  Exploring anisotropy and diverse magnetization dynamics in specimens with
vanishing magnetic moments presents a significant challenge using traditional
magnetometry, as the low resolution of existing techniques hinders the ability
to obtain accurate results. In this study, we delve deeper into the examination
of magnetic anisotropy and quasi-static magnetization dynamics in \mrg\,(MRG)
thin films, as an example of a compensated ferrimagnetic half-metal, by
employing anomalous Hall effect measurements within a tetragonal crystal
lattice system. Our research proposes an innovative approach to accurately
determine the complete set of anisotropy constants of these MRG thin films. To
achieve this, we perform anomalous Hall voltage curve fitting, using torque
models under the macrospin approximation, which allow us to obtain out-of-plane
anisotropy 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 weaker
in-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 to
validate the efficacy of the macrospin model in capturing the magnetic behavior
of MRG thin films. Furthermore, our investigation substantiates that the
complex quasi-static magnetization dynamics of MRG thin films can be
effectively modelled using a combination of hysteronic and torque models. This
approach facilitates the exploration of both linear and non-linear quasi-static
magnetization dynamics, in the presence of external magnetic field and/or
current-induced effective fields, generated by the spin-orbit torque and spin
transfer torque mechanisms.
