The anomalous Hall effect (AHE) and anomalous Nernst effect (ANE) are the transverse transport phenomena in magnetic materials, which reflect the Berry curvature arising from the electronic structure near the Fermi level. Lattice strain provides a direct means to tune these effects by modifying the electronic structure; however, disentangling the strain-induced effect through the Berry curvature modulations in multicomponent materials is challenging due to complexities arising from extrinsic contributions by impurities and disorder, as well as difficulties in simple direct comparison with first-principles calculations. In this study, we focus on Fe, a prototypical single element ferromagnet with a well-established electronic structure, and tune the sign and magnitude of the strain in epitaxial thin films of by varying the substrates and deposition conditions to investigate the strain effect on the AHE and ANE. Scaling law analysis revealed that the intrinsic anomalous Hall conductivity (AHC) exhibits a clear tetragonal distortion (c/a) dependence, in good agreement with theoretical calculations based on Berry curvature modification. In contrast, the anomalous Nernst conductivity (ANC) shows a pronounced deviation from the theoretical values and markedly different c/a dependence. These results demonstrate a crucial difference in the physical origin between the AHC and the ANC in the Fe films; the AHC is predominantly governed by intrinsic mechanisms, whereas the ANC is strongly influenced by the extrinsic contribution.
Antiferromagnets with tunable phase transitions are promising for future spintronics applications. We investigated spin-dependent transport properties of FeRh thin films, which show a temperature driven antiferromagnetic-to-ferromagnetic phase transition. Epitaxial FeRh films grown on MgO (001) substrates exhibit a clear magnetic and electronic phase transition. By performing anomalous Hall and anomalous Nernst effect measurements over a wide range of temperatures, we demonstrate that the thermally driven transition shows distinctly different transverse transport on both side of the phase tran…
Modulation of the Nernst Thermoelectrics by Regulating the Anomalous Hall and Nernst Angles
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；Key Laboratory of Magnetic Molecules and Magnetic Information Materials of Ministry of Education & Research Institute of Materials Science, Shanxi Normal University（山西师范大学磁性分子与磁信息材料教育部重点实验室及材料科学研究所）
In this study, we implemented a finite-difference algorithm for computing anomalous Hall and Nernst conductivity. Based on the expression to evaluate the Berry curvature in an insulating system [J. Phys. Soc. Jpn. 74 1674(2005)], we extended the methods to a metallic system. We calculated anomalous Hall conductivity and Nernst conductivity in a two-dimensional ferromagnetic material FeCl$_2$ and three-dimensional ferromagnetic transition metals bcc-Fe, hcp-Co, and fcc-Ni. Our results are comparable to previously reported results computed by Kubo-formula or Wannier representation. To evaluate a…
Based on first-principles calculations, the anomalous Hall (AHC) and anomalous Nernst conductivities (ANC) of the XMnP (X=Ti, Zr, Hf) compounds were evaluated, and the possibility to tailor such properties by changing the magnetization directions was also investigated. We observed that nodal lines and small gap areas consist the dominant contributions to AHC and ANC, where the significant variations in AHC and ANC when altering the magnetization direction originate from the whole Brillouin zone. Our studies gave a promising clue on engineering magnetic intermetallic compounds for tunable trans…
MnP and FeP are show complex magnetic spiral states with geometric phase contributions to the anomalous Hall effect and the topological Hall effect, where both have thermoelectric Nernst counterparts. We use state of the art first principle calculations to show that both Hall and Nernst effects are enhanced in MnP and FeP due to the temperature dependent magnetic texture. At ambient pressure the inversion breaking crystals shows a transition from a double-spiral helimagnetic phase to a topologically trivial magnetic phase. This helimagnetic structure is determined by exchange frustration and t…
The interplay of magnetism and topology opens up the possibility for exotic linear response effects, such as the anomalous Hall effect and the anomalous Nernst effect, which can be strongly enhanced by designing a strong Berry curvature in the electronic structure. It is even possible to utilize this to create a quantum anomalous Hall state at high temperatures by reducing the dimensionality. Magnetic Heusler compounds are a promising class of materials for this purpose because they grow in thin films, have a high Curie temperature, and their electronic structure hosts strong topological featu…
The generation of spin and orbital currents is of crucial importance in the field of spin-orbitronics. In this work, using relativistic density functional theory and the Kubo linear-response formalism, we systematically investigate the spin Hall and orbital Hall effects for 40 monoatomic metals. The spin Hall conductivity (SHC) and orbital Hall conductivity (OHC) are computed as a function of the electrochemical potential and the influence of the spin-orbit interaction strength is also investigated. Our calculations predict a rather small OHC in $sp$ metals, but a much larger OHC in $d$-band m…
Synthesis of crystallographically well-defined thin films of topological materials is important for unraveling their mesoscale quantum properties and for device applications. Mn$_3$Ge, an antiferromagnetic Weyl semimetal with a chiral magnetic structure on a Kagome lattice, is expected to have enhanced Berry curvature around Weyl nodes near the Fermi energy, leading to large anomalous Hall / Nernst effects and a large spin-Hall effect. Using magnetron sputtering, we have grown epitaxial thin films of hexagonal D0$_{19}$ Mn$_3$Ge that are flat and continuous. Large anomalous Nernst and inverse …
The anomalous Hall conductivity (AHC) and anomalous Nernst conductivity (ANC) are two prominent transport phenomena in ferromagnetic materials of a topological nature. Based on first-principles calculations, we evaluated the AHC and ANC of 35 cubic ferromagnetic antiperovskites (APVs) and observed giant AHC and ANC as large as 1128 S/cm and 6.27 AK-1m-1 for Co3LiN and Co3PtN, respectively. Detailed analysis reveals that the origin of giant ANC can be attributed to the occurrence of Weyl nodes near the Fermi energy, as demonstrated for Co3PtN. Interestingly, both the magnitude and sign of AHC a…
Anomalous Hall effect (AHE) and anomalous Nernst effect (ANE) in a variety of ferromagnetic metals including pure metals, oxides, and chalcogenides, are studied to obtain unified understandings of their origins. We show a universal scaling behavior of anomalous Hall conductivity $σ_{xy}$ as a function of longitudinal conductivity $σ_{xx}$ over five orders of magnitude, which is well explained by a recent theory of the AHE taking into account both the intrinsic and extrinsic contributions. ANE is closely related with AHE and provides us with further information about the low-temperature electro…
We study the anomalous Nernst effect (ANE) and anomalous Hall effect (AHE) in proximity-induced ferromagnetic palladium and platinum which is widely used in spintronics, within the Berry phase formalism based on the relativistic band structure calculations. We find that both the anomalous Hall ($σ_{xy}^A$) and Nernst ($α_{xy}^A$) conductivities can be related to the spin Hall conductivity ($σ_{xy}^S$) and band exchange-splitting ($Δ_{ex}$) by relations $σ_{xy}^A =Δ_{ex}\frac{e}{\hbar}σ_{xy}^S(E_F)'$ and $α_{xy}^A = -\frac{π^2}{3}\frac{k_B^2TΔ_{ex}}{\hbar}σ_{xy}^s(μ)"$, respectively. In particu…
The magnetic spin Hall effect (MSHE) is an anomalous charge-to-spin conversion phenomenon which occurs in ferromagnetic materials. In contrast to the conventional spin Hall effect (SHE), being a time-reversal even effect, the magnetic counterpart is time-reversal odd. In this work, we use ab initio calculations to investigate the MSHE for the bulk ferromagnets Fe, Co, and Ni. The magnitudes of the MSHE of Fe and Co are comparable to those of the SHE, but the MSHE is strongly dependent on the electron lifetime and the MSHE and SHE can moreover have opposite signs. For Ni the MSHE is smaller tha…
We theoretically study the thermoelectric transport properties of strained HgTe in the topological insulator phase. We developed a model for the system using a Dirac Hamiltonian including the effect of strain induced by the interface between HgTe and the CdTe substrate. The conductivity tensor was explored assuming the electrons are scattered by charge impurities, while the thermopower tensor was addressed using the Mott relation. Seebeck and Nernst responses exhibit remarkable enhancements in comparison with other two-dimensional Dirac materials, such as graphene, germanane, prosphorene and s…
Electric generation of spin current via spin Hall effect is of great interest as it allows an efficient manipulation of magnetization in spintronic devices. Theoretically, spin current can be also created by a temperature gradient, which is known as spin Nernst effect. Here, we report spin Nernst effect-induced transverse magnetoresistance in ferromagnet (FM)/non-magnetic heavy metal (HM) bilayers. We observe that the magnitude of transverse magnetoresistance (i.e., planar Nernst signal) in FM/HM bilayers is significantly modified by HM and its thickness. This strong dependence of transverse m…
Noncollinear antiferromagnets have recently been attracting considerable interest partly due to recent surprising discoveries of the anomalous Hall effect (AHE) in them and partly because they have promising applications in antiferromagnetic spintronics. Here we study the anomalous Nernst effect (ANE), a phenomenon having the same origin as the AHE, and also the spin Nernst effect (SNE) as well as AHE and the spin Hall effect (SHE) in noncollinear antiferromagnetic Mn$_3X$ ($X$ = Sn, Ge, Ga) within the Berry phase formalism based on {\it ab initio} relativistic band structure calculations. For…
Bismuth is an archetypal semimetal with gigantic spin-orbit coupling and it has been a major source material for the discovery of seminal phenomena in solid state physics for more than a century. In recent years, spin current transports in bismuth have also attracted considerable attention. In this paper, we theoretically study both spin Hall effect (SHE) and spin Nernst effect (SNE) in bismuth, based on relativistic band structure calculations. First, we find that there are three independent tensor elements of spin Hall conductivity (SHC) and spin Nernst conductivity (SNC), namely, $Z_{yx}^z$…
Motivated by the recent prediction of the Magnus Hall effect in systems with broken inversion symmetry, in this paper we study the Magnus Nernst effect and the Magnus thermal Hall effect. In presence of an in-built electric field, the self rotating wave-packets of electrons with finite Berry curvature generate a Magnus velocity perpendicular to both. This anomalous Magnus velocity gives rise to the Magnus Hall transport which manifests in all four electro-thermal transport coefficients. In this paper, we demonstrate the existence of the Magnus Nernst and Magnus thermal Hall effect in monolayer…
The Mott relation between the electrical and thermoelectric transport coefficients normally holds for phenomena involving scattering. However, the anomalous Hall effect (AHE) in ferromagnets may arise from intrinsic spin-orbit interaction. In this work, we have simultaneously measured AHE and the anomalous Nernst effect (ANE) in Ga1-xMnxAs ferromagnetic semiconductor films, and observed an exceptionally large ANE at zero magnetic field. We further show that AHE and ANE share a common origin and demonstrate the validity of the Mott relation for the anomalous transport phenomena.
Since spin currents can be generated, detected, and manipulated via the spin Hall effect (SHE), the design of strong SHE materials has become a focus in the field of spintronics. Because of the recent experimental progress also the spin Nernst effect (SNE), the thermoelectrical counterpart of the SHE, has attracted much interest. Empirically strong SHEs and SNEs are associated with $d$-band compounds, such as transition metals and their alloys -- the largest spin Hall conductivity (SHC) in a $p$-band material is $\sim 450$ $\left(\hbar/e\right)\left(Ω\cdot cm\right)^{-1}$ for a Bi-Sb alloy, wh…
Based on high-throughput first-principles calculations, we evaluated the anomalous Hall and anomalous Nernst conductivities of 266 transition-metal-based ferromagnetic compounds. Detailed analysis based on the symmetries and Berry curvatures reveals that the origin of singular-like behaviour of anomalous Hall/Nernst conductivities can be mostly attributed to the appearance of Weyl nodes or nodal lines located in the proximity of the Fermi energy, which can be further tailored by external stimuli such as biaxial strains and magnetic fields. Moreover, such calculations are enabled by the automat…
Improvement of a superconducting magnet system makes induction of a strong magnetic field easier. This fact gives us a possibility of energy conversion by the Nernst effect. As the first step to study the Nernst element, we measured the conductivity, the Hall coefficient, the thermoelectric power and the Nernst coefficient of the InSb, which is one of candidates of the Nernst elements. From this experiment, it is concluded that the Nernst coefficient is smaller than the theoretical values. On the other hand, the conductivity, the Hall coefficient ant the thermoelectric power has the values exp…
Exchange splitting as a descriptor for giant anomalous Hall and Nernst effects in ferromagnets
National Institute for Materials Science (NIMS)（物质材料研究机构）；Zhejiang Key Laboratory of Magnetic Materials and Applications, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences（中国科学院宁波材料技术与工程研究所磁材料与应用浙江省重点实验室）；Kyoto Institute of Technology（京都工艺纤维大学）
All-$d$ Heuslers are a category of novel compounds combining versatile functionalities such as caloric responses and spintronics with enhanced mechanical properties. Despite the promising transport properties (anomalous Hall (AHC) and anomalous Nernst (ANC) conductivities) shown in the conventional Co$_2$XY Heuslers with $p$-$d$ hybridization, the all-$d$ Heuslers with only $d$-$d$ hybridization open a new horizon to search for new candidates with outstanding transport properties. In this work, we evaluate the AHC and ANC for thermodynamically stable ferro/ferri-magnetic all-$d$-metal regular …
Ferrimagnetic Mn$_4$N is a promising material for heat flux sensors based on the anomalous Nernst effect (ANE) because of its sizable uniaxial magnetic anisotropy ($K_{\rm u}$) and low saturation magnetization ($M_{\rm s}$). We experimentally and theoretically investigated the ANE and anomalous Hall effect in sputter-deposited Mn$_4$N films. It was revealed that the observed negative anomalous Hall conductivity ($σ_{xy}$) could be explained by two different coexisting magnetic structures, that is, a dominant magnetic structure with high $K_{\rm u}$ contaminated by another structure with neglig…
The spin Hall effect allows generation of spin current when charge current is passed along materials with large spin orbit coupling. It has been recently predicted that heat current in a non-magnetic metal can be converted into spin current via a process referred to as the spin Nernst effect. Here we report the observation of the spin Nernst effect in W. In W/CoFeB/MgO heterostructures, we find changes in the longitudinal and transverse voltages with magnetic field when temperature gradient is applied across the film. The field-dependence of the voltage resembles that of the spin Hall magnetor…
Utilizing the first-principles density functional theory calculations together with group theory analyses, we systematically investigate the spin order-dependent magneto-optical effect (MOE), anomalous Hall effect (AHE), and anomalous Nernst effect (ANE) in a recently discovered two-dimensional room-temperature ferromagnet $1T$-CrTe$_2$. We find that the spin prefers an in-plane direction by the magnetocrystalline anisotropy energy calculations. The MOE, AHE, and ANE display a period of $2π/3$ when the spin rotates within the atomic plane, and they are forbidden if there exists a mirror plane …
The quaternary arsenide compounds XCuYAs (X=Zr, Hf; Y= Si, Ge) belong to the vast family of the 1111-type quaternary compounds, which possess outstanding physical properties ranging from $p$-type transparent semiconductors to high-temperature Fe-based superconductors. In this paper, we study the electronic structure topology, spin Hall effect (SHE) and spin Nernst effect (SNE) in these compounds based on density functional theory calculations. First we find that the four considered compounds are Dirac semimetals with the nonsymmorphic symmetry-protected Dirac line nodes along the Brillouin zon…
A novel process of spin conversion from a temperature gradient to a transverse voltage is addressed in this paper, viz. the anomalous Nernst effect (ANE) in a ferromagnetic metal. We report that an additional voltage is superposed on the conventional anomalous Nernst voltage in FePt crystalline thin films. The dynamics of the local magnetization is modulated by the heat current and excites spin waves. These generate a conduction electron spin current via s-d coupling, which flows along the temperature gradient, and the spin current is converted to a Nernst voltage by the inverse spin Hall effe…
Observation of the Nernst effect driven by longitudinal spin fluctuations
National Institute for Materials Science（国立材料研究所）；Research Institute for Interdisciplinary Science, Okayama University（冈山大学交叉科学研究所）；Department of Advanced Materials Science, Graduate School of Frontier Sciences, The University of Tokyo（东京大学前沿科学研究生院先进材料科学系）
We report the planar and anomalous Nernst effect in epitaxial thin films of spin polarized La2/3Sr1/3MnO3. The thermal counterpart of the anomalous Hall effect in this material (i.e. the anomalous Nernst effect) shows a extreme sensitivity to any parasitic thermal gradient, resulting in large asymmetric voltages under small temperature differences. This should be considered when interpreting the magnitude of the electrical response in nanostructures and devices that operate under high current densities. Finally, none of the observed magneto-thermoelectric signals is compatible with the observa…
In ferromagnetic solids, even in absence of magnetic field, a transverse voltage can be generated by a longitudinal temperature gradient. This thermoelectric counterpart of the Anomalous Hall effect (AHE) is dubbed the Anomalous Nernst effect (ANE). Expected to scale with spontaneous magnetization, both these effects arise because of the Berry curvature at the Fermi energy. Here, we report the observation of a giant ANE in a newly-discovered magnetic Weyl semimetal Co$_3$Sn$_2$S$_2$ crystal. Hall resistivity and Nernst signal both show sharp jumps at a threshold field and exhibit a clear hyste…
A large Berry curvature in the vicinity of the Fermi energy is required in order to obtain a large anomalous Hall and Nernst effect. This Berry curvature can be induced by Weyl points and gapped nodal lines. One of the possible mechanisms takes place in systems with a symmetry group where mirror planes lead to protected nodal line structures. When these mirror symmetries are broken, e. g. via fixing a magnetization direction, a gap in the former nodal line can create Weyl points and a large Berry curvature along the gapped lines. In this work we study this effect in a minimal effective model a…
A magnon Nernst effect, an antiferromagnetic analogue of the magnon Hall effect in ferromagnetic insulators, has been studied experimentally for a layered antiferromagnetic insulator MnPS3 in contact with two Pt strips. Thermoelectric voltage in the Pt strips grown on MnPS3 single crystals exhibits non-monotonic temperature dependence at low temperatures, which cannot be explained by electronic origins in Pt but can be ascribed to the inverse spin Hall voltage induced by a magnon Nernst effect. Control of antiferromagnetic domains in the MnPS3 crystal by magnetoelectric cooling is found to mod…
Materials exhibiting controllable magnetic phase transitions are currently in demand for many spintronics applications. Here we investigate from first principles the electronic structure and intrinsic anomalous Hall, spin Hall and anomalous Nernst response properties of the FeRh metallic alloy which undergoes a thermally driven antiferromagnetic-to-ferromagnetic phase transition. We show that the energy band structures and underlying Berry curvatures have important signatures in the various Hall effects. Specifically, the suppression of the anomalous Hall and Nernst effects in the AFM state an…
Harmonic measurements of the longitudinal and transverse voltages in Bi-Sb/Co bilayers are presented. A large second harmonic voltage signal due to the ordinary Nernst effect is observed. In experiments where a magnetic field is rotated in the film plane, the ordinary Nernst effect shows the same angular dependence in the transverse voltage as the damping-like spin-orbit torque and in the longitudinal voltage as the unidirectional spin-Hall magneto-resistance respectively. Therefore, the ordinary Nernst effect can be a spurious signal in spin-orbit torque measurements, leading to an overestima…
The longitudinal spin Seebeck effect is measured on the ferromagnetic insulator Fe$_3$O$_4$ with the ferromagnetic metal Co$_{0.2}$Fe$_{0.6}$B$_{0.2}$ (CoFeB) as the spin detector. By using a non-magnetic spacer material between the two materials (Ti), it is possible to decouple the two ferromagnetic materials and directly observe pure spin flow from Fe$_3$O$_4$ into CoFeB. It is shown, that in a single ferromagnetic metal the inverse spin Hall effect (ISHE) and anomalous Nernst effect (ANE) can occur simultaneously with opposite polarity. Using this and the large difference in the coercive fi…
Resolving the structure of energy bands in transport experiments is a major challenge in condensed matter physics and material science. Sometimes, however, traditional electrical conductance or resistance measurements only provide very small signals, and thus limit the ability to obtain direct band structure information. In this case, it has been proven beneficial to employ thermoelectric measurements which are sensitive to the first derivative of the density of states with respect to energy, rather than to its value itself. Due to the large interest in topological effects these days, it is im…
The topological kagome magnet (TKM) Fe3Sn2 exhibits unusual topological properties, flat electronic bands, and chiral spin textures, making it an exquisite materials platform to explore the interplay between topological band structure, strong electron correlations, and magnetism. Here we report the first synthesis of high-quality epitaxial (0001) Fe3Sn2 films with large intrinsic anomalous Hall effect close to that measured in bulk single crystals. In addition, we measured a large, anisotropic anomalous Nernst coefficient Syx of 1.26 μV/K, roughly 2-5x greater than that of common ferromagnets,…
Transition metal monosilicides CoSi, CoGe, RhSi and RhGe in the chiral cubic B20 structure have recently been found to host unconventional chiral fermions beyond spin-1/2 WFs, and also exhibit exotic physical phenomena such as long Fermi arc surface states, GME and quantized CPGE. Thus, exploring novel spin-related transports in these unconventional chiral fermion semimetals may open a new door for spintronics and spin caloritronics. In this paper, we study the intrinsic SHE and SNE in the CoSi family based on ab initio relativistic band structure calculations. First, we find that unlike nonch…
Utilizing the first-principles calculations together with the group theory analysis, we systematically investigate the magnetocrystalline anisotropy energy, magneto-optical effect, and anomalous transport properties (including anomalous Hall, Nernst, and thermal Hall effects) of monolayer and bilayer Fe$_n$GeTe$_2$ ($n$ = 3, 4, 5). The monolayer Fe$_n$GeTe$_2$ ($n$ = 3, 4, 5) exhibits the out-of-plane, in-plane, and in-plane ferromagnetic orders with considerable magnetocrystalline anisotropy energies of -3.17, 4.42, and 0.58 meV/f.u., respectively. Ferromagnetic order is predicted in bilayer …
The Hall effect can be extended by inducing a temperature gradient in lieu of electric field that is known as the Nernst (-Ettingshausen) effect. The recently discovered spin Nernst effect in heavy metals continues to enrich the picture of Nernst effect-related phenomena. However, the collection would not be complete without mentioning the valley degree of freedom benchmarked by the observation of the valley Hall effect. Here we show the experimental evidence of its missing counterpart, the valley Nernst effect. Using millimeter-sized WSe$_{2}$ mono-multi-layers and the ferromagnetic resonance…
