Nonequilibrium thermodynamics of the spin Seebeck and spin Peltier effects

Abstract

We study the problem of magnetization and heat currents and their associated thermodynamic forces in a magnetic system by focusing on the magnetization transport in ferromagnetic insulators like YIG. The resulting theory is applied to the longitudinal spin Seebeck and spin Peltier effects. By focusing on the specific geometry with one Y3Fe5O12 (YIG) layer and one Pt layer, we obtain the optimal conditions for generating large magnetization currents into Pt or large temperature effects in YIG. The theoretical predictions are compared with experiments from the literature permitting to derive the values of the thermomagnetic coefficients of YIG: the magnetization diffusion length lM ∼0.4 μm and the absolute thermomagnetic power coefficient εM∼10−2 TK−1

Thermodynamic transport theory of spin waves in ferromagnetic insulators

“…In the spin Seebeck effect, in which the ferromagnetic material is subjected to a uniform temperature gradient ∇T , the magnetization current source is j M S = −σ M M ∇T . The part of the current transmitted to the sensing layer depends on the coupling between the two materials and in particular it depends on the ratio v M = l M /τ M between the diffusion length and the time constant of each layer 29 . All the parameters contained in the continuity equation (2) and the constitutive equations (3) and (4) can be calculated on the basis of a microscopic theory.…”

“…1/2 , results to be related to material dependent parameters 29 . In the spin Seebeck effect, in which the ferromagnetic material is subjected to a uniform temperature gradient ∇T , the magnetization current source is j M S = −σ M M ∇T .…”

“…Therefore we describe the system by the scalar amplitudes M and H. By following the Johnson and Silsbee approach 29,35 , the thermodynamics of the ferromagnet is formulated by expressing the variation of the non equilibrium system enthalpy u e (s, H; M ) as a function of the entropy density s, of the magnetic field H and of the magnetization M :…”

“…The source of this conversion is the interaction between the d electrons in the ferromagnet and the s electrons in the metal which gives rise to an absorption of a magnon in the insulator and the corresponding generation of an electron spin flip in the metal [12][13][14][15][16][17][18] . While the assessment of the interface is well documented in the literature 10,[19][20][21] , the description of the transport of non equilibrium spin waves inside the bulk ferromagnet is still a debated issue [22][23][24][25][26][27][28][29] . The thermodynamic problem of the joint transport of heat and magnetic moment (thermo-magnetics) has its counterpart in the field of thermoelectricity where one has the joint transport of heat and charge.…”

“…This effective force has been worked out in the thermodynamic theory of Johnson and Silsbee 35 . In their approach the potential for the magnetization current is derived from purely thermodynamic grounds and it results to be given by H * = H − H eq , the difference between the magnetic field H and the field H eq (M ) corresponding to the equation of state at equilibrium 29 . When the theory of Johnson and Silsbee is applied to the problem of the transport of magnons, one finds that the potential H * is directly related to the chemical potential µ m associated with the magnon accumulation, that is H * = µ m /(2µ 0 µ B ).…”