Toward Controllable Quantum Transports and Novel Magnetic States in Eu1–xSrxMnSb2

Magnetic semimetals carry a great promise for potential applications in novel spintronic devices. Nevertheless, it is a challenging topic to realize the tunable topological states by the magnetism in a controllable way. Here, we report novel magnetic states and a tun-ability of the topological semimetallic states via controlling the Eu spin reorientation in Eu 1 − x Sr x MnSb 2 . Increasing the Sr concentration in this system induces a surprising reorientation of noncollinear Eu spins to the Mn moment’s direction and an appearance of topological semimetallic behavior. The Eu spin reorientations to distinct collinear antifer-1 are also by the ﬁeld, which are coupled to transport properties of the relativistic fermions generated the 2D Sb layers. These results suggest nonmagnetic element doping to the rare-earth element site may be an effective strategy to generate topological electronic states and new magnetic states in layered compounds involving spatially separated rare-earth and transition metal layers.


Introduction
Dirac/Weyl semimetals have attracted intense research interest due to their exotic quantum phenomena as well as promising applications in the next generation, more energy efficient electronic devices. [1][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 to tune and control resulting quantum transport properties. [4][5][6] To date, a couple of magnetic semimetals have been reported and most of the them were discovered in stoichiometric compounds, such as SrMnBi 2 7 , Mn 3 Sn 8 , RAlGe(R = rare earth) 9 , Co 3 Sn 2 S 2 10 , Co 2 MnGa 11, 12 , etc. Finding a strategy to control a topological state by tuning magnetism is highly desired and requires 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, magnetic and electronic phase diagrams in tunable magnetic topological materials.
A large family of ternary AMnCh 2 "112" compounds (A =alkali earth/rare earth elements, Ch = Bi or Sb) 6,7,[13][14][15] 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. AMnCh 2 (A=Ce, Pr, Nd, Eu, Sm; C=Bi or Sb) 15 and Eu layers are spatially separated, which makes them good candidates to explore the possible interplay between Dirac fermions and magnetism. For EuMnBi 2 , both Eu and Mn moments point to the out-of-plane direction and generate two AFM lattices in the ground state 15 . Previous studies have also shown that when the Eu AFM order undergoes a spin-flop transition in a moderate field range, the interlayer conduction is strongly suppressed, thus resulting in a stacked quantum Hall effect 15 . Interestingly, EuMnSb 2 exhibits distinct properties from EuMnBi 2 and conflicting results have been reported [16][17][18] . The magneto-transport properties reported by Yi et al. 16  Moreover, the magnetic structure of EuMnSb 2 is also thought to be distinct from that of EuMnBi 2 , with controversial reports on Eu and Mn moments being perpendicular 17 or canted to each other 18 .
It is therefore important to resolve the controversial magnetic and physical properties of EuMnSb 2 and to explore whether EuMnSb 2 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) 19,20 and RMnSbO (R=Pr or Ce) 21,22 , the moment of rareearth element ordered at low temperatures usually drives a Mn spin reorientation to its moment direction. Given there are two magnetic sublattices of Eu and Mn with an expected 4f -3d coupling between them in EuMnSb 2 , the chemical substitution of Eu by nonmagnetic element may achieve interesting magnetic states via tuning the magnetic interactions, which may control the transport and magneto-transport properties.
In this article, we report comprehensive studies on a tunable Dirac semimetal system Eu 1−x Sr x MnSb 2 , which exhibits a variety of novel magnetic states tunable by the Eu concentration, temperature and magnetic field. The evolution of magnetic states of this system is found to be coupled to quantum transport properties of Dirac fermions. Through single crystal X-ray diffraction, neutron scatter- Single-crystal x-ray and neutron diffraction measurements and neutron data analysis A crystal of x=0 was mounted onto a glass fibers using epoxy, which was in turn then mounted onto the goniometer of a Nonius KappaCCD diffractometer equipped with Mo Kα radiation (λ = 0.71073Å). After the data collection and subsequent data reduction, SIR97 was employed to give 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 refinement. 23 contamination from the Si-220 monochromator using its high resolution mode (bending 150) 25 .
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 Absorption Correction on integrated intensities was conducted carefully using WinGX package 26 .
The SARAH representational analysis program 27 and Bilbao crystallographic server 28 were used to derive the symmetry-allowed magnetic structures and magnetic space groups. The full data sets at different temperatures were analyzed using the refinement program FullProf suite 29 to obtain the structure and magnetic structures.
Magnetization, and magneto-transport 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 magneto-transport properties were measured in the 31 T resistivity magnets at the National High Magnetic Field Laboratory (NHMFL) in Tallahassee. The magnetic fields were applied parallel to out-of-plane direction to study the in-plane and out-of-plane magnetoresistance. The ρ in samples were made into hall bar shape and the ρ zz samples were in Corbino disk geometry. 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 EuMnSb 2 crystallizes in a tetragonal structure with space group P 4/nmm ( Fig. 1(b) and S1(e)) and nonstoichiometric composition EuMn 0.95 Sb 2 . The structural parameters of EuMn 0.95 Sb 2 obtained from the single crystal x-ray diffraction refinement at 293 K are summarized in show a clear lattice distortion and crystallize in the orthorhombic structure with the space group P nma, with a doubled unit cell along the out-of-plane direction ( Fig. 1(c-d) and S1(f)), similar to SrMnSb 2 6 . The structural parameters of Eu 1−x Sr x MnSb 2 (x=0, 0.2, 0.5 and 0.8) at 5 K obtained from the fits to neutron diffraction data are summarized in Table I. It can be seen that the  is shown in the right panel of Fig. 1 (b). Whereas Mn preserves a C-type AFM order with an increased moment due to Eu-Mn coupling along the c T axis, the "+ + --" Eu spin ordering with moment along the a T axis breaks magnetic symmetry along the c T axis and leads to observed magnetic reflections with k = (0,0,1/2) T . Such a magnetic structure is consistent with the susceptibility measurements where χ c increases slightly and χ ab decreases rapidly for T < T 2 , suggesting an AFM moment oriented along the a T b T 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 EuMnSb 2 for which no k = (0,0,1/2) T magnetic peaks were observed below T 2 . The Eu moment's canting proposed in Ref. 12 is not found in our crystal for T < T 2 in our crystal (see Supplemental Information for detailed discussion).
In the x=0.2 sample, we observed pure magnetic peaks (010) O and (001) O in the orthorhombic structure as shown in Fig. 2(b), corresponding to (100) T in the tetragonal notation, below  Fig. 1(c)). This is consistent with the susceptibility measurement shown in Fig.   3(b) where both χ a and χ bc decrease below T 2 , implying that Eu spins may form a canted AFM order. Note that such a canted Eu order is not applicable in the corresponding T < T 2 temperature region of the x=0 parent compound. At 10 K, the canting angle between Mn and Eu is 41 (9)  As x increases to 0.8, the Mn magnetic transition occurs at a temperature T 1 ≈ 330 K as identified from the intensity of (010) O and a C-type Mn order AFM Mn is determined (see the left panel of Fig. 1(d)). Another increase of (010) O is found below T 2 ≈ 7 K. There is no appearance of magnetic scattering at the (300) O and (200) O or (600) O Bragg positions below T 2 (see Fig. 1 (d) and Fig. S5(c-d) in SI), indicating that Eu moments may point to the a O axis. We found a coexistence of Mn C-type AFM order with the "+ -+ -" Eu order with oriented moment along the same the a O axis as the Mn moment (AFM Mn,Eu, , see the right panel of Fig. 1 (d)), consistent with susceptibility measurements. As shown in Fig. 3(c), χ bc keeps increasing but χ a decreases rapidly upon cooling below 8 K, showing the opposite behavior to x=0. This indicates that the Eu moment mainly points to out-of-plane a O direction in x=0.8.
Electronic transport properties Next, we present the evolution of electronic transport properties with the Sr doping in Eu 1−x Sr x MnSb 2 . As shown in Fig. 3(d-f), both in-plane (ρ in ) and out-ofplane resistivity (ρ out ) exhibit metallic transport properties. At 2 K, the ρ out /ρ in reaches 128, 198 and 322, for x=0, x=0.2 and x=0.8, respectively. Such a rapid increase of electronic anisotropy indicates that Sr doping reinforces the quasi-2D electronic structure. In the x=0 sample, the slope of ρ out and ρ in decreases below T 2 , indicative of the coupling between the emergence of Eu order and transport properties, suggesting that the in-plane Eu "+ + --" order leads to suppressed metalicity. The metallic behavior in our EuMn 0.95 Sb 2 sample is different from the insulating behavior observed in the Sn-or Mn-doped nonstoichiometric samples 16,18 . This indicates that the chemical doping on Sb or Mn sites induces a metal-insulator transition, which is distinct from the effect of the Sr substitution for Eu.
However, the x=0.2 sample exhibits distinct transport behavior as compared to x=0 sample.
We observed a rapid decrease in ρ out and a slight increase in ρ in below T 2 , suggesting that the Eu canting to the a O axis with the Eu "+ -+ -" component significantly increases the interlayer conductivity along the a O direction between Sb layers but suppresses the intralayer conductivity on the b O c O plane, contrasted with the effect of of the sole in-plane Eu order on the transport properties as described above. Below T 3 , there is no obvious change in the out-of-plane resistivity, but an anomalous decrease of the in-plane resistivity is observed. This can be well interpreted from the SR of Eu from noncollinear to collinear order. Below T 3 , the out-of-plane Eu order is kept to be "+ -+ -", which is not expected to influence the interlayer conductivity. In contrast, the switch of the in-plane component from "+ + --" to "+ -+ -" induces the anomalous increase in the intralayer conductivity.
As for x=0.8, the Eu ordering does not influence the resistivity obviously below T 2 , which can be ascribed to the small portion of Eu occupancy (≈ 20 %). Thus, our results reveal an intimate coupling between the Eu magnetic order and transport properties in Eu 1−x Sr x MnSb 2 .
Nontrivial Berry phases Figure 4 (a-d) shows both in-plane and out-of-plane magnetoresistance (0)) under high magnetic fields applied along the out-of-plane direction.
For x=0, the ∆ρ out /ρ out is negative, whereas the in-plane ∆ρ in /ρ in is positive. The magnitudes for both ∆ρ out /ρ out and ∆ρ in /ρ in are small, and no strong Shubnikov-de Haas (SdH) oscillations are observed. For x=0.2, weak SdH oscillations are observed in both ∆ρ out /ρ out and ∆ρ in /ρ in . As the field increases, there is a sign reversal in ∆ρ in /ρ in , whereas the ∆ρ out /ρ out remains positive.
Remarkably, at 1.8 K that is below T 3 , a large jump in ∆ρ out /ρ out up to ≈ 4500 % occurs above µ 0 H t ≈ 18 T, followed by a rapid decrease above ≈ 27 T. The dramatic changes in ∆ρ out /ρ out are ascribed to a field-induced metamagnetic transition. Since this phenomenon does not occur in the T > T 2 temperature regime (e.g. 50 K), the field-induced magnetic transition should not originate from the Mn magnetic sublattice, but be related to the Eu magnetic sublattice, indicative of a vital role that the Eu magnetic order plays in the magneto-transport properties. The most possible origin of the enhanced ∆ρ out /ρ out above µ 0 H t is the field-induced Eu SR transition from canted moment direction in a O c O plane to the c O axis while the A-type "+ -+ -" Eu order remains, thus yielding a strong suppression of interlayer conductivity, as illustrated in the inset of Fig. 4 The increase of the Sr doping level enhances SdH oscillations significantly in both ∆ρ out /ρ out and ∆ρ in /ρ in for x=0.5 and 0.8, with much higher oscillation amplitudes at high magnetic fields.
∆ρ out /ρ out reaches ≈ 18000% at 31.5 T for x=0.8. We further analyzed the Berry phase (BP) φ B accumulated along cyclotron orbits and are able to extract φ B for x=0.5 and 0.8. From the linear fit of the Landau level fan diagram based on the oscillatory resistivity ρ in , we obtained intercept n 0 of 0.38 and 0.44 for x=0.5 and x=0.8, respectively, as shown in the insets of Fig. 4 (c-d). The corresponding Berry phases 2π× n 0 are 0.76 π for x=0.5 and 0.88 π for x=0.8. The fits to LL fan diagram based on the oscillatory resistivity ρ out for x=0.8 yield intercept n 0 of 0.57, with a corresponding Berry phases of 1.14 π. All of them are close to a nontrivial π Berry phase for a quasi 2D system. The non-trivial Berry phase provides the evidences that x=0. 5  Composition phase diagram From the combination of single crystal x-ray diffraction, neutron diffraction, magnetization, and magneto-transport measurements, we are able to establish the structural, magnetic and electronic phase diagram, as shown in Fig. 1 (a). While the x=0 parent compound with Mn deficiency is tetragonal with space group P 4/nmm, the Sr-doping induces an orthorhombic distortion. This is consistent with the previous reports on the orthorhombic structure in the doped nonstoichiometric samples 16,18  there is no another magnetic transition at T 3 observed in Ref. [18]. For our x=0.2 compound, the 2nd type of Eu SR from a noncollinear canted spin order to a collinear A-type canted spin order was found at lower temperature (denoted by AFM Mn,Eu,C2 in Fig. 1(a)). 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 orientedto the possible c O axis. The established phase diagram for Eu 1−x Sr x MnSb 2 as well as the comparison with the previous reports we made above [16][17][18] indicate that the structure, magnetic order and electronic properties of EuMnSb  Table I, which could in turn change the electronic band structure. Second, the different types of Eu spin reorientations driven by the Sr doping, temperature or magnetic field influence the electronic transport and magneto-transport properties significantly, indicating the band structure is sensitively dependent on the magnetism of the Eu sub-lattice. As such, the phase diagram presented in Fig. 1 (a) offers an excellent opportunity to explore the intimate interplay between band relativistic effect and magnetism.
Origin of various Eu spin reorientations Finally, we turn to discuss the origins of the complicated magnetic structures, in particular the Sr-doping and temperature induced Eu SR transition in Eu 1−x Sr x MnSb 2 . A common SR of rare earth is that the rare-earth element drives Mn moment parallel to its moment direction once the rare earth spins are ordered with preferred in-plane orientation at low temperatures, as reported in several compounds such as RMnAsO (R=Nd or Ce) 19,20 and RMnSbO (R=Pr or Ce) 21,22 . However, the Sr doping in Eu 1−x Sr x MnSb 2 generates a novel Eu SR with moment changing from the in-plane direction to the out-of-plane direction while Mn moment direction remains along the out-of-plane a O -axis.
The Mn 2+ moment, which commonly displays very weak single-ion anisotropy as expected for the L=0 of Mn 2+ (S = 5/2), favors orientation along the out-of-plane direction [19][20][21] , i.e., the c T axis in tetragonal structure or the a O axis in orthorhombic structure, forming the C-type AFM order in T 2 < T < T 1 of Eu 1−x Sr x MnSb 2 . The in-plane checker-board-like AFM structure of the C-type order suggests that the NN interaction J 1 is dominant, whereas in-plane next-nearestneighbor (NNN) interaction J 2 is very weak. In the context of J 1 − J 2 − J c model 32 , we conclude that J 1 > 0, J 2 < J 1 /2 and out-of-plane J c < 0 with negligible spin frustration in Mn sublattice.
Upon cooling to T < T 2 , Eu-Eu coupling starts to come into play and induces Eu ordering with preferred orientation of Eu 2+ (S = 7/2) within in plane 33,34 , either the a T b T plane in tetragonal structure or the b O c O plane in orthorhombic structure. Simultaneously, the Eu-Mn coupling also plays an important role by exerting an effective field, which has the tendency to influence As the temperature decreases below T 3 for x=0.2, a temperature-induced SR transition occurs. This may be ascribed to another type of Eu-Eu coupling that comes into play below T 3 . This retains "+ -+ -" out-of-plane component but switches in-plane component from "+ + --" to "+ -+ -", leading to collinear A-type AFM order of Eu spins in T < T 3 . Thus, the striking Eu spin reorientation driven by Sr doping and temperature indicates a strong Eu-Mn (4f -3d) couplings and results from their competitions to Eu-Eu couplings.

Figures
All the compounds exhibit metal-like transport properties as a function of temperature and they are also coupled to Eu order at T2 and T3. The non-trivial Berry phases indicative of Dirac semimetallic behaviors emerge with x ≥0.5. Magnetic structures determined from the ts to the neutron data for (b) x=0, (c) x=0.2 ( all the panels) and 0.5 (only left and middle panels), and (d) x=0.8. The dashed rectangular shows the Mn-Eu-Eu-Mn block where the SR of Eu can be seen.   (color online) Field dependence of out-of-plane magnetoresistance Δρout=ρout and inplane magnetoresistance Δρin=ρin for (a) x=0, (b) x=0.2, (c) x=0.5, and (d) x=0.8. The inset of Fig. (b) shows the eld-induced metamagnetic transition in Eu-sublattice, i.e., Eu spin ordering in and H < Hf and Hf < H < Hs. The inset of (c-d) shows the linear t of the Landau level fan diagram based on the oscillatory resistivity ρin for x=0.5 and 0.8.