Magnetic Phase Diagram Slightly below the Saturation Field in the StackedJ1–J2Model in the Square Lattice with theJCInterlayer Coupling

Abstract

We study the effect of adding interlayer coupling to the square lattice, $J_1$-$J_2$ Heisenberg model in high external magnetic field. In particular, we consider a cubic lattice formed from stacked $J_1$-$J_2$ layers, with interlayer exchange coupling $J_{\text{C}}$. For the 2-dimensional model ($J_{\text{C}}=0$) it has been shown that a spin-nematic phase appears close to the saturation magnetic field for the parameter range $-0.4 \lesssim J_2/J_1$ and $J_2>0$. We determine the phase diagram for 3-dimensional model at high magnetic field by representing spin flips out of the saturated state as bosons, considering the dilute boson limit and using the Bethe-Salpeter equation to determine the first instability of the saturated paramagnet. Close to the highly frustrated point $J_2/J_1\sim0.5$, we find that the spin-nematic state is stable even for $|J_{\text{C}}/J_1|\sim 1$. For larger values of $J_2/J_1$, interlayer coupling favors a broad, phase-separated region. Further increase of $|J_{\text{C}}|$ stabilizes a collinear antiferromagnet, which is selected via the order-by-disorder mechanism.