The spectra of the E-edge absorption and the magnetic circular dichroism (MCD) for ferromagnetic Ni and Fe are calculated on the basis of a tight-binding approximation including the spin-orbit interaction. The calculated spectra are in good agreement with the experiments and the previous band calculations near the photothreshold.
Based on first-principles vector spin-density total-energy calculations of the magnetic and electronic structure of Cr and Mn transition-metal monolayers on the triangular lattice of a (111) oriented Cu surface, we propose for Mn a three-dimensional noncollinear spin structure on a two-dimensional triangular lattice as magnetic ground state. This new spin structure is a multiple spin-density wave of three row-wise antiferromagnetic spin states and comes about due to magnetic interactions beyond the nearest neighbors and due to higher order spin interactions (i.e., four spin). The magnetic ground state of Cr is a coplanar noncollinear periodic 120 ± Néel structure. DOI: 10.1103/PhysRevLett.86.1106 In the frontier field of nanomagnetism, understanding the effect of frustration on magnetic properties is one of the current key issues. Exchange bias [1], for example, is a technologically important effect for the magnetic recording industry and the magnetoelectronics, for which frustration plays an important role. In magnetic systems the term frustration refers to the inability to satisfy the competing exchange interactions between neighboring atoms. Frustration is known to be responsible for a number of diverse phenomena such as spin-glass behavior, noncollinear and incommensurate magnetic order, and unusual critical properties. One of the most evident examples of frustration is the so-called geometric frustration of an antiferromagnet on a triangular lattice. In fact, triangular antiferromagnets can be crystallized, e.g., in the form of stacked antiferromagnets. Typical compounds are RbNiCl 3 , VCl 2 , or CuCrO 2 [2], and they are localized spin systems. The magnetic properties of these triangular antiferromagnets are almost exclusively described within the framework of model Hamiltonians, the simplest of which is the classical Heisenberg modelwhere J ij describes the pairwise (two-spin) exchange interaction between spins at lattice sites i and j. S is the classical spin vector related to the magnetic moment vector m of localized atomic moments m 2gm B S. Localized spin systems are often well described by restricting the interaction to the antiferromagnetic nearestneighbor (n.n.) one, J ij 0 for all i, j, except for J ͑n.n.͒ J 1 (J 1 , 0). In this case the minimum energy configuration is the periodic 120 ± Néel state in the ͑ p 3 3 p 3 ͒R30 ±[3] unit cell (cf. Fig. 1b), a two-dimensional noncollinear structure with three atoms per surface unit cell, which consists of coplanar spins forming 6120 ± angles between nearest neighbors.Until now there has been no investigation of twodimensional (2D) itinerant antiferromagnets on a triangular lattice beyond model Hamiltonians. In itinerant magnets, the electrons that are responsible for the formation of the magnetic state do participate in the formation of the Fermi surface and hop across the lattice. Thus, it is by no means clear how far a short-ranged n.n. interaction or even how far the Heisenberg model can go in giving a sufficiently good description of the physics of i...
We study the orbital moment and the magnetic circular dichroism ͑MCD͒ at the K edge for ferromagnetic Co on the basis of a tight-binding model including the spin-orbit interaction. We find that the MCD spectra have negative values near the photothreshold up to ϳ7 eV in agreement with the experiment. The spin-orbit interaction of the 3d states plays a dominant role in generating the MCD spectra, similar to the previous study for Ni and Fe. We show that a positive peak grows at the vicinity of the photothreshold in the MCD spectra with decreasing values of the occupied electron number from that for Co within the fcc structure. When the atomic value is used for the spin-orbit coupling coefficient, the intensity of the MCD spectra and the orbital moment are nearly half the experimental values. We remove this discrepancy by taking account of the enhancement effect due to the intra-atomic Coulomb interaction.
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