Incommensurate magnetism in CrB$_2$ is studied in terms of a spin model based on density functional theory calculations. Heisenberg exchange interactions derived from the paramagnetic phase using the disordered local moment theory show significant differences compared with those resulting from the treatment of the material as a ferromagnet; of these two methods, the disordered local moment theory is found to give a significantly more realistic description. We calculate strongly ferromagnetic interactions between Cr planes but largely frustrated interactions within Cr planes. Although we find that the ground state ordering vector is sensitive to exchange interactions over a large number of neighbour shells, the $q$-vector of the incommensurate spin spiral state is satisfactorily reproduced by the theory ($0.213$ compared with the known ordering vector $0.285\times (2\pi)/(a/2)$ along $\Gamma-{\rm K}$). The strong geometric frustration of the exchange interactions causes a rather low N\'eel temperature (about 97 K), also in good agreement with experiment.

中文翻译：

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CrB$_2$ 中不相称的磁排序

CrB$_2$中的不相称磁性是根据基于密度泛函理论计算的自旋模型来研究的。使用无序局部矩理论从顺磁相衍生的海森堡交换相互作用与将材料作为铁磁体处理所产生的相互作用显示出显着差异；在这两种方法中，发现无序局部矩理论给出了更现实的描述。我们计算了 Cr 平面之间的强铁磁相互作用，但 Cr 平面内的相互作用很大程度上受挫。尽管我们发现基态有序向量对大量相邻壳层上的交换相互作用很敏感，但该理论令人满意地再现了不相称的自旋螺旋状态的$q$-向量（$0. 213$ 与沿 $\Gamma-{\rm K}$) 的已知排序向量 $0.285\times (2\pi)/(a/2)$ 相比。交换相互作用的强烈几何挫折导致相当低的 N'eel 温度（约 97 K），也与实验很好地吻合。