Thermodynamic Evidence for Multiple Field-Induced Phases in an Anisotropic Kagome Antiferromagnet

Kagome antiferromagnets are predicted to host exotic field-induced phases, yet experimental identification of their thermodynamic signatures remains challenging. Here we combine specific heat (C) and ultrasound measurements up to 36 T and down to 0.5 K to map the $H-T$ phase diagram of the anisotropic kagome magnet Y₃Cu₉(OH)₁₉Cl₈. We show that the suppression of long-range antiferromagnetic order with field at ~ 15 T approximately coincides with the onset of the unconventional $1/6$ (or $1/9$) magnetization plateau previously observed in this system. The attenuation (and sound velocity) then intriguingly increases down to 0.5 K just at μ₀H = 15 T, and $C/T$ becomes temperature independent. Moreover, our measurements are consistent with the opening of a spin gap Δ₀3.5± 0.3 K within the plateau and reveal a further compressible (ungapped) phase beyond the plateau phase, unveiling a rich sequence of field-induced phases in this quantum magnet.