Thermoelectric effects in magnetic nanostructures

We model and evaluate the Peltier and Seebeck effects in magnetic multilayer nanostructures by a finite-element theory of thermoelectric properties. We present analytical expressions for the thermopower and the current-induced temperature changes due to Peltier cooling/heating. The thermopower of a magnetic element is in general spin polarized, leading to spin-heat coupling effects. Thermoelectric effects in spin valves depend on the relative alignment of the magnetization directions and are sensitive to spin-flip scattering as well as inelastic collisions in the normal-metal spacer.

Figure 1

Schematic of a spin-valve structure connected to reservoirs at different chemical potentials and/or temperatures ($f_{L\left(R\right)}$ are the Fermi-Dirac distribution functions). Charge and heat flows through the normal-metal spacer $\left(N\right)$ are functions of the angle between the magnetization directions $\left(\theta \right)$ in the ferromagnets.

Figure 2

(Color online) Magnetothermoelectric power as a function of relative angle between the magnetizations in a $\text{Fe}\left|\text{Cr}\right|\text{Fe}$ (001) spin valve with dirty interfaces. The MTP is significantly different for the strong (full line) and weak (dotted line) thermalizations in the normal-metal spacer.

Figure 3

(Color online) Same as Fig. 2 but for a $\text{Co}\left|\text{Cu}\right|\text{Co}$ (110) spin valve with clean interfaces.

Figure 4

(Color online) Magneto-Peltier cooling as a function of the angle between the magnetizations in the hypothetical bcc $\text{Co}\left|\text{Cr}\right|\text{Fe}$ (001) spin valve. $R_0{I}_p\left(\theta \right)$ is the cooling power which compensates local Joule heating. The signal $R_0\left[I_p\left(\pi \right)-I_p\left(0\right)\right]$ is significantly different for strong (full line) and weak (dotted line) thermalizations in the normal-metal spacer.

Figure 5

(Color online) Same as Fig. 4 but for an asymmetric $\text{Co}\left|\text{Cu}\right|\text{Co}$ (001) spin valve with one clean and one disordered interface.

Figure 6

(Color online) Illustration of the local charge and spin chemical potentials in a ${\text{F}}_A\left|\text{N}\right|{\text{F}}_B$ spin valve biased by a voltage difference for both parallel $\left(\uparrow \uparrow \right)$ and antiparallel $\left(\uparrow \downarrow \right)$ alignments of the magnetizations. ${\text{F}}_B\left(P=0.8,{\lambda }_B=0.1,S_B=-1\mu \text{V}/\text{K}\right)$ has been chosen to have weak spin-flip scattering and thermopower compared with ${\text{F}}_A\left(P=0.8,{\lambda }_A=10,S_A=-20\mu \text{V}/\text{K}\right)$. The thin normal-metal spacer is chosen to be highly conductive $\left({\rho }_N⪡{\rho }_{A\left(B\right)}=10\mu \Omega \text{cm}\right)$ and to have a thermopower equal to that of ${\text{F}}_B$. Note that spin accumulation is assumed to vanish at the two ends (at reservoirs).

Figure 7

(Color online) Illustration of local temperature distribution in the voltage-biased ${\text{F}}_A\left|\text{N}\right|{\text{F}}_B$ spin-valve structure as in Fig. 6 for both parallel $\left(\uparrow \uparrow \right)$ and antiparallel $\left(\uparrow \downarrow \right)$ alignments of the magnetizations. The different temperature profiles correspond to (a) $P^{\prime }⪡P\left(P_S=-0.8\right)$ and (b) $P^{\prime }⪢P\left(P_S=-1.8\right)$. For the parallel alignment of the magnetizations the Peltier cooling is insensitive to spin flips and reaches its maximum in the central node.