Extrinsic spin Nernst effect from first principles

Thermally generated spin current in the topological insulator Bi2Se3

We present measurements of thermally generated transverse spin currents in the topological insulator Bi2Se3, thereby completing measurements of interconversions among the full triad of thermal gradients, charge currents, and spin currents. We accomplish this by comparing the spin Nernst magneto-thermopower to the spin Hall magnetoresistance for bilayers of Bi2Se3/CoFeB. We find that Bi2Se3 does generate substantial thermally driven spin currents. A lower bound for the ratio of spin current density to thermal gradient is [Formula: see text] = (4.9 ± 0.9) × 106 [Formula: see text], and a lower bound for the magnitude of the spin Nernst ratio is -0.61 ± 0.11. The spin Nernst ratio for Bi2Se3 is the largest among all materials measured to date, two to three times larger compared to previous measurements for the heavy metals Pt and W. Strong thermally generated spin currents in Bi2Se3 can be understood via Mott relations to be due to an overall large spin Hall conductivity and its dependence on electron energy.

Disorder- and Topology-Enhanced Fully Spin-Polarized Currents in Nodal Chain Spin-Gapless Semimetals

Recently discovered high-quality nodal chain spin-gapless semimetals MF_{3} (M=Pd, Mn) feature an ultraclean nodal chain in the spin up channel residing right at the Fermi level and displaying a large spin gap leading to a 100% spin polarization of transport properties. Here, we investigate both intrinsic and extrinsic contributions to anomalous and spin transport in this class of materials. The dominant intrinsic origin is found to originate entirely from the gapped nodal chains without the entanglement of any other trivial bands. The side-jump mechanism is predicted to be negligibly small, but intrinsic skew scattering enhances the intrinsic Hall and Nernst signals significantly, leading to large values of respective conductivities. Our findings open a new material platform for exploring strong anomalous and spin transport properties in magnetic topological semimetals.

Seebeck effect in nanomagnets

We present a theory of the Seebeck effect in nanomagnets with dimensions smaller than the spin diffusion length, showing that the spin accumulation generated by a temperature gradient strongly affects the thermopower. We also identify a correction arising from the transverse temperature gradient induced by the anomalous Ettingshausen effect and an induced spin-heat accumulation gradient. The relevance of these effects for nanoscale magnets is illustrated byab initiocalculations on dilute magnetic alloys.

Giant spin Seebeck effect in two-dimensional ferromagnetic CrI3 monolayer

Spin Seebeck effect (SSE) is a key factor in the spin caloritronics field, and extensive studies have been performed for potential spin thermoelectric modulator device applications. However, the performance of spin current generation was not high enough, and this is due to the weak yield of the SSE. Despite the many studies for the SSE in bulk materials, no reports are available yet in the pure two-dimensional (2D) ferromagnetic material. Hereby, we investigated the SSE of two-dimensional ferromagnetic CrI₃ using the Boltzmann transport approach allowing diffusive scattering. We obtained a giant effective spin Seebeck effect of 1450 μV K^-1, and this value is at least 4-5 times larger than previously reported values in bulk systems. Therefore, our finding may suggest that 2D CrI₃ can be a potential material to open another perspective for 2D materials in the spin caloritronics field.

Identification of spin effects in the anomalous Righi-Leduc effect in ferromagnetic metals

The emerging of spin caloritronics leads to a series of new spin-thermal related effects, such as spin Seebeck effect (SSE), spin Nernst effect (SNE) and their corresponding inverse effects. Anomalous Righi–Leduc effect (ARLE) describes that a transverse temperature gradient can be induced by a longitudinal heat flow in ferromagnets. The driving force and the response of the ARLE are all involved with heat. It is curious if spin effects mediate the heat transport and provide extra influence. In this work, we investigate the ARLE and the interplay between the heat current, charge current, and spin current via linear response theory. We identified that spin effects do have clear roles in heat transport, which can be confirmed by phase shifts of voltage output varying with the direction of magnetization. Our formulas fit the experimental data very well. Moreover, we discuss more configuration of magnetization which is expected to be tested in the future. It should be emphasized that the present formalism including spin effects is out of the theory based on magnon transport, which may be conspicuous in the devices within the spin diffusion length.

Berry Phase Effects in Dipole Density and the Mott Relation

We provide a unified semiclassical theory for thermoelectric responses of any observable represented by an operator θ[over ^] that is well defined in periodic crystals. The Einstein and Mott relations are established generally in the presence of Berry phase effects for various physical realizations of θ[over ^] in electronic systems, including the familiar case of the electric current as well as the currently controversial cases of the spin polarization and spin current. The magnetization current, which has been proven indispensable in the thermoelectric response of electric current, is generalized to the cases of various θ[over ^]. In our theory the dipole density of a physical quantity emerges and plays a vital role, which contains not only the statistical sum of the dipole moment of θ[over ^] but also a Berry phase correction.

Nonlocal Detection of Out-of-Plane Magnetization in a Magnetic Insulator by Thermal Spin Drag

We demonstrate a conceptually new mechanism to generate an in-plane spin current with out-of-plane polarization in a nonmagnetic metal, detected by nonlocal thermoelectric voltage measurement. We generate out-of-plane (∇T_{OP}) and in-plane (∇T_{IP}) temperature gradients, simultaneously, acting on a magnetic insulator-Pt bilayer. When the magnetization has a component oriented perpendicular to the plane, ∇T_{OP} drives a spin current into Pt with out-of-plane polarization due to the spin Seebeck effect. ∇T_{IP} then drags the resulting spin-polarized electrons in Pt parallel to the plane against the gradient direction. This finally produces an inverse spin Hall effect voltage in Pt, transverse to ∇T_{IP} and proportional to the out-of-plane component of the magnetization. This simple method enables the detection of the perpendicular magnetization component in a magnetic insulator in a nonlocal geometry.

Anomalous spin Nernst effect in Weyl semimetals

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. Because the spin current is a tensor, it has three elements with the spin direction pointing to the x, y  and z directions when the spin current flows along the transverse lead. By using the tight-binding Hamiltonian combined with the nonequilibrium Green's function method, the three elements of the spin current in the transverse leads and the spin Nernst coefficients are obtained. The results show that the spin Nernst effect in the Weyl semimetal has an essential difference to the traditional Nernst effect: we found that the z direction spin current is zero without the magnetic field while it appears under the magnetic field, and the x and y  direction spin currents in the two transverse leads flow out or in together, in contrast to the traditional spin Nernst effect, in which the spin current is induced by the spin-orbit coupling and flows out from one lead and flows in on the other. We call it the anomalous spin Nernst effect. In addition, we show that the Weyl semimetals have inversion-type symmetry, mirror-reversal-type symmetry and electron-hole-type symmetry, which lead to the spin Nernst coefficients being either odd or even functions of the Fermi energy, the magnetic field and the transverse terminals. Moreover, the spin Nernst effect in the Weyl semimetals are strongly anisotropic and its coefficients are strongly dependent on both the direction of thermal gradient and the direction of the transverse lead connection. Three non-equivalent connection modes (x-z, z-x and x-y  modes) are studied in detail, and the spin Nernst coefficients for three different modes exhibit very different behaviors. These strongly anisotropic behaviors of the spin Nernst effect can be used as the characterization of magnetic Weyl semimetals.

Observation of transverse spin Nernst magnetoresistance induced by thermal spin current in ferromagnet/non-magnet bilayers

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, pure 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/non-magnetic heavy metal bilayers. We observe that the magnitude of transverse magnetoresistance in the bilayers is significantly modified by heavy metal and its thickness. This strong dependence of transverse magnetoresistance on heavy metal evidences the generation of thermally induced pure spin current in heavy metal. Our analysis shows that spin Nernst angles of W and Pt have the opposite sign to their spin Hall angles. Moreover, our estimate implies that the magnitude of spin Nernst angle would be comparable to that of spin Hall angle, suggesting an efficient generation of spin current by the spin Nernst effect.

The spin Nernst effect in tungsten

The spin Hall effect allows the 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 nonmagnetic metal can be converted into spin current via a process referred to as the spin Nernst effect. 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 magnetoresistance. A comparison of the temperature gradient-induced voltage and the spin Hall magnetoresistance allows direct estimation of the spin Nernst angle. We find the spin Nernst angle of W to be similar in magnitude but opposite in sign to its spin Hall angle. Under an open-circuit condition, this sign difference results in the spin current generation larger than otherwise. These results highlight the distinct characteristics of the spin Nernst and spin Hall effects, providing pathways to explore materials with unique band structures that may generate large spin current with high efficiency.

Observation of the spin Nernst effect

The observation of the spin Hall effect triggered intense research on pure spin current transport. With the spin Hall effect, the spin Seebeck effect and the spin Peltier effect already observed, our picture of pure spin current transport is almost complete. The only missing piece is the spin Nernst (-Ettingshausen) effect, which so far has been discussed only on theoretical grounds. Here, we report the observation of the spin Nernst effect. By applying a longitudinal temperature gradient, we generate a pure transverse spin current in a Pt thin film. For readout, we exploit the magnetization-orientation-dependent spin transfer to an adjacent yttrium iron garnet layer, converting the spin Nernst current in Pt into a controlled change of the longitudinal and transverse thermopower voltage. Our experiments show that the spin Nernst and the spin Hall effect in Pt are of comparable magnitude, but differ in sign, as corroborated by first-principles calculations.

Spin and charge Nernst effect in a four-terminal quantum dot ring

Based on the Keldysh nonequilibrium Green's function technique, we study the spin and charge Nernst effect in a four-terminal quantum dot (QD) ring device, in which the Rashba spin-orbit interaction (RSOI) is taken into the QDs and the magnetic field penetrates the ring. We find that only with the assistance of RSOI, can the pure spin Nernst effect occur by applying a thermal bias without any magnetic field or ferromagnetic materials in the system. Under certain RSOI and magnetic field strengths, spin-down or spin-up currents can be driven from terminal 2 or 4. The sign and the magnitude of the spin currents or voltages can be modulated by adjusting the RSOI-induced phase factor and the magnetic flux. Moreover, the magnitude of the Nernst effect can be remarkably enhanced by the intra-dot Coulomb blockade. The Nernst coefficient is predicted to be more than two times larger than the case of zero Coulomb interaction. Our results indicate that such a four-terminal QD ring may be used as a manipulative thermoelectric generator.

Transport equations of energy for ferromagnetic insulators in contact with electrodes

A phenomenological derivation of the transport equations for ferromagnetic moments and associated energy and heat is proposed. The model describes the transfer of energy through an interface composed of a ferromagnetic insulator in contact with normal electrodes. A reduction method applied to the ferromagnetic degrees of freedom allows a two-channel model to be defined for the transport of magnetic moments. It is shown that a heat current flowing into the insulating ferromagnet-produced e.g. by electromagnetic resonance, thermal gradient, magneto-mechanical or magneto-optical excitations-can generate a magneto-voltaic potential and a pure spin-current in the non-ferromagnetic electrode.

Theory of the spin Seebeck effect

The spin Seebeck effect refers to the generation of a spin voltage caused by a temperature gradient in a ferromagnet, which enables the thermal injection of spin currents from the ferromagnet into an attached nonmagnetic metal over a macroscopic scale of several millimeters. The inverse spin Hall effect converts the injected spin current into a transverse charge voltage, thereby producing electromotive force as in the conventional charge Seebeck device. Recent theoretical and experimental efforts have shown that the magnon and phonon degrees of freedom play crucial roles in the spin Seebeck effect. In this paper, we present the theoretical basis for understanding the spin Seebeck effect and briefly discuss other thermal spin effects.