By developing models of increasing complexity, we show that a model without single-ion anisotropy (SIA) cannot explain the magnetic properties of $J_{\mathrm{eff}}=1/2 {\mathrm{Tb}}^{3+}$ moments in the orthorhombically distorted, honeycomb material ${\mathrm{Tb}}_2{\mathrm{Ir}}_3{\mathrm{Ga}}_9$. In four different models for the magnetization of a single honeycomb layer, the only sources of anisotropy are symmetric exchange interactions $J_{n\alpha \beta }=J_{n\beta \alpha }$ along three different bonds $n$, an anisotropic $\underline{g}$ tensor, and a Dzyalloshinskii-Moriya interaction (asymmetric exchange) that produces the observed canted moment along $\mathbf{b}$. With 21 parameters, the best such model yields ${\chi }^2=0.065$, which is substantially smaller than ${\chi }^2=0.112$ obtained using a Heisenberg model containing six parameters including easy-axis anisotropy. However, models without SIA fail to reproduce the linear dependence of the magnetization with a field perpendicular to the Ising axis while predicting a saturation magnetization that is far too low. Due to the complex crystal-field environments, we argue that SIA is necessary to study low-symmetry, three-dimensional $J_{\mathrm{eff}}=1/2$ materials containing ${\mathrm{Tb}}^{3+}$ ions.

中文翻译：

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单离子各向异性对于研究Tb2Ir3Ga9中Jeff=12的Tb3+矩在蜂窝晶格上的磁行为是必要和合适的

通过开发越来越复杂的模型，我们表明没有单离子各向异性 (SIA) 的模型无法解释 $J_{\mathrm{效果}}=1/2 {\mathrm{结核病}}^{3+}$ 正交扭曲蜂窝材料中的矩 ${\mathrm{结核病}}_2{\mathrm{红外线}}_3{嘎}_9$. 在单个蜂窝层磁化的四种不同模型中，各向异性的唯一来源是对称交换相互作用$J_{n\alpha \beta }=J_{n\beta \alpha }$ 沿着三个不同的债券 $n$, 各向异性 $\underline{G}$ 张量和 Dzyalloshinskii-Moriya 相互作用（不对称交换）产生观察到的倾斜力矩 $\mathbf{乙}$. 有 21 个参数，最好的这样的模型产生${\chi }^2=0.065$，远小于 ${\chi }^2=0.112$使用包含六个参数（包括易轴各向异性）的海森堡模型获得。然而，没有 SIA 的模型无法重现磁场与 Ising 轴垂直的磁化强度的线性相关性，同时预测饱和磁化强度太低。由于复杂的晶体场环境，我们认为 SIA 对于研究低对称性、三维$J_{\mathrm{效果}}=1/2$ 包含的材料 ${\mathrm{结核病}}^{3+}$ 离子。