Thermoelectric Detection of Spin Waves

We report on the thermoelectric detection of spin waves in Permalloy stripes via the anomalous Nernst effect. Spin waves are locally excited by a dynamic magnetic field generated from a microwave current flowing in a coplanar waveguide placed on top of a Permalloy stripe, which acts as a waveguide for spin waves. Electric contacts at the ends of the Permalloy stripe measure a dc voltage generated along the stripe. Magnetic field sweeps for different applied microwave frequencies reveal, with a remarkable signal-to-noise ratio, an electric voltage signature characteristic of spin-wave excitations. The symmetry of the signal with respect to the applied magnetic field direction indicates that the anomalous Nernst effect is responsible; Seebeck effects, anisotropic magnetoresistance, and voltages due to spin-motive forces are excluded. The dissipation of spin waves causes local heating that drains into the substrate, giving rise to a temperature gradient perpendicular to the sample plane, resulting in the anomalous Nernst voltage.

Figure 1

(a), (b) Schematic of the sample. The spin-wave waveguide is 2 mm long, $20\mu \mathrm{m}$ wide, and made from 100 nm thick Permalloy on a GaAs substrate. The coplanar waveguide for rf excitation and the leads for dc voltage measurements are made from 150 nm thick Au. The CPW has a signal linewidth of $10\mu \mathrm{m}$ and a signal-to-ground-line separation of $5\mu \mathrm{m}$. (c) Illustration of the $z$ distribution of the dissipated power and resulting temperature profile.

Figure 2

Voltage measured between the ends of the Permalloy stripe as a function of the magnetic field applied perpendicular to the stripe for frequencies from 4 GHz to 20 GHz in 1 GHz steps. The dotted line shows a theoretical estimate of the relative power dissipated by the spin waves. The inset shows the peak position vs applied frequency with a fit to the Kittel equation.

Figure 3

(a) Detected voltage for different in-plane angles of the applied magnetic field. For 0°, the magnetic field is perpendicular to the Py stripe; for 90°, $\overrightarrow{H}$ is parallel. (b) Thermoelectric voltage detected while heating the CPW with a dc current for different values of the magnetic field applied perpendicular to the Py stripe.

Figure 4

(a) Magnetic field sweeps for excitation at 10 GHz for microwave powers ranging from $-9\mathrm{dBm}$ to 18 dBm in 3 dBm steps. (b) Maximum of the detected voltage (red squares) and voltage at a magnetic field of 360 Oe as a function of the applied microwave power. (c) Upper red line, spin-wave dispersion for $H=1014\mathrm{Oe}$ and wave vector perpendicular to $\overrightarrow{M}$; lower blue lines, spin-wave band for $H=360\mathrm{Oe}$. The green horizontal lines mark the excitation frequency $\nu$ and the parametrically excited spin waves at $\nu /2$.