Thermodynamics of the up-up-down phase of the $S=\frac{1}{2}$ triangular-lattice antiferromagnet ${\mathrm{Cs}}_2\mathrm{Cu}{\mathrm{Br}}_4$

The specific heat and magnetocaloric effect are used to probe the field-induced up-up-down (UUD) phase of ${\mathrm{Cs}}_2\mathrm{Cu}{\mathrm{Br}}_4$, a quasi-two-dimensional spin-$\frac{1}{2}$ triangular antiferromagnet with near-maximal frustration. The transitions between the commensurate UUD phase and the incommensurate phases adjacent to it are clearly first order, at least at low temperatures. The shape of the magnetic phase diagram shows that the UUD phase is stabilized by quantum fluctuations, not by thermal fluctuations as in the corresponding phase of classical spins. The magnon gaps determined from the specific heat are considerably larger than those expected for a Heisenberg antiferromagnet.