In solids, electrons carry both charge and spin. The arrangement of these spins in a material largely determines its magnetic properties, such as whether it is ferromagnetic, antiferromagnetic, or something more exotic. Because the full many-electron problem is extremely complex, physicists often use spin models that focus only on the spin degrees-of-freedom. A representative example is the Heisenberg model, which contains only bilinear spin-spin interactions. However, recently discovered magnetic phenomena cannot be explained solely by the bilinear interaction. Specifically, higher-order interactions, such as the biquadratic interaction, play a crucial role in stabilizing complex magnetic structures.

To build realistic spin models from first principles, it is necessary to extract bilinear and higher-order terms in a reliable manner. The spin cluster expansion (SCE) combined with disordered local moment (DLM) method is discussed. In the SCE–DLM approach, one considers a “virtual” disordered paramagnetic state as a reference and expands the energy in terms of spin configurations, which allows bilinear, biquadratic, and higher-order interactions to be obtained by a systematic expansion. The use of a disordered reference state also avoids biasing the results toward any specific magnetically ordered phase. Previously, this framework was formulated only for specific Green’s function-based first-principles methods based on localized basis functions. Therefore, a method that is independent of basis functions is highly desirable.

Our study formulates the SCE–DLM method in terms of first-principles tight-binding models. Because our formulation requires only tight-binding parameters, the SCE–DLM framework for extracting higher-order spin interactions can be integrated with a wide range of first-principles codes employing various basis sets for constructing tight-binding models.

We tested our approach on simple model systems and typical metallic magnets, such as Fe and Co. We then applied the method to more complex materials, such as Co1/3TaS2, which hosts a noncoplanar spin structure, and potassium electrosodalite, where antiferromagnetism arises from electrons localized in vacant spaces in its crystal structure. In both cases, the spin interactions derived from our framework successfully reproduced the experimental observations, including magnetic structures and transition temperatures. Conventional methods were not suitable for these compounds, highlighting the versatility of our method.

The SCE–DLM method can be combined with high-throughput density functional theory calculations and automated search techniques to accelerate the discovery and design of functional magnetic materials, including candidates for antiferromagnetic spintronics and low-power devices based on topological spin textures.

(Written by Tatsuto Hatanaka on behalf of all the authors.)

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