Abstract
The anomalous Hall effect (AHE) and its thermoelectric counterpart, the anomalous Nernst effect (ANE), are two transverse transport coefficients that are intensely studied in condensed matter physics. While conventional wisdom links AHE and ANE to ferromagnetism, recent achievements reveal that they can emerge in nonmagnetic and antiferromagnetic topological materials with a diversity of mechanisms—many of which await further elucidation. Here, both an unconventional AHE (UAHE) that does not scale with the magnetization and a sizable ANE ( ≈ 1.8 μV K−1) are shown to be possessed by the metallic tetragonal antiferromagnet SmMnBi2. Electronic band structure of SmMnBi2 is investigated by angle-resolved photoemission spectroscopy and first-principles calculations. It is demonstrated that the UAHE reflects the intrinsic Berry curvature contribution stemming from the spin-canted antiferromagnetism, whereas the ANE is possibly further amplified by extrinsic mechanisms. These results identify SmMnBi2 as a promising candidate for exploring unusual transverse transport effects and the extremely rich underlying physics.
Similar content being viewed by others
Introduction
Anomalous transverse transport denotes the transverse electrical (the anomalous Hall effect, AHE), thermoelectric (the anomalous Nernst effect, ANE), and thermal (the anomalous Righi–Leduc effect) responses that are not caused by the Lorentz force experienced by the electrons subjected to magnetic fields (H). The most common case of anomalous transverse transport occurs in the ferromagnets, wherein the anomalous transport coefficients are proportional to the magnetization (M); it is well established that such behavior can arise from both intrinsic (which reflects the non-zero Berry curvature in the electronic system) and extrinsic (which is related to the scattering process) origins1. In ferromagnets, the validity of both the intrinsic and extrinsic mechanisms for the anomalous transport are guaranteed by the spin-orbit coupling (SOC) effect and the broken time-reversal symmetry (TRS)2,3,4. On the other hand, in a collinear antiferromagnet, despite the breaking of TRS, the intrinsic anomalous coefficients are usually forced to be zero because the momentum-space integral of Berry curvature is nullified in the presence of a combined symmetry, i.e., the combination of time-reversal operation and other unitary space group operations such as fractional translation or inversion operation5,6. Whilst it is the conventional notion that anomalous transverse transport is less important in antiferromagnets, large anomalous terms were recently observed in the transverse responses in antiferromagnetic (AFM) materials with peculiar noncollinear or noncoplanar spin configurations and non-trivial band topology, most notably Mn3Sn7, Mn3Ge8, YbMnBi29,10, YMn6Sn611, and CoNb3S612.
In comparison to ferromagnets, a zero (or rather weak7,8,12) net magnetization at H = 0 in antiferromagnets provides good opportunities for realizing high-performance integrated devices without perturbing stray fields. Most importantly, even with much smaller amplitudes of low-field M, several AFM compounds exhibit remarkable AHE and ANE that are not proportional to M; this behavior is in sharp contrast to the cases in most ferromagnets1 and the heavy-fermion antiferromagnets wherein the extrinsic anomalous terms dominate13. The possible origins of such “unconventional” anomalous transport include the “topological” transverse responses stemming from long-period noncoplanar chiral spin textures (e.g., Skyrmions) that introduces real-space Berry curvature14; the field-tuning of topological band crossings (e.g., Weyl nodes) and anticrossings in the electronic structures15,16, which are main sources contributing to the momentum-space Berry curvature; interplay between SOC and special crystal symmetry17,18; domain wall effects19, and so on. Overall, the correspondence between the symmetry of the system (depending on magnetic configurations) and the topological characterizations of the electronic bands (determining the behavior of itinerant electrons) plays an essential role in provoking the enriched phenomena of anomalous transport in topological antiferromagnets, consequently opens up a broad avenue in the design and fine control of advanced devices.
In this work, we present a combined transport, angle-resolved photoemission spectroscopy (ARPES), and first-principles study in a recently discovered20 member of the Mn-based RMnPn2 family, namely SmMnBi2; where R is a divalent rare-earth or alkaline-earth metal ion, Pn is Sb or Bi21,22,23,24. The RMnPn2 series of materials have been established as prototypical topological semimetals with AFM order of the Mn spins (Mn2+, 3d5, S = 5/2), hence serving as good candidates for investigating the interplay between magnetism and band topology23,24,25,26. In particular, it has been pointed out that in YbMnBi2, a small canting of the Mn spins in the C-type AFM configuration lifts the twofold band degeneracy, resulting in a Weyl semimetal state that is characterized by considerably large AHE and ANE6,9,24. Compared to other well-studied members in the RMnPn2 series, SmMnBi2 is unique: although it also hosts the Pn (here Pn = Bi) square sheets that engender the topological nontriviality in this series21,22,24,27, it crystallizes in a tetragonal crystal structure different from all other Mn-112 materials20, which leads to a more complicated electronic band structure.
We report, to the best of our knowledge, for the first time the observation of unconventional AHE (UAHE) and large ANE in SmMnBi2. These effects are detected in a configuration (H∥c) in which the anomalous terms in YbMnBi2 disappear9, suggesting that their occurrence is closely related to the details of magnetic structures. Based on the experimental results and first-principles calculations, we propose that SmMnBi2 is an AFM topological metal in the magnetically ordered phase below TN = 235 K; the UAHE arises from the non-zero momentum-space Berry curvature invoked by the canted spin configuration in the AFM state, whereas the anomalous terms persisting above TN can originate from magnetic fluctuations and/or peculiar extrinsic mechanisms. The ANE also contains extrinsic contributions which render its value much larger than the simple expectation for an intrinsic ANE. The coexistence of intrinsic and extrinsic mechanisms for anomalous transverse transport and their intricate relationship with magnetism make SmMnBi2 a fertile playground to explore the rich physics in magnetic topological phases of matter.
Results
Sample characterization
High-quality SmMnBi2 single crystals were synthesized by a self-flux method (Experimental section). The single-crystal X-ray diffraction (XRD) pattern (Supplementary Fig. 1) confirms that the shiny surface of our plate-shaped samples (top panel of Fig. 1a) corresponds to the crystal plane (001). Analysis of the results of single crystal XRD experiment that utilizes a four-circle goniometer provides detailed structure information for SmMnBi2 (Supplementary Tables 1 and 2). It is shown that SmMnBi2 crystallizes into a tetragonal structure (space group I4/mmm, No.139) as illustrated in Fig. 1a, with the lattice constants a = b = 4.506 Å, c = 20.597 Å; these results are consistent with previous work20. Compared with other members in the RMnPn2 family22,23,24,26, SmMnBi2 shares similar structural features, such as the periodic stacking of -Mn/SmBi/Bi/SmBi- layers along the crystallographic c-axis. It is believed that the Bi/Sb square net gives rise to the topologically nontrivial electronic state in RMnPn2, which is controlled by the spin configuration of Mn sublattice; in the cases of a collinear AFM order, the electronic states near the Fermi energy EF are characterized by the presence of highly anisotropic Dirac cones21,27. Nonetheless, the crystal structure of SmMnBi2 exhibits remarkable difference from other RMnPn2 compounds in the sense that it shows a MnBi4 square-planar coordination geometry (highlighted by the purple dashed lines in Fig. 1a), in stark contrast to the typical tetrahedra coordination in all other members. With such structural discrepancy, distinct electronic structure and physical properties are also expected for SmMnBi2.
We first look into the magnetic properties. The temperature (T)-dependent magnetic susceptibility (χ) curves displayed in Fig. 1b show that the onset of irreversibility between the zero-field-cooled (ZFC) and field-cooled (FC) curves at T = 235 K is accompanied by a weak kink on the H∥c curves (no evidence for additional magnetic transitions can be resolved from χ(T) up to 400 K, see Supplementary Fig. 2a). Such features match those of the AFM transition temperature TN previously reported for other Mn-112 materials21,26,28,29, thus we conclude that TN = 235 K in SmMnBi2. A small jump in the specific heat at the same temperature (Fig. 1e) supports this identification. Based on the χ(T) and the isothermal magnetization (M–H) data (Fig. 1c and Supplementary Fig. 2b), we can further comment on the nature of magnetism in SmMnBi2. First, the difference between ZFC and FC magnetizations, together with the nonlinear M–H profile, point towards a canted AFM order below TN, similar to the case in YbMnBi29,24,30, SrMnSb222,31, and Ca1−xNaxMnBi232; the magnetic moment per Mn atom is only 0.1–0.15 μB (μB is Bohr magneton) at μ0H = 7 T at the lowest T for both H∥c (Fig. 1c) and H⊥c (Supplementary Fig. 2b), suggesting that the polarized/ferromagnetic (FM) component remains small compared to the total moment for Mn2+ (typically 3–5μB). The more prominent kink at ~75 K in χ(T) for H⊥c (Fig. 1b) may arise from a variation in spin canting angle. Second, the larger suppression of χc compared to χab at low T, which is widely observed in other Mn-112 compounds21,31, implies that the Mn spins are aligned predominantly along the c-axis (with the above referred small canting-induced FM component lying in the ab-plane). The tiny hysteresis loops appearing at low H and high temperatures (inset of Fig. 1c) are probably attributed to residual spin clusters formed above TN, or some impurity-related extrinsic effects31.
The T dependence of zero-field resistivity ρxx displayed in Fig. 1d exhibits metallic behavior with a relatively high residual resistivity [ρxx(0 K) = ρ0 ≃ 110 μΩ cm]. The Seebeck coefficient Sxx is negative between 10 and 300 K (Fig. 1d), indicative of dominant electron-type carriers. The linear-in-T behavior of Sxx below ~ 30 K is consistent with the diffusion thermopower in metals; the nonmonotonic T dependence at higher temperatures suggests multiband transport, as also seen in SrMnBi233. Sxx reaches ~6 μV K−1 near room temperature (300 K). The magnetoresistance (MR) ρxx(H) and magnetothermopower (MTP) Sxx(H) (Supplementary Figs. 3a, b) both show features that can be understood within a single-carrier-type picture: the positive MR and MTP decline rapidly with increasing H and evolves into a saturation at moderate fields34,35. Such behaviors, together with the relatively large ρ0 and small MR, depict SmMnBi2 as a multiband metal with low carrier mobilities and poor electron-hole compensation.
Anomalous Hall and anomalous Nernst effects
Most intriguingly, the Hall resistivity ρxy of SmMnBi2 develops a striking nonmonotonic H-profile that is distinct from common metals. As shown in Fig. 2a, the amplitude of negative ρxy increases promptly at low H, reaching its maximum at a magnetic field that gradually shifts to higher values with increasing T (μ0H ≃ 0.06 T at 10 K and μ0H ≃ 1.3 T at 300 K); above this maximum, ρxy decreases in a trend roughly tracking the inverse magnetic field (1/μ0H), forming a skewed (or tilted) peak that becomes broader upon warming. This behavior of ρxy is unlikely to reflect the ordinary band-filling contribution. Neither it can be ascribed to the conventional AHE since it does not trace the profile of M(H) (Fig. 1c). To clarify the origin of the unusual Hall signal, we plot the Hall conductivity σxy [\(=-{\rho }_{xy}/({\rho }_{xx}^{2}+{\rho }_{xy}^{2})\)] against H in Fig. 2b. σxy(H) exhibits a notable low-H resonance-like peak that also undergoes broadening with increasing T. A resonant feature in σxy has been discussed in the framework of the single-band Drude model, wherein the reciprocal of the peak position in H provides an estimation of carrier mobility36,37. For SmMnBi2, such approach yields a very high mobility of ~104 cm2 V−1 s−1 (Supplementary Fig. 4a), in sharp contrast to the low mobility in SmMnBi2 indicated by the low Hall angle (Supplementary Fig. 4b). We conclude that the low-H tilted-peak-like features in ρxy and σxy are not caused by Lorentz force-induced orbital motion of highly mobile band electrons (see further discussions in Supplementary Note 1 for the explicit preclusion of ordinary contribution).
Alternatively, it is more reasonable to assign these features to a rare case of intrinsic UAHE that is exceptionally sensitive to the application of a weak H. For the intrinsic mechanism, the anomalous Hall conductivity \({\sigma }_{xy}^{{{{{{{{\rm{A}}}}}}}}}\) is directly given by the integral of Berry curvature in the momentum space, thus it is usually considered as an inherent property of the electronic bands that is independent of or weakly depends on T1. Consequently, a scaling relation between the AHE and the square of longitudinal resistivity, \({\rho }_{xy}^{{{{{{{{\rm{A}}}}}}}}}\propto {\rho }_{xx}^{2}\), often holds empirically for intrinsic AHE according to a simple Drude analysis1. We test this scaling in Fig. 2c, and it confirms that the maximal value of ρxy, \({\rho }_{xy}^{\max }\), is proportional to \({\rho }_{xx}^{2}\) in a broad range of T up to T ≃ TN. The validity of \({\rho }_{xy}-{\rho }_{xx}^{2}\) scaling, together with the weakly-T-dependent peak value of σxy (inset of Fig. 2c), imply an intrinsic AHE originating from nonvanishing Berry curvature of the electronic bands in SmMnBi2, at least for T < TN. (We note that the overall behavior of UAHE in SmMnBi2 resembles the spin-canting-induced intrinsic AHE observed in another AFM metal, EuCd2As238). Such a large Berry curvature effect will leave its footprints in the transverse thermoelectric response, i.e., a sizable ANE4. This is exactly what we observed with H∥c and an in-plane thermal gradient: the Nernst signal Sxy evolves in H with a unique skewed-peak profile similar to ρxy, showing a sharp increase in weak H and a continuous reduction at higher H (Fig. 2d). The amplitude of Nernst response in SmMnBi2 reaches 1.8 μV K−1 at its maximum, a remarkably large value for an AFM metal; we attribute it to a dominant ANE term (see Supplementary Note 1 and Supplementary Fig. 4d for arguments against normal Nernst). The observation of both intrinsic UAHE and ANE in SmMnBi2 is highly suggestive of a topologically nontrivial electronic structure that has an intimate connection with the field-tunable magnetism.
ARPES measurements and first-principles calculations
We investigate the electronic band structure of SmMnBi2 by methods of ARPES and first-principles calculations based on the density functional theory (DFT, see Supplementary Notes 2 and 3 for the details of calculation). The Fermi surface (FS) contour in the surface Brillouin zone (BZ) (Fig. 3a) probed by ARPES is presented in Fig. 3b. It reveals a few notable characteristics: a diamond-shaped contour around \(\overline{\Gamma }\), a diamond-like loop consisting of elongated FS pockets between \(\overline{\Gamma }\) and \(\overline{{{{{{{{\rm{M}}}}}}}}}\), and spot-like FS pockets around the \(\overline{{{{{{{{\rm{X}}}}}}}}}\) points. We note that the overall features of FS contours share many similarities with the ARPES results of other members in the RMnPn2 series21,27,39; in particular, the diamond-like FS loop in most of the Mn-112 compounds contains four anisotropic FSs possessing massive Dirac holes, whereas the small pockets at the X/Y points can also show Dirac-type dispersions. The massive Dirac fermions hosted by these FSs contribute to most of the intriguing physical properties in RMnPn2 materials21,23. For SmMnBi2, a direct identification of Dirac(-like) bands by ARPES measurements is hampered by the terraced surface of the cleaved single crystals. As shown in Fig. 3d–i, the ARPES-resolved bands largely track the dispersions given by DFT calculations along the \(\overline{\Gamma }-\overline{{{{{{{{\rm{M}}}}}}}}}\) and \(\overline{\Gamma }-\overline{{{{{{{{\rm{X}}}}}}}}}\) paths (see also Supplementary Fig. 8); in particular, the electron Fermi surface pockets centered at \(\overline{\Gamma }\) are clearly observed (Fig. 3d, e). On the other hand, ARPES and DFT results show some discrepancies along the \(\overline{{{{{{{{\rm{M}}}}}}}}}-\overline{{{{{{{{\rm{X}}}}}}}}}\) direction (Fig. 3f, i). A detailed discussion on the comparison between calculations and ARPES data is presented in Supplementary Note 4.
The band structure attained from the first-principles calculations relies on the spin configurations. Here, we consider two types of canted AFM orderings with Mn spins aligning predominantly along the c-axis but maintaining a small in-plane FM component, as revealed by the magnetization measurements (Fig. 1b, c). Illustrations of the two orderings, i.e., C-type22,24 and G-type21,23 AFM structures, are presented in Supplementary Fig. 5. The FM component is fixed to the [100] direction in our calculations. Whilst both C-type and G-type AFM orders can be established in the RMnPn2 series, we can further identify that the canted G-type order is a more plausible spin configuration for SmMnBi2. This argument is based on the observations of nonzero \({\sigma }_{xy}^{{{{{{{{\rm{A}}}}}}}}}\) (Fig. 2b) and anomalous Nernst conductivity \({\alpha }_{xy}^{{{{{{{{\rm{A}}}}}}}}}\) (Supplementary Fig. 3c): in the case of canted C-type AFM order, a glide plane perpendicular to the in-plane FM moments (and parallel to c) is preserved; the in-plane AHC (\({\sigma }_{xy}^{{{{{{{{\rm{A}}}}}}}}}\)) is forced to zero by the corresponding mirror operation (Supplementary Fig. 5e); by contrast, no mirror or glide plane parallel to c-axis exists in the canted G-type AFM structure and a nonzero AHC is thus permitted (see Supplementary Note 3). The DFT calculation results of the band structure in SmMnBi2 considering the canted G-type AFM order (with a canting angle θ = 10∘) is displayed in Fig. 4a. Compared to most of the typical RMnPn2 materials wherein the bands crossing the Fermi level EF are mainly attributed to the Bi-2 atoms within the Bi square nets21,24,27, the spectral weights of Bi-1 (Bi atoms in the MnBi4 polyhedra) p states and Mn d states are higher in SmMnBi2, resulting in a much more complicated FS structure with a large number of FS pockets and sheets constituting a diamond-like profile (Fig. 4d). The calculated FS contour (Fig. 3c) and band dispersions with this canted AFM configuration capture most of the main features observed in the ARPES experiment (Supplementary Note 4).
Our DFT calculations provide solid evidence for intrinsic UAHE in SmMnBi2. The energy-dependent AHC tensor elements (\({\sigma }_{xy}^{{{{{{{{\rm{A}}}}}}}}}\), \({\sigma }_{yz}^{{{{{{{{\rm{A}}}}}}}}}\) and \({\sigma }_{xz}^{{{{{{{{\rm{A}}}}}}}}}\)), calculated from the integrals of corresponding Berry curvature components on the first BZ (Supplementary Note 3), are shown in Fig. 4b. Large values of both \({\sigma }_{yz}^{{{{{{{{\rm{A}}}}}}}}}\) and \({\sigma }_{xy}^{{{{{{{{\rm{A}}}}}}}}}\) are confirmed, whereas \({\sigma }_{xz}^{{{{{{{{\rm{A}}}}}}}}}\) is considerably smaller. In particular, the amplitude of \({\sigma }_{xy}^{{{{{{{{\rm{A}}}}}}}}}\) in the vicinity of EF reached 60–70 S cm−1, in good agreement with the experimental result (Fig. 2b). This consistency unequivocally verifies the Berry-curvature origin of the AHC. In absence of the spin canting, our calculations reveal that SmMnBi2 with collinear G-type AFM order is a topological metal candidate with multiple band crossings along the Γ–X direction that are protected by the mirror symmetry; these crossings form nodal loops in the kx − ky plane (Supplementary Fig. 6). The spin canting destroys the mirror symmetry and opens gaps along the nodal loops. As has been proposed for numerous magnetic topological materials, gapped Dirac nodal lines and the remaining band touching points (e.g., Weyl nodes) serve as effective sources for abundant Berry curvature that leads to sizable AHC40,41. In addition, the Berry curvature distribution map for the kz = 0 plane (Fig. 4c) indicates that besides the gapped nodal loops, the bands around Γ (mostly associated with Mn d and Bi-1 p orbitals, Fig. 4a) contribute significantly to the nonzero Berry curvature flux; this is similar to the case in YbMnBi26,9.
Discussion
The remarkable skewed-peak profile of ρxy(H) in SmMnBi2 (which is distinct from the behavior of M) is uncommon for an intrinsic AHE. The peculiar H dependence resembles that of THE originating from real-space Berry curvature induced by large spin textures in Skyrmion lattices14. In SmMnBi2, our experimental and theoretical explorations suggest that the momentum-space Berry curvature still makes the predominant contribution. As mentioned above, the emergence of intrinsic AHE in SmMnBi2 relies on spin canting, which results in broken mirror symmetry. Thereby, the drastic variation of AHE (and AHC) under H can be naturally assigned to the field-modulated spin canting effect. We elucidate that apart from the well-known SOC-driven AHE, spin chirality also plays an essential role in contributing to the intrinsic AHE in the canted AFM state: when a spin-chirality period remains comparable to the lattice parameters, the Berry curvature derived from spin chirality can be effectively linked to band anti-crossings and/or Weyl nodes in the momentum space42,43,44. Whereas the scalar spin chirality delineated by noncoplanar spin textures44 may not be relevant in SmMnBi2, a recent proposal points out that the vector chirality produced by a small relative canting between neighboring spins can give rise to intense uncompensated momentum-space Berry curvature in both FM and AFM materials45. Our theoretical analysis presented in Supplementary Note 5 corroborates the presence of nonzero AHC in the spin-canted AFM state of SmMnBi2 even without SOC, which is presumably attributed to such vector chirality among canted spins45; the AHC is further enhanced by the inclusion of SOC (Supplementary Fig. 9), implying that both the vector spin chirality and the SOC effect contribute to the momentum space Berry curvature (and consequently the intrinsic AHE). We further note that a change of θ from 10° to 5° results in a decrease of \({\sigma }_{xy}^{{{{{{{{\rm{A}}}}}}}}}\) at EF, underlining the effective manipulation of AHE through the field control of spin canting (Supplementary Fig. 10, more discussions in Supplementary Note 5). Indeed, both the spin-chirality term and the SOC term of AHE can be highly sensitive to the modification of spin canting38.
Aside from the spin canting, field tuning of the positions of Weyl nodes through exchange splitting of energy bands can also lead to strongly nomonotonic UAHE; this mechanism has been discussed in a few magnetic topological materials, especially those hosting magnetic rare-earth ions15,16,46. A strong effective Zeeman field stemming from the large polarized magnetic moments under H is crucial for realizing such band tuning. For SmMnBi2, however, the absence of rare-earth magnetism and the complicated band structure near EF make it difficult to verify this mechanism.
The UAHE in SmMnBi2 survives above TN (Fig. 2a, b), with no suppression in its amplitude but a deviation of the \({\rho }_{xy}-{\rho }_{xx}^{2}\) scaling (Fig. 2c). We suggest that short-ranged canted AFM order can persist in the paramagnetic state above TN46; application of H may stabilize the spin chirality related to the short-ranged order and introduce nonzero momentum-space Berry curvature. The generally unchanged shape of ρxy(H) curves for T > TN with a broadened tilted peak supports the above picture. Additionally, we can not exclude the contribution of extrinsic mechanism for the high-T signals: in a background of thermally fluctuating spins, a skew scattering process evolving chiral spin clusters is expected to induce pronounced AHE47,48.
The realization of a sizable ANE in SmMnBi2 is more fascinating since it has only been achieved in a few antiferromagnets (e.g., Mn3Sn49, Mn3Ge50, YbMnBi29,10, YMn6Sn611, and TbPtBi51). In Fig. 5a, we compared the amplitudes of anomalous Nernst signal measured in several typical FM and AFM materials9,11,49,50,52,53,54,55,56,57,58, including SmMnBi2. Conventional FM metals are characterized by a weak ANE (<1 μV K−1). Magnetic topological materials exhibit much stronger ANE due to the Berry curvature contributed by Weyl nodes and gapped Dirac band-touchings. Among the AFM compounds listed in Fig. 5a, SmMnBi2 is featured by an ANE (1.8 μV K−1 at its maximum and 1.6 μV K−1 at 300 K) larger than the noncollinear antiferromagnets Mn3X (X = Sn, Ge)49,50, comparable to that in YMn6Sn611 but smaller than the maximum ANE observed in YbMnBi29,10. Nonetheless, the giant ANE ≃ 6–15 μV K−1 in YbMnBi2 is measured with H in-plane and the voltage drop V along the c-axis, whereas for SmMnBi2, we detect the ANE with a more conventional measurement configuration, i.e., H∥c and ∇T, V both in-plane. Such contrast is caused by different symmetry groups in the magnetically ordered states of the two compounds (see Supplementary Note 3).
With compelling evidence of intrinsic UAHE in SmMnBi2, it is natural to expect that the ANE is also attributed to the momentum-space Berry curvature (i.e., an intrinsic ANE). However, the origin of ANE herein is indeed more complex. If both electric and thermoelectric anomalous transverse terms are linked to the Berry curvature of band electrons, a qualitative analysis yields \(| {\alpha }_{xy}^{{{{{{{{\rm{A}}}}}}}}}/{\sigma }_{xy}^{{{{{{{{\rm{A}}}}}}}}}| \simeq ({k}_{{{{{{{{\rm{B}}}}}}}}}/e)\langle {\lambda }_{{{{{{{{\rm{F}}}}}}}}}^{2}/{\Lambda }^{2}\rangle\), where kB is the Boltzmann constant, λF the Fermi wavelength, and Λ the thermal de Broglie wavelength of electrons57,58. With T increasing towards room temperature, λF and Λ become comparable, consequently the ratio \(| {\alpha }_{xy}^{{{{{{{{\rm{A}}}}}}}}}/{\sigma }_{xy}^{{{{{{{{\rm{A}}}}}}}}}|\) is set by a universal constant ~kB/e = 86 μV K−1. Although the derivation uses an oversimplified single-band 2D model, such universal relation is revealed to be valid for several well-studied magnetic topological materials. As illustrated in Fig. 5b, the high-T ratio of \(| {\alpha }_{ij}^{{{{{{{{\rm{A}}}}}}}}}/{\sigma }_{ij}^{{{{{{{{\rm{A}}}}}}}}}|\) for Mn3X (X = Sn, Ge)49,50, Co3Sn2S257, and Co2MnGa58 all approaches the threshold kB/e (dashed line) from the lower side; in sharp contrast, the ratio in YbMnBi29,10 and SmMnBi2 strongly exceeds the kB/e threshold. Isotherms of αxy/σxy curves plotted against H (Supplementary Fig. 3d) imply that the ratio in SmMnBi2 exceeds kB/e over broad ranges of T and H. Considering the distinct FS morphologies in YbMnBi29,24 and SmMnBi2 (Supplementary Fig. 11), the analogous notable breakdown of the empirical kB/e relation in two materials is less likely to have a band origin (multiband effect, FS anisotropy, linear band dispersion, etc). Instead, we suggest that it is more reasonable to assign this violation to extrinsic contributions (e.g., skew scattering), which can give rise to a considerable enhancement in the transverse thermoelectric response but only enter \({\sigma }_{xy}^{{{{{{{{\rm{A}}}}}}}}}\) as a marginal component59. As such, for both YbMnBi2 and SmMnBi2, the giant ANE is probably dominated by the extrinsic mechanism(s), while the AHE still has a predominant intrinsic origin. Further studies are required to clarify the cause of this putative dichotomy in the origins of anomalous transverse transport coefficients.
Conclusions
In summary, we give the first report on the magnetic, transport, and spectroscopic properties of the magnetic topological material candidate SmMnBi2. This compound is corroborated to be a metallic antiferromagnet exhibiting pronounced anomalous transverse responses in both electrical transport and thermoelectricity. The long-range AFM order occurs at TN = 235 K, with spins largely along the easy c-axis but having a small canting towards the ab-plane. Unconventional AHE and large ANE with unique field dependence are observed both above and below TN. Most interestingly, our results hint at an extraordinary scenario that different mechanisms are responsible for the AHE and ANE: scaling relation and DFT-calculation considering the spin-canting effect confirm the intrinsic origin of AHE described by the contribution of momentum-space Berry curvature, whereas a plausible extrinsic origin of ANE amplifies the Nernst signal significantly, as indicated by the breakdown of the empirical rule \(| {\alpha }_{xy}^{{{{{{{{\rm{A}}}}}}}}}/{\sigma }_{xy}^{{{{{{{{\rm{A}}}}}}}}}| \sim {k}_{{{{{{{{\rm{B}}}}}}}}}/e\). We mention that the anomalous transport behavior of SmMnBi2 shares similarities with that of YbMnBi2, in spite of the different crystal structures, FS geometries, and (supposedly) magnetic configurations for the two materials. Such unusual consistency singles out spin canting as an essential factor in the occurrence of large AHE and ANE in antiferromagnets. The potential presence of multiple origins of anomalous off-diagonal transport in SmMnBi2 renders it an ideal platform for investigating the interplay between the enriched underlying physical mechanisms, which can definitely benefit the future development of electronic, spintronic, and thermoelectric devices that utilize transverse responses in application purposes.
Methods
Sample growth and characterization
Single crystals of SmMnBi2 were synthesized using a bismuth self-flux method. Initially, a mixture of samarium lumps (99.5%; the surface was polished to remove the oxidation layer), manganese powder (99.9%), and bismuth lumps (99.999%) with an atomic ratio of 1:1:10 were loaded into an alumina crucible. The crucible was sealed into a quartz tube under a high vacuum. The tube was heated to 1100 °C and maintained for 12 h to homogenize the melt, then it was slowly cooled to 500 °C over a time period of 7 days. Millimeter-sized single crystals with rectangular plate shapes and shiny surfaces were obtained after the removal of the excess bismuth flux by centrifugation. The stoichiometry of the samples was confirmed using an EDX mounted on the field emission scanning electronic microscope (FESEM), Sirion200. The single-crystal XRD pattern was measured by the X-ray diffractometer (SmartLab-9, Rigaku Corp.) with Cu Kα1 radiation and a fixed graphite monochromator. Magnetic properties of SmMnBi2 were characterized using a Quantum Design MPMS3 system. The valence of Sm in our samples was determined to be +2 by electron paramagnetic resonance, thus we conclude that the Sm ions are nonmagnetic and the magnetic moments in SmMnBi2 are fully attributed to the Mn2+ ions. Specific heat measurements were performed in a Quantum Design Physical Property Measurement System (PPMS-9T).
Electrical transport measurements
Electrical transport measurements were performed in a Quantum Design Physical Property Measurement System (PPMS-9T). The longitudinal resistivity ρxx and Hall resistivity ρxy were measured simultaneously in a standard Hall bar configuration. Contact leads were made by platinum wires attached to the SmMnBi2 sample using silver paste (DuPont 4922N). Data of ρxx and ρxy were symmetrized and anti-symmetrized with respect to the magnetic field, respectively, to remove the error caused by contact misalignment. The noise level of PPMS converts to an experimental error below 0.01 μΩ cm for electrical resistivity measurements.
Thermoelectric measurements
Thermoelectric measurements were performed utilizing a home-built high-resolution thermoelectric puck which is inserted into the PPMS. An AC method based on the differential thermocouple configuration was adopted to eliminate the DC background noise. The temperature gradient was generated by a chip resistor (1 kΩ) attached to the top of the sample; a low-frequency AC heating current was applied by a Keithley 6221 current source. To ensure good thermal contact, the end of the sample was glued to a copper block by cigarette paper soaked with diluted VGE varnish. A pair of type-E thermocouples were attached to the surface sample by thermal joint compound or stycast 2850 to measure the temperature gradient. The longitudinal (Seebeck) and transverse (Nernst) voltage signals were measured by two pairs of electrical contacts made from thin silver wires. The voltage signals were collected by a Keithley 2182A nanovoltmeter. The contribution of silver wire to the total Seebeck effect was subtracted, referring to the reported thermopower curve of silver60.
Angle-resolved photoelectron spectroscopy
ARPES experiments were performed at BL03U of Shanghai Synchrotron Radiation Facility61 and the Stanford Synchrotron Radiation Lightsource (SSRL). High-quality SmMnBi2 single crystals with a typical size of 1 mm × 1 mm were cleaved in situ. The measurements were carried out at 6.5 K with a base pressure better than 5 × 10−11 Torr, using both linear horizontally and linear vertically polarized lights with varying photon energies. Data shown in Fig. 3 were collected using a photon energy of 82 eV.
Data availability
The data that support the findings of this study are available from the corresponding authors upon reasonable request.
Code availability
The codes used to analyze the data are available from the corresponding authors upon reasonable request.
References
Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys. 82, 1539–1592 (2010).
Jungwirth, T., Niu, Q. & MacDonald, A. H. Anomalous Hall effect in ferromagnetic semiconductors. Phys. Rev. Lett. 88, 207208 (2002).
Yao, Y. G. et al. First principles calculation of anomalous Hall conductivity in ferromagnetic bcc Fe. Phys. Rev. Lett. 92, 037204 (2004).
Xiao, D., Yao, Y. G., Fang, Z. & Niu, Q. Berry-phase effect in anomalous thermoelectric transport. Phys. Rev. Lett. 97, 026603 (2006).
Chen, H., Niu, Q. & MacDonald, A. H. Anomalous Hall effect arising from noncollinear antiferromagnetism. Phys. Rev. Lett. 88, 207208 (2014).
Le, C., Felser, C. & Sun, Y. Design strong anomalous Hall effect via spin canting in antiferromagnetic nodal line materials. Phys. Rev. B 104, 125145 (2021).
Nakatsuji, S., Kiyohara, N. & Higo, T. Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature. Nature 527, 212–215 (2015).
Nayak, A. K. et al. Large anomalous Hall effect driven by a nonvanishing Berry curvature in the noncolinear antiferromagnet Mn3Ge. Sci. Adv. 2, e1501870 (2016).
Pan, Y. et al. Giant anomalous Nernst signal in the antiferromagnet YbMnBi2. Nat. Mater. 21, 203–209 (2022).
Guo, X., Li, X., Zhu, Z. & Behnia, K. Onsager reciprocal relation between anomalous transverse coefficients of an anisotropic antiferromagnet. Phys. Rev. Lett. 131, 246302 (2023).
Roychowdhury, S. et al. Large room temperature anomalous transverse thermoelectric effect in Kagome antiferromagnet YMn6Sn6. Adv. Mater. 34, 2201350 (2022).
Ghimire, N. J. et al. Large anomalous Hall effect in the chiral-lattice antiferromagnet CoNb3S6. Nat. Commun. 9, 3280 (2018).
Luo, Y. et al. Pressure-tuned quantum criticality in the antiferromagnetic Kondo semimetal CeNi2−δAs2. Proc. Natl Acad. Sci. USA 112, 13520–13524 (2015).
Kurumaji, T. et al. Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet. Science 365, 914–918 (2019).
Shekhar, C. et al. Anomalous Hall effect in Weyl semimetal half-heusler compounds RPtBi (R= Gd and Nd). Proc. Natl Acad. Sci. USA 115, 9140–9144 (2018).
Takahashi, K. S. et al. Anomalous Hall effect derived from multiple Weyl nodes in high-mobility EuTiO3 films. Science 4, eaar7880 (2018).
Betancourt, R. D. G. et al. Spontaneous anomalous Hall effect arising from an unconventional compensated magnetic phase in a semiconductor. Phys. Rev. Lett. 130, 036702 (2023).
Šmejkal, L., González-Hernández, R., Jungwirth, T. & Sinova, J. Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets. Sci. Adv. 6, eaaz8809 (2020).
Yang, H. Y. et al. Noncollinear ferromagnetic Weyl semimetal with anisotropic anomalous Hall effect. Phys. Rev. B 103, 115143 (2021).
Krishnan, S. & Besara, T. A new topological semimetal candidate: SmMnBi2. Acta Cryst. 77, 577–583 (2021).
Park, J. et al. Anisotropic Dirac fermions in a Bi square net of SrMnBi2. Phys. Rev. Lett. 107, 126402 (2011).
Liu, J. Y. et al. A magnetic topological semimetal Sr1−yMn1−zSb2 (y, z< 0.1). Nat. Mater. 16, 905–910 (2017).
Masuda, H. et al. Quantum Hall effect in a bulk antiferromagnet EuMnBi2 with magnetically confined two-dimensional Dirac fermions. Sci. Adv. 2, e1501117 (2016).
Borisenko, S. et al. Time-reversal symmetry breaking type-II Weyl state in YbMnBi2. Nat. Commun. 10, 3424 (2019).
Soh, J.-R. et al. Magnetic structure of the topological semimetal YbMnSb2. Phys. Rev. B 104, L161103 (2021).
Guo, Y. F. et al. Coupling of magnetic order to planar Bi electrons in the anisotropic Dirac metals AMnBi2 (A= Sr, Ca). Phys. Rev. B 90, 075120 (2014).
Feng, Y. et al. Strong anisotropy of Dirac cones in SrMnBi2 and CaMnBi2 revealed by angle-resolved photoemission spectroscopy. Sci. Rep. 4, 5385 (2014).
Li, L. et al. Electron-hole asymmetry, Dirac fermions, and quantum magnetoresistance in BaMnBi2. Phys. Rev. B 93, 115141 (2016).
Zhu, F. et al. Magnetic structures, spin-fop transition, and coupling of Eu and Mn magnetism in the Dirac semimetal EuMnBi2. Phys. Rev. Res. 2, 043100 (2020).
Liu, J. Y. et al. Unusual interlayer quantum transport behavior caused by the zeroth Landau level in YbMnBi2. Nat. Commun. 8, 646 (2017).
Liu, Y. et al. Crystal growth, microstructure, and physical properties of SrMnSb2. Phys. Rev. B 99, 054435 (2019).
Yang, R. et al. Spin-canting-induced band reconstruction in the Dirac material Ca1−xNaxMnBi2. Phys. Rev. Lett. 124, 137201 (2020).
Wang, K., Wang, L. & Petrovic, C. Large magnetothermopower effect in dirac materials (Sr/Ca)MnBi2. Appl. Phys. Lett. 100, 112111 (2012).
Liang, T. et al. Evidence for massive bulk Dirac fermions in Pb1−xSnxSe from Nernst and thermopower experiments. Nat. Commun. 4, 2696 (2013).
Pippard, A. B. Magnetoresistance in Metals (Cambridge University Press, 1989).
Qu, D.-X., Hor, Y. S., Xiong, J., Cava, R. J. & Ong, N. P. Quantum oscillations and Hall anomaly of surface states in the topological insulator Bi2Te3. Science 329, 821–824 (2010).
Liang, T. et al. Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd3As2. Nat. Mater. 24, 280–284 (2015).
Cao, X. et al. Giant nonlinear anomalous Hall effect induced by spin-dependent band structure evolution. Phys. Rev. Res. 4, 023100 (2022).
Rong, H. et al. Electronic structure examination of the topological properties of CaMnSb2 by angle-resolved photoemission spectroscopy. Phys. Rev. B 103, 245104 (2021).
Li, P. et al. Giant room temperature anomalous Hall effect and tunable topology in a ferromagnetic topological semimetal Co2MnAl. Nat. Commun. 11, 3476 (2020).
Liu, E. et al. Giant anomalous Hall effect in a ferromagnetic kagome-lattice semimetal. Nat. Phys. 14, 1125–1131 (2018).
Hirschberger, M. et al. Geometrical Hall effect and momentum-space Berry curvature from spin-reversed band pairs. Phys. Rev. B 103, L041111 (2021).
Hayashi, Y. et al. Magneto-optical spectroscopy on Weyl nodes for anomalous and topological Hall effects in chiral MnGe. Nat. Commun. 12, 5974 (2021).
Li, X., Koo, J., Zhu, Z., Behnia, K. & Yan, B. Field-linear anomalous Hall effect and Berry curvature induced by spin chirality in the kagome antiferromagnet Mn3Sn. Nat. Commun. 14, 1642 (2023).
Kipp, J. et al. The chiral Hall effect in canted ferromagnets and antiferromagnets. Commun. Phys. 4, 99 (2021).
Ma, J.-Z. et al. Spin fluctuation induced Weyl semimetal state in the paramagnetic phase of EuCd2As2. Sci. Adv. 5, eaaw4718 (2019).
Ishizuka, H. & Nagaosa, N. Spin chirality induced skew scattering and anomalous Hall effect in chiral magnets. Sci. Adv. 4, eaap9962 (2018).
Uchida, M. et al. Above-ordering-temperature large anomalous Hall effect in a triangular-lattice magnetic semiconductor. Sci. Adv. 7, eabl5381 (2021).
Li, X. et al. Anomalous Nernst and Righi-Leduc effects in Mn3Sn: Berry curvature and entropy flow. Phys. Rev. Lett. 119, 056601 (2017).
Wuttke, C. et al. Berry curvature unravelled by the anomalous Nernst effect in Mn3Ge. Phys. Rev. B 100, 085111 (2019).
Wang, H. et al. Large magneto-transverse and longitudinal thermoelectric effects in the magnetic Weyl semimetal TbPtBi. Adv. Mater. 35, 2206941 (2023).
Hanasaki, N. et al. Anomalous Nernst effects in pyrochlore molybdates with spin chirality. Phys. Rev. Lett. 100, 106601 (2008).
Weischenberg, J., Freimuth, F., Blügel, S. & Mokrousov, Y. Scattering-independent anomalous Nernst effect in ferromagnets. Phys. Rev. B 87, 060406 (2013).
Ramos, R. et al. Anomalous Nernst effect of Fe3O4 single crystal. Phys. Rev. B 90, 054422 (2014).
Ikhlas, M. et al. Large anomalous Nernst effect at room temperature in a chiral antiferromagnet. Nat. Phys. 13, 1085–1090 (2017).
Sakai, A. et al. Giant anomalous Nernst effect and quantum-critical scaling in a ferromagnetic semimetal. Nat. Phys. 14, 1119–1124 (2018).
Ding, L. et al. Intrinsic anomalous Nernst effect amplified by disorder in a half-metallic semimetal. Phys. Rev. X 9, 041061 (2019).
Xu, L. et al. Anomalous transverse response of Co2MnGa and universality of the room-temperature αijA/σijA ratio across topological magnets. Phys. Rev. B 101, 180404 (2020).
Papaj, M. & Fu, L. Enhanced anomalous Nernst effect in disordered Dirac and Weyl materials. Phys. Rev. B 103, 075424 (2021).
Lee, C. C. & Schroeder, P. A. Phonon drag thermopower in silver alloys. Philos. Mag. 25, 1161 (1972).
Yang, Y. C. et al. High-resolution ARPES endstation for in situ electronic structure investigations at SSRF. Nucl. Sci. Tech. 32, 31 (2021).
Acknowledgements
The authors thank Yimin Xiong, Aifeng Wang, Xiaoyuan Zhou, Zhenyu Wang, Tao Wu, and Jianjun Ying for insightful discussions. The authors also gratefully acknowledge Xuguang Liu, Jiafu Chen, and Maosheng Ma for assistance in the sample characterizations performed at the Instruments Center for Physical Science, University of Science and Technology of China. This work was financially supported by the National Key R&D Program of the MOST of China (Grant No. 2022YFA1602602), the National Natural Science Foundation of China (Grants Nos. 12274390, 12488201, 12222402 and 12204449), the Fundamental Research Funds for the Central Universities (Grants Nos. WK3510000014, WK3510000012, WK3510000015, and WK2030000035), the International Partnership Program of the Chinese Academy of Sciences (Grant No. 123GJHZ2022035MI), the Anhui Initiative in Quantum Information Technologies (AHY160000) and the Basic Research Program of the Chinese Academy of Sciences Based on Major Scientific Infrastructures (No. JZHKYPT-2021-08). Y.Y. acknowledges support from the China Postdoctoral Science Foundation (Grant No.2022M723068). Z.T.L. and D.W.S. acknowledge the National Natural Science Foundation of China (Grants Nos. U2032208 and 12004405). Use of the Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515. Part of this research used Beamline 03U of the Shanghai Synchrotron Radiation Facility, which is supported by the ME2 Project under Contract No. 11227902 from the National Natural Science Foundation of China. The DFT calculations in this work are supported by the Beijing Super Cloud Computing Center (BSCC) and the Supercomputing Center of the University of Science and Technology of China.
Author information
Authors and Affiliations
Contributions
K.T. grew the samples with the help from M.S. K.T. performed the electrical transport, magnetization, specific heat, and thermoelectric measurements with help from N.Z., H.-P.L., and H.-Y.L. J.S., Z.L., D.S., and J.H. performed the ARPES measurements. K.T., J.H., and Z.X. analyzed the experimental data. Y.Y., Y.G., and R.W. performed the theoretical analysis and calculations. Z.X. and X.-H.C. supervised the project. K.T. and Z.X. wrote the paper with input from Y.Y., J.S., D.S., R.W., Y.G., and J.H. All authors have given approval to the final version of the paper.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Communications Materials thanks the anonymous reviewers for their contribution to the peer review of this work. Primary Handling Editor: Aldo Isidori. A peer review file is available.
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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Tang, K., Yang, Y., Shen, J. et al. Unconventional anomalous Hall effect and large anomalous Nernst effect in antiferromagnet SmMnBi2. Commun Mater 5, 89 (2024). https://doi.org/10.1038/s43246-024-00525-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s43246-024-00525-0
- Springer Nature Limited