Ferromagnetic-antiferromagnetic coexisting ground states and exchange bias effects in $\bf{MnBi_4Te_7}$ and $\bf{MnBi_6Te_{10}}$

Natural superlattice structures $\rm{(MnBi_2Te_4)(Bi_2Te_3)}$$_n$ ($n$ = 1, 2,...), in which magnetic $\rm{MnBi_2Te_4}$ layers are separated by nonmagnetic $\rm{Bi_2Te_3}$ layers, hold band topology, magnetism and reduced interlayer coupling, providing a promising platform for the realization of exotic topological quantum states. However, their magnetism in the two-dimensional limit, which is crucial for further exploration of quantum phenomena, remains elusive. Here, complex ferromagnetic (FM)-antiferromagnetic (AFM) coexisting ground states that persist up to the 2-septuple layers (SLs) limit are observed and comprehensively investigated in $\rm{MnBi_4Te_7}$ ($n$ = 1) and $\rm{MnBi_6Te_{10}}$ ($n$ = 2). The ubiquitous Mn-Bi site mixing modifies or even changes the sign of the subtle inter-SL magnetic interactions, yielding a spatially inhomogeneous interlayer coupling. Further, a tunable exchange bias effect is observed in $\rm{(MnBi_2Te_4)(Bi_2Te_3)}$$_n$ ($n$ = 1, 2), arising from the coupling between the FM and AFM components in the ground state. Our work highlights a new approach toward the fine-tuning of magnetism and paves the way for further study of quantum phenomena in $\rm{(MnBi_2Te_4)(Bi_2Te_3)}$$_n$ ($n$ = 1, 2,...) as well as their magnetic applications.Comment: 9 pages, 4 figure