Ordered phases of the anisotropic kagome-lattice antiferromagnet in a magnetic field

The antiferromagnetic Heisenberg model on an anisotropic kagome lattice may be a good minimal model for real magnetic systems as well as a limit from which the isotropic case can be better understood. We therefore study the nearest-neighbor Heisenberg antiferromagnet on an anisotropic kagome lattice in a magnetic field. Such a system should be well described by weakly interacting spin chains, and we motivate a general form for the interaction by symmetry considerations and by perturbatively projecting out the interchain spins. In the spin-$1∕2$ case, we find that the system exhibits a quantum phase transition from a ferrimagnetic ordered state to an $XY$ ordered state as the field is increased. Finally, we discuss the appearance of magnetization plateaux in the ferrimagnetic phase.

Figure 1

The anisotropic kagome lattice with antiferromagnetic coupling $J$ between nearest-neighbor chain spins ($S$ spins) and coupling $J^{\prime }$ between $S$ spins and interchain spins ($I$ spins). We make the approximation that the $I$ spins are fully polarized by the external magnetic field.

Figure 2

The generating symmetries of the space group $cmm$ of the anisotropic kagome lattice: (a) translations, (b) rotations by $\pi$ about the hexagon centers, and (c) reflections through a vertical line passing through the hexagon centers.

Figure 3

An example of a ferrimagnetically ordered ground state of the spin-$1∕2$ system with magnetization $m\lesssim 1∕5$ and ${\lambda }_z<0$.

Figure 4

The $XY$ antiferromagnetically ordered ground state that occurs for both the spin-$1∕2$ and spin-1 systems in a large enough field (${\lambda }_{\perp }<0$ case shown).

Figure 5

Schematic graph of the magnetization curve and phases of the spin-$1∕2$ system. Note the possible plateau just below the crossover point. The shaded region indicates the parameter space where our model does not apply.