The thermodynamics of irreversible processes in continuous media predicts the existence of a Magnetic Nernst effect that results from a magnetic analog to the Seebeck effect in a ferromagnet and magnetophoresis occurring in a paramagnetic electrode in contact with the ferromagnet. Thus, a voltage that has DC and AC components is expected across a Pt electrode as a response to the inhomogeneous magnetic induction field generated by magnetostatic waves of an adjacent YIG slab subject to a temperature gradient. The voltage frequency and dependence on the orientation of the applied magnetic induction field are quite distinct from that of spin pumping.
Dirac and Weyl semimetals display a host of novel properties. In Cd$_3$As$_2$, the Dirac nodes lead to a protection mechanism that strongly suppresses backscattering in zero magnetic field, resulting in ultrahigh mobility ($\sim$ 10$^7$ cm$^2$ V$^{-1}$ s$^{-1}$). In applied magnetic field, an anomalous Nernst effect is predicted to arise from the Berry curvature associated with the Weyl nodes. We report observation of a large anomalous Nernst effect in Cd$_3$As$_2$. Both the anomalous Nernst signal and transport relaxation time $τ_{tr}$ begin to increase rapidly at $\sim$ 50 K. This suggests a…
We consider the Nernst-Ettingshausen (NE) effect in the presence of semiclassically strong magnetic fields for a quasi-two dimensional system with a parabolic or linear dispersion of carriers. We show that the occurring giant oscillations of the NE coefficient are coherent with the recent experimental observation in graphene, graphite and bismuth. In the 2D case we find the exact shape of these oscillations and show that their magnitude decreases/increases with enhancement of the Fermi energy for Dirac fermions/normal carriers. With a crossover to 3D spectrum the phase of oscillations shifts, …
We study the spin Nernst effect of a mesoscopic four-terminal cross-bar device with the Rashba spin-orbit interaction (SOI) in the absence of a magnetic field. The interplay between the spin Nernst effect and the seebeck coefficient is investigated for a wide range of the Rashba SOI. When no peaks appeared in the seebeck coefficient, an oscillatory spin Nernst effect still occurs. In addition, the disorder effect on the spin Nernst effect is also studied. We find that the spin Nernst effect can be enhanced up to threefold by disorder. Besides, due to the interface effect, the counter propagati…
We study the Nernst effect and the spin Nernst effect, that a longitudinal thermal gradient induces a transverse voltage and a spin current. A mesoscopic four-terminal cross-bar device having the Rashba spin-orbit interaction (SOI) under a perpendicular magnetic field is considered. For zero SOI, the Nernst coefficient peaks when the Fermi level crosses the Landau Levels. In the presence of the SOI, the Nernst peaks split, and the spin Nernst effect appears and exhibits a series of oscillatory structures. The larger SOI is or the weaker magnetic field is, the more pronounced the spin Nernst ef…
The derivation for the transport coefficients of an electron system in the presence of temperature gradient and the electric and magnetic fields are presented. The Nernst conductivity and the transverse thermoelectric power of the Dirac fermions in graphene under charged impurity scatterings and weak magnetic field are calculated on basis of the self-consistent Born approximation. The result is compared with so far the available experimental data.
We propose theoretically a new effect, i.e. nonlinear planar Nernst effect (NPNE), in nonmagnetic topological insulator (TI) Bi2Te3 in the presence of an in-plane magnetic field. We find that the Nernst current scales quadratically with temperature gradient but linearly with magnetic field and exhibits a cosine dependence of the orientation of the magnetic field with respect to the direction of the temperature gradient. The NPNE has a quantum origin arising from the conversion of a nonlinear transverse spin current to a charge current due to a joint result of hexagonal warping effect, spin-mom…
We report measurements of the thermopower $S$ and Nernst signal $S_{yx}$ in graphene in a magnetic field $H$. Both quantities show strong quantum oscillations vs. the gate voltage $V_g$. Our measurements for Landau Levels of index $n\ne 0$ are in quantitative agreement with the edge-current model of Girvin and Jonson (GJ). The inferred off-diagonal thermoelectric conductivity $α_{yx}$ comes close to the quantum of Amps per Kelvin. At the Dirac point ($n=0$), however, the width of the peak in $α_{yx}$ is very narrow. We discuss features of the thermoelectric response at the Dirac point includin…
The spin Nernst effect describes a transverse spin current induced by the longitudinal thermal gradient in a system with the spin-orbit coupling. Here we study the spin Nernst effect in a mesoscopic four-terminal cross-bar Weyl semimetal device under a perpendicular magnetic field. By using the tight-binding Hamiltonian combining with the nonequilibrium Green's function method, the three elements of the spin current in the transverse leads and then spin Nernst coefficients are obtained. The results show that the spin Nernst effect in the Weyl semimetal has the essential difference with the tra…
Magnon spin Hall systems could hardly show experimentally observable particle and thermal transport phenomena intrinsically due to the spin cancellation. Here we demonstrated that the magnon spin Hall systems can exhibit magnon Nernst effect and thermal Hall effect under external magnetic field by considering two typical systems, i.e. the antiferromagnetically (AFM) coupled bilayer honeycomb ferromagnets and monolayer collinear honeycomb antiferromagnet. The both systems experience magnetic phase transitions from AFM phase to a field-polarized phase via a spin-flop (SF) phase or directly. In b…
By generalizing the Kubo-Streda formula for calculating electrical conductivities to the thermoelectric coefficients, we theoretically study the anomalous Nernst effect (ANE) on the surface of a topological insulator induced by a finite concentration of magnetic impurities. The ANE is found to be modulated by the impurity scattering and thermal fluctuations, simultaneously, and so exhibits rich structures in the energy space. While the anomalous Hall conductivity is half-integer quantized with the Fermi level across the magnetic-impurity-induced gap, the anomalous Nernst signal (ANS) is fully …
The thermoelectric power, including the Nernst and Seebeck effects, in graphene nanoribbon is studied. By using the non-equilibrium Green function combining with the tight-binding Hamiltonian, the Nernst and Seebeck coefficients are obtained. Due to the electron-hole symmetry, the Nernst coefficient is an even function of the Fermi energy while the Seebeck coefficient is an odd function regardless of the magnetic field. In the presence of a strong magnetic field, the Nernst and Seebeck coefficients are almost independent of the chirality and width of the nanoribbon, and they show peaks when th…
We calculate the magnetic-field dependence (oscillations) of the Nernst coefficient in bismuth at low temperatures for the case when the magnetic field is directed along the trigonal axis of the crystal. In the calculations we take into account the scattering of the electrons and holes in bismuth on impurities and the dependence of this scattering on the magnetic field. The results of these calculations are compared with the experimental data recently published.
We theoretically investigate topological spin transport of the magnon-polarons in bilayer magnet with two-dimensional square lattices. Our theory is motivated by recent reports on the van der Waals magnets which show the reversible electrical switching of the interlayer magnetic order between antiferromagnetic and ferromagnetic orders. The magnetoelastic interaction opens band gaps and allows the interband transition between different excitation states. In the layered antiferromagnet, due to the interband transition between the magnon-polaron states, the spin Berry curvature which allows the t…
We investigate transverse magnetic heat transport on the surface of a topological insulator on which a ferromagnet is attached. We present general expressions of the Nernst coefficient and the thermal Hall conductivity, which are reduced to simple forms at low temperatures. It is shown that the Nernst coefficient and the thermal Hall conductivity show non-monotonous dependence on temperature. At low temperature, they have linear dependence on temperature. From the behavior of the Nernst coefficient at low temperature, one can estimate the magnitude of the gap induced by time-reversal symmetry …
Geometric oscillations of local Hall and Nernst effects in ballistic graphene at weak magnetic fields
Abrikosov Center for Theoretical Physics, MIPT（莫斯科物理技术学院阿布里科索夫理论物理中心）；Institute of Physics of DFRS of the RAS（俄罗斯科学院达吉斯坦共和国科学中心物理研究所）；School of Science, Westlake University（西湖大学理学院）
A valley-contrasting Berry curvature in bilayer transition metal dichalcogenides with spin-orbit coupling can generate valley magnetization when the inversion symmetry is broken, for example, by an electric field, regardless of time-reversal symmetry. A nontrivial Berry curvature can also lead to anomalous transport responses, such as the anomalous Hall effect and the anomalous Nernst effect. Applied to a bilayer WSe$_2$, an electric field can tune the Berry curvature and orbital magnetic moment, which has important consequences for the orbital magnetization and the anomalous Nernst responses.…
In the presented report, the Nernst-Ettingshausen effect in layered conductors is investigated. Considering a Fermi surface (FS) consisting of a slightly corrugated cylinder and two corrugated planes distributed periodically in the momentum space, the thermoelectric effects are considered under general assumptions for the value of a magnetic breakdown probability. As a result of an external generalized force, the FS sheets in layered conductors with a multisheet FS appear to be so close that the charge carriers (as a result of magnetic breakdown) can move from one FS sheet to another. In addit…
Cyclotron resonance of a Landau-quantized graphene can absorb significant amount of infrared light. However, application of this phenomenon to the photodetector had been limited due to the lack of efficient photon to charge conversion scheme. Here, we demonstrate the detection of cyclotron resonance in a partially metal-masked monolayer graphene two-terminal device using photo-Nernst effect. Due to the presence of the mask, incident infrared light is irradiated on only one-half of the graphene channel. This partial irradiation creates a temperature gradient perpendicular to the graphene channe…
We theoretically investigate a pure spin Hall current driven by a longitudinal temperature gradient, i.e., the spin Nernst effect (SNE), in a paramagnetic state of a collinear antiferromagnetic insulator with the Dzyaloshinskii-Moriya interaction. The SNE in a magnetic ordered state in such an insulator was proposed by Cheng {\it et al.} [R. Cheng, S. Okamoto, and D. Xiao, Phys. Rev. Lett. 117, 217202 (2016)]. Here we show that the Dzyaloshinskii-Moriya interaction can generate a pure spin Hall current even without magnetic ordering. By using a Schwinger boson mean-field theory, we calculate t…
The ideal reversible thermodynamic cycle visualization of the Nernst effect in Laughlin geometry, excluding the kinetic contribution is proposed. The Ettingshausen effect is also treated in the fashion using the reverse cycle. The corresponding values of the off-diagonal thermoelectric coefficients are expressed through the ratio of the entropy budget per magnetic flux. Our approach enlightens the profound thermodynamic origin of the relation between the Nernst effect and magnetization currents.
We measured the anomalous-Nernst effect and anisotropic magnetoresistive heating in a lateral multiterminal Permalloy/Copper spin valve using all-electrical lock-in measurements. To interpret the results, a three-dimensional thermoelectric finite-element-model is developed. Using this model, we extract the heat profile which we use to determine the anomalous Nernst coefficient of Permalloy Rn=0.13 and also determine the maximum angle of theta=8 degrees of the magnetization prior to the switching process when an opposing non-collinear 10$^{\circ}$ magnetic field is applied.
We study the manifestation of the Nernst effect in the Corbino disk subjected to the normal external magnetic field and to the radial temperature gradient. The Corbino geometry offers a precious opportunity for the direct measurement of the magnetization currents that are masked by kinetic contributions to the Nernst current in the conventional geometry. The magnetization currents, also referred to as the edge currents, are independent on the conductivity of the sample which is why they can be conveniently described within the thermodynamic approach. They can be related to the Landau thermodyn…
Magnon spin Nernst effect was recently proposed as an intrinsic effect in antiferromagnets, where spin diffusion and boundary spin transmission have been ignored. However, diffusion processes are essential to convert a bulk spin current into boundary spin accumulation, which determines the spin injection rate into detectors through imperfect transmission. We formulate a diffusive theory to describe the detection of magnon spin Nernst effect with boundary conditions reflecting real device geometry. Thanks to the spin diffusion effect, the output signals in both electronic and optical detection …
We introduce a simple model for an engine based on the Nernst effect. In the presence of a magnetic field, a vertical heat current can drive a horizontal particle current against a chemical potential. For a microscopic model invoking classical particle trajectories subject to the Lorentz force, we prove a universal bound 3-2*sqrt(2) simeq 0.172 for the ratio between maximum efficiency and Carnot efficiency. This bound, as the slightly lower one 1/6 for efficiency at maximum power, can indeed be saturated for large magnetic field and small fugacity irrespective of the aspect ratio.
We investigate the Nernst effect in a mesoscopic two-dimensional electron system (2DES) at low magnetic fields, before the onset of Landau level quantization. The overall magnitude of the Nernst signal agrees well with semi-classical predictions. We observe reproducible mesoscopic fluctuations in the signal which diminish significantly with an increase in temperature. We also show that the Nernst effect exhibits an anomalous component which is correlated with an oscillatory Hall effect. This behavior may be able to distinguish between different spin-correlated states in the 2DES.
We study electronic transport in graphene under the influence of a transversal magnetic field $\f{B}(\f{r})=B(x)\f{e}_z$ with the asymptotics $B(x\to\pm\infty)=\pm B_0$, which could be realized via a folded graphene sheet in a constant magnetic field, for example. By solving the effective Dirac equation, we find robust modes with a finite energy gap which propagate along the fold -- where particles and holes move in opposite directions. Exciting these particle-hole pairs with incident photons would then generate a nearly perfect charge separation and thus a strong magneto-thermoelectric (Nerns…
Anomalous Nernst effect, a result of charge current driven by temperature gradient, provides a probe of the topological nature of materials due to its sensitivity to the Berry curvature near the Fermi level. Fe3GeTe2, one important member of the recently discovered two-dimensional van der Waals magnetic materials, offers a unique platform for anomalous Nernst effect because of its metallic and topological nature. Here, we report the observation of large anomalous Nernst effect in Fe3GeTe2. The anomalous Hall angle and anomalous Nernst angle are about 0.07 and 0.09 respectively, far larger than…
Weyl semimetals host linear energy dispersions around Weyl nodes, as well as monopoles of Berry curvature in momentum space around these points. These features give rise to unique transport signatures in a Weyl semimetal, such as transverse transport without an applied magnetic field, known as anomalous transport. The type-II Weyl semimetal, recently experimentally demonstrated in several materials, is classified by a tilting of the Weyl nodes. This paper provides a theoretical study on thermoelectric transport in time-reversal breaking type-II Weyl semimetals. Our results examine the balance …
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…
Nernst effect is the transverse electric field due to a longitudinal thermal gradient in presence of magnetic field. Its magnitude was recently studied up to 33 T in a bismuth single crystal with a magnetic field oriented along the trigonal axis . In addition to quantum oscillations of the Nernst response, a rich structure with several additional peaks was also detected when the magnetic field exceeded the quantum limit, which is of the order of 10 T in this configuration. The origin of these high-field Nernst anomalies is a subject of ongoing research. Very recently, Seradjeh, Wu, and Phillip…
It is theoretically predicted that the Nernst coefficient is strongly suppressed and the thermal conductance is quantized in the quantum Hall regime of the two-dimensional electron gas. The Nernst effect is the induction of a thermomagnetic electromotive force in the $y$ direction under a temperature bias in the $x$ direction and a magnetic field in the $z$ direction. The quantum nature of the Nernst effect is analyzed with the use of a circulating edge current and is demonstrated numerically. The present system is a physical realization of the non-equilibrium steady state.
We predict that a temperature gradient can induce a magnon-mediated intrinsic torque and a transverse spin current in systems with non-trivial magnon Berry curvature. With the help of a microscopic linear response theory of nonequilibrium magnon-mediated torques and spin currents we identify the interband and intraband components that manifest in ferromagnets with Dzyaloshinskii-Moriya interactions and magnetic textures. To illustrate and assess the importance of such effects, we apply our theory to the magnon-mediated spin Nernst and torque responses in a kagome lattice ferromagnet.
We report a measurement for the anomalous Nernst effects induced by a temperature gradient in [CoSiB/Pt] multilayer films with perpendicular magnetic anisotropy. The Nernst voltage shows a characteristic hysteresis which reflects the magnetization of the film as in the case of the anomalous Hall effects. With a local heating geometry, we also measure the dependence of the anomalous Nernst voltage on the distance d from the heating element. It is roughly proportional to 1/d^1.3, which can be conjectured from the expected temperature gradient along the sample from the heat equation.
The anomalous Hall and Nernst effects are considered theoretically within Matsubara-Green's function formalism. The effective Hamiltonian of a magnetized two-dimensional electron gas with cubic Rashba spin-orbit interaction may describe transport properties of electronic states at the interfaces or surfaces of perovskite oxides or another type of heterostructures that, due to symmetry, may be described by the same effective model. In the quasi-ballistic limit, both effects are determined by the topological (Fermi sea) contribution whereas the states at the Fermi level gives a negligibly small …
Transverse magneto-thermoelectric effects are studied in permalloy thin films grown on MgO and GaAs substrates and compared to those grown on suspended SiN membranes. The transverse voltage along platinum strips patterned on top of the permalloy films is measured vs. the external magnetic field as a function of angle and temperature gradient. After the identification of the contribution of the planar and anomalous Nernst effects, we find an upper limit for the transverse spin Seebeck effect, which is several orders of magnitude smaller than previously reported.
The magnon transport driven by thermal gradient in a perpendicularly magnetized honeycomb lattice is studied. The system with the nearest-neighbor pseudodipolar interaction and the next-nearest-neighbor Dzyaloshinskii-Moriya interaction (DMI) has various topologically nontrivial phases. When an in-plane thermal gradient is applied, a transverse in-plane magnon current is generated. This phenomenon is termed as the anomalous magnon Nernst effect that closely resembles the anomalous Nernst effect for an electronic system. The anomalous magnon Nernst coefficient and its sign are determined by the…
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 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.
Spin and valley dependent anomalous Nernst effect are analyzed for monolayer MoS2 and other group-VI dichalcogenides. We find that pure spin and valley currents can be generated perpendicular to the applied thermal gradient in the plane of these two-dimensional materials. This effect provides a versatile platform for applications of spin caloritronics. A spin current purity factor is introduced to quantify this effect. When time reversal symmetry is violated, e.g. two-dimensional materials on an insulating magnetic substrate, a dip-peak feature appears for the total Nernst coefficient. For the…
In this Letter, we study the spin Nernst effect (SNE) of magnons in the nonlinear response regime. We derive the formula for the nonlinear magnon spin Nernst current by solving the Boltzmann equation and find out that it is described by an extended Berry curvature dipole of magnons. The nonlinear magnon SNE is expected to occur in various Néel antiferromagnets without Dzyaloshinskii-Moriya interaction. In particular, the nonlinear spin Nernst current in the honeycomb and diamond lattice antiferromagnets can be controlled by strain/pressure.
In this Letter, we study the magnetic transport in AA-stacked bilayer honeycomb chiral magnets coupled either ferromagnetically or antiferromagnetically. For both couplings, we observe chirality-induced gaps, chiral protected edge states, magnon Hall and magnon spin Nernst effects of magnetic spin excitations. For ferromagnetically coupled layers, thermal Hall and spin Nernst conductivities do not change sign as function of magnetic field or temperature similar to single-layer honeycomb ferromagnetic insulator. In contrast, for antiferromagnetically coupled layers, we observe a sign change in …
Photocurrent measurements provide a powerful means of studying the spatially resolved optoelectronic and electrical properties of a material or device. Generally speaking there are two classes of mechanism for photocurrent generation: those involving separation of electrons and holes, and thermoelectric effects driven by electron temperature gradients. Here we introduce a new member in the latter class: the photo-Nernst effect. In graphene devices in a perpendicular magnetic field we observe photocurrent generated uniformly along the free edges, with opposite sign at opposite edges. The signal…
We identify and investigate thermal spin transport phenomena in sputter-deposited Pt/NiFe$_2$O$_{\textrm{4-x}}$ ($4\geq x \geq 0$) bilayers. We separate the voltage generated by the spin Seebeck effect from the anomalous Nernst effect contributions and even disentangle the intrinsic anomalous Nernst effect (ANE) in the ferromagnet (FM) from the ANE produced by the Pt that is spin polarized due to its proximity to the FM. Further, we probe the dependence of these effects on the electrical conductivity and the band gap energy of the FM film varying from nearly insulating NiFe$_2$O$_4$ to metalli…
Localized laser heating creates temperature gradients in all directions and thus leads to three-dimensional electron flux in metallic materials. Temperature gradients in combination with material magnetization generate thermomagnetic voltages. The interplay between these direction-dependent temperature gradients and the magnetization along with their control enable to manipulate the generated voltages, e.g. in magnetic nanodevices. We identify the anomalous Nernst effect (ANE) generated on a nanometer length scale by micrometer sized temperature gradients in magnetic tunnel junctions (MTJs). I…
The magneto-thermoelectric properties of Heusler compound thin films are very diverse. Here, we discuss the anomalous Nernst response of Co$_2$MnGa thin films. We systematically study the anomalous Nernst coefficient as a function of temperature, and we show that unlike the anomalous Hall effect, the anomalous Nernst effect in Co$_2$MnGa strongly varies with temperature. We exploit the on-chip thermometry technique to quantify the thermal gradient, which enables us to directly evaluate the anomalous Nernst coefficient. We compare these results to a reference CoFeB thin film. We show that the 5…
