Classical simulations of magnetic structures for chromium clusters: Size effects

Abstract

Classical (Heisenberg) simulations show that the total magnetization of the lowest-energy states of clusters made of antiferromagnetically coupled chromium atoms is planar, rather than collinear, depending on the arrangement of the atoms. Although the model Hamiltonian is not restrictive, many cluster configurations of various numbers of atoms do not use all three directions for the spins. This result confirms the conclusion drawn from the local-spin DFT calculation by Kohl and Bertsch that clusters of N ≤ 13 have non-collinear magnetic moments. The present simulations show non-collinear spin ordering also for bigger clusters, designed to be as spherical as possible following the bcc arrangement, when atoms interact both with the nearest and next-nearest neighbours. Depending on the signs of the coupling constants frustration appears. The advantage of the discrete model, despite the simplicity, is that very large clusters and magnetization at finite temperatures can be studied. This model predicts that clusters with specific numbers of atoms interacting only with the nearest neighbours have collinear spins as in the bulk. We also apply the model to simulate the destruction of the anti-ferromagnetic ordering by thermal fluctuations. This model shows no unique magnetization of mixed F e 0.33 Cr 0.67 , which is consistent with experimental observations.

Theory of ground states for classical Heisenberg spin systems VI

“…In Eq. ( 124) we have inserted the previous results for M (2) , E (2) , and E (4) , see ( 76), (79), and ( 116), together with (120).…”

“…We assume that the eigenspace E 0 of  µν (λ (0) , γ 0 ) corresponding to the lowest eigenvalue x 0 is three-dimensional and hence the subspace E 1 according to (48) will be two-dimensional. Let (ξ (1) , ξ (2) ) be a fixed orthonormal basis in E 1 .…”

“…According to (136) these eigenvectors y (1,a) are orthogonal to 1 and hence lie in E 1 . They can hence be expanded into the orthonormal basis (ξ (1) , ξ (2) ):…”

“…It follows that the vector κ (2) lies in the subspace spanned by ran(K) and 1 and hence is orthogonal to E 1 or, equivalently, to ξ (1) and ξ (2) :…”

Multicanonical sampling of the space of states of ℋ(2, n)-vector models

“…The wide spectrum of applied and fundamental problems, general function, immense field of applications, elegance, and obvious simplicity of the WL method have been the reason for the widest variety of its applications in statistical physics, biophysics, and other fields starting from spin systems [2,[4][5][6][7][8][9][10][11], quantum systems [12], atomic clusters [13,14], dipole [15] and spin [16] glasses, liquid crystals [17], fluids [18], XY model [19], the Blume-Capel model [20], the Potts model [21], biomolecules [22], protein folding [23], polymer films [24], as well as in many other fields of science, for example, in solving optimization problems [25], development of combinatorial number theory [26], and others.…”