Fourfold Anisotropic Magnetoresistance and Unconventional Critical Exponents in Twinned FePd$_2$Te$_2$

As a special material symmetry operation, crystal twins usually influence physical properties. Here, detailed electrical transport and magnetic measurements were performed to reveal twinning effect on properties of van der Waals ferromagnet FePd$_2$Te$_2$. Orthorhombic crystal domains were observed in polarized optical microscopy and fixed $\pi$/2 angle between adjacent domains suggests a phase transition origin of the twins. FePd$_2$Te$_2$ exhibits fourfold in-plane anisotropic magnetoresistance. It is attributed to antiferromagnetic coupling component near atomically flat twin boundary and pseudo four-fold symmetry from perpendicular Fe chains. Intense magnetic domain motion is suggested by Hopkinson effect observed in magnetic susceptibility. A set of unusual critical exponents $\beta$ = 0.866, $\gamma$ = 1.043, $\delta$ = 2.20 cannot be classified in any universal class predicted by renormalized group. Deviation from standard model reflects the non-saturating magnetization and slow growth of spontaneous magnetization resulting from crystal domain walls. These results show that additional symmetry from twins and twin boundary have a significant effect on electrical transport and magnetic properties of FePd$_2$Te$_2$. There is much room to modulate physical properties of twinned van der Waals ferromagnets through twins.