Magnetism of small Cr clusters: Interplay between structure, magnetic order, and electron correlations

Abstract

The magnetic properties of small Cr N clusters ͑N Յ 6͒ are investigated in the framework of densityfunctional theory. The interplay between electron correlations, cluster structure, and magnetic order is quantified by performing fully spin-unrestricted calculations allowing for noncollinear spin arrangements within both the local-spin-density approximation ͑LSDA͒ and the generalized-gradient approximation ͑GGA͒. The possible transition or saddle-point states are identified by determining the vibrational frequencies from diagonalizing the dynamical matrix. In agreement with previous studies, a dimer-based growth pattern is found in all considered low-lying isomers with very short equilibrium bond lengths ͑typically d eq GGA = 1.55-1.65 Å͒ alternating with relative long ones ͑typically d eq GGA = 2.75-2.85 Å͒ in the relaxed geometries. Strong local magnetic moments ជ i are, in general, obtained for the relaxed geometries ͑e.g., ͉ i GGA ͉Ӎ2 B in Cr 4 ͒, which show a collinear magnetic order with antiparallel ͑parallel͒ alignment of the ជ i along the short ͑long͒ bonds. In contrast to the GGA, the LSDA yields vanishing magnetization density in some cases ͉͑ i LSDA ͉ =0 ∀ i for N = 2 and 4͒. Despite quantitative differences, both LSDA and GGA functionals always yield collinear ground-state solutions for the fully relaxed structures. In fact, noncollinear spin arrangements are found only for particular symmetric ͑nondimerized͒ geometries. However, the structures are not local minima and involve considerably large excitation energies. The results clearly indicate that the magnetic frustration, which one would physically expect in compact antiferromagnetic spin systems, is solved by dimerization rather than by noncollinearity of the local moments.

Noncollinear magnetism in transition metal nanostructures: Exchange interaction and local environment effects in free and deposited clusters

“…A well-known example is the dimerization of Cr clusters. 31,32 By taking the optimal structures obtained in DFT, 9,30,33 SCTB calculations yield similar results. It is interesting to notice that for n d = 7, we found other NC solutions with higher energy.…”

“…It should be noticed, however, that noncollinearity is not the only mechanism for solving such magnetic frustration effects. Indeed, previous DFT calculations on Cr clusters 31,32 have shown that the actual ground state of Cr N magnetic corresponds to strongly dimerized structures with collinear local moments that are antiparallel along the short nearest-neighbors bonds (NN's) and eventually parallel along long bonds (next NN's). It is important to remark that the SCTB approach reproduces these trends very well.…”

“…Furthermore, it is important to remark that our NC results are in agreement with previous DFT results for the equilateral triangle with approximately bulk NN distances. 32,33 The general trends on the onset of NC magnetism found in the triangle cannot be extended straightforwardly to larger more complex triangular geometries, since the onset of noncollinear magnetism is often the result of subtle systemspecific details of the electronic structure, which preclude easy generalizations. 34 Figure 3 shows representative collinear and noncollinear magnetic arrangements obtained for a five-atom TM clus- ter having regular triangular-bipyramid structure.…”

Magnetism of Cr Impurities Embedded in Cu fcc Matrix: Density Functional Calculations

“…Ruiz-Diaz et al [6] have studied free Cr clusters using Vienna ab initio simulation package [21,22], they studied dimers, trimers, tetramers, pentamers and hexamer, using Local Spin Density Approximation of Vosko-Wilk-Nussair (LSDA-VWN) [23] and Generalized Gradient Approximation of Perdew-Burke-Ernzerhof (GGA-PBE) [17]. With the aim of comparing our results with those of Ruiz-Diaz et al, we show the results in Figs.…”

“…Its half-filled valence configuration leads to a large magnetic moment and strong interatomic bond [5]. Chromium clusters have been studied extensively in various configurations: free (pure [6] and doped with other atoms [7]) and deposited (in magnetic [8,9] and non-magnetic substrates [10,11]). Also experimental work was carried out with free [12] and deposited clusters on gold [13].…”