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Thermopower and Thermally Induced Domain Wall Motion in (Ga,Mn)As

We study two reciprocal thermal effects in the ferromagnetic semiconductor (Ga,Mn)As by scattering theory: domain wall motion induced by a temperature gradient as well as heat currents pumped by a moving domain wall. The effective out-of-plane thermal spin transfer torque parameter $P_Q β_{Q}$, which governs the coupling between heat currents and a magnetic texture, is found to be of the order of unity. Unpinned domain walls are predicted to move at speed 10 m/s in temperature gradients of the order 10 ${\rm K/ μm}$. The cooling power of a moving domain wall only compensates the heating due to friction losses at ultra-low domain wall velocities of about 0.07 m/s. The Seebeck coefficient is found to be of the order 100-500 ${\rm μV / K}$ at T=10 K, in good agreement with recent experiment.