Quantum fluctuations in ferromagnetic and antiferromagnetic spin-spiral structures

Abstract Quantum fluctuations in two-dimensional S = 1 ∕ 2 ferromagnetic and antiferromagnetic spin-spiral structures are studied by the double-time Green’s function method. Independent exchange and Dzyaloshinsky-Moriya interactions in the two film directions ( ∥ and ⊥ ) lead to different spin-spiral structures characterized by the pitch angles θ ∥ and θ ⊥ . Quantum fluctuations occur under the influence of Dzyaloshinsky-Moriya interaction, and increase when going from the ferromagnetic to one of the three antiferromagnetic states (Neel or collinear antiferromagnet) θ = 0 ∘ → 18 0 ∘ . Thereby, the quantum fluctuations are quantified by the decrease of the magnetization M = 〈 S z 〉 . Despite the expected growth of the quantum fluctuations with increasing θ , a drastic rise of quantum fluctuations is investigated when the Dzyaloshinsky-Moriya interaction D → η , η ∈ { ∥ , p e r p } , along one direction, either ∥ or ⊥ , becomes dominant. In this case, the 2D character of the system becomes quasi 1D, and the magnetization breaks down. In that scenario, the magnetization M gets comparable to the magnetization value of a 1D spin chain. To understand the occurrence of the quantum fluctuations, the change of the eigenenergies with changing Dzyaloshinsky-Moriya interactions is investigated.