Intrinsic orbital Hall conductivity is expressed via orbital Berry curvature and quantum metric with term-by-term match to charge Hall geometry.
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Chiral crystals with screw symmetry undergo a spontaneous spin-selective structural phase transition driven by handedness-dependent phonon renormalization, producing helical spin density waves and chiral lattice distortions.
Phonon-mediated spin-spin interactions in insulators produce temperature-dependent anisotropic couplings with oscillatory spatial decay, potentially accounting for weak ferromagnetism in chiral compounds when inversion symmetry is broken.
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Intrinsic orbital Hall effect in a nonuniform electric field
Intrinsic orbital Hall conductivity is expressed via orbital Berry curvature and quantum metric with term-by-term match to charge Hall geometry.
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Phonon mediated spin-spin interactions
Phonon-mediated spin-spin interactions in insulators produce temperature-dependent anisotropic couplings with oscillatory spatial decay, potentially accounting for weak ferromagnetism in chiral compounds when inversion symmetry is broken.