NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2020, 11 (1), P. 65–77
Fully self-consistent calculations of magnetic structure within non-collinear Alexander–Anderson model
A.V. Ivanov – Saint Petersburg State University, 199034, Saint Petersburg, Russia; Science Institute and Faculty of Physical Sciences, U. of Iceland, 107 Reykjavık, Iceland; email@example.com
P. F. Bessarab – Science Institute and Faculty of Physical Sciences, U. of Iceland, 107 Reykjavık, Iceland; ITMO University, 197101 Saint Petersburg, Russia
H. Jónsson – Science Institute and Faculty of Physical Sciences, U. of Iceland, 107 Reykjavık, Iceland; Department of Applied Physics, Aalto University, FI-00076 Espoo, Finland
V. M. Uzdin – ITMO University, 197101 Saint Petersburg, Russia
An implementation of the non-collinear Alexander–Anderson model for itinerant electrons in magnetic systems is presented where self-consistency is reached for specified directions of the magnetic moments. This is achieved by means of Lagrange multipliers and a variational principle for determining the transverse and longitudinal components of the magnetic moments as well as the average number of d-electrons using direct optimisation. Various optimisation algorithms are compared and the limited memory Broyden–Fletcher–Goldfarb–Shanno algorithm is found to give the best performance. An application to antiferromagnetic Cr crystal is presented where spin-dynamics and curvature of the energy surface are calculated to compare results obtained with and without the constraints on the orientation of the magnetic moments.
Keywords: itinerant magnetism, Alexander–Anderson model, non-stationary configurations, constraints.