Stabilization of the long-range magnetic ordering by dipolar and magnetoelastic interactions in two-dimensional ferromagnets

Long‐range order in two‐dimensional ferromagnets: Magnetoelastic effects

“…(12) and (13)) as found in Ref. [9] for quantum S = 1 ferromagnet by the Hubbard operators technique (taking S = 1 in Eqs. (14)- (16)).…”

“…The differences are: (i) in Ref. [9] the term −h d ka, appearing in Eq. (20), was discarded; and (ii) the magnetoelastic field h me ≈ 3λ 2 /4E differs from that obtained here (Eq.…”

“…The former inconsistency comes from the method of calculation: in Ref. [9] the spontaneous deformations were found by minimizing the free energy obtained solving the quantum problem, while here we used the phenomenological approach. This difference is not essential, especially at large S. Therefore, for the case of an isotropic ferromagnet Eq.…”

“…Later this statement was proved for S = 1 Heisenberg ferromagnet and XY model [8]. The influence of magnetoelastic coupling and dipolar interaction on long-range order in ferromagnets has also been studied [9].…”

Сверхтвердая Магнитная Фаза В Двумерном Изингоподобном Антиферромагнетике С Большой Одноионной Анизотропией

“…Что же касается квантовых флукту-аций, то они конечны, поскольку сходимость интеграла флуктуаций для всех однородных состояний обеспечива-ется учетом магнитодипольного взаимодействия [48][49][50][51] и влиянием внешнего магнитного поля. Поэтому тео-рема Мермина−Вагнера о реализации дальнего маг-нитного порядка в двумерных системах не применима для рассматриваемой модели.…”