Quantum-Uncertainty-Governed Spin Dynamics in s-d Coupled Systems

TL;DR

The paper addresses quantum fluctuations in spin dynamics of s-d coupled systems, where itinerant electrons exchange angular momentum with localized moments. It develops a full quantum treatment of s–d scattering, extending the Landau–Lifshitz–Gilbert framework to include quantum and thermal noise, and introduces a quantum random field that yields a quantum effective temperature $T_Q$; this reveals regimes where quantum fluctuations dominate and can be amplified via VCMA for binary MTJ readout. Key contributions include identifying an intrinsic channel for transferring spin quantum fluctuations, deriving a quantum master equation and corresponding Fokker–Planck description, and proposing VCMA-assisted amplification to enable MTJ-based QTRNG with readout through TMR. The work offers a microscopic framework for fluctuation-driven spin dynamics and provides a practical pathway toward spin-based quantum true random number generation, with tunable randomness via current, angle, and temperature, though challenges such as noise sources and device integration remain.

Abstract

We investigate quantum fluctuation effects arising from the Heisenberg uncertainty principle governing angular momentum operators in the full dynamical evolution of disentanglement-entanglement-disentanglement between itinerant electrons and localized magnetic moments under the s-d exchange interaction. Beyond the conventional deterministic spin-transfer torque, we identify an intrinsic channel for the transfer of spin quantum fluctuations. By extending the Landau-Lifshitz-Gilbert equation to include both quantum and thermal stochastic fields, we reveal a temperature regime where quantum fluctuations dominate spin dynamics. Furthermore, voltage-controlled magnetic anisotropy can exponentially amplify these quantum fluctuation signals, enabling their binary detection via tunneling magnetoresistance in magnetic tunnel junctions. These results establish a microscopic framework for quantum fluctuation-driven spin dynamics and provide a fundamental route toward spin-based quantum true random number generation.

Figures (3)

• Figure 1: The scattering between a local magnetic moment and an incident electron due to the s-d exchange interaction. (a) The Feynman diagrams for the scattering events of a local magnetic moment with a spin-polarized electron. The flip of a spin-polarized electron from the spin-down (spin-up) state to the spin-up (spin-down) state corresponds to the generation (annihilation) of a magnon in the local magnetic moment. (b) The process where an electron and a local magnetic moment transition from non-entanglement to entanglement, and then to disentanglement.
• Figure 2: Schematic illustration of amplifying the spin quantum fluctuation by virtue of the VCMA effect in the MTJ. (a) The P state and the AP state separated by an energy barrier. (b) By reducing the energy barrier through the VCMA effect, spin fluctuations are converted into the state switching signals. (c) Upon removal of the voltage, the state of the MTJ relaxes to one of the stable states with equal probability under ideal conditions
• Figure 3: Magnetization switching probability of the free layer versus energy barrier. In the simulation, the initial magnetization state of the free layer $\hbox{\boldmath$\mathrm{m}$} _{\rm f}=(\sin(\pi/180),0,\cos(\pi/180))$, the VCMA voltage pulse width $T _{\rm1}=20$ ns, the polarized current intensity $I=2$ mA with a pulse width $T _{\rm2}=115$ ps, the transmission coefficient $\chi=1$, and the applied magnetic fields (a) $\hbox{\boldmath$\mathrm{H}$} _{\rm ext}=(30000,0,0)$ A/m and (b) $\hbox{\boldmath$\mathrm{H}$} _{\rm ext}=(-30000,0,0)$ A/m. Each data point in the switching probability is obtained from 100 random dynamic simulations under the same conditions.