romagnets is presented that clearly outlines the close connection between these two quantities. The theory is used to study the magnetocrystalline anisotropy in transitionmetal monolayers. The importance of the crystal-field energy and of the filling of the valence band is emphasized. For the first time the orbital contribution to the magnetization in monolayers is estimated; it is shown that it may produce an anisotropy in the magnetization of the order of 0. 1~~ per atom. A perturbative theory of magnetocrystalline anisotropy and orbital moment in itinerant fer-I

The long-range ordered surface alloy Bi=Ag 111 is found to exhibit a giant spin splitting of its surface electronic structure due to spin-orbit coupling, as is determined by angle-resolved photoelectron spectroscopy. First-principles electronic structure calculations fully confirm the experimental findings. The effect is brought about by a strong in-plane gradient of the crystal potential in the surface layer, in interplay with the structural asymmetry due to the surface-potential barrier. As a result, the spin polarization of the surface states is considerably rotated out of the surface plane. DOI: 10.1103/PhysRevLett.98.186807 PACS numbers: 73.20.At, 71.70.Ej, 79.60.ÿi In nonmagnetic solids, electronic states of opposite spin orientation are often implicitly taken to be degenerate (Kramers' degeneracy). However, spin degeneracy is a consequence of both time-reversal and inversion symmetry. If one of the latter is broken, the degeneracy can be lifted by, e.g., the spin-orbit (SO) interaction. This is, for example, the case in crystals that lack a center of inversion in the bulk (Dresselhaus effect) [1,2]. But also a structural inversion asymmetry, as it shows up at surfaces or interfaces, can lead to spin-split electronic states [RashbaBychkov (RB) effect] [3]. In particular, clean surfaces of noble metals show spin-split surface states, where the splitting increases with the strength of the atomic SO coupling (cf. Ag and Au in Table I). The splitting can be further enhanced by adsorption of adatoms [9][10][11][12]. Hence, using morphology and chemistry to tune the spin splitting of twodimensional electronic states is a promising path to create a new class of nanoscale structures suitable for spintronic devices. Doping GaAs by only a few percent with Bi atoms has been shown to strongly increase the spin-orbit splitting energy 0 [13]. However, a value for the Rashba-Bychkov type spin splitting has not been reported.The Au(111) L-gap surface state is the paradigm of a Rashba-Bychkov system with a spin splitting of a few tens of meV, that was investigated in detail by means of spinand angle-resolved photoelectron spectroscopy (ARPES) [14]. The nonrelativistic Hamilton operator of the spinorbit interaction,can be expressed for a two-dimensional gas of free electrons (in the xy plane) asin which the Rashba parameter R is essentially determined by the gradient of the potential V in z direction,and is the vector of Pauli matrices. This model reproduces remarkably well the very characteristic dispersion of the spin-split surface-state bands of Au(111). The spin polarizations P of the split and completely polarized (jPj 100%) electronic states lie axially symmetric within the surface plane (P ? k k ? e z ). Time-reversal symmetry requires P k k ÿP ÿk k and E k k E ÿk k . The two main contributions to the spin splitting are a strong atomic SO interaction and a potential gradient along the surface normal (z direction). By adsorption of noble gases and oxygen, the spin splitting was successfully enhanced by increasing ...

A theory of interlayer exchange coupling is presented. A detailed and comprehensive discussion of the various aspects of the problem is given. The interlayer exchange coupling is described in terms of quantum interferences due to confinement in ultrathin layers. This approach provides both a physically transparent picture of the coupling mechanism, and a suitable scheme for discussing the case of a realistic system. This is illustrated for the Co/Cu/Co(OOI) system. The cases of metallic and insulating spacers are treated in a unified manner by introducing the concept of the complex Fermi surface.

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We have calculated Heisenberg exchange parameters for bcc-Fe, fcc-Co, and fcc-Ni using the non-relativistic spin-polarized Green function technique within the tight-binding linear muffin-tin orbital method and by employing the magnetic force theorem to calculate total energy changes associated with a local rotation of magnetization directions. We have also determined spinwave stiffness constants and found the dispersion curves for metals in question employing the Fourier transform of calculated Heisenberg exchange parameters. Detailed analysis of convergence properties of the underlying lattice sums was carried out and a regularization procedure for calculation of the spin-wave stiffness constant was suggested. Curie temperatures were calculated both in the mean-field approximation and within the Green function random phase approximation. The latter results were found to be in a better agreement with available experimental data.PACS numbers: 71.15.-m, 75.10.-b, 75.30.Ds of the relevant physical quantities such as spin-wave stiffness, Curie temperature T C , etc., for comparison with experimental data.It is therefore of a great importance to develop an ab initio, parameter-free, scheme for the description of ferromagnetic metals at T > 0 K. Such an approach must be able to go beyond the ground state and to take into account excited states, in particular the magnetic excitations responsible for the decrease of the magnetization with temperature and for the phase transition at T = T C . Although density functional theory can be formally extended to non-zero temperature, there exists at present no practical scheme allowing to implement it. One therefore has to rely on approximate approaches. The approximations to be performed must be chosen on the basis of physical arguments.In itinerant ferromagnets, it is well known that magnetic excitations are basically of two different types: (i) Stoner excitations, in which an electron is excited from an occupied state of the majority-spin band to an empty state of the minority-spin band and creates an electron-hole pair of triplet spin. They are associated with longitudinal fluctuations of the magnetization; (ii) the spin-waves or magnons, which correspond to collective transverse fluctuations of the direction of the magnetization. Near the bottom of the excitation spectrum, the density of states of magnons is considerably larger than that of corresponding Stoner excitations, so that the thermodynamics in the low-temperature regime is completely dominated by magnons and Stoner excitations can be neglected. Therefore it seems reasonable to extend this approximation up to the Curie temperature, and to estimate the latter by neglecting Stoner excitations. This is a good approximation for ferromagnets with a large exchange splitting such as Fe and Co, but it is less justified for Ni which has a small exchange splitting.The purpose of the present paper is to describe the spin-wave properties of transition metal itinerant ferromagnets at ab initio level. With thermodynamic propertie...

We discuss the anomalous Hall effect in a two-dimensional electron gas subject to a spatially varying magnetization. This topological Hall effect (THE) does not require any spin-orbit coupling, and arises solely from Berry phase acquired by an electron moving in a smoothly varying magnetization. We propose an experiment with a structure containing 2D electrons or holes of diluted magnetic semiconductor subject to the stray field of a lattice of magnetic nanocylinders. The striking behavior predicted for such a system (of which all relevant parameters are well known) allows to observe unambiguously the THE and to distinguish it from other mechanisms. PACS numbers: 73.20.Fz; 72.15.Rn; 72.10.Fk After half a century of theoretical efforts, the Hall effect of ferromagnets (usually called anomalous or extraordinary Hall effect) remains a puzzling and controversial topic. Until recently, it was considered that it originates from the combined effect of exchange and spin-orbit (SO) interactions. Two mechanisms of anomalous Hall effect (AHE) have been identified (the skew scattering [1,2] and side-jump [3]) and studied thoroughly [4]. Recently, a new point of view has been proposed [5], in which the AHE is expressed in terms of a Berry curvature in momentum space. However, one should note that a generally accepted theory treating on an equal footing all the above mentioned contributions to the SO-induced AHE is still missing.Recently, it has been suggested that (in addition to the above mentioned SO-induced mechanism) a new mechanism may give rise to a non-vanishing Hall effect in ferromagnets having a topologically non-trivial (chiral) spin-texture, such as manganites or pyrochlore-type compounds [6]. To distinguish this mechanism from the SObased mechanism, we shall refer to it hereafter as the topological Hall effect (THE).Several theoretical papers have been devoted to the THE. In order to explain the AHE observed in manganites, a model of 3D ferromagnet with thermally excited skyrmion strings (topological dipoles)has been proposed [7], showing that a THE can be induced by the Berry phase [8] related to the spatial variation of magnetization in the vicinity of the string. The case of disordered ferromagnets in the limit of small exchange splitting has been addressed in Ref. 9. In both cases, in order to get a net topological field (or chirality), the SO-coupling must be invoked. Even when the net topological field vanishes, a nonvanishing THE may be obtained, as discussed for a 2D kagomé lattice or a 3D pyrochlore lattice [10].All the above mentioned discussions of the THE concern systems with spin-chirality at the microscopic scale (e.g., pyrochlore lattice) or due to skyrmion-strings. In both cases, quantitative experimental information on the chirality is not easily available. Furthermore, the SOmechanism is usually also present, which makes complicate the quantitative interpretation of the observations.In the present Letter, we propose to investigate the THE in nanostructures, namely in a 2D electron (or hole) ...

The structure and properties of a geometrically constrained magnetic wall in a constriction separating two wider regions are studied theoretically. They are shown to differ considerably from those of an unconstrained wall, so that the geometrically constrained magnetic wall truly constitutes a new kind of magnetic wall, besides the well known Bloch and Néel walls. In particular, the width of a constrained wall can become very small if the characteristic length of the constriction is small, as is actually the case in an atomic point contact. This provides a simple, natural explanation for the large magnetoresistance observed in ferromagnetic atomic point contacts. PACS numbers: 75.60.Ch, 75.70.Kw, 75.70.Pa The investigation of magnetic nanostructures is one of the major current subjects in magnetism. This interest is stimulated, on one hand, by the great progress in nanofabrication techniques and magnetic characterization methods and, on the other hand, by the perspective of technological applications for magnetic storage of information of unprecedented density.A major question to be addressed in this field of research is: How does the micromagnetic structure (i.e., domains, walls, etc.) respond to geometrical constraints on the nanometer scale?In an unconstrained system such as in a bulk ferromagnet, as first pointed out by Bloch, the wall structure is determined by a competition between exchange and anisotropy energies [1]. The exact structure of the Bloch wall has been calculated by Landau and Lifshitz [2]. In a ferromagnetic thin film with in-plane easy magnetization axis, as shown by Néel [3], the dipolar interaction leads to a new kind of wall, known as a Néel wall, in which the structure is determined by a competition between exchange, anisotropy, and dipolar energies.In this Letter, I consider the problem of the structure and energy of a magnetic wall in a constriction separating two regions of wider cross section. This encompasses various situations of great physical interest such as a narrow constriction fabricated in a magnetic ultrathin film by lithographic techniques, or a constriction in a wire.I point out that when the cross section of the constriction is much smaller than that of the wide region, the structure of the wall becomes almost independent of the material parameters such as magnetization, exchange stiffness, and anisotropy constant and is determined mostly by the geometry of the constriction. The wall energy consists mostly of exchange energy. Thus, geometrically constrained magnetic walls appear as a new kind of magnetic walls, with properties completely different from those of Bloch and Néel walls. In particular, the width of the geometrically constrained magnetic walls is essentially given by the length of the constriction, which can be considerably smaller than the width of a Bloch or Néel wall.In the limit of a point contact of atomic dimensions, the width of the wall would also be of atomic dimensions. This fact has important physical consequences: in particular, the contribution ...

Effective pair exchange interactions between Mn atoms in III-V and group-IV diluted magnetic semiconductors are determined from a two-step first-principles procedure. In the first step, the self-consistent electronic structure of a system is calculated for a collinear spin structure at zero temperature with the substitutional disorder treated within the framework of the coherent-potential approximation. The effective exchange pair interactions are then obtained in a second step by mapping the total energies associated with rotations of magnetic moments onto an effective classical Heisenberg Hamiltonian using the magnetic force theorem and one-electron Green functions. The formalism is applied to Ga 1Ϫx Mn x As alloys with and without As antisites, and to Ge 1Ϫx Mn x alloys recently studied experimentally. A detailed study of the behavior of pair exchange interactions as a function of the distance between magnetic atoms as well as a function of the concentrations of the magnetic atoms and compensating defects is presented. We have found that due to disorder and the half-metallic character of the system the pair exchange interactions are exponentially damped with increasing distance between the Mn atoms. The exchange interactions between Mn atoms are ferromagnetic for distances larger than the ones corresponding to the averaged nearest-neighbor Mn-Mn distance. The pair exchange interactions are also reduced with increasing concentrations of the Mn atoms and As antisites. As a simple application of the calculated exchange interactions we present mean-field estimates of Curie temperatures.