Introduction

Dirac/Weyl semimetals have attracted intense research interest due to their exotic quantum phenomena, as well as their promise for applications in next generation, more energy-efficient electronic devices1,2,3. Magnetic Dirac/Weyl semimetals are especially attractive since the coupling of Dirac/Weyl fermions to the additional spin degree of freedom may open up a new avenue for tuning and controlling the resulting quantum transport properties4,5,6. To date, several magnetic semimetals have been reported, and most of them were discovered in stoichiometric compounds, such as SrMnBi27, Mn3Sn8, RAlGe(R = rare earth)9, Co3Sn2S210,11, and Co2MnGa12,13. Finding a strategy to control a topological state by tuning magnetism is highly desirable and requires a clear understanding of the interplay between the magnetism and the topological electronic state. This goal can be achieved by investigating the coupling between the structure and magnetic and electronic phase diagrams in tunable magnetic topological materials.

The large family of ternary AMnCh2 “112” compounds (A = alkali earth/rare earth elements, Ch = Bi or Sb)6,7,14,15,16 are particularly interesting since a few of them have been reported to be magnetic Dirac semimetals where the Bi or Sb layers host relativistic fermions. AMnCh2 (A = Ce, Pr, Nd, Eu, Sm; C = Bi or Sb)14,16,17,18 possesses two magnetic sublattices, formed by the magnetic moments of rare earth A and Mn, respectively, in contrast with other compounds, which have only Mn magnetic lattice in this family. The conducting Bi/Sb layers and the insulating magnetic Mn–Bi(Sb) and Eu layers are spatially separated, which makes them good candidates for exploring the possible interplay between Dirac fermions and magnetism. For EuMnBi2, both the Eu and Mn moments point in the out-of-plane direction and generate two AFM lattices in the ground state16. Previous studies have also shown that when the Eu AFM order undergoes a spin-flop transition in a moderate field range, interlayer conduction is strongly suppressed, thus resulting in a stacked quantum Hall effect. Interestingly, EuMnSb2 exhibits distinct properties from EuMnBi2, and conflicting results have been reported17,18,19. The magnetotransport properties reported by Yi et al.17 are not indicative of a Dirac semimetallic state, while Soh et al.18 observed linear band dispersion near the Fermi level in Angle-resolved photoemission spectroscopy measurements of EuMnSb2 and claimed that it may be a Dirac semimetal. Moreover, the magnetic structure of EuMnSb2 is thought to be distinct from that of EuMnBi2, with controversial reports on Eu and Mn moments being perpendicular18 or canted to each other19. It is therefore important to resolve the controversy about the magnetic and physical properties of EuMnSb2 and to explore whether EuMnSb and its derivatives could host Dirac fermions. Additionally, it is known that in many-layered compounds involving spatially separated rare earth and manganese layers such as RMnAsO (R = Nd or Ce)21,22 and RMnSbO (R = Pr or Ce)22,23, the moment of rare earth elements ordered at low temperatures usually drives Mn spin reorientation to its moment direction. Given that there are two magnetic sublattices of Eu and Mn with an expected 4f–3d coupling between them in EuMnSb2, the chemical substitution of Eu by nonmagnetic elements may achieve interesting magnetic states by tuning the magnetic interactions, which may control the transport and magnetotransport properties.

In this article, we report comprehensive studies on a tunable Dirac semimetal system Eu1−xSrxMn1−zSb2, which exhibits a variety of novel magnetic states tunable by the Eu concentration, temperature, and magnetic field. The evolution of the magnetic states of this system is found to be coupled to the quantum transport properties of Dirac fermions. Through single-crystal X-ray diffraction, neutron scattering, magnetic and high-field transport measurements, we established a rich phase diagram of the crystal structure, magnetism, and electronic properties of Eu1−xSrxMn1−zSb2. The increase in Sr concentration in Eu1−xSrxMn1−zSb2 induces not only lattice symmetry breaking and surprising Eu spin reorientation to the Mn moment direction but also topological semimetallic states for x ≥ 0.5. Furthermore, the quantum transport properties can be tuned by the different Eu spin reorientations to collinear AFM orders induced by the temperature and external magnetic field. The in-plane and out-of-plane components of the canted Eu magnetic order are found to influence the intralayer and interlayer conductivities of Dirac fermions generated by the 2D Sb layers, respectively. These results establish a new unique material platform for exploring Dirac band tuning by magnetism.

Materials and methods

Crystal growth

The Eu1−xSrxMn1−zSb2 single crystals were grown using a self-flux method. The starting materials with stoichiometric mixtures of Eu/Sr, Mn, and Sb elements, i.e., EuMnSb2, Eu0.8Sr0.2MnSb2, Eu0.5Sr0.5MnSb2, and Eu0.2Sr0.8MnSb2, were put into small alumina crucibles and sealed in individual quartz tubes in an argon gas atmosphere. The tube was heated to 1050 °C for 2 days, followed by subsequent cooling to 650 °C at a rate of 2 °C/h. Plate-like single crystals were obtained. The compositions of all the single crystals were examined using energy-dispersive X-ray spectroscopy. The composition of the x = 0 parent compound was also characterized by fitting to single-crystal X-ray diffraction data.

Single-crystal X-ray and neutron diffraction measurements and neutron data analysis

A crystal of x = 0 was mounted onto glass fibers using epoxy, which was then mounted onto the goniometer of a Nonius KappaCCD diffractometer equipped with Mo Kα radiation (λ = 0.71073 Å). After the data collection and subsequent data reduction, SIR97 was employed to provide a starting model, SHELXL97 was used to refine the structural model, and the data were corrected using extinction coefficients and weighting schemes during the final stages of refinement24,25. To investigate the crystal and magnetic structures, neutron diffraction measurements were conducted with the four circle neutron diffractometer (FCD) located in the High Flux Isotope Reactor at Oak Ridge National Laboratory. To further distinguish between tetragonal and orthorhombic structures for x = 0, neutrons with a monochromatic wavelength of 1.003 Å without λ/2 contamination are used via the silicon monochromator from (bent Si-331)26. For other Eu1−xSrxMn1−zSb2 (x = 0.2, 0.5, 0.8) crystals, we employed neutrons with a wavelength of 1.542 Å involving 1.4% λ/2 contamination from the Si-220 monochromator using its high resolution mode (bending 150)26. The crystal and magnetic structures were investigated in different temperature windows. The order parameter of a few important nuclear and magnetic peaks was measured. Data were recorded over a temperature range of 4 < T < 340 K using a closed-cycle refrigerator available at the FCD. Due to the involvement of the high-absorbing europium in the Eu1−xSrxMn1−zSb2 crystals, proper neutron absorption corrections to the integrated intensities of the nuclear/magnetic peaks are indispensable. The dimensions of the faces for each crystal were measured, and a face index absorption correction of the integrated intensities was conducted carefully using the WinGX package27. The SARAh representational analysis program28 and Bilbao crystallographic server29 were used to derive the symmetry-allowed magnetic structures and magnetic space groups. The full datasets at different temperatures were analyzed using the refinement program FullProf suite30 to obtain the structure and magnetic structures.

Magnetization and magnetotransport measurements

The temperature and field dependence of the magnetization were measured in a superconducting quantum interference device magnetometer (Quantum Design) in magnetic fields up to 7 T. The transport measurements at zero magnetic field were performed with a four-probe method using Physical Property Measurement Systems (PPMS). The high-field magnetotransport properties were measured in 31 T resistivity magnets at the National High Magnetic Field Laboratory (NHMFL) in Tallahassee. The magnetic fields were applied parallel to the out-of-plane direction to study the in-plane and out-of-plane magnetoresistance. The ρin samples were made into Hall bar shapes, and the ρout samples were in the Corbino disk geometry. The Berry phase was extracted from the Landau fan diagram. The integer Landau levels are assigned to the magnetic field positions of resistivity minima in SdH oscillations, which correspond to the minimal density of state.

Results and discussion

Crystal structures

Both single-crystal X-ray and neutron diffraction reveal that the parent compound EuMnSb2 crystallizes in a tetragonal structure with space group P4/nmm (Figs. 1a and S1e) and nonstoichiometric composition EuMn0.95Sb2. The structural parameters of EuMn0.95Sb2 obtained from the single-crystal X-ray diffraction refinement at 293 K are summarized in Tables SI and SII. Note that the structure of EuMn0.95Sb2 is similar to that of CaMnBi231 but different from the I4/mmm in the tetragonal structure of EuMnBi216 and the previously reported orthorhombic structure of EuMnSb217,19. The energy-dispersive X-ray spectroscopy analysis shows that there are also less than 5% Mn deficiencies in the Sr-doped compounds with z∼0.01, 0.05, and 0.02 for x = 0.2, 0.5, and 0.8, respectively.

Fig. 1: Magnetic structures of Eu1−xSrxMn1−zSb2.
figure 1

Magnetic structures determined from the fits to the neutron data for a x = 0, b x = 0.2 (all the 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.

Full size image

Interestingly, the Sr-doped Eu1−xSrxMn1−zSb2 (x = 0.2, 0.5, and 0.8) shows a clear lattice distortion and crystallizes in the orthorhombic structure with the space group Pnma, with a doubled unit cell along the out-of-plane direction (Figs. 1b, c and S1f), similar to SrMnSb26. Thus, the Sr do** at the Eu site in EuMn0.95Sb2 induces symmetry breaking from tetragonal P4/nmm to Pnma. Our systematic studies on Sr-doped EuMn1−zSb2 and comparison with previous reports on the parent compound suggest that the structural difference between our x = 0 sample and the samples reported in the literature17,19 arises from the nonstoichiometric compositions and/or flux-induced chemical do**. The sample reported in ref. 17 involves Sn do** at the Sb sites due to the use of Sn flux, which yields a composition of Eu0.992Mn1.008Sb1.968Sn0.73. In ref. 19, the composition was reported to be EuMn1.1Sb2, which implies that a significant amount of Mn antisite defects may exist at the Sb sites. In contrast, our parent compound x = 0 is characterized by only a small degree of Mn deficiency. Such composition differences from the previously reported samples explain why our x = 0 sample is tetragonal, whereas the samples reported in the literature are orthorhombic. This also indicates that chemical do** at the Eu, Mn, or Sb sites in EuMnSb2 could induce orthorhombic distortion.

The structural parameters of Eu1−xSrxMn1−zSb2 (x = 0, 0.2, 0.5, and 0.8) at 5 K obtained from the fits to neutron diffraction data are summarized in Table 1. It can be seen that Sr do** induces a slight decrease in the out-of-plane lattice constant and an increase in the in-plane lattice constants. More details about the determination of crystal structures of all the Eu1−xSrxMn1−zSb2 compounds can be found in the Supplemental Information.

Table 1 Structural parameters of Eu1−xSrxMn1−zSb2 with x = 0, 0.2, 0.5, and 0.8 at 5 K obtained through the fitting of the single-crystal neutron diffraction data. For x = 0, space group: P4/nmm. Atomic positions: Eu(2c): (0.25, 0.25, z), Mn(2a): (0.75, 0.25, 0), Sb1(2b): (0.75, 0.25, 0.5), Sb2(2c):(0.25, 0.25, z). For x > 0 compounds: Space group: Pnma. Eu/Sr(4c): (x, 0.25, z), Mn(4c): (x, 0.25, z), Sb1(4c):(x, 0.25, z), Sb1(4c): (x, 0.25, z).
Full size table

Determination of magnetic structures

In general, determining the complicated magnetic structures in Eu-containing compounds is difficult due to the strong neutron absorption of europium. Proper neutron absorption correction of the neutron diffraction data is critical. We employed single-crystal neutron diffraction to solve the complicated magnetic structures of Eu1−xSrxMn1−zSb2 below 340 K. The refined moments, Mn–Eu canting angle, and reliability factors of the refinements of the neutron data after neutron absorption correction are summarized in Table 2 (see the Supplemental Information for more details).

Table 2 Refined magnetic moments, Mn–Eu angles, and reliable factors of Eu1−xSrxMn1−zSb2 with x = 0, 0.2, 0.5, and 0.8 at different temperatures.
Full size table

Figure 2a–d shows the temperature dependences of a few representative nuclear and/or magnetic reflections of Eu1−xSrxMn1−zSb2. For the x = 0 parent compound, the presence of the pure magnetic peak at (100)T below T1 at 330 K indicates one magnetic transition. The absence of an anomaly at T1 in susceptibility measurements (see Fig. 3a) may be ascribed to the possible strong spin fluctuations above T1 that tend to smear out any anomalies in the susceptibility as in other Mn-based compounds6,20,22. For T < T1, a C-type AFM order of Mn spins (AFMMn) with the propagation vector k = (0,0,0)T and the moment along the cT axis is determined without Eu ordering, as illustrated in the left panel of Fig. 1a. Upon cooling below T2 at 22 K, there is an increase in magnetic peak intensities such as (100)T and (101)T with k = (0,0,0)T and, simultaneously, new magnetic reflections with a propagation vector k = (0,0,1/2)T from the Eu sublattice appear.

Fig. 2: Neutron results on nuclear and magnetic peaks of Eu1−xSrxMn1−zSb2.
figure 2

Temperature dependence of intensities at the representative 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.

Full size image
Fig. 3: Susceptibility and resistivity of Eu1−xSrxMn1−zSb2.
figure 3

Temperature dependence of the susceptibility of a x = 0 with a magnetic field of 0.1 T parallel to the out-of-plane cT and in-plane aTbT directions and b x = 0.2, c x = 0.5, and d x = 0.8 with the field parallel to the out-of-plane aO and in-plane bOcO directions. Temperature dependence of the out-of-plane resistivity ρout and in-plane longitudinal resistivity ρin at zero magnetic field for e x = 0, f x = 0.2, g x = 0.5 and h x = 0.8.

Full size image

Interestingly, we observed strong magnetic peaks (0, 0, L/2)T (L = odd number) below T2 (see the inset of Fig. 2a). This excludes the possibility of Eu moments pointing in the out-of-plane axis seen in EuMnBi216,32. The determined magnetic structure for T < T2 denoted by AFMMn,Eu,⊥is shown in the right panel of Fig. 1a. Whereas Mn preserves a C-type AFM order with an increased moment due to Eu-Mn coupling along the cT axis, the “+ + − −” Eu spin ordering with the moment along the aT axis breaks the magnetic symmetry along the cT axis and leads to observed magnetic reflections with k = (0,0,1/2)T. Such a magnetic structure is consistent with the susceptibility measurements in Fig. 3a, where χc increases slightly and χab decreases rapidly for T < T2, suggesting an AFM moment oriented along the aTbT plane. Note that the magnetic structure determined here is different from the “+-+-” A-type Eu order proposed on the basis of diffraction experiments on a polycrystalline sample of EuMnSb2, for which no k = (0,0,1/2)T magnetic peaks were observed below T2. The Eu moment canting proposed in ref. 19 is not found in our crystal for T < T2 (see the Supplemental Information for a detailed discussion).

In the x = 0.2 compound, the temperature dependence of the pure magnetic peak (010)O in the orthorhombic structure, corresponding to the (100)T in the tetragonal notation, shows a clear magnetic transition at the T1 of 330 K, as shown in Fig. 2b. A similar C-type AFM order (AFMMn) with k = (0,0,0)O was determined and is displayed in the left panel in Fig. 1b. Upon cooling below T2 at 21 K, new magnetic peaks indexed by (H, K, L) (H = odd integers), for instance (700)O, corresponding to (0 0 3.5)T, are observed (see inset of Fig. 2b). All the magnetic peaks can be described by the AFM order at k = (0,0,0)O in the orthorhombic notation due to the doubled unit cell in contrast to x = 0. Within the temperature range of T3 < T < T2, we find a canted and noncollinear Eu spin order confined within the aOcO plane with a “+ + − −’ component along the cO axis and a “+ − + −” component along the aO axis, coexisting with the C-type Mn AFM order with moments along the aO axis (denoted by AFMMn,Eu,C1, the middle panel in Fig. 1b). This is consistent with the susceptibility measurement shown in Fig. 3b, where both χa and χbc decrease below T2, implying that Eu spins may form a canted AFM order. Note that such a canted Eu order is not applicable in the corresponding T < T2 temperature region of the x = 0 parent compound. At 10 K, the canting angle between Mn and Eu is 41(9)°. The susceptibility measurements show that χa increases but χbc decreases anomalously below T3 at 7 K, indicative of another magnetic transition. Interestingly, there is a decrease in the (300)O peak intensity, with a concurrent increase in the intensity of the nuclear peak (600)O for T < T3. This strongly indicates a Eu spin-reorientation transition to a Eu spin order without magnetic symmetry breaking along the aO axis. When the C-type Mn order is unchanged, a canted and collinear magnetic structure with A-type “+ − + −” Eu spin order along both the aO and cO axes (AFMMn,Eu,C2) occurs with a Mn–Eu canting angle of 40(7)° at 4 K, as shown in the right panel of Fig. 1b. At 4 K, the Mn and Eu moments are found to be 3.75(45) and 5.26(50) µB, respectively, indicative of Mn2+ (S = 5/2) and Eu2+ (S = 7/2).

When x is increased to 0.5 or 0.8, the Eu lattice exhibits only a single AFM transition as revealed from the susceptibility measurements shown in Fig. 3c, with T2 at 17 K for x = 0.5 and 8 K for x = 0.8. For the x = 0.5 sample, both the (010)O and (001)O magnetic peaks appear below T1. Upon cooling below T2 at 15 K, the (010)O peak intensity further increases, while there is no obvious change in the (001)O peak (see Fig. 2c and Fig. S5a, b). Furthermore, there is an increase in the peak intensity (300)O due to the magnetic contribution but no obvious change in the peak intensities of (200)O or (600)O. These features are similar to those at x = 0.2. We indeed obtain similar magnetic structures in the x = 0.5 sample, as shown in the left panel (AFMMn) and middle panel (AFMMn,Eu,C1) in Fig. 1b for T2 < T < T1 and T3 < T < T2, respectively. Note that the canting angle between Eu and Mn moments decreases to 24(8)° at 5 K.

As x increases to 0.8, the Mn magnetic transition occurs at a T1 of 330 K as identified from the intensity of (010)O, and a C-type Mn order AFMMn is determined (see the left panel of Fig. 1c). Another increase in (010)O is found below T2 ≈ 7 K. There is no appearance of magnetic scattering at the (300)O and (200)O or (600)O Bragg positions below T2 (see the inset of Fig. 2d and Fig. S5c in SI), indicating that Eu moments may point to the aO axis. We find a coexistence of C-type Mn AFM order with the “+ − + −” Eu order with an oriented moment along the same aO axis as the Mn moment (AFMMn,Eu,, see the right panel of Fig. 1c), consistent with susceptibility measurements. As shown in Fig. 3d, Xbc keeps increasing, but Xa decreases rapidly upon cooling below 8 K, showing behavior opposite to that of x = 0. This indicates that the Eu moment mainly points in the out-of-plane aO direction at x = 0.8.

Electronic transport properties

Next, we present the evolution of the electronic transport properties with Sr do** in Eu1−xSrxMn1−zSb2. As shown in Fig. 3e–h, both the in-plane longitudinal resistivity ρin and out-of-plane resistivity ρout exhibit metallic transport properties. At 2 K, ρout/ρin reaches 128, 198 and 322 for x = 0, x = 0.2 and x = 0.8, respectively. Such a rapid increase in electronic anisotropy indicates that Sr do** reinforces the quasi-2D electronic structure. In the x = 0 sample (see Figs. 3e and S7a), the slope of ρout and ρin decreases below T2, indicative of the coupling between the emergence of Eu order and the transport properties, suggesting that the in-plane Eu “+ + - -” order leads to suppressed metallicity. The metallic behavior in our EuMn0.95Sb2 sample is different from the insulating behavior observed in the Sn- or Mn-doped nonstoichiometric samples17,19. This indicates that chemical do** at Sb or Mn sites induces a metal-insulator transition that is distinct from the effect of Sr substitution for Eu.

However, the x = 0.2 sample exhibits transport behavior distinct from that of the x = 0 sample. We observe a rapid decrease in ρout and a slight increase in ρin below T2 (see Figs. 3f and S7b), suggesting that the Eu canting to the aO axis with the Eu “+ − + −” component significantly increases the interlayer conductivity along the aO direction between Sb layers but suppresses the intralayer conductivity on the bOcO plane, in contrast with the effect of the sole in-plane Eu order on the transport properties described above. Below T3, there are no obvious changes in the out-of-plane resistivity, but an anomalous decrease in the in-plane resistivity is observed. This can be attributed to the SR of Eu from noncollinear to collinear order. Below T3, the out-of-plane Eu order is kept at “+ − + −”, which is not expected to influence the interlayer conductivity. In contrast, the switch of the in-plane component from “+ + − −” to “+ − + −” induces an anomalous increase in the intralayer conductivity.

When x increases to 0.5, the “+ − + −” component of the Eu order along the aO axis direction also induces an increase in the interlayer conductivity below T2 (see Figs. 3g and S7c), but the increase is weaker than that at x = 0.2. Furthermore, the weak decrease in the intralayer conductivity at x = 0.2 is hardly observed near T2 at x = 0.5. Both are ascribed to the reduction in Eu occupancy to ≈ 50% at x = 0.5, which weakens the effect of Eu order on the transport properties. For x = 0.8, the Eu ordering does not obviously influence the resistivity below T2, as shown in Figs. 3h and S7d, which can be ascribed to the low Eu occupancy (≈ 20%). Thus, our results reveal an intimate coupling between the Eu magnetic order and transport properties in Eu1−xSrxMn1−zSb2.

Nontrivial Berry phases

Figure 4a–d shows both in-plane and out-of-plane magnetoresistance (MR = [ρ (B) − ρ (0)]/ρ (0)) under high magnetic fields applied along the out-of-plane direction. For x = 0, ∆ρout/ρout is negative, whereas the in-plane ∆ρin/ρin is positive. The magnitudes for both ∆ρout/ρout and ∆ρin/ρin are small, and no strong Shubnikov-de Haas (SdH) oscillations are observed. For x = 0.2, weak SdH oscillations are observed in both ∆ρout/ρout and ∆ρin/ρin. As the field increases, there is a sign reversal in ρin/ρin, whereas ∆ρout/ρout remains positive. Remarkably, at 1.8 K, which is below T3, a large jump in ∆ρout/ρout up to 4500% occurs above a µ0Ht of 18 T. The dramatic changes in ∆ρout/ρout near µ0Ht of 18 T are ascribed to a field-induced metamagnetic transition. Since this phenomenon does not occur in the T > T2 temperature regime (e.g., 50 K), the field-induced magnetic transition does not originate from the Mn magnetic sublattice but is related to the Eu magnetic sublattice, which is indicative of the vital role that the Eu magnetic order plays in the magnetotransport properties. The most likely origin of the enhanced ∆ρout/ρout above µ0Ht of 18 T is the field-induced Eu SR transition from the canted moment direction in the aOcO plane to the cO axis, while the A-type “+ − + −” Eu order remains, thus strongly suppressing interlayer conductivity, as illustrated in the inset of Fig. 4b. Note that this is different from the field-induced spin-flop transition of the “+ + − −” Eu order from the out-of-plane cO axis to the in-plane direction in EuMnBi216. Above ∼ 28 T, the rapid decrease in ∆ρout/ρout may indicate the full polarization of Eu spins to the external field direction, i.e., the aO axis, similar to the scenario seen in EuMnBi216. Further high-field magnetization measurements are required to confirm these metamagnetic transitions.

Fig. 4: High field magnetoresistance of Eu1−xSrxMn1−zSb2.
figure 4

Field dependence of the out-of-plane magnetoresistance ∆ρout/ρout and in-plane magnetoresistance ∆ρin/ρin 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 sublattice, i.e., Eu spin ordering in and H < Hf and Hf < H < Hs. The insets of c, d show the linear fit of the Landau level fan diagram based on both the oscillatory resistivity ρin and the second derivative of the resistivity -d2ρn/dB2 for x = 0.5 and based on only the oscillatory resistivity ρin for x = 0.8.

Full size image

An increase in the Sr do** level significantly enhances SdH oscillations in both ∆ρout/ρout and ∆ρin/ρin for x = 0.5 and 0.8, respectively, with much higher oscillation amplitudes at high magnetic fields. ∆ρout/ρout reaches ≈ 18,000% at 31.5 T for x = 0.8. We further analyze the Berry phase (BP) ϕB accumulated along cyclotron orbits and are able to extract ϕB for x = 0.5 and 0.8. Based on the field dependence data of ρin measured in a 14 T PPMS, which show well-resolved SdH oscillations in Fig. S8a, we obtain the second derivative of resistivity -d2ρin/dB2 and the oscillatory component of ρin after background subtraction. The oscillation peaks and valleys obtained from both analyses are well-matched, 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 nonmagnetic Sr induces Dirac semimetallic behavior that is closely associated with the controllable Eu magnetic order.

Unlike the x = 0.2 sample, the x = 0.5 and 0.8 samples do not show large jumps in ρout/ρout in the field up to 31 T. This indicates the absence of field-induced metamagnetic transitions in both compounds. Therefore, the nontrivial Berry phase may be intrinsic for x = 0.5 and 0.8 compounds. In addition, compared to SrMnSb2, with only an ordered Mn moment, the x = 0.5 and 0.8 samples exhibit distinct Eu orders coexisting with Mn orders, and the increase in Eu canting angle is accompanied by stronger quantum oscillations.

Composition phase diagram

From the combination of single-crystal X-ray diffraction, neutron diffraction, magnetization, and magnetotransport measurements, we are able to establish the structural, magnetic, and electronic phase diagram, as illustrated in Fig. 5. While the x = 0 parent compound with Mn deficiency is tetragonal with the space group P4/mmm, Sr do** induces an orthorhombic distortion. This is consistent with previous reports on the orthorhombic structure in doped nonstoichiometric samples17,19. Notably, our EuMn0.95Sb2 sample forms a magnetic structure with perpendicular Mn and Eu moments at the ground state and does not exhibit topological semimetallic behavior, different from previous reports on samples with different compositions17,18,19. Sr substitution for Eu in EuMnSb2 induces a slight decrease in T1 but suppresses T2 significantly. Furthermore, an increase in Sr concentration drives an unusual Eu SR from the in-plane to the out-of-plane direction and simultaneously induces the appearance of Dirac semimetallic behaviors. A higher Eu canting angle characterized by a smaller Eu–Mn angle is accompanied by stronger quantum SdH oscillations. Our results show that Eu spin canting can be driven by chemical do**, which could explain the observation of Eu canting in a doped nonstoichiometric sample19. Note that no other magnetic transition is observed at T3 in ref. 19 For our x = 0.2 compound, a 2nd type of Eu SR from a noncollinear canted spin order to a collinear A-type canted spin order is found at lower temperature (denoted by AFMMn,Eu,C2 in Fig. 5). Furthermore, the Eu order at the base temperature can be easily tuned by the external magnetic field to another type of SR, leading to a canted AFM state with the moments oriented to the possible cO axis. The established phase diagram for Eu1−xSrxMn1−zSb2 as well as the comparison with the previous reports we made above17,18,19 indicate that the structure, magnetic order, and electronic properties of EuMnSb2 are easily perturbed by chemical do** at any of the Eu, Mn, and Sb sites, indicating that the lattice, spin and charge degrees of freedom are strongly coupled in this material. This could account for the conflicting results reported in the literature17,18,19 regarding the structure, magnetic, and electronic transport properties of EuMnSb2 and implies that the nonstoichiometry must be taken into account to understand the intrinsic crystal and magnetic structure and magnetotransport properties of EuMnSb2.

Fig. 5: Composition phase diagram of Eu1−xSrxMn1−zSb2 with the structural and magnetic transitions, Eu–Mn moment angle α and nontrivial Berry phase (BH) extracted from the fits to ρin.
figure 5

T1, T2, and T3 label the magnetic transition temperatures. The distinct magnetic structures (AFMMn, AFMMn,Eu,⊥, AFMMn,Eu,C1, AFMMn,Eu,C2, and AFMMn,Eu,//) are displayed in Fig. 1b–d. AFMMn,Eu, // and AFMMn,Eu,⊥ indicate the parallel and perpendicular moments of Mn and Eu, respectively. AFMMn,Eu,C1 and AFMMn,Eu,C2 show the two distinct canted moments between Mn and Eu. The evolution of the violet color illustrates the gradual decrease in the Eu–Mn moment angles. A higher Eu canting angle of (90o − α), i.e., a smaller α, is accompanied by stronger quantum SdH oscillations. All the compounds exhibit metal-like transport properties as a function of temperature, and they are also coupled to the Eu order at T2 and T3. The nontrivial Berry phases indicative of Dirac semimetallic behaviors emerge for x ≥ 0.5.

Full size image

While chemical do** at Sb or Mn sites17,19 in nonstoichiometric samples induces a tetragonal-orthorhombic structural transition, as in our Eu1−xSrxMn1−zSb2 (x > 0), such do** induces a metal–insulator transition yielding insulating behavior. This indicates that do** at the Sb or Mn sites may be detrimental to forming semimetallic behavior in EuMnSb2 derivatives. In contrast, our phase diagram clearly shows that Sr do** at the Eu site is the driving force of the Dirac semimetallic behavior in Eu1−xSrxMn1−zSb2, as discussed below. First, Sr do** at the Eu site lowers the lattice symmetry and modifies the structural parameters, as summarized in Table 1, which could in turn change the electronic band structure. Second, the different types of Eu spin reorientations driven by Sr do**, temperature, or magnetic field significantly influence the electronic transport and magnetotransport properties, indicating that the band structure is sensitively dependent on the magnetism of the Eu sublattice. As such, the phase diagram presented in Fig. 5 offers an excellent opportunity to explore the intimate interplay between the band relativistic effect and magnetism.

Origin of various Eu spin reorientations

Finally, we discuss the origins of the complicated magnetic structures, in particular, the Sr-do** and temperature-induced Eu SR transition in Eu1−xSrxMn1−zSb2. A common SR in rare earth elements occurs because the rare earth element drives the Mn moment parallel to its moment direction once the rare earth spins are ordered with preferred in-plane orientation at low temperatures, as reported for several compounds such as RMnAsO (R = Nd or Ce)20,21 and RMnSbO (R = Pr or Ce)22,23. However, Sr do** in Eu1−xSrxMn1−zSb2 generates a novel Eu SR where the moment changes from the in-plane direction to the out-of-plane direction while the Mn moment direction remains along the out-of-plane aO axis.

The Mn2+ moment, which commonly displays very weak single-ion anisotropy as expected for the L = 0 of Mn2+ (S = 5/2), favors orientation along the out-of-plane direction20,21,22, i.e., the cT axis in the tetragonal structure or the aO axis in the orthorhombic structure, forming C-type AFM order in T2 < T < T1 of Eu1−xSrxMn1−zSb2. The in-plane checkerboard-like AFM structure of the C-type order suggests that the NN interaction J1 is dominant, whereas the in-plane next-nearest-neighbor (NNN) interaction J2 is very weak. In the context of the J1–J2–Jc model33, we conclude that J1 > 0, J2 < J1/2 and out-of-plane Jc < 0 with negligible spin frustration in the Mn sublattice. Upon cooling to T < T2, Eu-Eu coupling starts to come into play and induces Eu ordering with a preferred orientation of Eu2+ (S = 7/2) in plane34,

References

  1. Xu, S.-Y. et al. Discovery of a Weyl fermion semimetal and topological fermi arcs. Science 349, 613–617 (2015).

    Article  CAS  Google Scholar 

  2. Lu, L. et al. Experimental observation of Weyl points. Science 349, 622–624 (2015).

    Article  CAS  Google Scholar 

  3. Lv, B. Q. et al. Experimental discovery of Weyl semimetal TaAs. Phys. Rev. X 5, 031013 (2015).

    Google Scholar 

  4. Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three dimensional solids. Rev. Mod. Phys. 90, 15001 (2018).

    Article  CAS  Google Scholar 

  5. Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermi arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B. 83, 205101 (2011).

    Article  Google Scholar 

  6. Liu, J. Y. et al. A magnetic topological semimetal Sr1−yMn1−zSb2. Nat. Mater. 16, 905 (2017).

    Article  CAS  Google Scholar 

  7. Park, J. et al. Anisotropic Dirac fermions in a Bi square net of SrMnBi2. Phys. Rev. Lett. 107, 126402 (2011).

    Article  Google Scholar 

  8. Nakatsuji, S., Kiyohara, N. & Higo, T. Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature. Nature 527, 212 (2015).

    Article  CAS  Google Scholar 

  9. Chang, G. et al. Magnetic and noncentrosymmetric Weyl fermion semimetals in the RAlGe family of compounds (R = rare earth). Nature 527, 212 (2015).

    Google Scholar 

  10. Liu, E. et al. Giant anomalous Hall effect in a ferromagnetic kagome-lattice semimetal. Nat. Phys. 14, 1125 (2018).

    Article  CAS  Google Scholar 

  11. Zhang, Q. et al. Unusual exchange couplings and intermediate temperature Weyl state in Co3Sn2S2. Phys. Rev. Lett. 127, 117201 (2021).

    Article  CAS  Google Scholar 

  12. Sakai, A. et al. Giant anomalous Nernst effect and quantum-critical scaling in a ferromagnetic semimetal. Nat. Phys. 14, 1119 (2018).

    Article  CAS  Google Scholar 

  13. Belopolski, I. et al. Discovery of topological Weyl fermion lines and drumhead surface states in a room temperature magnet. Science 365, 1278 (2019).

    Article  CAS  Google Scholar 

  14. Wollesen, P., Jeitschko, W., Brylak, M. & Dietrich, L. Ternary antimonides LnM1−xSb2 with Ln = La−Nd, Sm, Gd, Tb and M = Mn, Co, Au, Zn, Cd. J. Alloy. Compd. 245, L5–L8 (1996).

    Article  CAS  Google Scholar 

  15. Borisenko, S. et al. Time-reversal symmetry breaking type-II Weyl state in YbMnBi2. Nat. Commun. 10, 3424 (2019).

    Article  Google Scholar 

  16. Masuda, H. et al. Quantum Hall effect in a bulk antiferromagnet EuMnBi2 with magnetically confined two-dimensional Dirac fermions. Sci. Adv. 2, e1501117 (2016).

    Article  Google Scholar 

  17. Yi, C. et al. Large negative magne-toresistance of a nearly Dirac material: Layered antimonide EuMnSb2. Phys. Rev. B 96, 205103 (2017).

    Article  Google Scholar 

  18. Soh, J.-R. et al. Magnetic and electronic structure of Dirac semimetal candidate EuMnSb2. Phys. Rev. B 100, 174406 (2019).

    Article  CAS  Google Scholar 

  19. Gong, D. et al. Canted Eu magnetic structure in EuMnSb2. Phys. Rev. B 101, 224422 (2020).

    Article  CAS  Google Scholar 

  20. Zhang, Q., Tian, W., Peterson, S. G., Dennis, K. W. & Vaknin, D. Spin reorientation and Ce–Mn coupling in antiferromagnetic oxypnictide CeMnAsO. Phys. Rev. B 91, 064418 (2015).

    Article  Google Scholar 

  21. Emery, N. et al. Variable temperature study of the crystal and magnetic structures of the giant magnetoresistant materials LmnAsO (L = La, Nd). Phys. Rev. B 83, 144429 (2011).

    Article  Google Scholar 

  22. Zhang, Q. et al. Structure and magnetic properties of LnMnSbO (Ln = La and Ce). Phys. Rev. B 93, 094413 (2016).

    Article  Google Scholar 

  23. Kimber, S. A. J. et al. Local moments and symmetry breaking in metallic PrMnSbO. Phys. Rev. B 82, 100412 (2010).

    Article  Google Scholar 

  24. Altomare, A. et al. SIR97: A new tool for crystal structure determination and refinement. J. Appl. Crystallogr. 32, 115–119 (1999).

    Article  CAS  Google Scholar 

  25. Sheldrick, G. M. A short history of SHELX. Acta Crystallogr. Sect. A 64, 112122 (2008).

    Article  Google Scholar 

  26. Chakoumakos, B. C. et al. Four-circle single-crystal neutron diffractometer at the High Flux Isotope reactor. J. Appl. Crystallogr. 44, 655–658 (2011).

    Article  CAS  Google Scholar 

  27. Farrugia, L. J. Wingx and ortep for windows: An update. J. Appl. Crystallogr. 45, 849–854 (2012).

    Article  CAS  Google Scholar 

  28. Wills, A. A new protocol for the determination of magnetic structures using simulated annealing and representational analysis (SARAh). Phys. B 276–278, 680–681 (2000).

    Article  Google Scholar 

  29. Perez-Mato, J. M. et al. Symmetry-based computational tools for magnetic crystallography. Annu. Rev. Mater. Res. 45, 217–248 (2015).

    Article  CAS  Google Scholar 

  30. Rodrguez-Carvajal, J. Recent advances in magnetic structure determination by neutron powder diffraction. Physica B 192, 55–69 (1993).

    Article  Google Scholar 

  31. Zhang, A. et al. Interplay of Dirac electrons and magnetism in CaMnB2 and SrMnB2. Nat. Commun. 7, 13833 (2016).

    Article  CAS  Google Scholar 

  32. Zhu, F. et al. Magnetic structures, spin-flop transition, and coupling of Eu and Mn magnetism in the Dirac semimetal EuMnBi2. Phys. Rev. Res. 2, 043100 (2020).

    Article  CAS  Google Scholar 

  33. Johnston, D. C. et al. Magnetic exchange interactions in BaMn2As2: A case study of the J1–J2–Jc Heisenberg model. Phys. Rev. B 84, 094445 (2011).

    Article  Google Scholar 

  34. Herrero-Martin, J. et al. Magnetic structure of EuFe2As2 as determined by resonant X-ray scattering. Phys. Rev. B 80, 134411 (2009).

    Article  Google Scholar 

  35. **ao, Y. et al. Magnetic structure of EuFe2As2 determined by single-crystal neutron diffraction. Phys. Rev. B 80, 174424 (2009).

    Article  Google Scholar 

Download references

Acknowledgements

Q.Z. J.L, A.P., and J.F.D. acknowledge the support for the materials preparation, measurements of the magnetization, transport and magnetotransport properties, and neutron scatting experiments from the US DOE under EPSCoR Grant No. DESC0012432 with additional support from the Louisiana board of regents. The use of the High Flux Isotope Reactor at Oak Ridge National Laboratory was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Scientific User Facilities Division. D.A.T. is sponsored by the DOE Office of Science, Laboratory Directed Research and Development Program (LDRD) of Oak Ridge National Laboratory, managed by UT-Battelle, LLC for the U.S. Department of Energy (Project ID 9566). A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by the National Science Foundation Cooperative Agreement No. DMR-1644779 and the State of Florida.

Author information

Author notes

  1. These authors contributed equally: Qiang Zhang, **yu Liu.

Authors and Affiliations

  1. Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA

    Qiang Zhang, Huibo Cao & D. Alan Tennant

  2. Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA, 70803, USA

    Qiang Zhang, Adam Phelan & J. F. DiTusa

  3. Department of Physics and Engineering Physics, Tulane University, New Orleans, LA, 70118, USA

    **yu Liu & Zhiqiang Mao

  4. National High Magnetic Field Laboratory, Tallahassee, FL, 32310, USA

    David Graf

  5. Shull Wollan Center, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA

    D. Alan Tennant

  6. Quantum Science Center, Oak Ridge, TN, 37831, USA

    D. Alan Tennant

  7. Department of Physics, Pennsylvania State University, University Park, PA, 16802, USA

    Zhiqiang Mao

Authors
  1. Qiang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. **yu Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Huibo Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Adam Phelan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. David Graf
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. J. F. DiTusa
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. D. Alan Tennant
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Zhiqiang Mao
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Q.Z. and J.L. contributed equally to this paper. J.L. and Z.M. prepared and characterized the high-quality single crystals. A.P. conducted single-crystal X-ray measurements and data analysis on x = 0. Q.Z., H.C., J.D., and D.A.T. performed the neutron experiments. D.G. assisted with the high-field magnetotransport measurements, while J.L. and Z.M. analyzed the magnetization and magnetotransport data. Q.Z. analyzed the neutron data and wrote the paper with input from all the authors.

Corresponding author

Correspondence to Qiang Zhang.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Rights and permissions

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 the Creative Commons 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/.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, Q., Liu, J., Cao, H. et al. Toward tunable quantum transport and novel magnetic states in Eu1−xSrxMn1−zSb2 (z < 0.05). NPG Asia Mater 14, 22 (2022). https://doi.org/10.1038/s41427-022-00369-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1038/s41427-022-00369-5

  • Springer Japan KK