SSA: Spin Space Averaging
Definition:Method to compute atomic forces at finite magnetic temperatures.
Explanation:The SSA technique [1] is based on an adiabatic decoupling of the (fast) magnetic and (slow) atomic degrees of freedom. Within this method, the magnetic configuration space is coarse grained using different magnetic snapshots. Effective forces are obtained by an energy weighted average over these configurations as sketched below. As an example of the high temperature paramagnetic state, the configurations are typically constructed with the concept of special quasi-random structures (→SQS) to ensure that the supercells to largest possible extend represent a disordered distribution of spin-up and spin-down atoms over the lattice.

The method has been implemented in the widely used phonopy package [2] and has been applied to Fe [1,2] as well as to more complex alloys, such as CrN [3].

At present, the direct application of the SSA concept to partially disordered magnetic configurations (e.g. for bcc Fe below the Curie temperature) is computationally too expensive. However, a combination of the SSA method with Quantum Monte Carlo (→QMC) simulations for the spin Hamiltonian turns out to be a successful strategy [4]. The application to Fe indicates a strong magnon-phonon coupling over a large temperature range.
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Sketch of the SSA method. Effective forces (left) are obtained by averaging forces from individual magnetic configurations. Images adopted from Ref. [1].
References:[1] F. Körmann, A. Dick, B. Grabowski, T. Hickel, and J. Neugebauer, Phys. Rev. B 85, 125104 (2012).
[2] Y. Ikeda, A. Seko, A. Togo, and I. Tanaka, Phys. Rev. B 90, 134106 (2014).
[3] L. Zhou, F. Körmann, D. Holec, M. Bartosik, B. Grabowski, J. Neugebauer, and P. H. Mayrhofer, Phys. Rev. B 90, 184102 (2014).
[4] F. Körmann, B. Grabowski, B. Dutta, T. Hickel, L. Mauger, B. Fultz, and J. Neugebauer, Phys. Rev. Lett. 113, 165503 (2014).