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Exploring anisotropy and diverse magnetization dynamics in specimens withvanishing magnetic moments presents a significant challenge using traditionalmagnetometry, as the low resolution of existing techniques hinders the abilityto obtain accurate results. In this study, we delve deeper into the examinationof magnetic anisotropy and quasi-static magnetization dynamics in \mrg\,(MRG)thin films, as an example of a compensated ferrimagnetic half-metal, byemploying anomalous Hall effect measurements within a tetragonal crystallattice system. Our research proposes an innovative approach to accuratelydetermine the complete set of anisotropy constants of these MRG thin films. Toachieve this, we perform anomalous Hall voltage curve fitting, using torquemodels under the macrospin approximation, which allow us to obtain out-of-planeanisotropy constants $K_1=4.0\times10^4$ J m$^{-3}$ ($K_1/M=0.655$\,T) and$K_2=2.54\times10^4$ J m$^{-3}$ ($K_2/M=0.416$\,T), along with a weakerin-plane anisotropy constant $K_3=3.48\times10^3$ J m$^{-3}$($K_3/M=0.057$\,T). By additionally employing first-order reversal curves(FORC) and classical Preisach hysteresis (hysterons) models, we are able tovalidate the efficacy of the macrospin model in capturing the magnetic behaviorof MRG thin films. Furthermore, our investigation substantiates that thecomplex quasi-static magnetization dynamics of MRG thin films can beeffectively modelled using a combination of hysteronic and torque models. Thisapproach facilitates the exploration of both linear and non-linear quasi-staticmagnetization dynamics, in the presence of external magnetic field and/orcurrent-induced effective fields, generated by the spin-orbit torque and spintransfer torque mechanisms.

Quasi-static magnetization dynamics in a compensated ferrimagnetic half-metal -- Mn$_2$Ru$_x$Ga