Magnetoelastic effects and magnetization plateaus in two-dimensional systems

We show the importance of both strong frustration and spin-lattice coupling for the stabilization of magnetization plateaus in translationally invariant two-dimensional systems. We consider a frustrated spin-1/2 Heisenberg model coupled to adiabatic phonons under an external magnetic field. At zero magnetization, simple structures with two or at most four spins per unit cell are stabilized, forming dimers or $2\times 2$ plaquettes, respectively. A much richer scenario is found in the case of magnetization $m=1∕2$, where larger unit cells are formed with nontrivial spin textures and an analogy with the corresponding classical Ising model is detectable. Specific predictions on lattice distortions and local spin values can be directly measured by x rays and nuclear magnetic resonance experiments.

Figure 1

Ground-state phase diagram of the $J_1\text{−}{J}_2\text{−}{J}_3$ model for $m=0$, $K=10$, and $J_2=0$ (a) or $J_2=0.5$ (b). See text for the precise description of the various phases.

Figure 2

The same as in Fig. 1 but for $m=1∕2$.

Figure 3

Magnetic structure factor at $m=1∕2$ along a closed path in the Brillouin zone [$\Gamma =(0,0)$, $M=(0,\pi )$, and $X=(\pi ,\pi )$] for the $J_1\text{−}{J}_2$ Heisenberg model $(J_3=0)$ on a $4\times 4$ (empty dots) and a $6\times 6$ (full dots) rigid lattice along the magnetic field (left panels) and in the orthogonal plane (right panels) for $J_2=0.2$ in the upper panels and $J_2=1.1$ in the lower ones.

Figure 4

Distortion pattern of the $J_1\text{−}{J}_2\text{−}{J}_3$ Heisenberg model on the $4\times 4$ lattice at $m=1∕2$ in the “trapezoidal” phase at $J_2=0.5$, $J_3=0.2$, and $\alpha =3.5$ (a) and in the “classical Ising” phase at $J_2=0.5$, $J_3=0.4$, and $\alpha =\sqrt{10}$ (b). Distortion pattern of the Ising model on the $8\times 8$ cluster at $J_2=0.5$, $J_3=0.4$, and $\alpha =\sqrt{10}$ (c). Stars mean $⟨S_i^z⟩\sim 0$, while empty and full dots indicate positive and negative local magnetization close or equal to the maximal value 1/2, respectively.

Figure 5

Behavior of local magnetization $⟨S_i^z⟩$ as a function of $J_3$ at $m=1∕2$ and $\alpha =\sqrt{10}$ for $J_2=0$ (upper panel) and $J_2=0.5$ (lower panel).

Figure 6

Distortion pattern of the nearest-neighbor classical Ising model at $\alpha =\sqrt{10}$.

Figure 7

Distortion pattern of the $J_1\text{−}{J}_2\text{−}{J}_3$ classical Ising model at $J_2=0.5$, $J_3=0$, and $\alpha =\sqrt{10}$.