Noncollinear magnetic ordering in small chromium clusters

Abstract

We investigate noncollinear effects in antiferromagnetically coupled clusters using the general, rotationally invariant form of local spin-density theory. The coupling to the electronic degrees of freedom is treated with relativistic non-local pseudopotentials and the ionic structure is optimized by Monte-Carlo techniques. We find that small chromium clusters (N ≤ 13) strongly favor noncollinear configurations of their local magnetic moments due to frustration. This effect is associated with a significantly lower total magnetization of the noncollinear ground states, ameliorating the disagreement between Stern-Gerlach measurements and previous collinear calculations for Cr12 and Cr13. Our results further suggest that the trend to noncollinear configurations might be a feature common to most antiferromagnetic clusters.

Classical simulations of magnetic structures for chromium clusters: Size effects

“…This discrete model lets us study the magnetization of both small and large clusters containing magic and ordinary numbers of atoms, and frustration (Section 3). The agreement between our findings and those obtained with more sophisticated models [5,16] for very small clusters (containing up to 13 atoms), justifies the model and lets us predict properties of bigger clusters since our model can be exploited for bulk materials as well. Clusters at finite temperatures can also be studied with this model, which is not achievable with the quantum methods available at present.…”

“…[5], Fig.1, which has been used to generate the connectivity list for the 5-cluster; 6a and 6b are given in Fig.1 and Fig.2; 9 = one body-centered cube; 12 = one body-centered cube plus 3 adjacent cube-centers, the data are computed with the first Hamiltonian; 12' = 12 computed with the second Hamiltonian; 13 = symmetrized 12 with a fourth adjacent cube-centre; 27-cluster is build by surrounding the centre atom with 3 shells having 8, 6, and 12 atoms; 30 has 3 cube centers adjacent to the 27-cluster; 39 has a shell of 12 atoms around 27; 51 has a shell of 24 atoms around the 27-cluster. For collinearity, i.e.…”

“…The Heisenberg model describes properties that depend on the structure, not on the spin (integer or half-integer) itself [15]. The anti-ferromagnetic interaction between chromium atoms had been understood [4] to generate a problem known as non-collinear magnetic ordering, studied later by Kohl and Bertsch [5], Fujima [16] in the frame of general rotationally invariant forms of the local spin-density theory.…”

“…Clusters of a few atoms possess unique properties that cannot be observed in the corresponding bulk materials: enhanced moments [1,2], an altered temperature dependence of the magnetization [3], non-collinear effects [4,5,6,7]. A complex non-collinear nature of low temperature magnetic configurations whose stability increases with disorder, unusual scaling behaviour of the magnetic energy as a function of particle concentration, a possibility of long range magnetic order due to dipolar interactions, and complexity of the hysteresis loops have been found in [8].…”

Noncollinear magnetism in density functional calculations

“…13 Some noncollinear DFT calculations have been published dealing with magnetic crystals, 5,10 and with fourth period transition metal clusters. 11,14,15,16 In all cases, the realization of the LSDA and GGA employed in noncollinear calculations is the same as that developed for collinear spin systems.…”