Orbital magnetic octupole in crystalline solids and anomalous Hall response to a nonuniform electric field
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911347018563584 |
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| author | Sato, Takumi Hayami, Satoru |
| author_facet | Sato, Takumi Hayami, Satoru |
| contents | Magnetic multipole moments beyond dipoles have emerged as key descriptors of unconventional electromagnetic responses in crystalline solids. However, a gauge-invariant bulk expression for orbital magnetic multipole moments has remained elusive, hindering a unified understanding of their physical consequences. Here we formulate a gauge-invariant expression for the orbital magnetic octupole moment in periodic crystals and investigate its behavior in a minimal model of $d$-wave altermagnets. We show that the orbital magnetic octupole is naturally linked to a higher-rank Hall response induced by spatially nonuniform electric fields, leading to a generalized Středa-type relation. Finally, we demonstrate that such a Hall response can arise even when symmetry forbids the conventional anomalous Hall effect against uniform electric fields, thereby providing an illustrative response characteristic to altermagnets. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_24269 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orbital magnetic octupole in crystalline solids and anomalous Hall response to a nonuniform electric field Sato, Takumi Hayami, Satoru Mesoscale and Nanoscale Physics Magnetic multipole moments beyond dipoles have emerged as key descriptors of unconventional electromagnetic responses in crystalline solids. However, a gauge-invariant bulk expression for orbital magnetic multipole moments has remained elusive, hindering a unified understanding of their physical consequences. Here we formulate a gauge-invariant expression for the orbital magnetic octupole moment in periodic crystals and investigate its behavior in a minimal model of $d$-wave altermagnets. We show that the orbital magnetic octupole is naturally linked to a higher-rank Hall response induced by spatially nonuniform electric fields, leading to a generalized Středa-type relation. Finally, we demonstrate that such a Hall response can arise even when symmetry forbids the conventional anomalous Hall effect against uniform electric fields, thereby providing an illustrative response characteristic to altermagnets. |
| title | Orbital magnetic octupole in crystalline solids and anomalous Hall response to a nonuniform electric field |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2512.24269 |