In order to study spin-wave excitations of itinerant ferromagnets a relativistic first-principles method based on the adiabatic approach is presented. The derivatives of the free energy up to second order with respect of the polar and azimuthal angles are derived within the framework of the magnetic force theorem and the fully relativistic Korringa-Kohn-Rostoker method. Exchange and spin-orbit coupling are thus incorporated on equal footing in the Hamiltonian. Furthermore, a detailed comparison to classical spin Hamiltonians is given and it is shown that the magnetocrystalline anisotropy energy contains contributions from both the on-site anisotropy and the off-site exchange coupling terms. The method is applied to an Fe monolayer on Cu͑001͒ and Au͑001͒ surfaces and for a Co monolayer on Cu͑001͒. The calculations provide with the gap at zero wave number due to the spin-orbit coupling and uniaxial anisotropy energies in good agreement with the results of the band energy difference method. It is pointed out that the terms in the spin-wave Hamiltonian related to the mixed partial derivatives of the free energy, absent within a nonrelativistic description, introduce an asymmetry in the magnon spectrum with respect to two in-plane easy axes. Moreover, in the case of an in-plane magnetized system the long-wavelength magnons are elliptically polarized due to the difference of the second-order uniaxial and fourth-order in-plane magnetic anisotropy.

We present a first-principles theory of the variation of magnetic anisotropy, K, with temperature, T, in metallic ferromagnets. It is based on relativistic electronic structure theory and calculation of magnetic torque. Thermally induced local moment magnetic fluctuations are described within the relativistic generalization of the disordered local moment theory from which the T dependence of the magnetization, m, is found. We apply the theory to a uniaxial magnetic material with tetragonal crystal symmetry, L1 0-ordered FePd, and find its uniaxial K consistent with a magnetic easy axis perpendicular to the Fe/ Pd layers for all m and proportional to m 2 for a broad range of values of m. This is the same trend that we have previously found in L1 0-ordered FePt and which agrees with experiment. We also study a magnetically soft cubic magnet, the Fe 50 Pt 50 solid solution, and find that its small magnetic anisotropy constant K 1 rapidly diminishes from 8 eV to zero. K 1 evolves from being proportional to m 7 at low T to m 4 near the Curie temperature. The accounts of both the tetragonal and cubic itinerant electron magnets differ from those extracted from single ion anisotropy models and instead receive clear interpretations in terms of two ion anisotropic exchange.

We raise the possibility that the chiral degeneracy of the magnons in ultrathin films can be lifted due to the presence of Dzyaloshinskii-Moriya interactions. By using simple symmetry arguments, we discuss under which conditions such a chiral asymmetry occurs. We then perform relativistic first principles calculations for an Fe monolayer on W(110) and explicitly reveal the asymmetry of the spin-wave spectrum in case of wave-vectors parallel to the (001) direction. Furthermore, we quantitatively interpret our results in terms of a simplified spin-model by using calculated DzyaloshinskiiMoriya vectors. Our theoretical prediction should inspire experiments to explore the asymmetry of spin-waves, with a particular emphasis on the possibility to measure the Dzyaloshinskii-Moriya interactions in ultrathin films. It is by now well-established that relativistic effects play a fundamental role in the magnetism of nanostructures, in particular, for thin films and finite deposited nanoparticles. Over the past two decades, a vast number of experimental and theoretical studies has been published to explore related phenomena such as magnetic anisotropies, spin-reorientation phase transitions, and non-collinear magnetic orderings. [1,2,3,4,5] The antisymmetric exchange interaction between two magnetic atoms,, where M i and M j denote the spin-moments of the atoms labeled by i and j, has been proposed 50 years ago by Dzyaloshinskii [6] and Moriya [7]. The D ij is called the Dzyaloshinskii-Moriya vector being identical to zero if the sites i and j experience inversion symmetry. It has been put forward just about ten years ago that an enhanced Dzyaloshinskii-Moriya interaction (DMI) at surfaces or interfaces can give rise to novel phenomena in nanomagnetism such as to noncollinear interlayer coupling, [8,9] to unidirectional competing magnetic anisotropies, [10] or to stabilization of non-collinear (chiral) magnetic orderings. [11,12] A breakthrough on this field happened when the resolution of spin-polarized scanning tunneling microscopy enabled to detect magnetic pattern formation on the atomic scale in monolayer-thin films. Such periodic modulations have been observed for Mn monolayers deposited on W(110) and W(001) and, could successfully be interpreted in terms of a combination of relativistic first principles calculations and a simple micromagnetic model as the consequence of large DM interactions. [13,14]. Using the same theoretical basis it was even possible to explain the homochirality of the domain walls in two monolayers of Fe on W(110), [15] in agreement with previous experimental observation. [16] In this Letter, we investigate a consequence of the DM interactions on the spin-wave spectra in ultrathin films, not yet explored in the literature. We argue that the chiral degeneracy of the spin-wave (SW) spectrum can be lifted due to the Dzyaloshinskii-Moriya interactions and discuss under which conditions such a chiral asymmetry occurs. Based on relativistic first principles calculations, we explicitly evidence the asy...

Theoretical predictions of the magnetic anisotropy of antiferromagnetic materials are demanding due to a lack of experimental techniques which are capable of a direct measurement of this quantity. At the same time it is highly significant due to the use of antiferromagnetic components in magneto-resistive sensor devices where the stability of the antiferromagnet is of upmost relevance. We perform an ab-initio study of the ordered phases of IrMn and IrMn3, the most widely used industrial antiferromagnets. Calculating the form and the strength of the magnetic anisotropy allows the construction of an effective spin model, which is tested against experimental measurements regarding the magnetic ground state and the Néel temperature. Our most important result is the extremely strong second order anisotropy for IrMn3 appearing in its frustrated triangular magnetic ground state, a surprising fact since the ordered L12 phase has a cubic symmetry. We explain this large anisotropy by the fact that cubic symmetry is locally broken for each of the three Mn sub-lattices. While the magnetic anisotropy (MA) of ferromagnets is a well investigated quantity, both experimentally as well as theoretically, it is much less understood in case of antiferromagnets. This lack of knowledge is on the one hand due to a lack of experimental techniques which are capable of a direct measurement of this quantity. On the other hand, theoretical first principles calculations of magnetic anisotropy effects are quite challenging as they require the use of fully relativistic spin density functional theory.Interest in the MA of antiferromagnets comes from the fact that these compounds are important components of GMR sensors used, e.g., in hard disc read heads. Antiferromagnetic materials are employed in these devices to form antiferromagnet/ferromagnet bilayers exhibiting exchange bias 1 , a shift of the hysteresis loop of the ferromagnet, providing a pinned layer which fixes the magnetization of the reference layer of a GMR sensor. The stability of the antiferromagnet is most crucial for the stability of exchange bias and hence the functioning of the device 2,3 . Industrially the antiferromagnet IrMn is widely used because of the large exchange bias and thermal stability that can be obtained with this material.From experimental investigations of the exchange bias effect it is concluded that IrMn must have a rather large MA. Recent estimates of the MA of IrMn concerned the mean blocking temperature T B , the temperature at which the exchange bias shift changes sign upon thermal activation. From T B the intrinsic MA can be inferred if the particle size distribution is known; such a procedure has recently been reported and the room temperature MA energy of IrMn was estimated at 5.5×10 6 erg/cc 4 and even 2.8×10 7 erg/cc 5 depending on the seed layer and, consequently, the texture of the IrMn.In this letter, we address several features of the MA of IrMn alloys starting from first principles. In terms of simple symmetry considerations we predict the form...