Spin Transfer due to Quantum Magnetization Fluctuations

We utilize a nanoscale magnetic spin-valve structure to demonstrate that current-induced magnetization fluctuations at cryogenic temperatures result predominantly from the quantum fluctuations enhanced by the spin transfer effect. The demonstrated spin transfer due to quantum magnetization fluctuations is distinguished from the previously established current-induced effects by a nonsmooth piecewise-linear dependence of the fluctuation intensity on current. It can be driven not only by the directional flows of spin-polarized electrons, but also by their thermal motion and by scattering of unpolarized electrons. This effect is expected to remain non-negligible even at room temperature, and entails a ubiquitous inelastic contribution to spin-polarizing properties of magnetic interfaces.

Figure 1

(a) Schematic of the tested spin-valve nanopillar. Gray: Permalloy (Py) free layer $F1$ and polarizer $F2$. Orange: Cu electrodes and spacer $N$. (b) Effect of STT on thermal magnetization fluctuations. Top (bottom): Spin transfer due to scattering of the majority (minority) electron by the magnetization results in a decrease (increase) of thermal fluctuations. Vectors show the direction of the fluctuating magnetization and the magnetic moment of the scattered electron. (c) Magnetoelectronic hysteresis loop. (d) Differential resistance vs current, at the labeled fields. Inset: Critical current $I_c$ for the onset of auto-oscillation vs field determined from the experimental data (symbols), and the calculation (curve). All measurements were performed at 3.4 K.

Figure 2

(a) Differential resistance vs current, at the labeled values of field and $T=3.4\mathrm{K}$. Symbols, data; lines, best linear fits performed separately for $I<0$ and $I>0$. (b) Differential resistance (symbols, right scale) and the calculated total magnon population (curve, left scale) vs $B$ at $I=0$. (c) Scattering of the majority (top) and the minority (bottom) electron by magnetization experiencing only quantum fluctuations. Vectors show the direction of the fluctuating magnetization and the magnetic moment of the scattered electron. (d) Population of the magnon mode with frequency $\omega$ vs current, in the classical limit $k_{B}T/\hslash \omega =200$ and in the quantum limit $k_{B}T/\hslash \omega =0.01$, for $p=1$. Symbols, classical result based on Eq. (1); curves, quantum result based on Eq. (3).

Figure 3

(a) Symbols: differential resistance vs current at the labeled values of temperature and $B=1\mathrm{T}$. Curves: results of fitting with a piecewise-linear dependence convolved with a Gaussian whose width is used as an adjustable parameter. The data are offset for clarity. Inset: temperature dependence of the Gaussian width extracted from the fitting (symbols), and $\mathrm{\Delta }I=1.9k_{B}T/e{R}_0$ (line). (b) Top: at $T=0$, the Fermi distribution of scattered electrons is steplike. Bias current shifts the distribution, driving the spin transfer. Bottom: at finite $T$, scattering of thermal electrons and holes occurs even at zero bias, equivalent to bias distribution of width $k_{B}T/e$.

Figure 4

(a) The calculated slope $dN/dI$ vs $T$, at $B=1\mathrm{T}$. Vertical dashed line marks the crossover temperature $T_x$ between the quantum and the classical spin transfer regimes. (b) Symbols: The slope $dR/dI$ of resistance vs current at $I=0$ and $B=1\mathrm{T}$. Line: best linear fit of the data.