Six magnetization plateau phases in a spin-1/2 distorted kagome antiferromagnet: application to $\rm{Y}_3\rm{Cu}_9(\rm{OH})_{19}\rm{Cl}_8$

Abstract: A recently discovered kagome antiferromagnet $\rm{Y}3\rm{Cu}_9(\rm{OH}){19}\rm{Cl}8$ has attracted significant interest due to its unique kagome lattice structure and magnetic properties. The kagome lattice has three types of exchange interactions: one hexagonal coupling and two different triangular couplings. Previous studies have shown that its ground state is significantly different from that predicted for the undistorted kagome lattice, forming a coplanar spin state with a commensurate magnetic wave vector ${\mathbf Q}=(1/3,1/3)$. Two separate studies have proposed distinct sets of exchange interaction parameters for this compound. In this study, we investigate the ground state of the spin-1/2 Heisenberg kagome model with three types of nearest-neighbor exchange interactions under a magnetic field by exact diagonalization using the Lanczos method. We reveal that clear magnetization plateaus at $M/M{\rm sat}$=1/3, 5/9, and 7/9 are present under both parameter sets, which are identified as magnon crystal states based on their spin structures. Our findings suggest that these plateaus could potentially be experimentally confirmed with magnetization measurements on $\rm{Y}3\rm{Cu}_9(\rm{OH}){19}\rm{Cl}8$ under a magnetic field of approximately 300 T, achievable with state-of-the-art magnetic field generators. In order to get a deeper understanding of magnetism of $\rm{Y}_3\rm{Cu}_9(\rm{OH}){19}\rm{Cl}8$, we perform additional calculations by varying these interactions. Consequently, we discover additional plateau phases at $M/M{\rm sat}$=1/3, 5/9, and 7/9, each distinctly different from the magnon crystal states.