A new direction in magnetic nanostructure research has evolved by combining the control of heat currents and spin currents which is known as spin caloritronics. Phenomena in spin caloritronics are interesting from the point of view of fundamental as well as applied physics as they offer the opportunity to manipulate the spin degree of freedom with heat.
Schematic of temperature gradient ($T_1>T_2$) inducing magnetisation dynamics (magnetisation is denoted m).
Occurring in the same system heat currents and spin currents can be expected to interact mutually. To introduce a coupling between both we propose an action functional including the coupling of the scalar temperature field and its derivatives with respect to the spatial coordinates to the magnetization and its variation in space. Applying variational principles enables to derive the relevant equation of motion for the temperature as well the magnetization which are now coupled. This allows to investigate how magnetic systems behave when the temperature distribution is varied. Regarding this, the choice of the boundary conditions and the shape of the initially distributed temperature are particularly important and influence the spin wave dispersion relation as well as spin wave damping.
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