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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, that so far has only been discussed 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 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.
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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 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 with its spin Hall angle. Interestingly, under an open circuit condition, such sign difference results in 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.
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 effect is. The results also show that the Nernst and spin Nernst coefficients are sensitive to the detailed characteristics of the sample and the contacts. In addition, the Nernst effect is found to survive in strong disorder than the spin Nernst effect does.
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 Greens 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 traditional one: The z direction spin currents 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 flows out or flows in together, in contrary 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. So we call it the anomalous spin Nernst effect. In addition, we show that the Weyl semimetals have the center-reversal-type symmetry, the mirror-reversal-type symmetry and the electron-hole-type symmetry, which lead to the spin Nernst coefficients being odd function or even function 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.
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 of the magnon spin Nernst effect with boundary conditions reflecting real device geometry. Thanks to the diffusion effect, the output signals in both electronic and optical detection grow rapidly with an increasing system size in the transverse dimension, which eventually saturate. Counterintuitively, the measurable signals are even functions of magnetic field, yielding optical detection more reliable than electronic detection.
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 propagating of the charge current to the direction of the temperature gradient is possible for a nonuniform system.
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