Abstract
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.
Highlights
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
Wegrowe et al found an angular dependence between the transverse temperature gradient and the direction of magnetization (formula (16) in Ref.25) based on the magnons transport
Comparing Eq (15) to Eq (16) in Ref.[25], there are two extra terms of2-angle term and a term independent of magnetization angles. These terms stem from extra spin caloritronic effects which can not be captured in a formalism based on magnon transport
Summary
−∇μs , to spin electrochemical potential current density Js , particle cgurarrdeinent dt e∇nμsintyaJnndan∇TdT are the corresponding heat current density Jq , respectively, and T is the temperature. The first term is coming from the diagonal components of Aqq which describes the generated heat current by a temperature gradient. It is the coefficient of conventional Fourier law. SrRL which involves is characterized by tpwt os different longitudinal-transverse r and describes that a transverse joint heat current can be generated when applying a spin current in longitudinal direction and will be converted into temperature gradient via thermal resistance. The other longitudinal–transverse effect is expressed by srRL which illustrates that heat current is firstly generated by spin current via spin Peltier effect and is converted into the transverse temperature gradient through anomalous Righi–Leduc effect. We can identify the role of spin-thermal effects by identifying the extra angular dependence
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