Diffusion-jump model for the combined Brownian and Néel relaxation dynamics of ferrofluids in the presence of external fields and flow.

Relaxation of suspended magnetic nanoparticles occurs via Brownian rotational diffusion of the particle as well as internal magnetization dynamics. The latter is often modeled by the stochastic Landau-Lifshitz equation, but its numerical treatment becomes prohibitively expensive in many practical applications due to a timescale separation between fast, Larmor-type precession and slow, barrier-crossing dynamics. Here, a diffusion-jump model is proposed to take advantage of the timescale separation and to approximate barrier-crossings as thermally activated jump processes that occur alongside rotational diffusion. The predictions of our diffusion-jump model are compared to reference results obtained by solving the stochastic Landau-Lifshitz equation coupled to rotational Brownian motion. Good agreement is found in the regime of high-energy barriers where Néel relaxation can be considered a thermally activated rare event. While many works in the field have neglected Néel relaxation altogether, our approach opens the possibility to efficiently include Néel relaxation also into interacting many-particle models.