Cascade of Magnetic-Field-Induced Quantum Phase Transitions in a Spin-$\frac{1}{2}$ Triangular-Lattice Antiferromagnet

We report magnetocaloric and magnetic-torque evidence that in ${\mathrm{Cs}}_2{\mathrm{CuBr}}_4$—a geometrically frustrated Heisenberg $S=\frac{1}{2}$ triangular-lattice antiferromagnet—quantum fluctuations stabilize a series of spin states at simple increasing fractions of the saturation magnetization $M_s$. Only the first of these states—at $M=\frac{1}{3}{M}_s$—has been theoretically predicted. We discuss how the higher fraction quantum states might arise and propose model spin arrangements. We argue that the first-order nature of the transitions into those states is due to strong lowering of the energies by quantum fluctuations, with implications for the general character of quantum phase transitions in geometrically frustrated systems.

Figure 1

(a) Evolution of the temperature difference between the sample and thermal reservoir due to the magnetocaloric effect at 180 mK, with arrows indicating the field-sweep directions. (b) Derivative of magnetic torque with respect to $H$ at temperatures near 400 mK. To produce a torque, the magnetic field was slightly tilted away from the $c$ axis toward the $b$ axis, by the angle indicated for each curve. (c) Magnetic phase diagram deduced from the magnetocaloric-effect data taken at various temperatures. Circles indicate second-order phase boundaries, whereas other symbols except the open diamonds indicate first-order boundaries. Open diamonds are the positions of the large features near $H_s$ and do not indicate a phase boundary. Lines are guides to the eye. Data for $H\le 18\mathrm{T}$ are from Ref. 10, where open circles are from specific heat.

Figure 2

Collinear states on the triangular lattice at $M/Ms=\frac{1}{3}$, $\frac{1}{2}$, $\frac{5}{9}$, and $\frac{2}{3}$. Arrows indicate down spins antiparallel to the magnetic field. Vertices with no arrows indicate up spins pointing in the direction of the field, with broken lines marking rows containing both spins and solid lines marking rows of only up spins. The $A$ phase may resemble the $M/Ms=\frac{1}{2}$ state, albeit not collinear.

Figure 3

Ground-state energy $\mathcal{E}$ of a frustrated quantum-mechanical Heisenberg antiferromagnet as a function of magnetization $M$. (a) Macroscopic behavior of $\mathcal{E}(M)$, exhibiting a cusp at a gapped ground state $P$. (b) Microscopic, extremely expanded view of the region near $P$, revealing quantum-mechanically discrete ground states (dots). (c) Macroscopic behavior, when the transitions to state $P$ are first order. (d) Corresponding microscopic view. In (a) and (c), the magnetic fields are in dimensionless units.