Magnon-drag and field-direction dependent thermopower in low-damping ferromagnetic ${\mathrm{Co}}_{25}{\mathrm{Fe}}_{75}$ alloy thin films

Recent experimental and theoretical work has focused new interest on magnon contributions to transport properties of metallic ferromagnets. Here we present the Seebeck coefficient, or thermopower, measured from $78\text{to}325K$ for ${\mathrm{Co}}_x{\mathrm{Fe}}_{1-x}$ thin films and discuss the role of the Gilbert damping parameter, ${\alpha }_{\mathrm{GD}}$, on electron-magnon interactions. These measurements are made with micromachined Si-N thermal isolation platforms that allow excellent control of the thermal gradient applied to a thin film. We first present zero-field measurements of the absolute Seebeck coefficient, ${\alpha }_{\text{abs}}$, for two films with $x=0.25$, the alloy composition previously shown to have low damping and long-lived spin excitations, and a third film with $x=50$ where ${\alpha }_{\mathrm{GD}}$ is higher, and more typical of other 3D alloy ferromagnets. We compare these to pure Co and Fe films, and to simple expectations from the electronic DOS. This indicates that a large additional thermopower appears where spin excitations are long-lived. This additional zero-field thermopower can be explained by magnon drag, where momentum is transferred from thermal, exchange-dominated magnons to the electron system. We then present the dependence of the thermopower on the direction of an applied in-plane magnetic field. Comparison of this magnetothermopower (MTP) to anisotropic magnetoresistance (AMR) measured via four-wire electrical resistance measured on the same films shows, as in previous measurements of thermal conductivity in the same samples, a field-direction dependent contribution to thermopower. The MTP also allows improved estimation of the electronic diffusion thermopower, which then allows us to construct a plausible model for the zero-field thermopower of the low-damping films that adds the theoretically predicted magnon drag, and matches measured ${\alpha }_{\text{abs}}$ well at low $T$. The field-direction dependent contribution, not previously observed, also suggests interaction of electrons with the lower wave-vector dipole or dipole-exchange dominated magnetostatic spin waves, which is an alternate manifestation of magnon drag.