Temperature-switched anomaly in the spin Seebeck effect in ${\mathrm{Gd}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$

The magnon-polaron induced anomaly has recently been observed in the magnetic field dependence of the spin seebeck effect in ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ [T. Kikkawa et al., Phys. Rev. Lett. 117, 207203 (2016)]. In the present theoretical work, we show that such an anomaly in ${\mathrm{Gd}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ depends strongly on the temperature, and it exists only at high temperature but disappears at low temperature. The finite-temperature magnon-polaron anomaly results from the distortion of the magnon dispersion driven by thermal magnon excitation. In contrast to the scenario in ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$, the anomaly in ${\mathrm{Gd}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ can present either single-peak or double-peak features at different temperatures.

Figure 1

(a) Full spin wave spectrum at zero temperature with clockwise and anticlockwise modes distinguished by red and blue, respectively. Zoom in the low-frequency regime (b) without and (c) with external magnetic field. The light blue curves represent the dispersion relations of the transverse (TA) and longitudinal (LA) acoustic phonon.

Figure 2

Group velocity of ${\alpha }_1$ mode as function of temperature and wave vector. The contour curves show the values of 1, 2, and 3 km/s and transverse sound speed $c_t$.

Figure 3

(a) The spin Seebeck coefficient as a function of magnetic field at different temperatures. (b) The magnetic fields at the enhanced peaks from self-consistent calculation (solid dots) and estimated from zero temperature velocity $v_m=v_t$ (open triangles). In the calculation we take $\eta =100$.

Figure 4

Spin wave spectra at 100 and 150 K with different values of magnetic field. The insets zoom in the tangential regions. The yellow arrows in (b) and in (e) and (f) denote the inflection point and the touching points, respectively.