Odd-Even Layer-Number Effect and Layer-Dependent Magnetic Phase Diagrams in MnBi_{2}Te_{4}

Abstract

Recently reported with nontrivial topological properties and magnetic orders, MnBi_{2}Te_{4} is an intrinsic, magnetic topological insulator which holds promise for exploring exotic quantum phenomena such as the quantum anomalous Hall effect. However, the layer-dependent magnetism of MnBi_{2}Te_{4}, which is fundamental and crucial for further exploration of related quantum phenomena in this system, remains elusive. Here, by using polar reflective magnetic circular dichroism spectroscopy, we show that few-layered MnBi_{2}Te_{4} exhibits an evident odd-even layer-number effect, i.e., the oscillations of the coercivity of the hysteresis loop (at μ_{0}H_{c}) and the spin-flop transition (at μ_{0}H_{1}), concerning the Zeeman energy and magnetic anisotropy energy. Noticeably, an anomalous magnetic hysteresis loop is observed in the even-number septuple-layered MnBi_{2}Te_{4}, which might be attributed to the thickness-independent surface-related magnetization. A linear-chain model is applied to elucidate this odd-even layer-number effect of the spin-flop field and to determine the evolution of the magnetic states when subjected to an external magnetic field. A mean-field method further allows us to fully map the MnBi_{2}Te_{4} flake’s magnetic phase diagrams in the parameter space of the magnetic field, layer number, and, especially, temperature. By harnessing the unusual layer-dependent magnetic properties, our work paves the way for further study of quantum phenomena of MnBi_{2}Te_{4}.