Spin Quadrupolar Order in d -wave Unconventional Magnetism

作者：Jian-Keng Yuan, Zhiming 志明 Pan 潘, Congjun Wu · 发表于：Chinese Physics Letters · 年份：2026 · DOI：10.1088/0256-307x/43/9/090703 · 研究领域：Topological Materials and Phenomena、Organic and Molecular Conductors Research、Advanced Condensed Matter Physics

Abstract Unconventional magnetism represents a class of metallic states whose Fermi surfaces exhibit spin-dependent splittings under the nontrivial representations of the rotation group. The d -wave α -phase of unconventional magnetism provides a continuum realization of the nonrelativistic spin-splitting physics described in crystals within the framework of altermagnetism; the two share the same symmetry under rotation. In this work, we investigate how the associated momentum-space spin quadrupole manifests itself in the real-space spin structure of a crystal. Within linear-response theory, we calculate the spin-charge cross-susceptibility of the d -wave state in a weak nonmagnetic periodic scalar potential. The combined symmetry of the d -wave α -phase requires the response to change sign between two symmetry-related reciprocal-lattice vectors, producing an intra-unit-cell d -wave spin-density modulation without enlarging the unit cell. The resulting real-space spin modulation is induced by the scalar lattice potential rather than being a consequence of spontaneous symmetry breaking. It thus provides a real-space linear-response signature of the even-parity momentum-space spin multipole.