Equation of motion and the constraining field in ab initio spin dynamics

Abstract

It is generally accepted that the effective magnetic field acting on a magnetic moment is given by the gradient of the energy with respect to the magnetization. However, in ab initio spin dynamics within the adiabatic approximation, the effective field is also known to be exactly the negative of the constraining field, which acts as a Lagrange multiplier to stabilize an out-of-equilibrium, non-collinear magnetic configuration. We show that for Hamiltonians without mean-field parameters both of these fields are exactly equivalent, while there can be a finite difference for mean-field Hamiltonians. For density-functional theory (DFT) calculations the constraining field obtained from the auxiliary Kohn-Sham Hamiltonian is not exactly equivalent to the DFT energy gradient. This inequality is highly relevant for both ab initio spin dynamics and the ab initio calculation of exchange constants and effective magnetic Hamiltonians. We argue that the effective magnetic field and exchange constants have the highest accuracy in DFT when calculated from the energy gradient and not from the constraining field.

arXiv comment9 pages, 5 figures

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Cited by in corpus (8)

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• A Self-Adaptive First-Principles Approach for Magnetic Excited States
• Spin dynamics from a constrained magnetic Tight-Binding model
• Linear Response Based Theories for Dzyaloshinskii-Moriya Interactions
• Adiabatic spin dynamics and effective exchange interactions from constrained tight-binding electronic structure theory: Beyond the Heisenberg regime