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Toward tunable quantum transport and novel magnetic states in Eu1−xSrxMn1−zSb2 (z < 0.05)

Toward tunable quantum transport and novel magnetic states in Eu1−xSrxMn1−zSb2 (z < 0.05) Magnetic semimetals are very promising for potential applications in novel spintronic devices. Nevertheless, realizing tunable topological states with magnetism in a controllable way is challenging. Here, we report novel magnetic states and the tunability of topological semimetallic states through the control of Eu spin reorientation in Eu Sr Mn Sb . 1−x x 1−z 2 Increasing the Sr concentration in this system induces a surprising reorientation of noncollinear Eu spins to the Mn moment direction and topological semimetallic behavior. The Eu spin reorientations to distinct collinear antiferromagnetic orders are also driven by the temperature/magnetic field and are coupled to the transport properties of the relativistic fermions generated by the 2D Sb layers. These results suggest that nonmagnetic element doping at the rare earth element site may be an effective strategy for generating topological electronic states and new magnetic states in layered compounds involving spatially separated rare earth and transition metal layers. Introduction the coupling between the structure and magnetic and Dirac/Weyl semimetals have attracted intense research electronic phase diagrams in tunable magnetic topological interest due to their exotic quantum phenomena, as well materials. as their promise for applications in next generation, more The large family of ternary AMnCh “112” compounds 1–3 6,7,14–16 energy-efficient electronic devices . Magnetic Dirac/ (A= alkali earth/rare earth elements, Ch = Bi or Sb) Weyl semimetals are especially attractive since the cou- are particularly interesting since a few of them have been pling of Dirac/Weyl fermions to the additional spin degree reported to be magnetic Dirac semimetals where the Bi or of freedom may open up a new avenue for tuning and Sb layers host relativistic fermions. AMnCh (A = Ce, Pr, 4–6 14,16–18 controlling the resulting quantum transport properties . Nd, Eu, Sm; C = Bi or Sb) possesses two magnetic To date, several magnetic semimetals have been reported, sublattices, formed by the magnetic moments of rare and most of them were discovered in stoichiometric earth A and Mn, respectively, in contrast with other 7 8 compounds, such as SrMnBi ,Mn Sn , RAlGe(R = rare compounds, which have only Mn magnetic lattice in this 2 3 9 10,11 12,13 earth) ,Co Sn S , and Co MnGa . Finding a family. The conducting Bi/Sb layers and the insulating 3 2 2 2 strategy to control a topological state by tuning magnetism magnetic Mn–Bi(Sb) and Eu layers are spatially separated, is highly desirable and requires a clear understanding of which makes them good candidates for exploring the the interplay between the magnetism and the topological possible interplay between Dirac fermions and magnet- electronic state. This goal can be achieved by investigating ism. For EuMnBi , both the Eu and Mn moments point in the out-of-plane direction and generate two AFM lattices in the ground state . Previous studies have also shown Correspondence: Qiang Zhang (zhangq6@ornl.gov) that when the Eu AFM order undergoes a spin-flop Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA transition in a moderate field range, interlayer conduction Department of Physics and Astronomy, Louisiana State University, Baton is strongly suppressed, thus resulting in a stacked quan- Rouge, LA 70803, USA tum Hall effect. Interestingly, EuMnSb exhibits distinct Full list of author information is available at the end of the article These authors contributed equally: Qiang Zhang, Jinyu Liu. © The Author(s) 2022 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to theCreativeCommons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. 1234567890():,; 1234567890():,; 1234567890():,; 1234567890():,; Zhang et al. NPG Asia Materials (2022) 14:22 Page 2 of 11 properties from EuMnBi , and conflicting results have stoichiometric mixtures of Eu/Sr, Mn, and Sb elements, 17–19 been reported . The magnetotransport properties i.e., EuMnSb ,Eu Sr MnSb ,Eu Sr MnSb , and 2 0.8 0.2 2 0.5 0.5 2 reported by Yi et al. are not indicative of a Dirac Eu Sr MnSb , were put into small alumina crucibles 0.2 0.8 2 semimetallic state, while Soh et al. observed linear band and sealed in individual quartz tubes in an argon gas dispersion near the Fermi level in Angle-resolved photo- atmosphere. The tube was heated to 1050 °C for 2 days, emission spectroscopy measurements of EuMnSb and followed by subsequent cooling to 650 °C at a rate of 2 °C/ claimed that it may be a Dirac semimetal. Moreover, the h. Plate-like single crystals were obtained. The composi- magnetic structure of EuMnSb is thought to be distinct tions of all the single crystals were examined using from that of EuMnBi , with controversial reports on Eu energy-dispersive X-ray spectroscopy. The composition of and Mn moments being perpendicular or canted to each the x = 0 parent compound was also characterized by other . It is therefore important to resolve the controversy fitting to single-crystal X-ray diffraction data. about the magnetic and physical properties of EuMnSb and to explore whether EuMnSb and its derivatives could Single-crystal X-ray and neutron diffraction measurements host Dirac fermions. Additionally, it is known that in and neutron data analysis many-layered compounds involving spatially separated A crystal of x = 0 was mounted onto glass fibers using rare earth and manganese layers such as RMnAsO (R= epoxy, which was then mounted onto the goniometer of a 21,22 22,23 Nd or Ce) and RMnSbO (R= Pr or Ce) , the Nonius KappaCCD diffractometer equipped with Mo Kα moment of rare earth elements ordered at low tempera- radiation (λ = 0.71073 Å). After the data collection and tures usually drives Mn spin reorientation to its moment subsequent data reduction, SIR97 was employed to pro- direction. Given that there are two magnetic sublattices of vide a starting model, SHELXL97 was used to refine the Eu and Mn with an expected 4f–3d coupling between structural model, and the data were corrected using them in EuMnSb , the chemical substitution of Eu by extinction coefficients and weighting schemes during the 24,25 nonmagnetic elements may achieve interesting magnetic final stages of refinement . To investigate the crystal states by tuning the magnetic interactions, which may and magnetic structures, neutron diffraction measure- control the transport and magnetotransport properties. ments were conducted with the four circle neutron dif- In this article, we report comprehensive studies on a fractometer (FCD) located in the High Flux Isotope tunable Dirac semimetal system Eu Sr Mn Sb , Reactor at Oak Ridge National Laboratory. To further 1−x x 1−z 2 which exhibits a variety of novel magnetic states tunable distinguish between tetragonal and orthorhombic struc- by the Eu concentration, temperature, and magnetic field. tures for x = 0, neutrons with a monochromatic wave- The evolution of the magnetic states of this system is length of 1.003 Å without λ/2 contamination are used via found to be coupled to the quantum transport properties the silicon monochromator from (bent Si-331) . For of Dirac fermions. Through single-crystal X-ray diffrac- other Eu Sr Mn Sb (x = 0.2, 0.5, 0.8) crystals, we 1−x x 1−z 2 tion, neutron scattering, magnetic and high-field trans- employed neutrons with a wavelength of 1.542 Å invol- port measurements, we established a rich phase diagram ving 1.4% λ/2 contamination from the Si-220 mono- of the crystal structure, magnetism, and electronic prop- chromator using its high resolution mode (bending erties of Eu Sr Mn Sb The increase in Sr con- 150) . The crystal and magnetic structures were inves- 1−x x 1−z 2. centration in Eu Sr Mn Sb induces not only lattice tigated in different temperature windows. The order 1−x x 1−z 2 symmetry breaking and surprising Eu spin reorientation parameter of a few important nuclear and magnetic peaks to the Mn moment direction but also topological semi- was measured. Data were recorded over a temperature metallic states for x ≥ 0.5. Furthermore, the quantum range of 4 < T < 340 K using a closed-cycle refrigerator transport properties can be tuned by the different Eu spin available at the FCD. Due to the involvement of the high- reorientations to collinear AFM orders induced by the absorbing europium in the Eu Sr Mn Sb crystals, 1−x x 1−z 2 temperature and external magnetic field. The in-plane proper neutron absorption corrections to the integrated and out-of-plane components of the canted Eu magnetic intensities of the nuclear/magnetic peaks are indis- order are found to influence the intralayer and interlayer pensable. The dimensions of the faces for each crystal conductivities of Dirac fermions generated by the 2D Sb were measured, and a face index absorption correction of layers, respectively. These results establish a new unique the integrated intensities was conducted carefully using material platform for exploring Dirac band tuning by the WinGX package . The SARAh representational 28 29 magnetism. analysis program and Bilbao crystallographic server were used to derive the symmetry-allowed magnetic Materials and methods structures and magnetic space groups. The full datasets at Crystal growth different temperatures were analyzed using the refine- The Eu Sr Mn Sb single crystals were grown ment program FullProf suite to obtain the structure and 1−x x 1−z 2 using a self-flux method. The starting materials with magnetic structures. Zhang et al. NPG Asia Materials (2022) 14:22 Page 3 of 11 Magnetization and magnetotransport measurements in the orthorhombic structure with the space group Pnma, The temperature and field dependence of the magnetiza- with a doubled unit cell along the out-of-plane direction tion were measured in a superconducting quantum inter- (Figs. 1b, c and S1f), similar to SrMnSb . Thus, the Sr ference device magnetometer (Quantum Design) in doping at the Eu site in EuMn Sb induces symmetry 0.95 2 magnetic fields up to 7 T. The transport measurements at breaking from tetragonal P4/nmm to Pnma. Our sys- zero magnetic field were performed with a four-probe tematic studies on Sr-doped EuMn −zSb and comparison 1 2 method using Physical Property Measurement Systems with previous reports on the parent compound suggest (PPMS). The high-field magnetotransport properties were that the structural difference between our x=0sample 17,19 measured in 31 T resistivity magnets at the National High and the samples reported in the literature arises from Magnetic Field Laboratory (NHMFL) in Tallahassee. The the nonstoichiometric compositions and/or flux-induced magnetic fields were applied parallel to the out-of-plane chemical doping. The sample reported in ref. involves direction to study the in-plane and out-of-plane magne- Sn doping at the Sb sites due to the use of Sn flux, which toresistance. The ρ samples were made into Hall bar yields a composition of Eu Mn Sb Sn .In in 0.992 1.008 1.968 0.73 shapes, and the ρ samples were in the Corbino disk ref. , the composition was reported to be EuMn Sb , out 1.1 2 geometry. The Berry phase was extracted from the Landau which implies that a significant amount of Mn antisite fan diagram. The integer Landau levels are assigned to the defects may exist at the Sb sites. In contrast, our parent magnetic field positions of resistivity minima in SdH oscil- compound x = 0 is characterized by only a small degree of lations, which correspond to the minimal density of state. Mn deficiency. Such composition differences from the previously reported samples explain why our x=0sample Results and discussion is tetragonal, whereas the samples reported in the litera- Crystal structures ture are orthorhombic. This also indicates that chemical Both single-crystal X-ray and neutron diffraction reveal doping at the Eu, Mn, or Sb sites in EuMnSb could induce that the parent compound EuMnSb crystallizes in a tet- orthorhombic distortion. ragonal structure with space group P4/nmm (Figs. 1aand The structural parameters of Eu Sr Mn Sb (x = 0, 1−x x 1−z 2 S1e) and nonstoichiometric composition EuMn Sb . 0.2, 0.5, and 0.8) at 5 K obtained from the fits to neutron 0.95 2 The structural parameters of EuMn Sb obtained from diffraction data are summarized in Table 1. It can be seen 0.95 2 the single-crystal X-ray diffraction refinement at 293 K are that Sr doping induces a slight decrease in the out-of- summarized in Tables SI and SII. Note that the structure of plane lattice constant and an increase in the in-plane EuMn lattice constants. More details about the determination of Sb is similar to that of CaMnBi but different 0.95 2 2 from the I4/mmm in the tetragonal structure of EuMnBi crystal structures of all the Eu Sr Mn Sb com- 2 1−x x 1−z 2 and the previously reported orthorhombic structure of pounds can be found in the Supplemental Information. 17,19 EuMnSb . The energy-dispersive X-ray spectroscopy analysis shows that there are also less than 5% Mn defi- Determination of magnetic structures ciencies in the Sr-doped compounds with z∼0.01, 0.05, and In general, determining the complicated magnetic 0.02 for x = 0.2, 0.5, and 0.8, respectively. structures in Eu-containing compounds is difficult due Interestingly, the Sr-doped Eu Sr Mn Sb (x = 0.2, to the strong neutron absorption of europium. Proper 1−x x 1−z 2 0.5, and 0.8) shows a clear lattice distortion and crystallizes neutron absorption correction of the neutron diffraction Fig. 1 Magnetic structures of Eu Sr Mn Sb . Magnetic structures determined from the fits to the neutron data for a x = 0, b x = 0.2 (all the 1−x x 1−z 2 panels) and 0.5 (only left and middle panels), and c x = 0.8. The dashed rectangle shows the Mn–Eu–Eu–Mn block where the SR of Eu can be seen. Zhang et al. NPG Asia Materials (2022) 14:22 Page 4 of 11 Table 1 Structural parameters of Eu Sr Mn Sb with simultaneously, new magnetic reflections with a propa- 1−x x 1−z 2 x = 0, 0.2, 0.5, and 0.8 at 5 K obtained through the fitting gation vector k = (0,0,1/2) from the Eu sublattice appear. of the single-crystal neutron diffraction data. For x = 0, Interestingly, we observed strong magnetic peaks (0, 0, space group: P4/nmm. Atomic positions: Eu(2c): (0.25, 0.25, L/2) (L = odd number) below T (see the inset of Fig. 2a). T 2 z), Mn(2a): (0.75, 0.25, 0), Sb1(2b): (0.75, 0.25, 0.5), Sb2(2c): This excludes the possibility of Eu moments pointing in (0.25, 0.25, z). For x > 0 compounds: Space group: Pnma. 16,32 the out-of-plane axis seen in EuMnBi . The deter- Eu/Sr(4c): (x, 0.25, z), Mn(4c): (x, 0.25, z), Sb1(4c):(x, 0.25, z), mined magnetic structure for T < T denoted by AFM 2 Mn, Sb1(4c): (x, 0.25, z). is shown in the right panel of Fig. 1a. Whereas Mn Eu,⊥ preserves a C-type AFM order with an increased moment x = 0 x = 0.2 x = 0.5 x = 0.8 due to Eu-Mn coupling along the c axis, the “++ −−” Lattice constants Eu spin ordering with the moment along the a axis a 4.343 (6) 22.348 (3) 22.27 (42) 22.28 (41) breaks the magnetic symmetry along the c axis and leads to observed magnetic reflections with k = (0,0,1/2) . Such b 4.343 (6) 4.347 (5) 4.411 (14) 4.412 (14) a magnetic structure is consistent with the susceptibility c 11.169 (13) 4.383 (4) 4.434 (24) 4.438 (28) measurements in Fig. 3a, where χ increases slightly and Atom χ decreases rapidly for T < T , suggesting an AFM ab 2 Eu z 0.729(5) x 0.113 (4) 0.113 (5) 0.112 (4) moment oriented along the a b plane. Note that the T T magnetic structure determined here is different from the z 0.781 (5) 0.789 (7) 0.806 (3) “+-+-” A-type Eu order proposed on the basis of dif- Mn x 0.253 (7) 0.249 (4) 0.242 (4) fraction experiments on a polycrystalline sample of z 0.323 (3) 0.279 (7) 0.292 (4) EuMnSb , for which no k = (0,0,1/2) magnetic peaks 2 T Sb1 x 0.0019 (8) 0.0011 (7) 0.0042 (9) were observed below T . The Eu moment canting pro- posed in ref. is not found in our crystal for T < T (see z 0.233 (6) 0.264 (4) 0.298 (7) the Supplemental Information for a detailed discussion). Sb2 z 0.156(7) x 0.324 (5) 0.325 (5) 0.324 (6) In the x = 0.2 compound, the temperature dependence z 0.829 (5) 0.768 (4) 0.818 (5) of the pure magnetic peak (010) in the orthorhombic Reliable factors structure, corresponding to the (100) in the tetragonal notation, shows a clear magnetic transition at the T of Rf 8.75 6.67 6.18 7.59 330 K, as shown in Fig. 2b. A similar C-type AFM order 2 0.28 0.28 1.21 0.83 (AFM ) with k = (0,0,0) was determined and is dis- Mn O played in the left panel in Fig. 1b. Upon cooling below T at 21 K, new magnetic peaks indexed by (H, K, L)(H = data is critical. We employed single-crystal neutron odd integers), for instance (700) , corresponding to (0 0 diffraction to solve the complicated magnetic structures 3.5) , are observed (see inset of Fig. 2b). All the magnetic of Eu Sr Mn Sb below 340 K. The refined peaks can be described by the AFM order at k = (0,0,0) 1−x x 1−z 2 O moments, Mn–Eu canting angle, and reliability factors in the orthorhombic notation due to the doubled unit cell of the refinements of the neutron data after neutron in contrast to x = 0. Within the temperature range of T < absorption correction are summarized in Table 2 (see T < T ,we find a canted and noncollinear Eu spin order the Supplemental Information for more details). confined within the a c plane with a “++ −−’ com- O O Figure 2a–d shows the temperature dependences of a ponent along the c axis and a “+ − + −” component few representative nuclear and/or magnetic reflections of along the a axis, coexisting with the C-type Mn AFM Eu Sr Mn Sb . For the x = 0 parent compound, the order with moments along the a axis (denoted by 1−x x 1−z 2 O presence of the pure magnetic peak at (100) below T1at AFM the middle panel in Fig. 1b). This is con- T Mn,Eu,C1, 330 K indicates one magnetic transition. The absence of sistent with the susceptibility measurement shown in an anomaly at T in susceptibility measurements (see Fig. 3a) Fig. 3b, where both χ and χ decrease below T , implying 1 a bc 2 may be ascribed to the possible strong spin fluctuations that Eu spins may form a canted AFM order. Note that above T that tend to smear out any anomalies in the such a canted Eu order is not applicable in the corre- 6,20,22 susceptibility as in other Mn-based compounds . For sponding T < T temperature region of the x = 0 parent T < T , a C-type AFM order of Mn spins (AFM ) with compound. At 10 K, the canting angle between Mn and 1 Mn the propagation vector k = (0,0,0) and the moment along Eu is 41(9)°. The susceptibility measurements show that χ T a the c axis is determined without Eu ordering, as illu- increases but χ decreases anomalously below T at 7 K, T bc 3 strated in the left panel of Fig. 1a. Upon cooling below T indicative of another magnetic transition. Interestingly, at 22 K, there is an increase in magnetic peak intensities there is a decrease in the (300) peak intensity, with a such as (100) and (101) with k = (0,0,0) and, concurrent increase in the intensity of the nuclear peak T T T Zhang et al. NPG Asia Materials (2022) 14:22 Page 5 of 11 Table 2 Refined magnetic moments, Mn–Eu angles, and reliable factors of Eu Sr Mn Sb with x = 0, 0.2, 0.5, and 0.8 1−x x 1−z 2 at different temperatures. x = 0 x = 0.2 x = 0.5 x = 0.8 T (K) 170 5 60 10 4 50 5 5 Mn moments M (x = 0) 2.99 (29) 4.63 (21) M (x > 0) 3.70 (46) 3.66 (32) 3.75 (45) 3.74 (15) 3.76 (17) 3.80 (22) Eu moments M 4.08 (34) 3.89 (69) 4.84 (55) 5.17 (62) M 5.25 (43) 3.52 (34) 3.30 (86) 2.23 (29) |M | 5.25 (43) 5.38 (34) 5.26 (50) 5.32 (50) 5.17 (62) total Mn–Eu moment angle( ) 90 (7) 41 (9) 40 (7) 24 (8) 0 Reliable factors RF (k = (0, 0, 0)) 9.53 8.75 7.64 7.55 6.67 5.32 6.18 7.59 χ (k = (0, 0, 0)) 0.27 0.28 0.13 0.29 0.28 0.31 1.26 0.83 RF (k = (0, 0, 1/2)) 8.93 χ (k = (0, 0, 1/2)) 0.26 Fig. 2 Neutron results on nuclear and magnetic peaks of Eu Sr Mn Sb . Temperature dependence of intensities at the representative 1−x x 1−z 2 nuclear and/or magnetic peak positions for a x = 0, b x = 0.2, c x = 0.5, and d 0.8. The insets show a comparison of the nuclear/magnetic peaks at different temperatures. The 2nd weak peak with a smaller omega in the rocking curves for x = 0 is due to the presence of another tetragonal domain rather than an orthorhombic domain in the crystal. The very weak (300) peak in d results from the λ/2 contamination of neutrons. The vertical lines indicate the locations of the magnetic transition temperatures. (600) for T < T . This strongly indicates a Eu spin- aMn–Eu canting angle of 40(7)° at 4 K, as shown in the O 3 reorientation transition to a Eu spin order without mag- right panel of Fig. 1b. At 4 K, the Mn and Eu moments are netic symmetry breaking along the a axis. When the found to be 3.75(45) and 5.26(50) µ , respectively, indi- O B 2+ 2+ C-type Mn order is unchanged, a canted and collinear cative of Mn (S = 5/2) and Eu (S = 7/2). magnetic structure with A-type “+ − + −” Eu spin order When x is increased to 0.5 or 0.8, the Eu lattice exhibits along both the a and c axes (AFM ) occurs with only a single AFM transition as revealed from the O O Mn,Eu,C2 Zhang et al. NPG Asia Materials (2022) 14:22 Page 6 of 11 Fig. 3 Susceptibility and resistivity of Eu Sr Mn Sb . Temperature dependence of the susceptibility of a x = 0 with a magnetic field of 0.1 T 1−x x 1−z 2 parallel to the out-of-plane c and in-plane a b directions and b x = 0.2, c x = 0.5, and d x = 0.8 with the field parallel to the out-of-plane a and in- T T T O plane b c directions. Temperature dependence of the out-of-plane resistivity ρ and in-plane longitudinal resistivity ρ at zero magnetic field for O O out in e x = 0, f x = 0.2, g x = 0.5 and h x = 0.8. susceptibility measurements shown in Fig. 3c, with T at Eu moment mainly points in the out-of-plane a direc- 2 O 17 K for x = 0.5 and 8 K for x = 0.8. For the x = 0.5 sam- tion at x = 0.8. ple, both the (010) and (001) magnetic peaks appear O O below T . Upon cooling below T at 15 K, the (010) peak Electronic transport properties 1 2 O intensity further increases, while there is no obvious Next, we present the evolution of the electronic trans- change in the (001) peak (see Fig. 2c and Fig. S5a, b). port properties with Sr doping in Eu Sr Mn Sb .As O 1−x x 1−z 2 Furthermore, there is an increase in the peak intensity shown in Fig. 3e–h, both the in-plane longitudinal resis- (300) due to the magnetic contribution but no obvious tivity ρ and out-of-plane resistivity ρ exhibit metallic O in out change in the peak intensities of (200) or (600) . These transport properties. At 2 K, ρ /ρ reaches 128, 198 and O O out in features are similar to those at x = 0.2. We indeed obtain 322 for x = 0, x = 0.2 and x = 0.8, respectively. Such a similar magnetic structures in the x = 0.5 sample, as rapid increase in electronic anisotropy indicates that Sr shown in the left panel (AFM ) and middle panel doping reinforces the quasi-2D electronic structure. In the Mn (AFM ) in Fig. 1b for T < T < T and T < T < T , x = 0 sample (see Figs. 3e and S7a), the slope of ρ and Mn,Eu,C1 2 1 3 2 out respectively. Note that the canting angle between Eu and ρ decreases below T , indicative of the coupling between in 2 Mn moments decreases to 24(8)° at 5 K. the emergence of Eu order and the transport properties, As x increases to 0.8, the Mn magnetic transition occurs suggesting that the in-plane Eu “++ --” order leads to at a T of 330 K as identified from the intensity of (010) , suppressed metallicity. The metallic behavior in our 1 O and a C-type Mn order AFM is determined (see the left EuMn Sb sample is different from the insulating Mn 0.95 2 panel of Fig. 1c). Another increase in (010) is found behavior observed in the Sn- or Mn-doped nonstoichio- 17,19 below T ≈ 7 K. There is no appearance of magnetic metric samples . This indicates that chemical doping scattering at the (300) and (200) or (600) Bragg at Sb or Mn sites induces a metal-insulator transition that O O O positions below T (see the inset of Fig. 2d and Fig. S5c in is distinct from the effect of Sr substitution for Eu. SI), indicating that Eu moments may point to the a axis. However, the x = 0.2 sample exhibits transport behavior We find a coexistence of C-type Mn AFM order with the distinct from that of the x = 0 sample. We observe a rapid “+ − + −” Eu order with an oriented moment along the decrease in ρ and a slight increase in ρ below T (see out in 2 same a axis as the Mn moment (AFM , see the right Figs. 3f and S7b), suggesting that the Eu canting to the a O Mn,Eu, O panel of Fig. 1c), consistent with susceptibility measure- axis with the Eu “+ − + −” component significantly ments. As shown in Fig. 3d, X keeps increasing, but X increases the interlayer conductivity along the a direc- bc a O decreases rapidly upon cooling below 8 K, showing tion between Sb layers but suppresses the intralayer behavior opposite to that of x = 0. This indicates that the conductivity on the b c plane, in contrast with the effect O O Zhang et al. NPG Asia Materials (2022) 14:22 Page 7 of 11 Fig. 4 High field magnetoresistance of Eu Sr Mn Sb . Field dependence of the out-of-plane magnetoresistance Δρ /ρ and in-plane 1−x x 1−z 2 out out magnetoresistance Δρ /ρ for a x = 0, b x = 0.2, c x = 0.5, and d x = 0.8. The inset of b shows the field-induced metamagnetic transition in the Eu in in sublattice, i.e., Eu spin ordering in and H < H and H < H < H . The insets of c, d show the linear fit of the Landau level fan diagram based on both the f f s 2 2 oscillatory resistivity ρ and the second derivative of the resistivity -d ρ /dB for x = 0.5 and based on only the oscillatory resistivity ρ for x = 0.8. in n in of the sole in-plane Eu order on the transport properties coupling between the Eu magnetic order and transport described above. Below T , there are no obvious changes properties in Eu Sr Mn Sb . 3 1−x x 1−z 2 in the out-of-plane resistivity, but an anomalous decrease in the in-plane resistivity is observed. This can be attrib- Nontrivial Berry phases uted to the SR of Eu from noncollinear to collinear order. Figure 4a–d shows both in-plane and out-of-plane Below T , the out-of-plane Eu order is kept at “+ − + −”, magnetoresistance (MR = [ρ (B) − ρ (0)]/ρ (0)) under which is not expected to influence the interlayer con- high magnetic fields applied along the out-of-plane ductivity. In contrast, the switch of the in-plane compo- direction. For x = 0, Δρ /ρ is negative, whereas the out out nent from “++ −−” to “+ − + −” induces an in-plane Δρ /ρ is positive. The magnitudes for both in in anomalous increase in the intralayer conductivity. Δρ /ρ and Δρ /ρ are small, and no strong out out in in When x increases to 0.5, the “+ − + −” component of Shubnikov-de Haas (SdH) oscillations are observed. For the Eu order along the a axis direction also induces an x = 0.2, weak SdH oscillations are observed in both Δρ / O out increase in the interlayer conductivity below T (see ρ and Δρ /ρ . As the field increases, there is a sign 2 out in in Figs. 3g and S7c), but the increase is weaker than that at reversal in ρ /ρ , whereas Δρ /ρ remains positive. in in out out x = 0.2. Furthermore, the weak decrease in the intralayer Remarkably, at 1.8 K, which is below T , a large jump in conductivity at x = 0.2 is hardly observed near T at x = Δρ /ρ up to 4500% occurs above a µ H of 18 T. 2 out out 0 t 0.5. Both are ascribed to the reduction in Eu occupancy to The dramatic changes in Δρ /ρ near µ H of 18 T are out out 0 t ≈ 50% at x = 0.5, which weakens the effect of Eu order on ascribed to a field-induced metamagnetic transition. Since the transport properties. For x = 0.8, the Eu ordering does this phenomenon does not occur in the T > T tempera- not obviously influence the resistivity below T , as shown ture regime (e.g., 50 K), the field-induced magnetic tran- in Figs. 3h and S7d, which can be ascribed to the low Eu sition does not originate from the Mn magnetic sublattice occupancy (≈ 20%). Thus, our results reveal an intimate but is related to the Eu magnetic sublattice, which is Zhang et al. NPG Asia Materials (2022) 14:22 Page 8 of 11 indicative of the vital role that the Eu magnetic order Composition phase diagram plays in the magnetotransport properties. The most likely From the combination of single-crystal X-ray diffrac- origin of the enhanced Δρ /ρ above µ H of 18 T is the tion, neutron diffraction, magnetization, and magneto- out out 0 t field-induced Eu SR transition from the canted moment transport measurements, we are able to establish the direction in the a c plane to the c axis, while the structural, magnetic, and electronic phase diagram, as O O O A-type “+ − + −” Eu order remains, thus strongly sup- illustrated in Fig. 5. While the x = 0 parent compound pressing interlayer conductivity, as illustrated in the inset with Mn deficiency is tetragonal with the space group P4/ of Fig. 4b. Note that this is different from the field- mmm, Sr doping induces an orthorhombic distortion. induced spin-flop transition of the “++ −−” Eu order This is consistent with previous reports on the orthor- from the out-of-plane c axis to the in-plane direction in hombic structure in doped nonstoichiometric sam- 16 17,19 EuMnBi . Above ∼ 28 T, the rapid decrease in Δρ / ples . Notably, our EuMn Sb sample forms a 2 out 0.95 2 ρ may indicate the full polarization of Eu spins to the magnetic structure with perpendicular Mn and Eu out external field direction, i.e., the a axis, similar to the moments at the ground state and does not exhibit topo- scenario seen in EuMnBi . Further high-field magneti- logical semimetallic behavior, different from previous 17–19 zation measurements are required to confirm these reports on samples with different compositions .Sr metamagnetic transitions. substitution for Eu in EuMnSb induces a slight decrease An increase in the Sr doping level significantly in T but suppresses T significantly. Furthermore, an 1 2 enhances SdH oscillations in both Δρ /ρ and Δρ / increase in Sr concentration drives an unusual Eu SR from out out in ρ for x = 0.5 and 0.8, respectively, with much higher the in-plane to the out-of-plane direction and simulta- in oscillation amplitudes at high magnetic fields. Δρ /ρ neously induces the appearance of Dirac semimetallic out out reaches ≈ 18,000% at 31.5 T for x = 0.8. We further behaviors. A higher Eu canting angle characterized by a analyze the Berry phase (BP) ϕ accumulated along smaller Eu–Mn angle is accompanied by stronger quan- cyclotron orbits and are able to extract ϕ for x = 0.5 and tum SdH oscillations. Our results show that Eu spin 0.8. Based on the field dependence data of ρ measured canting can be driven by chemical doping, which could in in a 14 T PPMS, which show well-resolved SdH oscilla- explain the observation of Eu canting in a doped tions in Fig. S8a, we obtain the second derivative of 2 2 resistivity -d ρ /dB and the oscillatory component of in ρ after background subtraction. The oscillation peaks in and valleys obtained from both analyses are well-mat- ched, as shown in Fig. S8b. With six oscillation valleys assigned to integer Landau levels (LLs) and five peaks assigned to half integer LLs, a Landau index fan diagram can be established, from which a nontrivial Berry phase of 0.8 π can be unambiguously extracted, as displayed in the inset of Fig. 4c. As shown in Fig. 4d, we extract a Berry phase of 0.88 π for the x = 0.8 compound. The Berry phases in both the x = 0.5 and 0.8 samples are apparently close to an ideal Berry phase for a quasi-2D system. The nontrivial Berry phase provides evidence that x = 0.5 and 0.8 harbor relativistic Dirac fermions. Our results clearly show that the substitution of Eu by Fig. 5 Composition phase diagram of Eu Sr Mn Sb with the 1−x x 1−z 2 nonmagnetic Sr induces Dirac semimetallic behavior structural and magnetic transitions, Eu–Mn moment angle α and that is closely associated with the controllable Eu nontrivial Berry phase (BH) extracted from the fits to ρ . T , T , in 1 2 magnetic order. and T label the magnetic transition temperatures. The distinct Unlike the x = 0.2 sample, the x = 0.5 and 0.8 samples magnetic structures (AFM , AFM , AFM , AFM , and Mn Mn,Eu,⊥ Mn,Eu,C1 Mn,Eu,C2 AFM are displayed in Fig. 1b–d. AFM and AFM do not show large jumps in ρ /ρ in the field up to Mn,Eu,//) Mn,Eu, // Mn,Eu,⊥ out out indicate the parallel and perpendicular moments of Mn and Eu, 31 T. This indicates the absence of field-induced meta- respectively. AFM and AFM show the two distinct Mn,Eu,C1 Mn,Eu,C2 magnetic transitions in both compounds. Therefore, the canted moments between Mn and Eu. The evolution of the violet nontrivial Berry phase may be intrinsic for x = 0.5 and 0.8 color illustrates the gradual decrease in the Eu–Mn moment angles. A compounds. In addition, compared to SrMnSb , with only higher Eu canting angle of (90 − α), i.e., a smaller α, is accompanied by stronger quantum SdH oscillations. All the compounds exhibit an ordered Mn moment, the x = 0.5 and 0.8 samples metal-like transport properties as a function of temperature, and they exhibit distinct Eu orders coexisting with Mn orders, and are also coupled to the Eu order at T and T . The nontrivial Berry 2 3 the increase in Eu canting angle is accompanied by phases indicative of Dirac semimetallic behaviors emerge for x ≥ 0.5. stronger quantum oscillations. Zhang et al. NPG Asia Materials (2022) 14:22 Page 9 of 11 nonstoichiometric sample . Note that no other magnetic the moment changes from the in-plane direction to the out- transition is observed at T in ref. For our x = 0.2 of-plane direction while the Mn moment direction remains compound, a 2nd type of Eu SR from a noncollinear along the out-of-plane a axis. 2+ canted spin order to a collinear A-type canted spin order The Mn moment, which commonly displays very is found at lower temperature (denoted by AFM in weak single-ion anisotropy as expected for the L =0of Mn,Eu,C2 2+ Fig. 5). Furthermore, the Eu order at the base temperature Mn (S = 5/2), favors orientation along the out-of-plane 20–22 can be easily tuned by the external magnetic field to direction , i.e., the c axis in the tetragonal structure another type of SR, leading to a canted AFM state with the or the a axis in the orthorhombic structure, forming moments oriented to the possible c axis. The established C-type AFM order in T < T < T of Eu Sr Mn Sb O 2 1 1−x x 1−z 2. phase diagram for Eu Sr Mn Sb as well as the The in-plane checkerboard-like AFM structure of the 1−x x 1−z 2 17–19 comparison with the previous reports we made above C-type order suggests that the NN interaction J is indicate that the structure, magnetic order, and electronic dominant, whereas the in-plane next-nearest-neighbor properties of EuMnSb are easily perturbed by chemical (NNN) interaction J is very weak. In the context of the 2 2 doping at any of the Eu, Mn, and Sb sites, indicating that J –J –J model , we conclude that J >0, J < J /2 and out- 1 2 c 1 2 1 the lattice, spin and charge degrees of freedom are of-plane J < 0 with negligible spin frustration in the Mn strongly coupled in this material. This could account for sublattice. Upon cooling to T < T , Eu-Eu coupling starts 17–19 the conflicting results reported in the literature to come into play and induces Eu ordering with a pre- 2+ 34,35 regarding the structure, magnetic, and electronic trans- ferred orientation of Eu (S = 7/2) in plane , either port properties of EuMnSb and implies that the non- the a b plane in the tetragonal structure or the b c 2 T T O O stoichiometry must be taken into account to understand plane in the orthorhombic structure. Simultaneously, the the intrinsic crystal and magnetic structure and magne- Eu–Mn coupling also plays an important role by exerting totransport properties of EuMnSb . an effective field that has the tendency to influence the 17,19 While chemical doping at Sb or Mn sites in non- Mn/Eu moment directions. The increase in Sr con- stoichiometric samples induces a tetragonal-orthorhombic centration on the Eu site weakens Eu–Eu coupling and structural transition, as in our Eu Sr Mn Sb (x>0), destabilizes the preferred orientation of the Eu spins. 1−x x 1−z 2 such doping induces a metal–insulator transition yielding Thus, as x increases to 0.2, the effective field from Eu–Mn insulating behavior. This indicates that doping at the Sb or coupling tends to drive the Eu moment toward the Mn Mn sites may be detrimental to forming semimetallic beha- moment direction. The competition of Eu–Eu and vior in EuMnSb Eu–Mn couplings induces spin frustration in the Eu derivatives. In contrast, our phase diagram clearly shows that Sr doping at the Eu site is the driving force sublattice and leads to a canted Eu order with the moment of the Dirac semimetallic behavior in Eu Sr Mn Sb ,as in the ac plane stabilized in T < T < T . An increase in Sr 1−x x 1−z 2 3 2 discussed below. First, Sr doping at the Eu site lowers the doping has a tendency to further drive the Eu moment tilt lattice symmetry and modifies the structural parameters, as toward the a axis due to weakened Eu–Eu coupling, as summarized in Table 1, which could in turn change the shown by a lower Eu–Mn angle for x = 0.5. As the Sr electronic band structure. Second, the different types of Eu doping increases to 0.8, the Eu–Mn coupling overwhelms spin reorientations driven by Sr doping, temperature, or the weak Eu–Eu coupling, which leads to an SR of Eu to magnetic field significantly influence the electronic transport the same moment direction as the Mn moment. This and magnetotransport properties, indicating that the band could account for the unusual Eu SR induced by Sr structure is sensitively dependent on the magnetism of the doping. As the temperature decreases below T for x = Eu sublattice. As such, the phase diagram presented in Fig. 5 0.2, a temperature-induced SR transition occurs. This may offers an excellent opportunity to explore the intimate be ascribed to another type of Eu–Eu coupling that comes interplay between the band relativistic effect and magnetism. into play below T . This retains the “+ − + −” out-of- plane component but switches the in-plane component Origin of various Eu spin reorientations from “++ −−” to “+ − + −”, leading to a collinear Finally,wediscuss theorigins of thecomplicated magnetic A-type AFM order of Eu spins in T < T . Thus, the structures, in particular, the Sr-doping and temperature- striking Eu spin reorientation driven by Sr doping and induced Eu SR transition in Eu Sr Mn Sb . A common temperature indicates strong Eu–Mn (4f–3d) couplings 1−x x 1−z 2 SR in rare earth elements occurs because the rare earth and results from their competition with Eu–Eu couplings. element drives the Mn moment parallel to its moment To summarize, we report the composition phase dia- direction once the rare earth spins are ordered with pre- gram of the crystal and magnetic structures and electronic ferred in-plane orientation at low temperatures, as reported transport properties of Eu Sr Mn Sb and the reali- 1−x x 1−z 2 for several compounds such as RMnAsO (R= Nd or zation of tunable topological semimetallic behavior by 20,21 22,23 Ce) and RMnSbO (R= Pr or Ce) . However, Sr controlling various spin reorientations by chemical sub- doping in Eu Sr Mn Sb generates a novel Eu SR where stitution, temperature, and/or an external magnetic field. 1−x x 1−z 2 Zhang et al. NPG Asia Materials (2022) 14:22 Page 10 of 11 The structure, magnetic order, and electronic properties Supplementary information The online version contains supplementary material available at https://doi.org/10.1038/s41427-022-00369-5. of the parent EuMnSb are easily perturbed by chemical doping, and therefore, the nonstoichiometry must be Received: 10 August 2021 Revised: 22 January 2022 Accepted: 2 February taken into account to determine its intrinsic structure and physical properties. While we found that nearly stoi- Published online: 11 March 2022 chiometric EuMnSb is not a topological semimetal, doping of nonmagnetic Sr on the Eu site induces an References intricate coupling between the structure, various Eu spin 1. Xu, S.-Y. et al. Discovery of a Weyl fermion semimetal and topological fermi arcs. Science 349,613–617 (2015). reorientations, and quantum transport properties, indi- 2. Lu, L. et al. Experimental observation of Weyl points. 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Toward tunable quantum transport and novel magnetic states in Eu1−xSrxMn1−zSb2 (z < 0.05)

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Abstract

Magnetic semimetals are very promising for potential applications in novel spintronic devices. Nevertheless, realizing tunable topological states with magnetism in a controllable way is challenging. Here, we report novel magnetic states and the tunability of topological semimetallic states through the control of Eu spin reorientation in Eu Sr Mn Sb . 1−x x 1−z 2 Increasing the Sr concentration in this system induces a surprising reorientation of noncollinear Eu spins to the Mn moment direction and topological semimetallic behavior. The Eu spin reorientations to distinct collinear antiferromagnetic orders are also driven by the temperature/magnetic field and are coupled to the transport properties of the relativistic fermions generated by the 2D Sb layers. These results suggest that nonmagnetic element doping at the rare earth element site may be an effective strategy for generating topological electronic states and new magnetic states in layered compounds involving spatially separated rare earth and transition metal layers. Introduction the coupling between the structure and magnetic and Dirac/Weyl semimetals have attracted intense research electronic phase diagrams in tunable magnetic topological interest due to their exotic quantum phenomena, as well materials. as their promise for applications in next generation, more The large family of ternary AMnCh “112” compounds 1–3 6,7,14–16 energy-efficient electronic devices . Magnetic Dirac/ (A= alkali earth/rare earth elements, Ch = Bi or Sb) Weyl semimetals are especially attractive since the cou- are particularly interesting since a few of them have been pling of Dirac/Weyl fermions to the additional spin degree reported to be magnetic Dirac semimetals where the Bi or of freedom may open up a new avenue for tuning and Sb layers host relativistic fermions. AMnCh (A = Ce, Pr, 4–6 14,16–18 controlling the resulting quantum transport properties . Nd, Eu, Sm; C = Bi or Sb) possesses two magnetic To date, several magnetic semimetals have been reported, sublattices, formed by the magnetic moments of rare and most of them were discovered in stoichiometric earth A and Mn, respectively, in contrast with other 7 8 compounds, such as SrMnBi ,Mn Sn , RAlGe(R = rare compounds, which have only Mn magnetic lattice in this 2 3 9 10,11 12,13 earth) ,Co Sn S , and Co MnGa . Finding a family. The conducting Bi/Sb layers and the insulating 3 2 2 2 strategy to control a topological state by tuning magnetism magnetic Mn–Bi(Sb) and Eu layers are spatially separated, is highly desirable and requires a clear understanding of which makes them good candidates for exploring the the interplay between the magnetism and the topological possible interplay between Dirac fermions and magnet- electronic state. This goal can be achieved by investigating ism. For EuMnBi , both the Eu and Mn moments point in the out-of-plane direction and generate two AFM lattices in the ground state . Previous studies have also shown Correspondence: Qiang Zhang (zhangq6@ornl.gov) that when the Eu AFM order undergoes a spin-flop Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA transition in a moderate field range, interlayer conduction Department of Physics and Astronomy, Louisiana State University, Baton is strongly suppressed, thus resulting in a stacked quan- Rouge, LA 70803, USA tum Hall effect. Interestingly, EuMnSb exhibits distinct Full list of author information is available at the end of the article These authors contributed equally: Qiang Zhang, Jinyu Liu. © The Author(s) 2022 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to theCreativeCommons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. 1234567890():,; 1234567890():,; 1234567890():,; 1234567890():,; Zhang et al. NPG Asia Materials (2022) 14:22 Page 2 of 11 properties from EuMnBi , and conflicting results have stoichiometric mixtures of Eu/Sr, Mn, and Sb elements, 17–19 been reported . The magnetotransport properties i.e., EuMnSb ,Eu Sr MnSb ,Eu Sr MnSb , and 2 0.8 0.2 2 0.5 0.5 2 reported by Yi et al. are not indicative of a Dirac Eu Sr MnSb , were put into small alumina crucibles 0.2 0.8 2 semimetallic state, while Soh et al. observed linear band and sealed in individual quartz tubes in an argon gas dispersion near the Fermi level in Angle-resolved photo- atmosphere. The tube was heated to 1050 °C for 2 days, emission spectroscopy measurements of EuMnSb and followed by subsequent cooling to 650 °C at a rate of 2 °C/ claimed that it may be a Dirac semimetal. Moreover, the h. Plate-like single crystals were obtained. The composi- magnetic structure of EuMnSb is thought to be distinct tions of all the single crystals were examined using from that of EuMnBi , with controversial reports on Eu energy-dispersive X-ray spectroscopy. The composition of and Mn moments being perpendicular or canted to each the x = 0 parent compound was also characterized by other . It is therefore important to resolve the controversy fitting to single-crystal X-ray diffraction data. about the magnetic and physical properties of EuMnSb and to explore whether EuMnSb and its derivatives could Single-crystal X-ray and neutron diffraction measurements host Dirac fermions. Additionally, it is known that in and neutron data analysis many-layered compounds involving spatially separated A crystal of x = 0 was mounted onto glass fibers using rare earth and manganese layers such as RMnAsO (R= epoxy, which was then mounted onto the goniometer of a 21,22 22,23 Nd or Ce) and RMnSbO (R= Pr or Ce) , the Nonius KappaCCD diffractometer equipped with Mo Kα moment of rare earth elements ordered at low tempera- radiation (λ = 0.71073 Å). After the data collection and tures usually drives Mn spin reorientation to its moment subsequent data reduction, SIR97 was employed to pro- direction. Given that there are two magnetic sublattices of vide a starting model, SHELXL97 was used to refine the Eu and Mn with an expected 4f–3d coupling between structural model, and the data were corrected using them in EuMnSb , the chemical substitution of Eu by extinction coefficients and weighting schemes during the 24,25 nonmagnetic elements may achieve interesting magnetic final stages of refinement . To investigate the crystal states by tuning the magnetic interactions, which may and magnetic structures, neutron diffraction measure- control the transport and magnetotransport properties. ments were conducted with the four circle neutron dif- In this article, we report comprehensive studies on a fractometer (FCD) located in the High Flux Isotope tunable Dirac semimetal system Eu Sr Mn Sb , Reactor at Oak Ridge National Laboratory. To further 1−x x 1−z 2 which exhibits a variety of novel magnetic states tunable distinguish between tetragonal and orthorhombic struc- by the Eu concentration, temperature, and magnetic field. tures for x = 0, neutrons with a monochromatic wave- The evolution of the magnetic states of this system is length of 1.003 Å without λ/2 contamination are used via found to be coupled to the quantum transport properties the silicon monochromator from (bent Si-331) . For of Dirac fermions. Through single-crystal X-ray diffrac- other Eu Sr Mn Sb (x = 0.2, 0.5, 0.8) crystals, we 1−x x 1−z 2 tion, neutron scattering, magnetic and high-field trans- employed neutrons with a wavelength of 1.542 Å invol- port measurements, we established a rich phase diagram ving 1.4% λ/2 contamination from the Si-220 mono- of the crystal structure, magnetism, and electronic prop- chromator using its high resolution mode (bending erties of Eu Sr Mn Sb The increase in Sr con- 150) . The crystal and magnetic structures were inves- 1−x x 1−z 2. centration in Eu Sr Mn Sb induces not only lattice tigated in different temperature windows. The order 1−x x 1−z 2 symmetry breaking and surprising Eu spin reorientation parameter of a few important nuclear and magnetic peaks to the Mn moment direction but also topological semi- was measured. Data were recorded over a temperature metallic states for x ≥ 0.5. Furthermore, the quantum range of 4 < T < 340 K using a closed-cycle refrigerator transport properties can be tuned by the different Eu spin available at the FCD. Due to the involvement of the high- reorientations to collinear AFM orders induced by the absorbing europium in the Eu Sr Mn Sb crystals, 1−x x 1−z 2 temperature and external magnetic field. The in-plane proper neutron absorption corrections to the integrated and out-of-plane components of the canted Eu magnetic intensities of the nuclear/magnetic peaks are indis- order are found to influence the intralayer and interlayer pensable. The dimensions of the faces for each crystal conductivities of Dirac fermions generated by the 2D Sb were measured, and a face index absorption correction of layers, respectively. These results establish a new unique the integrated intensities was conducted carefully using material platform for exploring Dirac band tuning by the WinGX package . The SARAh representational 28 29 magnetism. analysis program and Bilbao crystallographic server were used to derive the symmetry-allowed magnetic Materials and methods structures and magnetic space groups. The full datasets at Crystal growth different temperatures were analyzed using the refine- The Eu Sr Mn Sb single crystals were grown ment program FullProf suite to obtain the structure and 1−x x 1−z 2 using a self-flux method. The starting materials with magnetic structures. Zhang et al. NPG Asia Materials (2022) 14:22 Page 3 of 11 Magnetization and magnetotransport measurements in the orthorhombic structure with the space group Pnma, The temperature and field dependence of the magnetiza- with a doubled unit cell along the out-of-plane direction tion were measured in a superconducting quantum inter- (Figs. 1b, c and S1f), similar to SrMnSb . Thus, the Sr ference device magnetometer (Quantum Design) in doping at the Eu site in EuMn Sb induces symmetry 0.95 2 magnetic fields up to 7 T. The transport measurements at breaking from tetragonal P4/nmm to Pnma. Our sys- zero magnetic field were performed with a four-probe tematic studies on Sr-doped EuMn −zSb and comparison 1 2 method using Physical Property Measurement Systems with previous reports on the parent compound suggest (PPMS). The high-field magnetotransport properties were that the structural difference between our x=0sample 17,19 measured in 31 T resistivity magnets at the National High and the samples reported in the literature arises from Magnetic Field Laboratory (NHMFL) in Tallahassee. The the nonstoichiometric compositions and/or flux-induced magnetic fields were applied parallel to the out-of-plane chemical doping. The sample reported in ref. involves direction to study the in-plane and out-of-plane magne- Sn doping at the Sb sites due to the use of Sn flux, which toresistance. The ρ samples were made into Hall bar yields a composition of Eu Mn Sb Sn .In in 0.992 1.008 1.968 0.73 shapes, and the ρ samples were in the Corbino disk ref. , the composition was reported to be EuMn Sb , out 1.1 2 geometry. The Berry phase was extracted from the Landau which implies that a significant amount of Mn antisite fan diagram. The integer Landau levels are assigned to the defects may exist at the Sb sites. In contrast, our parent magnetic field positions of resistivity minima in SdH oscil- compound x = 0 is characterized by only a small degree of lations, which correspond to the minimal density of state. Mn deficiency. Such composition differences from the previously reported samples explain why our x=0sample Results and discussion is tetragonal, whereas the samples reported in the litera- Crystal structures ture are orthorhombic. This also indicates that chemical Both single-crystal X-ray and neutron diffraction reveal doping at the Eu, Mn, or Sb sites in EuMnSb could induce that the parent compound EuMnSb crystallizes in a tet- orthorhombic distortion. ragonal structure with space group P4/nmm (Figs. 1aand The structural parameters of Eu Sr Mn Sb (x = 0, 1−x x 1−z 2 S1e) and nonstoichiometric composition EuMn Sb . 0.2, 0.5, and 0.8) at 5 K obtained from the fits to neutron 0.95 2 The structural parameters of EuMn Sb obtained from diffraction data are summarized in Table 1. It can be seen 0.95 2 the single-crystal X-ray diffraction refinement at 293 K are that Sr doping induces a slight decrease in the out-of- summarized in Tables SI and SII. Note that the structure of plane lattice constant and an increase in the in-plane EuMn lattice constants. More details about the determination of Sb is similar to that of CaMnBi but different 0.95 2 2 from the I4/mmm in the tetragonal structure of EuMnBi crystal structures of all the Eu Sr Mn Sb com- 2 1−x x 1−z 2 and the previously reported orthorhombic structure of pounds can be found in the Supplemental Information. 17,19 EuMnSb . The energy-dispersive X-ray spectroscopy analysis shows that there are also less than 5% Mn defi- Determination of magnetic structures ciencies in the Sr-doped compounds with z∼0.01, 0.05, and In general, determining the complicated magnetic 0.02 for x = 0.2, 0.5, and 0.8, respectively. structures in Eu-containing compounds is difficult due Interestingly, the Sr-doped Eu Sr Mn Sb (x = 0.2, to the strong neutron absorption of europium. Proper 1−x x 1−z 2 0.5, and 0.8) shows a clear lattice distortion and crystallizes neutron absorption correction of the neutron diffraction Fig. 1 Magnetic structures of Eu Sr Mn Sb . Magnetic structures determined from the fits to the neutron data for a x = 0, b x = 0.2 (all the 1−x x 1−z 2 panels) and 0.5 (only left and middle panels), and c x = 0.8. The dashed rectangle shows the Mn–Eu–Eu–Mn block where the SR of Eu can be seen. Zhang et al. NPG Asia Materials (2022) 14:22 Page 4 of 11 Table 1 Structural parameters of Eu Sr Mn Sb with simultaneously, new magnetic reflections with a propa- 1−x x 1−z 2 x = 0, 0.2, 0.5, and 0.8 at 5 K obtained through the fitting gation vector k = (0,0,1/2) from the Eu sublattice appear. of the single-crystal neutron diffraction data. For x = 0, Interestingly, we observed strong magnetic peaks (0, 0, space group: P4/nmm. Atomic positions: Eu(2c): (0.25, 0.25, L/2) (L = odd number) below T (see the inset of Fig. 2a). T 2 z), Mn(2a): (0.75, 0.25, 0), Sb1(2b): (0.75, 0.25, 0.5), Sb2(2c): This excludes the possibility of Eu moments pointing in (0.25, 0.25, z). For x > 0 compounds: Space group: Pnma. 16,32 the out-of-plane axis seen in EuMnBi . The deter- Eu/Sr(4c): (x, 0.25, z), Mn(4c): (x, 0.25, z), Sb1(4c):(x, 0.25, z), mined magnetic structure for T < T denoted by AFM 2 Mn, Sb1(4c): (x, 0.25, z). is shown in the right panel of Fig. 1a. Whereas Mn Eu,⊥ preserves a C-type AFM order with an increased moment x = 0 x = 0.2 x = 0.5 x = 0.8 due to Eu-Mn coupling along the c axis, the “++ −−” Lattice constants Eu spin ordering with the moment along the a axis a 4.343 (6) 22.348 (3) 22.27 (42) 22.28 (41) breaks the magnetic symmetry along the c axis and leads to observed magnetic reflections with k = (0,0,1/2) . Such b 4.343 (6) 4.347 (5) 4.411 (14) 4.412 (14) a magnetic structure is consistent with the susceptibility c 11.169 (13) 4.383 (4) 4.434 (24) 4.438 (28) measurements in Fig. 3a, where χ increases slightly and Atom χ decreases rapidly for T < T , suggesting an AFM ab 2 Eu z 0.729(5) x 0.113 (4) 0.113 (5) 0.112 (4) moment oriented along the a b plane. Note that the T T magnetic structure determined here is different from the z 0.781 (5) 0.789 (7) 0.806 (3) “+-+-” A-type Eu order proposed on the basis of dif- Mn x 0.253 (7) 0.249 (4) 0.242 (4) fraction experiments on a polycrystalline sample of z 0.323 (3) 0.279 (7) 0.292 (4) EuMnSb , for which no k = (0,0,1/2) magnetic peaks 2 T Sb1 x 0.0019 (8) 0.0011 (7) 0.0042 (9) were observed below T . The Eu moment canting pro- posed in ref. is not found in our crystal for T < T (see z 0.233 (6) 0.264 (4) 0.298 (7) the Supplemental Information for a detailed discussion). Sb2 z 0.156(7) x 0.324 (5) 0.325 (5) 0.324 (6) In the x = 0.2 compound, the temperature dependence z 0.829 (5) 0.768 (4) 0.818 (5) of the pure magnetic peak (010) in the orthorhombic Reliable factors structure, corresponding to the (100) in the tetragonal notation, shows a clear magnetic transition at the T of Rf 8.75 6.67 6.18 7.59 330 K, as shown in Fig. 2b. A similar C-type AFM order 2 0.28 0.28 1.21 0.83 (AFM ) with k = (0,0,0) was determined and is dis- Mn O played in the left panel in Fig. 1b. Upon cooling below T at 21 K, new magnetic peaks indexed by (H, K, L)(H = data is critical. We employed single-crystal neutron odd integers), for instance (700) , corresponding to (0 0 diffraction to solve the complicated magnetic structures 3.5) , are observed (see inset of Fig. 2b). All the magnetic of Eu Sr Mn Sb below 340 K. The refined peaks can be described by the AFM order at k = (0,0,0) 1−x x 1−z 2 O moments, Mn–Eu canting angle, and reliability factors in the orthorhombic notation due to the doubled unit cell of the refinements of the neutron data after neutron in contrast to x = 0. Within the temperature range of T < absorption correction are summarized in Table 2 (see T < T ,we find a canted and noncollinear Eu spin order the Supplemental Information for more details). confined within the a c plane with a “++ −−’ com- O O Figure 2a–d shows the temperature dependences of a ponent along the c axis and a “+ − + −” component few representative nuclear and/or magnetic reflections of along the a axis, coexisting with the C-type Mn AFM Eu Sr Mn Sb . For the x = 0 parent compound, the order with moments along the a axis (denoted by 1−x x 1−z 2 O presence of the pure magnetic peak at (100) below T1at AFM the middle panel in Fig. 1b). This is con- T Mn,Eu,C1, 330 K indicates one magnetic transition. The absence of sistent with the susceptibility measurement shown in an anomaly at T in susceptibility measurements (see Fig. 3a) Fig. 3b, where both χ and χ decrease below T , implying 1 a bc 2 may be ascribed to the possible strong spin fluctuations that Eu spins may form a canted AFM order. Note that above T that tend to smear out any anomalies in the such a canted Eu order is not applicable in the corre- 6,20,22 susceptibility as in other Mn-based compounds . For sponding T < T temperature region of the x = 0 parent T < T , a C-type AFM order of Mn spins (AFM ) with compound. At 10 K, the canting angle between Mn and 1 Mn the propagation vector k = (0,0,0) and the moment along Eu is 41(9)°. The susceptibility measurements show that χ T a the c axis is determined without Eu ordering, as illu- increases but χ decreases anomalously below T at 7 K, T bc 3 strated in the left panel of Fig. 1a. Upon cooling below T indicative of another magnetic transition. Interestingly, at 22 K, there is an increase in magnetic peak intensities there is a decrease in the (300) peak intensity, with a such as (100) and (101) with k = (0,0,0) and, concurrent increase in the intensity of the nuclear peak T T T Zhang et al. NPG Asia Materials (2022) 14:22 Page 5 of 11 Table 2 Refined magnetic moments, Mn–Eu angles, and reliable factors of Eu Sr Mn Sb with x = 0, 0.2, 0.5, and 0.8 1−x x 1−z 2 at different temperatures. x = 0 x = 0.2 x = 0.5 x = 0.8 T (K) 170 5 60 10 4 50 5 5 Mn moments M (x = 0) 2.99 (29) 4.63 (21) M (x > 0) 3.70 (46) 3.66 (32) 3.75 (45) 3.74 (15) 3.76 (17) 3.80 (22) Eu moments M 4.08 (34) 3.89 (69) 4.84 (55) 5.17 (62) M 5.25 (43) 3.52 (34) 3.30 (86) 2.23 (29) |M | 5.25 (43) 5.38 (34) 5.26 (50) 5.32 (50) 5.17 (62) total Mn–Eu moment angle( ) 90 (7) 41 (9) 40 (7) 24 (8) 0 Reliable factors RF (k = (0, 0, 0)) 9.53 8.75 7.64 7.55 6.67 5.32 6.18 7.59 χ (k = (0, 0, 0)) 0.27 0.28 0.13 0.29 0.28 0.31 1.26 0.83 RF (k = (0, 0, 1/2)) 8.93 χ (k = (0, 0, 1/2)) 0.26 Fig. 2 Neutron results on nuclear and magnetic peaks of Eu Sr Mn Sb . Temperature dependence of intensities at the representative 1−x x 1−z 2 nuclear and/or magnetic peak positions for a x = 0, b x = 0.2, c x = 0.5, and d 0.8. The insets show a comparison of the nuclear/magnetic peaks at different temperatures. The 2nd weak peak with a smaller omega in the rocking curves for x = 0 is due to the presence of another tetragonal domain rather than an orthorhombic domain in the crystal. The very weak (300) peak in d results from the λ/2 contamination of neutrons. The vertical lines indicate the locations of the magnetic transition temperatures. (600) for T < T . This strongly indicates a Eu spin- aMn–Eu canting angle of 40(7)° at 4 K, as shown in the O 3 reorientation transition to a Eu spin order without mag- right panel of Fig. 1b. At 4 K, the Mn and Eu moments are netic symmetry breaking along the a axis. When the found to be 3.75(45) and 5.26(50) µ , respectively, indi- O B 2+ 2+ C-type Mn order is unchanged, a canted and collinear cative of Mn (S = 5/2) and Eu (S = 7/2). magnetic structure with A-type “+ − + −” Eu spin order When x is increased to 0.5 or 0.8, the Eu lattice exhibits along both the a and c axes (AFM ) occurs with only a single AFM transition as revealed from the O O Mn,Eu,C2 Zhang et al. NPG Asia Materials (2022) 14:22 Page 6 of 11 Fig. 3 Susceptibility and resistivity of Eu Sr Mn Sb . Temperature dependence of the susceptibility of a x = 0 with a magnetic field of 0.1 T 1−x x 1−z 2 parallel to the out-of-plane c and in-plane a b directions and b x = 0.2, c x = 0.5, and d x = 0.8 with the field parallel to the out-of-plane a and in- T T T O plane b c directions. Temperature dependence of the out-of-plane resistivity ρ and in-plane longitudinal resistivity ρ at zero magnetic field for O O out in e x = 0, f x = 0.2, g x = 0.5 and h x = 0.8. susceptibility measurements shown in Fig. 3c, with T at Eu moment mainly points in the out-of-plane a direc- 2 O 17 K for x = 0.5 and 8 K for x = 0.8. For the x = 0.5 sam- tion at x = 0.8. ple, both the (010) and (001) magnetic peaks appear O O below T . Upon cooling below T at 15 K, the (010) peak Electronic transport properties 1 2 O intensity further increases, while there is no obvious Next, we present the evolution of the electronic trans- change in the (001) peak (see Fig. 2c and Fig. S5a, b). port properties with Sr doping in Eu Sr Mn Sb .As O 1−x x 1−z 2 Furthermore, there is an increase in the peak intensity shown in Fig. 3e–h, both the in-plane longitudinal resis- (300) due to the magnetic contribution but no obvious tivity ρ and out-of-plane resistivity ρ exhibit metallic O in out change in the peak intensities of (200) or (600) . These transport properties. At 2 K, ρ /ρ reaches 128, 198 and O O out in features are similar to those at x = 0.2. We indeed obtain 322 for x = 0, x = 0.2 and x = 0.8, respectively. Such a similar magnetic structures in the x = 0.5 sample, as rapid increase in electronic anisotropy indicates that Sr shown in the left panel (AFM ) and middle panel doping reinforces the quasi-2D electronic structure. In the Mn (AFM ) in Fig. 1b for T < T < T and T < T < T , x = 0 sample (see Figs. 3e and S7a), the slope of ρ and Mn,Eu,C1 2 1 3 2 out respectively. Note that the canting angle between Eu and ρ decreases below T , indicative of the coupling between in 2 Mn moments decreases to 24(8)° at 5 K. the emergence of Eu order and the transport properties, As x increases to 0.8, the Mn magnetic transition occurs suggesting that the in-plane Eu “++ --” order leads to at a T of 330 K as identified from the intensity of (010) , suppressed metallicity. The metallic behavior in our 1 O and a C-type Mn order AFM is determined (see the left EuMn Sb sample is different from the insulating Mn 0.95 2 panel of Fig. 1c). Another increase in (010) is found behavior observed in the Sn- or Mn-doped nonstoichio- 17,19 below T ≈ 7 K. There is no appearance of magnetic metric samples . This indicates that chemical doping scattering at the (300) and (200) or (600) Bragg at Sb or Mn sites induces a metal-insulator transition that O O O positions below T (see the inset of Fig. 2d and Fig. S5c in is distinct from the effect of Sr substitution for Eu. SI), indicating that Eu moments may point to the a axis. However, the x = 0.2 sample exhibits transport behavior We find a coexistence of C-type Mn AFM order with the distinct from that of the x = 0 sample. We observe a rapid “+ − + −” Eu order with an oriented moment along the decrease in ρ and a slight increase in ρ below T (see out in 2 same a axis as the Mn moment (AFM , see the right Figs. 3f and S7b), suggesting that the Eu canting to the a O Mn,Eu, O panel of Fig. 1c), consistent with susceptibility measure- axis with the Eu “+ − + −” component significantly ments. As shown in Fig. 3d, X keeps increasing, but X increases the interlayer conductivity along the a direc- bc a O decreases rapidly upon cooling below 8 K, showing tion between Sb layers but suppresses the intralayer behavior opposite to that of x = 0. This indicates that the conductivity on the b c plane, in contrast with the effect O O Zhang et al. NPG Asia Materials (2022) 14:22 Page 7 of 11 Fig. 4 High field magnetoresistance of Eu Sr Mn Sb . Field dependence of the out-of-plane magnetoresistance Δρ /ρ and in-plane 1−x x 1−z 2 out out magnetoresistance Δρ /ρ for a x = 0, b x = 0.2, c x = 0.5, and d x = 0.8. The inset of b shows the field-induced metamagnetic transition in the Eu in in sublattice, i.e., Eu spin ordering in and H < H and H < H < H . The insets of c, d show the linear fit of the Landau level fan diagram based on both the f f s 2 2 oscillatory resistivity ρ and the second derivative of the resistivity -d ρ /dB for x = 0.5 and based on only the oscillatory resistivity ρ for x = 0.8. in n in of the sole in-plane Eu order on the transport properties coupling between the Eu magnetic order and transport described above. Below T , there are no obvious changes properties in Eu Sr Mn Sb . 3 1−x x 1−z 2 in the out-of-plane resistivity, but an anomalous decrease in the in-plane resistivity is observed. This can be attrib- Nontrivial Berry phases uted to the SR of Eu from noncollinear to collinear order. Figure 4a–d shows both in-plane and out-of-plane Below T , the out-of-plane Eu order is kept at “+ − + −”, magnetoresistance (MR = [ρ (B) − ρ (0)]/ρ (0)) under which is not expected to influence the interlayer con- high magnetic fields applied along the out-of-plane ductivity. In contrast, the switch of the in-plane compo- direction. For x = 0, Δρ /ρ is negative, whereas the out out nent from “++ −−” to “+ − + −” induces an in-plane Δρ /ρ is positive. The magnitudes for both in in anomalous increase in the intralayer conductivity. Δρ /ρ and Δρ /ρ are small, and no strong out out in in When x increases to 0.5, the “+ − + −” component of Shubnikov-de Haas (SdH) oscillations are observed. For the Eu order along the a axis direction also induces an x = 0.2, weak SdH oscillations are observed in both Δρ / O out increase in the interlayer conductivity below T (see ρ and Δρ /ρ . As the field increases, there is a sign 2 out in in Figs. 3g and S7c), but the increase is weaker than that at reversal in ρ /ρ , whereas Δρ /ρ remains positive. in in out out x = 0.2. Furthermore, the weak decrease in the intralayer Remarkably, at 1.8 K, which is below T , a large jump in conductivity at x = 0.2 is hardly observed near T at x = Δρ /ρ up to 4500% occurs above a µ H of 18 T. 2 out out 0 t 0.5. Both are ascribed to the reduction in Eu occupancy to The dramatic changes in Δρ /ρ near µ H of 18 T are out out 0 t ≈ 50% at x = 0.5, which weakens the effect of Eu order on ascribed to a field-induced metamagnetic transition. Since the transport properties. For x = 0.8, the Eu ordering does this phenomenon does not occur in the T > T tempera- not obviously influence the resistivity below T , as shown ture regime (e.g., 50 K), the field-induced magnetic tran- in Figs. 3h and S7d, which can be ascribed to the low Eu sition does not originate from the Mn magnetic sublattice occupancy (≈ 20%). Thus, our results reveal an intimate but is related to the Eu magnetic sublattice, which is Zhang et al. NPG Asia Materials (2022) 14:22 Page 8 of 11 indicative of the vital role that the Eu magnetic order Composition phase diagram plays in the magnetotransport properties. The most likely From the combination of single-crystal X-ray diffrac- origin of the enhanced Δρ /ρ above µ H of 18 T is the tion, neutron diffraction, magnetization, and magneto- out out 0 t field-induced Eu SR transition from the canted moment transport measurements, we are able to establish the direction in the a c plane to the c axis, while the structural, magnetic, and electronic phase diagram, as O O O A-type “+ − + −” Eu order remains, thus strongly sup- illustrated in Fig. 5. While the x = 0 parent compound pressing interlayer conductivity, as illustrated in the inset with Mn deficiency is tetragonal with the space group P4/ of Fig. 4b. Note that this is different from the field- mmm, Sr doping induces an orthorhombic distortion. induced spin-flop transition of the “++ −−” Eu order This is consistent with previous reports on the orthor- from the out-of-plane c axis to the in-plane direction in hombic structure in doped nonstoichiometric sam- 16 17,19 EuMnBi . Above ∼ 28 T, the rapid decrease in Δρ / ples . Notably, our EuMn Sb sample forms a 2 out 0.95 2 ρ may indicate the full polarization of Eu spins to the magnetic structure with perpendicular Mn and Eu out external field direction, i.e., the a axis, similar to the moments at the ground state and does not exhibit topo- scenario seen in EuMnBi . Further high-field magneti- logical semimetallic behavior, different from previous 17–19 zation measurements are required to confirm these reports on samples with different compositions .Sr metamagnetic transitions. substitution for Eu in EuMnSb induces a slight decrease An increase in the Sr doping level significantly in T but suppresses T significantly. Furthermore, an 1 2 enhances SdH oscillations in both Δρ /ρ and Δρ / increase in Sr concentration drives an unusual Eu SR from out out in ρ for x = 0.5 and 0.8, respectively, with much higher the in-plane to the out-of-plane direction and simulta- in oscillation amplitudes at high magnetic fields. Δρ /ρ neously induces the appearance of Dirac semimetallic out out reaches ≈ 18,000% at 31.5 T for x = 0.8. We further behaviors. A higher Eu canting angle characterized by a analyze the Berry phase (BP) ϕ accumulated along smaller Eu–Mn angle is accompanied by stronger quan- cyclotron orbits and are able to extract ϕ for x = 0.5 and tum SdH oscillations. Our results show that Eu spin 0.8. Based on the field dependence data of ρ measured canting can be driven by chemical doping, which could in in a 14 T PPMS, which show well-resolved SdH oscilla- explain the observation of Eu canting in a doped tions in Fig. S8a, we obtain the second derivative of 2 2 resistivity -d ρ /dB and the oscillatory component of in ρ after background subtraction. The oscillation peaks in and valleys obtained from both analyses are well-mat- ched, as shown in Fig. S8b. With six oscillation valleys assigned to integer Landau levels (LLs) and five peaks assigned to half integer LLs, a Landau index fan diagram can be established, from which a nontrivial Berry phase of 0.8 π can be unambiguously extracted, as displayed in the inset of Fig. 4c. As shown in Fig. 4d, we extract a Berry phase of 0.88 π for the x = 0.8 compound. The Berry phases in both the x = 0.5 and 0.8 samples are apparently close to an ideal Berry phase for a quasi-2D system. The nontrivial Berry phase provides evidence that x = 0.5 and 0.8 harbor relativistic Dirac fermions. Our results clearly show that the substitution of Eu by Fig. 5 Composition phase diagram of Eu Sr Mn Sb with the 1−x x 1−z 2 nonmagnetic Sr induces Dirac semimetallic behavior structural and magnetic transitions, Eu–Mn moment angle α and that is closely associated with the controllable Eu nontrivial Berry phase (BH) extracted from the fits to ρ . T , T , in 1 2 magnetic order. and T label the magnetic transition temperatures. The distinct Unlike the x = 0.2 sample, the x = 0.5 and 0.8 samples magnetic structures (AFM , AFM , AFM , AFM , and Mn Mn,Eu,⊥ Mn,Eu,C1 Mn,Eu,C2 AFM are displayed in Fig. 1b–d. AFM and AFM do not show large jumps in ρ /ρ in the field up to Mn,Eu,//) Mn,Eu, // Mn,Eu,⊥ out out indicate the parallel and perpendicular moments of Mn and Eu, 31 T. This indicates the absence of field-induced meta- respectively. AFM and AFM show the two distinct Mn,Eu,C1 Mn,Eu,C2 magnetic transitions in both compounds. Therefore, the canted moments between Mn and Eu. The evolution of the violet nontrivial Berry phase may be intrinsic for x = 0.5 and 0.8 color illustrates the gradual decrease in the Eu–Mn moment angles. A compounds. In addition, compared to SrMnSb , with only higher Eu canting angle of (90 − α), i.e., a smaller α, is accompanied by stronger quantum SdH oscillations. All the compounds exhibit an ordered Mn moment, the x = 0.5 and 0.8 samples metal-like transport properties as a function of temperature, and they exhibit distinct Eu orders coexisting with Mn orders, and are also coupled to the Eu order at T and T . The nontrivial Berry 2 3 the increase in Eu canting angle is accompanied by phases indicative of Dirac semimetallic behaviors emerge for x ≥ 0.5. stronger quantum oscillations. Zhang et al. NPG Asia Materials (2022) 14:22 Page 9 of 11 nonstoichiometric sample . Note that no other magnetic the moment changes from the in-plane direction to the out- transition is observed at T in ref. For our x = 0.2 of-plane direction while the Mn moment direction remains compound, a 2nd type of Eu SR from a noncollinear along the out-of-plane a axis. 2+ canted spin order to a collinear A-type canted spin order The Mn moment, which commonly displays very is found at lower temperature (denoted by AFM in weak single-ion anisotropy as expected for the L =0of Mn,Eu,C2 2+ Fig. 5). Furthermore, the Eu order at the base temperature Mn (S = 5/2), favors orientation along the out-of-plane 20–22 can be easily tuned by the external magnetic field to direction , i.e., the c axis in the tetragonal structure another type of SR, leading to a canted AFM state with the or the a axis in the orthorhombic structure, forming moments oriented to the possible c axis. The established C-type AFM order in T < T < T of Eu Sr Mn Sb O 2 1 1−x x 1−z 2. phase diagram for Eu Sr Mn Sb as well as the The in-plane checkerboard-like AFM structure of the 1−x x 1−z 2 17–19 comparison with the previous reports we made above C-type order suggests that the NN interaction J is indicate that the structure, magnetic order, and electronic dominant, whereas the in-plane next-nearest-neighbor properties of EuMnSb are easily perturbed by chemical (NNN) interaction J is very weak. In the context of the 2 2 doping at any of the Eu, Mn, and Sb sites, indicating that J –J –J model , we conclude that J >0, J < J /2 and out- 1 2 c 1 2 1 the lattice, spin and charge degrees of freedom are of-plane J < 0 with negligible spin frustration in the Mn strongly coupled in this material. This could account for sublattice. Upon cooling to T < T , Eu-Eu coupling starts 17–19 the conflicting results reported in the literature to come into play and induces Eu ordering with a pre- 2+ 34,35 regarding the structure, magnetic, and electronic trans- ferred orientation of Eu (S = 7/2) in plane , either port properties of EuMnSb and implies that the non- the a b plane in the tetragonal structure or the b c 2 T T O O stoichiometry must be taken into account to understand plane in the orthorhombic structure. Simultaneously, the the intrinsic crystal and magnetic structure and magne- Eu–Mn coupling also plays an important role by exerting totransport properties of EuMnSb . an effective field that has the tendency to influence the 17,19 While chemical doping at Sb or Mn sites in non- Mn/Eu moment directions. The increase in Sr con- stoichiometric samples induces a tetragonal-orthorhombic centration on the Eu site weakens Eu–Eu coupling and structural transition, as in our Eu Sr Mn Sb (x>0), destabilizes the preferred orientation of the Eu spins. 1−x x 1−z 2 such doping induces a metal–insulator transition yielding Thus, as x increases to 0.2, the effective field from Eu–Mn insulating behavior. This indicates that doping at the Sb or coupling tends to drive the Eu moment toward the Mn Mn sites may be detrimental to forming semimetallic beha- moment direction. The competition of Eu–Eu and vior in EuMnSb Eu–Mn couplings induces spin frustration in the Eu derivatives. In contrast, our phase diagram clearly shows that Sr doping at the Eu site is the driving force sublattice and leads to a canted Eu order with the moment of the Dirac semimetallic behavior in Eu Sr Mn Sb ,as in the ac plane stabilized in T < T < T . An increase in Sr 1−x x 1−z 2 3 2 discussed below. First, Sr doping at the Eu site lowers the doping has a tendency to further drive the Eu moment tilt lattice symmetry and modifies the structural parameters, as toward the a axis due to weakened Eu–Eu coupling, as summarized in Table 1, which could in turn change the shown by a lower Eu–Mn angle for x = 0.5. As the Sr electronic band structure. Second, the different types of Eu doping increases to 0.8, the Eu–Mn coupling overwhelms spin reorientations driven by Sr doping, temperature, or the weak Eu–Eu coupling, which leads to an SR of Eu to magnetic field significantly influence the electronic transport the same moment direction as the Mn moment. This and magnetotransport properties, indicating that the band could account for the unusual Eu SR induced by Sr structure is sensitively dependent on the magnetism of the doping. As the temperature decreases below T for x = Eu sublattice. As such, the phase diagram presented in Fig. 5 0.2, a temperature-induced SR transition occurs. This may offers an excellent opportunity to explore the intimate be ascribed to another type of Eu–Eu coupling that comes interplay between the band relativistic effect and magnetism. into play below T . This retains the “+ − + −” out-of- plane component but switches the in-plane component Origin of various Eu spin reorientations from “++ −−” to “+ − + −”, leading to a collinear Finally,wediscuss theorigins of thecomplicated magnetic A-type AFM order of Eu spins in T < T . Thus, the structures, in particular, the Sr-doping and temperature- striking Eu spin reorientation driven by Sr doping and induced Eu SR transition in Eu Sr Mn Sb . A common temperature indicates strong Eu–Mn (4f–3d) couplings 1−x x 1−z 2 SR in rare earth elements occurs because the rare earth and results from their competition with Eu–Eu couplings. element drives the Mn moment parallel to its moment To summarize, we report the composition phase dia- direction once the rare earth spins are ordered with pre- gram of the crystal and magnetic structures and electronic ferred in-plane orientation at low temperatures, as reported transport properties of Eu Sr Mn Sb and the reali- 1−x x 1−z 2 for several compounds such as RMnAsO (R= Nd or zation of tunable topological semimetallic behavior by 20,21 22,23 Ce) and RMnSbO (R= Pr or Ce) . However, Sr controlling various spin reorientations by chemical sub- doping in Eu Sr Mn Sb generates a novel Eu SR where stitution, temperature, and/or an external magnetic field. 1−x x 1−z 2 Zhang et al. NPG Asia Materials (2022) 14:22 Page 10 of 11 The structure, magnetic order, and electronic properties Supplementary information The online version contains supplementary material available at https://doi.org/10.1038/s41427-022-00369-5. of the parent EuMnSb are easily perturbed by chemical doping, and therefore, the nonstoichiometry must be Received: 10 August 2021 Revised: 22 January 2022 Accepted: 2 February taken into account to determine its intrinsic structure and physical properties. While we found that nearly stoi- Published online: 11 March 2022 chiometric EuMnSb is not a topological semimetal, doping of nonmagnetic Sr on the Eu site induces an References intricate coupling between the structure, various Eu spin 1. Xu, S.-Y. et al. Discovery of a Weyl fermion semimetal and topological fermi arcs. Science 349,613–617 (2015). reorientations, and quantum transport properties, indi- 2. Lu, L. et al. Experimental observation of Weyl points. 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