Microscopic Model Calculations for the Magnetization Process of Layered Triangular-Lattice Quantum Antiferromagnets

Magnetization processes of spin-$1/2$ layered triangular-lattice antiferromagnets (TLAFs) under a magnetic field $H$ are studied by means of a numerical cluster mean-field method with a scaling scheme. We find that small antiferromagnetic couplings between the layers give rise to several types of extra quantum phase transitions among different high-field coplanar phases. Especially, a field-induced first-order transition is found to occur at $H\approx 0.7H_s$, where $H_s$ is the saturation field, as another common quantum effect of ideal TLAFs in addition to the well-established one-third plateau. Our microscopic model calculation with appropriate parameters shows excellent agreement with experiments on ${\mathrm{Ba}}_3{\mathrm{CoSb}}_2{\mathrm{O}}_9$ [T. Susuki et al., Phys. Rev. Lett. 110, 267201 (2013)]. Given this fact, we suggest that the ${\mathrm{Co}}^{2+}$-based compounds may allow for quantum simulations of intriguing properties of this simple frustrated model, such as quantum criticality and supersolid states.

Figure 1

(a) Ground-state phase diagram of spin-$1/2$ easy-plane TLAFs on an independent layer with in-plane magnetic field, obtained by the $\mathrm{CMF}+\mathrm{S}$. (b) Emergent high-field states induced by interlayer coupling $J^{\prime }$ for $J_z/J=0.8$. The thick (thin) curves denote first- (second-) order transitions.

Figure 2

(a) Six-sublattice structure and the cluster decoupling with $N_C=6$. (b) Series of clusters used in the $\mathrm{CMF}+\mathrm{S}$.

Figure 3

Energy per site of candidate magnetic orders measured from that of the $\pi$-coplanar state for $J=J_z$ and $J^{\prime }=0$ within the $N_C=3$ approximation. The lower illustrations depict the spin configurations on an elementary triangle $ABC$.

Figure 4

Energy per site of candidate magnetic orders measured from that of the configuration (d) for $J=J_z$ and $J^{\prime }=0.025J$ within the $N_C=3$ approximation. The arrow locates a first-order transition that is absent in the 2D result. The inset shows an enlarged view of the high-field region. The lower illustrations depict the spin configurations on an elementary triangular prism $ABC-A^{\prime }{B}^{\prime }{C}^{\prime }$.

Figure 5

(a) Ground-state phase diagram for $J^{\prime }=0.025J$ and $N_C\to \infty$. The thick (thin) curves denote first- (second-) order transitions. (b) The magnetization curve $M$ and its field derivative $JdM/dH$ for $J^{\prime }=0.025J$ and $J_z/J=0.8$. The $\mathrm{CMF}+\mathrm{S}$ at zero temperature is compared to the classical-spin analysis and the experimental data of ${\mathrm{Ba}}_3{\mathrm{CoSb}}_2{\mathrm{O}}_9$ for $H\parallel ab$ at $T=1.3$ $\mathrm{K}\approx 0.07J$ [24, 47]. The values of the saturation field and the saturation magnetization are adjusted.