A spin-bond theory unifying non-relativistic spin splitting and emergent spin-orbit textures

• URL: http://arxiv.org/abs/2608.09644v1
• Date: Mon, 10 Aug 2026 14:22:59 GMT
• Title: A spin-bond theory unifying non-relativistic spin splitting and emergent spin-orbit textures
• Abstract summary: Non-relativistic spin textures are governed by unitary spin phases and Hermitian spin amplitudes.<n>Our theory uncovers a mixed non-commuting regime that emerges when the unitary and Hermitian sectors fail to commute.<n>By providing a microscopic foundation for such tuning, our theory paves the way for advanced applications, including field-free spin qubits.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Magnetic order with vanishing net magnetization can produce non-relativistic spin-split bands, broadly categorized into even-parity altermagnets and odd-parity \(p\)-wave magnets. Here, we introduce a spin-bond theory that unifies these seemingly distinct phenomena into a single algebraic framework. We demonstrate that non-relativistic spin textures are fundamentally governed by two components of the electronic bond: unitary spin phases and Hermitian spin amplitudes. The unitary sector generates odd-parity p-wave and emergent spin-orbit-like textures, while the Hermitian sector generates even-parity spin fields, including the uniform \(Γ\)-split and bond-structured altermagnetic limits. Beyond unifying known phases, our theory uncovers a mixed non-commuting regime that emerges when the unitary and Hermitian sectors fail to commute, revealing an underlying non-commuting spin-bond structure. This regime generates a non-coplanar spin texture characterized by an even-in-momentum transverse spin polarization, providing a direct spectroscopic fingerprint for spin- and angle-resolved photoemission spectroscopy. Furthermore, we establish that this synthetic spin-orbit coupling can be dynamically tuned by geometrically controlling the non-commutation of the bond sectors. By providing a microscopic foundation for such tuning, our theory paves the way for advanced applications, including field-free spin qubits.

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