Measuring Non-Markovianity in Ultrafast Magnetization Dynamics

Researchers have established a new quantitative method to measure non-Markovianity in magnetization dynamics at ultrafast timescales. The study utilizes thermodynamic entropy production rates to evaluate the inertial and open-system extensions of the traditional stochastic Landau-Lifshitz-Gilbert (LLG) equation, revealing that dynamics on the picosecond scale present significant memory effects that break the classical separation of timescales.

The Challenge of Picosecond Scales

Historically, magnetization dynamics in ferromagnets have been effectively described by the LLG equation, which models damped precessional motion in an effective magnetic field. However, recent experiments on crystalline cobalt thin films operating at the picosecond scale have revealed dynamical properties that the standard equation cannot capture. At these ultrafast scales, the time-scale separation between the magnetic system and the thermal bath is broken, requiring theoretical extensions such as the inertial LLG (iLLG) equation or the open-system LLG (os-LLG) equation. Until now, statistical physics lacked a direct metric to quantify exactly how non-Markovian (memory-dependent) these extended systems truly are.

Stochastic Thermodynamics and Entropy Production

To solve this problem, the team employed concepts from stochastic thermodynamics, specifically entropy production rates (EPR), as a detection tool. Through analytical proofs and numerical simulations based on 50,000 trajectories, the scientists demonstrated that the standard LLG equation produces strictly positive entropy rates, characterizing a purely Markovian evolution. In contrast, the iLLG and os-LLG dynamics exhibit temporary drops to negative entropy production rates. This phenomenon is the exact marker of non-Markovian dynamics.

“We find that, while the standard LLG equation exhibits strictly positive entropy production rates, inertial and open-system LLG dynamics display temporarily negative entropy production rates, which signal non-Markovian dynamics…”

Memory Quantification and Experimental Impact

Using newly defined metrics such as the “negative EPR window” and the “relative EPR window,” the study confirmed that experiments based on the os-LLG present the largest magnitude of non-Markovianity among the evaluated models. The research establishes that any magnetic system yielding a negative entropy production rate cannot be correctly modeled by the traditional LLG equation. The next theoretical and experimental steps point to the use of hot-electron bolometers to experimentally access this entropy production, and the need to expand the analysis to environments with additive noise and the full quantum regime.