Nematostriction in frustrated two-dimensional Heisenberg models

Abstract

We investigate the nematic phase transition in the Heisenberg $J_1$-$J_2$-model on square and triangular lattices, accounting for finite lattice compressibility and bond-length-dependent magnetic exchange. Using Nematic Bond Theory, a diagrammatic self-consistent method, we study the nematostriction that happens when the onset of nematic order in the spin-system drives a concomitant structural phase transition. We analyze the mechanisms by which the magnetoelastic couplings renormalize the critical temperature and modify the phonon spectrum. The magnetoelastic feeback can also alter fundamentally the nature of the phase transition. Specifically, on the square lattice, the transition shifts from continuous to weakly first-order (discontinuous) beyond a critical magnetoelastic coupling threshold. Conversely, on the triangular lattice, the transition remains discontinuous regardless of coupling strength.

Figures (10)

• Figure 1: Gibbs free energy per site vs. temperature for $J_2=1$ and zero magnetoelastic coupling. $N_x=256$. A linear function $a + bT$ with $a=0.7353$ and $b=-1.65029$ has been subtracted from $G/N$ in order to better visualize the crossing of the two branches at $T_c$.
• Figure 2: Main panel: Critical temperature as a function of $J_2$ for zero magnetoelastic couplings. $N_x=256$. Inset: Relative change in critical temperatures, $\Delta T_c/T_c \equiv (T_c(\tilde{g})-T_c(0))/T_c(0)$, for two sets of magnetoelastic couplings indicated by the legends.
• Figure 3: Critical temperatures $T_c$ vs. $\tilde{g}_1$ for $J_2=1$ (top panel) and $J_2=0.51$ (bottom panel), with $\tilde{g}_2=0$ and $N_x=256$. The different curves show results obtained under different conditions imposed on the self-consistent equations as indicated by the legends. Full means no extra conditions.
• Figure 4: Order parameters vs. $T$. Blue curve: Nematic order parameter. Pink curve: Orthorhombic strain $\epsilon_1$. Green curve: Volumetric strain $\epsilon_3$. $\epsilon_1$ and $\epsilon_3$ are multiplied by $10^3$. $(\tilde{g}_1,\tilde{g}_2)=(0.03,0)$, $N_x=256$. The inset shows $\epsilon_3 \times 10^3$ over a wider temperature range.
• Figure 5: Entropy discontinuity per spin $\Delta S/N$ vs. inverse linear system size $1/N_x$ at $J_2=1$. The black small circles show results for no magnetoelastic couplings $(\tilde{g}_i=0)$. The colored circles are for different magnetoelastic couplings $\tilde{g}_1$ as indicated by the legends. $\tilde{g}_2=0$.