Temperature evolution of the effective magnetic anisotropy in the MnCr\(_2\)O\(_4\) spinel

In this work we present a study of the low temperature magnetic phases of polycrystalline MnCr\(_2\)O\(_4\) spinel through dc magnetization and ferromagnetic resonance spectroscopy (FMR). Through these experiments we determined the main characteristic temperatures: T\(_C\) \(\sim\)41 K and T\(_H\) \(\sim\)18 K corresponding, respectively, to the ferrimagnetic order and to the low temperature helicoidal transitions. The temperature evolution of the system is described by a phenomenological approach that considers the different terms that contribute to the free energy density. Below the Curie temperature the FMR spectra were modeled by a cubic magnetocrystalline anisotropy to the second order, with \(K_1\) and \(K_2\) anisotropy constants that define the easy magnetization axis along the direction. At lower temperatures, the formation of a helicoidal phase was considered by including uniaxial anisotropy axis along the [1-10] propagation direction of the spiral arrange, with a \(K_u\) anisotropy constant. The values obtained from the fittings at 5 K are \(K_1\)=-2.3x10\(^4\) erg/cm\(^3\), \(K^2\)=6.4x10\(^4\) erg/cm\(^3\) and \(K_u\)=7.5x10\(^4\) erg/cm\(^3\).