Fast ab initio methods for the calculation of adiabatic spin wave spectra in complex systems

The interpretation of the physics of magnets with reduced dimensionality often requires information on the spin wave excitations at arbitrary wavelengths which is generally hard to obtain experimentally. Two powerful methods for the ab initio calculation of adiabatic spin-wave spectra are introduced, a frozen-magnon-torque method for systems with large exchange fields and a transverse-susceptibility method which may be used also for materials with smaller exchange fields. The efficiency of both methods results from the fact that the number of calculations required to obtain the spin-wave spectrum scales linearly with the number of basis atoms in the unit cell. Results are given for Fe, Co, Ni, permalloy Ni 3Fe, and CoFe, materials which are often used for thin-film technologies. DOI: 10.1103/PhysRevB.63. 100401 PACS number~s! : 75.30. Ds, 71.15. Ap, 71.15. Mb In recent years magnetism in reduced dimensionality has become extremely important because of the very rapid development of thin-film technologies for basic research and for applications in magnetotransport. Thereby, spin excitations like single-particle Stoner excitations or collective spinwave excitations 1 play a central role for thermostatic phenomena, but also for the transport phenomena because the spin-dependence of the inelastic mean free path of an excited hot electron is determined by spin-flip exchange scattering at these excitations. 2,3 A quantitative analysis of the various phenomena requires information about the spin-wave spectra which is often difficult to obtain experimentally. One example is the spin-dependent transport of hot electrons in a spin-valve transistor where in the ‘‘bulk’’ of the metallic components spin-flip exchange scattering at spin waves of all wavelengths occurs. Because the energies of shortwavelength spin waves in 3d transition metals are very large, it is difficult and costly to investigate the bulk spin wave spectra of various 3d magnets used in the devices by neutron-scattering experiments. A second example is the generation of magnons by hot electrons at the interfaces between the insulating barrier and the magnetic electrodes of magnetic tunnel junctions which is responsible for the reduction of the magnetoresistance. 4 Because the magnon spectrum at such an interface is hardly accessible by experiments, the quantitative analysis of the data so far must manage with a simple modelling of the spin-wave spectra by a Debye model. 4 Finally, the short-wavelength spin waves at surfaces or in ultrathin magnetic filmsof few magnetic monolayers contribute to the spin polarized electron energy loss spectrum. 3 Whereas low-energy spin waves in ultrathin films can be studied by ferromagnetic resonance 5 or by Brillouin scattering experiments, 6 the direct experimental determination of the short-wavelength spectrum is again difficult. From the above discussion it becomes obvious that a theoretical determination of spin wave spectra would be extremely helpful for a quantitative analysis of experimental data, especially for complex situations like compounds, surfaces and interfaces. Thereby, the methods of the ab initio electron theory have to be used to cope with the interplay between structure and exchange interactions in a selfconsistent manner which is not possible within phenomenological models like the Heisenberg model or the Hubbard Hamiltonian. 1 For a full account of the excitations in principle the dynamic transverse susceptibility x 12(q,v) had to be calculated 1 which contains both the single-particle Stoner excitations and the spin-wave excitations as well as their interference which determines, e.g., the lifetime of the magnons. This has been achieved by Savrasov 7 within the framework