It is demonstrated by means of density functional and ab-initio quantum chemical calculations, that transition metal -carbon systems have the potential to enhance the presently achievable area density of magnetic recording by three orders of magnitude. As a model system, Co 2 -benzene with a diameter of 0.5 nm is investigated. It shows a magnetic anisotropy in the order of 0.1 eV per molecule, large enough to store permanently one bit of information at temperatures considerably larger than 4 K. A similar performance can be expected, if cobalt dimers are deposited on graphene or on graphite. It is suggested that the subnanometer bits can be written by simultaneous application of a moderate magnetic and a strong electric field. PACS numbers: 31.15.es, 75.30.Gw, 75.75.+a Keywords: applications of density functional theory, magnetic anisotropy, magnetic properties of nanostructures 1 Long-term magnetic data storage requires that spontaneous magnetization reversals should occur significantly less often than once in ten years. This implies that the total magnetic anisotropy energy (MAE) of each magnetic particle should exceed 40 kT , 1 where k is the Boltzmann constant and T is the temperature. Among the elemental ferromagnets (Fe, Co, Ni, and Gd), cobalt metal shows the highest MAE, about 0.06 meV per atom in the hexagonal close packed structure. Thus, Co is the main ingredient of magnetic data storage materials at present. At room temperature, data loss due to fluctuations is avoided, if a Co grain contains not less than 40 k · 300 K/0.06 meV ≈ 15,000 atoms. In fact, the grain diameter of contemporary Co(Cr,Pt,SiO 2 ) recording media is close to 8 nm, each grain containing about 50,000 atoms and each bit being composed of some dozen grains.2 The grain size could be considerably reduced by using the intermetallic compounds FePt or CoPt with record MAE of almost 1 meV per atom in their structurally ordered L1 0 bulk phase. It is, however, hard to achieve the required ordered structure in nano-particles. 3Obviously, a further reduction of the bit size is primarily limited by the value of MAE per atom. Recent efforts to enhance this value were focused on single atoms or small clusters deposited on the surface of heavy metals. This approach combines two ideas: 4 Firstly, the magnitude of MAE is related to the size of the orbital moments. The latter are quenched for highly coordinated atoms but can be large if the coordination is low. Secondly, the magnitude of MAE is related to the strength of spin-orbit coupling which grows with atomic number. Considerable progress was achieved in this way by deposition of single Co atoms on a Pt surface, yielding a record MAE of 9 meV per Co atom. 5 Unfortunately, clusters of several Co atoms on Pt show a much smaller MAE per atom, roughly inversely proportional to the number of atoms. 5More recently, the magnetic properties of transition metal dimers came into the focus of interest. 6,7,8,9 Isolated magnetic dimers are the smallest chemical objects that possess a magnetic a...

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The effect of epitaxial strain on the cation distribution in spinel ferrites CoFe 2 O 4 and NiFe 2 O 4 is investigated by GGAþU total energy calculations. We obtain a very strong (moderate) tendency for cation inversion in NiFe 2 O 4 (CoFe 2 O 4 ), in agreement with experimental bulk studies. This preference for the inverse spinel structure is reduced by tensile epitaxial strain, which can lead to strong sensitivity of the cation distribution on specific growth conditions in thin films. Furthermore, we obtain significant energy differences between different cation arrangements with the same degree of inversion, providing further evidence for recently proposed short range B site order in [3][4][5][6][7] These applications require the growth of high quality thin films of CFO and NFO on suitable substrates. However, the electronic and magnetic properties of the corresponding films can depend strongly on substrate, film thickness, and specific preparation conditions, and eventually differ drastically from the corresponding bulk materials. For example, both increased and decreased saturation magnetizations have been reported for thin films of CFO and NFO grown on different substrates at different growth temperatures. [8][9][10] It has been suggested that the large increase in magnetization observed in some NFO films is due to the presence of Ni 2þ on the tetrahedrally coordinated cation sites of the spinel crystal structure. 8,9 The spinel crystal structure (space group Fd 3m) contains two inequivalent cation sites, the tetrahedrally coordinated A sites (T d ) and the octahedrally coordinated B sites (O h ). In the normal spinel structure, A and B sites are both occupied by a unique cation species. In the inverse spinel structure, the more abundant cation species (Fe 3þ in the present case) occupies the tetrahedral A sites and 50% of the octahedral B sites, whereas the remaining 50% of B sites are occupied by the other cation species (Co 2þ or Ni 2þ in the present case). In practice, site occupancies can vary between these two cases, depending on specific preparation conditions, and the inversion parameter k measures the fraction of less abundant cations on the B site sublattice, i.e., k ¼ 0 for the normal spinel structure and k ¼ 1 for complete inversion. Since in the ferrimagnetic Néel state of CFO and NFO, the magnetic moments of the A and B sublattices are oriented antiparallel to each other, small changes in k can lead to significant changes in magnetization.Here, we use first principles density functional theory to clarify whether epitaxial strain can influence the distribution of cations over the two different cation sites in CFO and NFO. Such epitaxial strain is generally incorporated in thin films due to the mismatch of lattice constants between the film material and the substrate, and often leads to drastic changes of properties compared to the corresponding bulk materials. 2 In order to accommodate different arrangements of cations on the tetrahedral and octahedral sites in our calculations, corresponding...

The inverse spinels CoFe2O4 and NiFe2O4, which have been of particular interest over the past few years as building blocks of artificial multiferroic heterostructures and as possible spin-filter materials, are investigated by means of density functional theory calculations. We address the effect of epitaxial strain on the magneto-crystalline anisotropy and show that, in agreement with experimental observations, tensile strain favors perpendicular anisotropy, whereas compressive strain favors in-plane orientation of the magnetization. Our calculated magnetostriction constants λ100 of about −220 ppm for CoFe2O4 and −45 ppm for NiFe2O4 agree well with available experimental data. We analyze the effect of different cation arrangements used to represent the inverse spinel structure and show that both LSDA+U and GGA+U allow for a good quantitative description of these materials. Our results open the way for further computational investigations of spinel ferrites.

Dimers are the smallest chemical objects that show magnetic anisotropy. We focus on 3d and 4d transition metal dimers that have magnetic ground states in most cases. Some of these magnetic dimers have a considerable barrier against re-orientation of their magnetization, the so-called magnetic anisotropy energy, MAE. The height of this barrier is important for technological applications, as it determines, e.g., the stability of information stored in magnetic memory devices. It can be estimated by means of relativistic density functional calculations. Our approach is based on a full-potential local-orbital method (FPLO) in a four-component Dirac-Kohn-Sham implementation. Orbital polarization corrections to the local density approximation are employed. They are discussed in the broader context of orbital dependent density functionals. Ground state properties (spin multiplicity, bond length, harmonic vibrational frequency, spin- and orbital magnetic moment, and MAE) of the 3d and 4d transition metal dimers are evaluated and compared with available experimental and theoretical data. We find exceptionally high values of MAE, close to 0.2 eV, for four particular dimers: Fe(2), Co(2), Ni(2), and Rh(2).

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We present calculations of magnetostriction constants for the spinel ferrites CoFe2O4 and NiFe2O4 using density functional theory within the GGA+U approach. Special emphasis is devoted to the influence of different possible cation distributions on the B site sublattice of the inverse spinel structure on the calculated elastic and magnetoelastic constants. We show that the resulting symmetrylowering has only a negligible effect on the elastic constants of both systems as well as on the magnetoelastic response of NiFe2O4, whereas the magnetoelastic response of CoFe2O4 depends more strongly on the specific cation arrangement. In all cases our calculated magnetostriction constants are in good agreement with available experimental data. Our work thus paves the way for more detailed first-principles studies regarding the effect of stoichiometry and cation inversion on the magnetostrictive properties of spinel ferrites.

Theoretical studies on M 13 (M = Fe, Co, Ni) and M 13 Pt n (for n = 3, 4, 5, 20) clusters including the spin-orbit coupling are done using density functional theory. The magnetic anisotropy energy (MAE) along with the spin and orbital moments are calculated for M 13 icosahedral clusters. The angle-dependent energy differences are modelled using an extended classical Heisenberg model with local anisotropies. From our studies, the MAE for Jahn-Teller distorted Fe 13 , Mackay distorted Fe 13 and nearly undistorted Co 13 clusters are found to be 322, 60 and 5 µeV/atom, respectively, and are large relative to the corresponding bulk values, (which are 1.4 and 1.3 µeV/atom for bcc Fe and fcc Co, respectively.) However, for Ni 13 (which practically does not show relaxation tendencies), the calculated value of MAE is found to be 0.64 µeV/atom, which is approximately four times smaller compared to the bulk fcc Ni (2.7 µeV/atom). In addition, MAE of the capped cluster (Fe 13 Pt 4 ) is enhanced compared to the uncapped Jahn-Teller distorted Fe 13 cluster.