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Precise modeling of the magnetization dynamics of nanoparticles with finitesize effects at fast varying temperatures is a computationally challengingtask. Based on the Landau-Lifshitz-Bloch (LLB) equation we derive a coarsegrained model for disordered ferrimagnets, which is both fast and accurate.First, we incorporate stochastic fluctuations to the existing ferrimagnetic LLBequation. Further, we derive a thermodynamic expression for the temperaturedependent susceptibilities, which is essential to model finite size effects.Together with the zero field equilibrium magnetization the susceptibilities areused in the stochastic ferrimagnetic LLB to simulate a $5\times10$ nm$^2$ferrimagnetic GdFeCo particle with 70 % FeCo and 30 % Gd under various externalapplied fields and heat pulses. The obtained trajectories agree well with thoseof an atomistic model, which solves the stochastic Landau-Lifshitz-Gilbertequation for each atom. Additionally, we derive an expression for theintergrain exchange field which couple the ferromagnetic sublattices of aferrimagnet. A comparison of the magnetization dynamics obtained from thissimpler model with those of the ferrimagnetic LLB equation shows a perfectagreement.

Stochastic ferrimagnetic Landau-Lifshitz-Bloch equation for finite magnetic structures