Magnon scattering in the transport coefficients of CoFe thin films

Resistivity $\rho$, thermopower $\mathcal{S}$, and thermal conductivity $\kappa$ were measured simultaneously on a set of CoFe alloy films. Variation of the Co content $x_{\mathrm{Co}}$ allows for a systematic tuning of the Fermi level through the band structure, and the study of the interplay between electronic and magnetic contributions to the transport coefficients. While band-structure and magnon effects in $\rho$ and $\kappa$ are rather weak, they turn out to be very significant in $\mathcal{S}$. A decomposition of $\mathcal{S}$ into Mott and magnon drag contributions results in a systematic evolution between the two limiting cases of pure Fe and pure Co. At low temperatures, we find an interesting sign change of the curvature of $\mathcal{S}\left(T\right)$ that indicates a corresponding sign change of the magnon drag.

Figure 1

(a) Resistivity $\rho \left(T\right)$ for several values of Co content $x_{\mathrm{Co}}$. (b) Optical image of a typical device. (c) The phonon contribution to the resistivity for $x_{\mathrm{Co}}=0.5$ (open circles) fitted to a Bloch-Wilson function for $T\le 100$ K (red line). Double-headed arrow: Estimated magnon contribution to $\rho \left(T\right)$. Blue line: Calculated resistivity taking into account chemical disorder and lattice vibrations for $x_{\mathrm{Co}}=0.5$ (see text). (d) Estimated ${\rho }_{\mathrm{mag}}$ for all samples (dots) vs temperature with ${\rho }_{\mathrm{mag}}$ for bulk Fe from Ref. [29] (orange line).

Figure 2

(a) Measured thermopower vs temperature for all ${\mathrm{Co}}_x{\mathrm{Fe}}_{1-x}$ samples from 26 to 296 K, labeled on the right by $\mathrm{at}.\%$ Co. (b) Mott-like contribution ${\mathcal{S}}_{\mathrm{Mott}}\left(T\right)$ (half-solid triangles) as a function of temperature. Inset: ${\mathcal{S}}_{\mathrm{Mott}}$ and ${\mathcal{S}}_{\mathrm{mag}}$ vs at. $\%$ Co at 296 K. (c) Magnon drag ${\mathcal{S}}_{\mathrm{mag}}\left(T\right)\propto T^{3/2}$ contribution (half-solid circles); literature values for bulk Co and Fe [24] are shown as lines. (d) Calculated thermopower taking into account chemical and vibrational disorder.

Figure 3

(a) Measured thermal conductivity of the ${\mathrm{Co}}_x{\mathrm{Fe}}_{1-x}$ films. (b) Calculated electronic contribution to ${\kappa }_{\mathrm{el}}$ including elastic scattering on lattice vibrations. (c) Extracted Lorenz number $L$ as a function of bath temperature. The horizontal line indicates the Sommerfeld value $L_0={\pi }^2/3·{(k_{\mathrm{B}}/e)}^2$. (d) Positive deviations from the Wiedemann-Franz law using the measured resistivity of the films with low Co content.