Magnetic Field-Induced Quantum Spin Liquids on Kagome Lattice

The kagome lattice provides a platform for investigating quantum spin liquid (QSL) phases. Experimentally, kagome-based materials such as herbertsmithite and YCu₃(OH)₆₊ₓBr₃₋ₓ have emerged as promising candidates for QSL states. Recently, YCu₃(OH)₆₊ₓBr₃₋ₓ and YCu₃(OD)₆₊ₓBr₃₋ₓ have exhibited a 1/9 magnetization plateau, maintaining a magnetically disordered state under finite external magnetic fields. In this regime, proposed ground states include the Z₃ spin liquid and a valence bond solid, though the nature of intermediate phases as a function of field strength remains unexplored. In this study, we examine the range of external magnetic fields, from the Dirac spin liquid (DSL) phase at zero field (h=0) to the Z₃ QSL, using a variational Monte Carlo approach. We find that the DSL phase remains stable up to a small finite field. In the intermediate field regime between the DSL and Z₃ QSL, the variational energy decreases as magnetization develops, with spinon up and down bands shifting in opposite directions, resulting in a finite spinon Fermi surface.