Saturation Field as a Direct Probe of Exchange and Single-Ion Anisotropies in Spin-1 Magnets

TL;DR

The paper addresses how exchange anisotropy and single-ion anisotropies shape field-induced order in layered spin-1 magnets. It develops an SU(3) bond-operator formalism to map spin-1 operators to bosons, derives the magnon spectrum, and obtains analytic expressions for the critical fields $h_{c1}$ and $h_{c2}$ and the magnon-BEC dome. A key finding is that the saturation field $h_{c2}$ encodes the anisotropies linearly via $h_{c2} = (z_1+\alpha z_2)(1+R) + D - 2D_x$, while $h_{c1}$ is less sensitive to axial terms; interlayer coupling shapes the dome extent. The results provide experimental diagnostics via high-field magnetization, inelastic neutron scattering, and THz spectroscopy, and suggest candidate quasi-2D Ni$^{2+}$ materials for testing symmetry-breaking mechanisms in spin-1 magnets.

Abstract

High magnetic fields provide a direct route to probe the anisotropies that govern spin dynamics in layered magnets. Using the SU(3) bond operator framework for spin 1 systems, we derive analytic expressions for the magnon spectrum and the critical fields delimiting the field induced ordered phase. We show that the upper critical field $h_{c2}$ carries a simple and quantitative fingerprint of both exchange anisotropy and single ion symmetry breaking, enabling high field experiments to serve as sensitive probes of microscopic anisotropy. We further map how these anisotropies, together with interlayer coupling, control the extent and location of the magnon Bose Einstein condensation dome. Our results provide experimentally accessible criteria for identifying symmetry breaking mechanisms in real spin 1 materials.

Figures (4)

• Figure 1: Staggered magnetization $M_y$ as a function of $h/J$ at $J=1$, $T=0$, $R=1$ and $\alpha = 0.086$. Solid lines correspond to $D_x = 0$, while dashed lines represent $D_x = 0.5$. The curves for $D = 6.6$, $D = 6.9$, and $D = 8$ are shown in blue, red, and purple, respectively.
• Figure 2: Uniform magnetization $m$ as a function of $h/J$ at $J=1$, $T=0$, $R=1$, and $\alpha = 0.086$. Solid, dashed and colored lines follow the scheme of Fig. \ref{['fig:dome']}.
• Figure 3: Phase diagram of $\alpha_c$ versus the critical fields $h_{c1}$ and $h_{c2}$ for $R=1$. Red curves correspond to $D=7$, and purple curves to $D=8$. Solid lines denote $D_x=0$, while dashed lines indicate $D_x=0.5$. For $R<1$ (not shown), the phase boundary shifts to larger $\alpha_c$ at fixed $h$.
• Figure 4: Phase diagram of $\alpha_c$ versus $h_{c1}$ for $D=7$. Red solid: $D_x=0$, $R=1$ (isotropic single-ion case). Red dashed: $D_x=0.5$, $R=1$ (single-ion distortion). Black solid: $D_x=0$, $R=0.5$. The curves illustrate how single-ion and exchange anisotropies shift the phase boundary; axes are labeled in the main panel.