Magnetic modelling for ultrafast simulations at the atomistic and micromagnetic scale make common use of Langevin Dynamics to model the effect of thermal fluctuations on the procession of the magnetic moment. Such a model is simple to add to any finite-temperature simulation: a Gaussian distribution scaled against a collection of material dependent parameters are included in the effective field term in the LLG spin Hamiltonian, and at pico-second timescales is uncorrelated in space or time 1.
In general, however, the thermal fluctuations in a material are correlated through collective occupation of electron, phonon, and magnon modes in the system. Analytical solutions for these relationships under conditions of non-equilibrium require simple materials or drastic approximations, conditions ill-suited to ultrafast ferri and antiferromagnetic materials. We present an improved thermostat for ultrafast atomistic scale magnetic simulations using a computationally determined conduction band environment based on semi-classical electron-electron and electron-phonon scattering events 2. Currently, our environment simulates charge and heat transport in metals on ultra-fast time scales during severe non-equilibrium caused from applied electric fields or laser-heating pulses. The electron-electron and electron-phonon relationship is parametrized into the relaxation time approximation using constants derived from experimental data 3. Our environment successfully reproduces the popular two-temperature model (TTM) used to simulate laser-heating of experimental samples (fig. 1), and currently reproduces the phenomena of effective Joule heating from applied external fields and super-diffusive electron transport. The current work lays the foundation for the inclusion of electron spin into the conduction band environment, offering the ability to include correlated spin effects not possible in Langevin Dynamics.
Figure 1. Simulated electron and lattice temperatures (solid) following laser exposure compared to the standard TTM (dash). The varying colours and dynamics are a result of varying the electron-electron scattering constant.