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.

Figure 1

(Color online) Magnetocaloric effect of ${\mathrm{Cs}}_2\mathrm{Cu}{\mathrm{Br}}_4$ in fields along the $c$ axis: temperature difference $\Delta T$ between sample and thermal reservoir during $0.2\mathrm{T}∕\min$ upward and downward field sweeps (thick and thin lines, respectively). Traces at different temperatures are offset for clarity. The overall separation between up- and down-sweep traces at the lowest temperatures is an uninteresting nuclear-spin effect.

Figure 2

(Color online) Magnetic specific heat of ${\mathrm{Cs}}_2\mathrm{Cu}{\mathrm{Br}}_4$ in zero magnetic field and in fields along the $c$ axis. A small phonon contribution, $7.94T^3\mathrm{mJ}∕\mathrm{K}\mathrm{mol}$, has been subtracted by scaling the specific heat of ${\mathrm{Cs}}_2\mathrm{Zn}{\mathrm{Br}}_4$ (Ref. 13). The lines are guides to the eye.

Figure 3

(Color online) Phase diagram of ${\mathrm{Cs}}_2\mathrm{Cu}{\mathrm{Br}}_4$ in magnetic fields along the $c$ axis, as deduced from magnetocaloric-effect (squares) and specific-heat (circles) measurements. Lines indicating the phase boundaries are guides to the eye.

Figure 4

Magnetic specific heat of ${\mathrm{Cs}}_2\mathrm{Cu}{\mathrm{Br}}_4$ in a $13.7\mathrm{T}$ field along the $c$ axis. The lines are calculations for gapped magnons, as discussed in the text.

Figure 5

(Color online) Dispersion ${ϵ}_0\left(\mathit{k}\right)$ of the $S_z=-1$ (solid lines) and $S_z=+1$ (broken line) classical magnon modes in the UUD state of a Heisenberg antiferromagnet on a triangular lattice, along the high-symmetry paths indicated with arrows in the reciprocal space at right. In the reciprocal space, the solid line outlines the first Brillouin zone of the three triangular sublattices, and the broken line that of the full lattice.