Magnetisation Dynamics

two images are shown. the top of the first shows a 2D lattice of atoms, coupling to a spin. in one case, the coupling is instantaneous, in the other, coupling also happens to a previous state. on the bottom the two different dynamics are illustrated on the bloch sphere, where the first case spirals uniformly towards equilibrium, the second shows additional oszillations. The other image shows amplitudes of spin oszillations, especially the nutation peak at around 4 THz, as described by the LLG, iLLG and non-Markovian LLG models, and experimental data. the non-Markovian LLG seems to fit the data best. — Photo: Felix Hartmann

The most widely used equation to describe magnetisation dynamics is the Landau-Lifshitz-Gilbert (LLG) equation, which predicts the precession and relaxation of a classical spin vector. In our group we study a generalised LLG equation which takes into account physically relevant additions to the LLG paradigm: coloured noise and memory effects. Our research explores how the dynamics and the equilibrium state of the spin vector is affected. In particular, we show how non-trivial spin-phonon interactions give raise to a complex THz-frequency spectrum, which has been measured experimentally also (see figure). These effects are not captured by the standard LLG equation dynamics and show the need to incorporate non-Markovian memory kernels on ultrashort timescales, where system and bath timescales are no longer well separated.

If you want to read more about the topic, you can start here:

Quantum Brownian Motion for Magnets, J. Anders, C.R.J. Sait, and S.A.R. Horsley., New J. Phys. 24 033020 (2022)
SpiDy.jl: open-source Julia package for the study of non-Markovian stochastic dynamics S. Scali et al., J. Open Source Softw. 9(97), 6263 (2024)
Accounting for quantum effects in atomistic spin dynamics M. Berritta, S. Scali, F. Cerisola, and J. Anders, Phys. Rev. B 109, 174441 (2024)
Anisotropic signatures in the spin-boson model, F. Hartmann , S. Scali, and J. Anders., Phys. Rev. B 108, 184402 (2023)
Intrinsic non-Markovian magnetisation dynamics, F. Hartmann, V. Unikandanunni, M. Bargheer, E.E. Fullerton, S. Bonetti, and J. Anders, arXiv quant-ph (2025)
Atomistic spin dynamics with quantum colored noise, F.C. Weber, F. Hartmann, M. Bargheer, J. Anders, and R.F.L. Evans, Phys. Rev. B (2025)