Cubic magnetocrystalline anisotropy-driven spin reorientation in TmIG detected by spin Hall magnetoresistance

The precise manipulation and detection of magnetization in magnetic insulators are essential for the development of next-generation spintronic devices. Here, using a heterostructure consisting of a heavy metal and a magnetic garnet thin film, i.e., (111)-oriented Pt/Tm_3Fe_5O_12 (TmIG), we reconstruct the three-dimensional magnetization reversal trajectory using spin Hall magnetoresistance (SMR). It is found that the SMR signal of the heterostructure exhibits abrupt jumps when the magnetic field is scanned along the out-of-plane direction, and this anomalous phenomenon persists at temperatures below 100 K. By employing a three-dimensional Stoner-Wohlfarth model, we demonstrate that this behavior originates from a discontinuous magnetization trajectory with a unique 3m symmetry, which is governed by the competition among the cubic magnetocrystalline anisotropy, magnetoelastic anisotropy, and the Zeeman energy. These results provide a novel strategy for detecting three-dimensional magnetization orientation in magnetic insulators and hold the potential to advance the development of low-energy-consumption spintronic devices.