Designing a Spin-Seebeck Diode

Using micromagnetic simulations, we have investigated spin dynamics in a spin-valve bilayer in the presence of a thermal gradient. The direction and the intensity of the gradient allow us to excite the spin wave modes of each layer selectively. This permits us to synchronize the magnetization precession of the two layers and to rectify the flows of energy and magnetization through the system. Our study yields promising opportunities for applications in spin caloritronics and nanophononics devices.

Figure 1

(a) Bilayer system studied in our simulations. The magnetization is decomposed into the static component $M_z$ and the transverse components $M_x$ and $M_y$, which precess at the Larmor frequency in the $x$-$y$ plane. A uniform thermal gradient is set along the $z$ axis. (b) Symmetric ($s$) and antisymmetric ($a$) precession states of the system.

Figure 2

(a) and (b) SW spectrum for $\ell =0$ and $\ell =+1$ modes, respectively. (c) Tabulation of the corresponding frequencies.

Figure 3

SW spectrum for different $\ell$ modes in the presence of the thermal gradient (expressed in K/nm). (a) and (b): positive gradient, (c) and (d) negative gradient. Positive (negative) gradients excite only the $s$ ($a$) modes.

Figure 4

Frequency of the SW modes as a function of a positive (a) and a negative (b) gradient. The lines are a guide to the eye.

Figure 5

(a) Rectification effect for magnetization and energy currents. The panels (b) and (c) show the power spectra computed for different gradients and illustrate the rectification effect. (b) For negative gradients, the modes $a_{01}$ and $s_{01}$ overlap, giving a partial phase-locking and a conductive state. (c) For positive gradients, there is no overlapping and the conduction is reduced.

Figure 6

(a) Phase difference $\mathrm{\Delta }\varphi$ between the oscillators vs time, computed for different thermal gradients. $\mathrm{\Delta }\varphi$ increases faster in the insulating region than in the conducting one, where the frequencies of the two oscillators become closer. (b) Corresponding power spectrum of the magnetization currents. In the conductive state, the spectrum is dominated by the zero frequency mode, which is barely visible in the insulating state. In the insulating state, the spectra are reduced by a factor 3 for better visibility.