Magnetic criticality and magnetocaloric response in MnBi$_2$Te$_4$ and MnBi$_4$Te$_7$

Abstract

MnBi$_2$Te$_4$ and MnBi$_4$Te$_7$ are antiferromagnetic topological insulators belonging to the MnBi$_{2n}$Te$_{3n+1}$ series, where structural layering provides a natural route to tune magnetic interaction in van der Waals magnets. Despite extensive interest in their topological properties, how the insertion of Bi$_2$Te$_3$ quintuple layers modifies magnetic critical fluctuations near the antiferromagnetic transition remains unresolved. Here, we combine scanning tunneling microscopy (STM), critical scaling analysis, and magnetocaloric measurements to directly correlate real-space structures with magnetic criticality. STM reveals atomically flat septuple-layer terraces in MnBi$_2$Te$_4$ whereas MnBi$_4$Te$_7$ displays coexisting septuple and quintuple layer terminations reflecting its alternating stacking sequence. MnBi$_2$Te$_4$ exhibits robust three-dimensional Ising-like critical behavior together with a distinct low-temperature first-order transition. In contrast, MnBi$_4$Te$_7$ displays crossover-dominated criticality arising from weakened interlayer exchange and competing magnetic phases. Correspondingly, the magnetocaloric response differs significantly between the two compounds. MnBi$_2$Te$_4$ shows dual-type magnetocaloric behavior with a sharp field-induced sign reversal of the isothermal magnetic entropy change ($-\Delta S_M$). It exhibits both inverse ($-\Delta S_M < 0$) and conventional ($-\Delta S_M > 0$) magnetocaloric effects. In contrast, MnBi$_4$Te$_7$ shows only conventional magnetocaloric response with a broad positive entropy peak. These results establish structural layering as a key parameter governing magnetic critical fluctuations and magnetocaloric behavior in MnBi$_{2n}$Te$_{3n+1}$ topological magnets.