Dephasing-Assisted Macrospin Transport

Abstract

Transport phenomena are ubiquitous in physics, and it is generally understood that the environmental disorder and noise deteriorates the transfer of excitations. There are, however, cases in which transport can be enhanced by fluctuations. In the present work, we show, by means of micromagnetics simulations, that transport efficiency in a chain of classical macrospins can be greatly increased by an optimal level of dephasing noise. We also demonstrate the same effect in a simplified model, the dissipative Discrete Nonlinear Schrödinger equation, subject to phase noise. Our results point towards the realization of a large class of magnonics and spintronics devices, where disorder and noise can be used to enhance spin-dependent transport efficiency.

Keywords: Discrete Nonlinear Schrödinger model; micromagnetic simulations; noise and transport; open systems.

Figure 1

Sketch of the system, consisting of 10 Py nano-disks coupled through the magneto-dipolar interaction. The magnetization in the first disk (input) is tilted away from equilibrium. The transport efficiency is the integrated Spin Wave (SW) power in the last disk (output).

Figure 2

Time-average of the SW powers of each collective mode, obtained by exciting the dynamics with a uniform time-dependent magnetic field with the frequencies of the modes until the system reaches a steady state. Simulations are performed at zero temperature. The total SW power of each profile is normalized to one for better comparison.

Figure 3

Total SW power P vs time for different values of the dephasing noise amplitude $\theta$ (a) and of the bath temperature T (b). One can see that in the first case P drops to zero and the magnetization aligns with the z axis, since the dephasing conserves the total power. In the second case, the bath temperature excites the dynamics and the system thermalizes with P increasing with the bath temperature T.

Figure 4

Effect of the dephasing noise on the dynamics of the macrospin chain: time evolution of the local SW power $p_{10}$ of the last disk for different values of $\theta$. Transmitted power is maximized for an optimal value around $\theta \approx 4$. Simulation parameters as given in the text.

Figure 5

(a) Efficiency E and (b) Kuramoto parameter K versus $\theta$. E increases of a factor 3 until $\theta =6$ and then decreases again, showing that transport can be effectively promoted by dephasing. On the other hand, K decreases monotonically with $\theta$. Thus, in the present case, transport is not related to phase synchronization.

Figure 6

Wavelet analysis of the complex spin amplitudes ${\psi }_n$ on the central disk ($n=5$, left panels) and on the last disk ($n=10$, right panels) for different values of $\theta$. Each plot shows the density map of the average square modulus $\langle |G_n(\omega ,t){|}^2\rangle$ of the Gabor transform (7) averaged over a sample of 32 independent realizations of the dyanamics. The parameter a has been set equal to $7.5$ ns${}^2$, optimized so as to maximize the resolution in both the time and frequency domains. Notice the difference in the density scales.

Figure 7

Average amplitude contributions $g_n\left(\tilde{\omega }\right)$ on site $n=5$ (a) and site $n=10$ (b) for $\tilde{\omega }={\omega }_1,{\omega }_2,{\omega }_3,{\omega }_4,{\omega }_5$ computed from data of Figure 6. Solid curves are obtained with $\delta \omega =0.25$ GHz, while the black dashed curve refers to $\delta \omega =2$ GHz.

Figure 8

Transport efficiency versus dephasing noise strength of a chain of $N=10$ damped discrete nonlinear Schrödinger equation (DNLS) oscillators evolving according to Equation (9). Simulations refer to $J=0.1$, $\alpha =0.008$, $\nu =1$ and linear frequencies $({\omega }_1^0,{\omega }_2^0,{\omega }_3^0,{\omega }_4^0,{\omega }_5^0)=(1,1.09,1.15,1.21,1.33)$. For each value of ${\theta }^{\prime }$, data are averaged over a set of 100 independent realizations of the dynamics.