najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2020-11-1-65-77najo-468Research ArticlePHYSICSФИЗИКАFully self-consistent calculations of magnetic structure within non-collinear Alexander–Anderson modelIvanovA. V.

199034, Saint Petersburg

107 Reykjav´ık

ali5@hi.isBessarabP. F.

107 Reykjav´ık

197101 Saint Petersburg

Jonsson´H.

107 Reykjav´ık

FI-00076 Espoo, Finland

UzdinV. M.

197101 Saint Petersburg

Saint Petersburg State University; Science Institute and Faculty of Physical Sciences, U. of IcelandRussian FederationScience Institute and Faculty of Physical Sciences, U. of Iceland; ITMO UniversityIrelandScience Institute and Faculty of Physical Sciences; Department of Applied Physics, Aalto UniversityIrelandITMO UniversityRussian Federation20203107202511165–77Copyright © Ivanov A.V., Bessarab P.F., Jonsson´ H., Uzdin V.M., 20252025Ivanov A.V., Bessarab P.F., Jonsson´ H., Uzdin V.M.Ivanov A.V., Bessarab P.F., Jonsson´ H., Uzdin V.M.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/468

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.

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The authors declare that there are no conflicts of interest present.