 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
quasirandom
structures
(→SQS)
to ensure that the
supercells to
largest possible
extend represent a
disordered
distribution of
spinup and
spindown 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 magnonphonon
coupling over a
large temperature
range. 
Picture / Figure / Diagram: 

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). 

