Orbital Magnetization — Modern Theory

The quantum-mechanical orbital magnetization of Bloch electrons requires Berry curvature and the orbital moment — it cannot be obtained from bulk charge alone

Model Parameters

M_orb = 0.00 μ_B/cell

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Modern theory of orbital magnetization (Thonhauser 2005, Xiao 2005, Ceresoli 2006): M_orb = (e/2ℏ) ∫_BZ [dk/(2π)²] f(ε_k) Ω_k (ε_k + ε̃_k), where Ω_k is the Berry curvature and ε̃_k is the orbital magnetic moment of the Bloch state. Unlike polarization (which is geometric), orbital magnetization has two contributions: the self-rotation of Bloch wavepackets (orbital moment), and the center-of-mass circulation of wavepackets (Berry curvature × energy). The anomalous Hall conductivity σ_xy = (e²/ℏ) ∫_BZ f_k Ω_k — same Berry curvature integral but without the energy weight.