Spin excitations in solids from abinitiomanybody perturbation theory
Spin excitations in solids from ab-initiomany-body perturbation theory 1, Arno Schindlmayr 2, Christoph Friedrich 1, and Stefan Blügel 1 Ersoy Sasioglu 1 Institutfür Festkörperforschung and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany 2 Department. Physik , Abstract Universität. Paderborn, 33095 Paderborn, Germany Wannier Functions Itinerant electron systems (Collective excitations) Density of states of Fe, Co and Ni (localized) MLWFs in Fe Unitary transformation matrix Maximally localized Wannier functions for entangled bands [3, 5, 6] The calculated average matrix elements of the screened Coulomb potential for 3 d transition metals are in good agreement with the FP-LMTO-Wannier scheme (filled spheres) [1, 7]. Fe On-site U, U’and J for Fe, Co and Ni T-Matrix in Wannier Basis Magnetic Excitations • Spin waves (delocalized) Energy window To study spin excitations in solids from first principles we have developed a computational scheme based on many-body perturbation theory within the fullpotential linearized augmented plane-wave (FLAPW) method and implement it in the SPEX code [1, 2]. The main quantity of interest is the dynamical transverse spin susceptibility, from which magnetic excitations, including singleparticle spin-flip Stoner excitations and collective spin-wave modes as well as their lifetimes, can be obtained. In order to describe spin waves we include appropriate vertex corrections in the form of a multiple scattering T-matrix, which describes the coupling of electrons and holes with different spins. To reduce the numerical cost for the calculation of the four-point T-matrix we exploit a transformation to maximally localized Wannier functions that takes advantage of the short spatial range of electronic correlation in the partially filled d or f orbitals of magnetic materials [3]. As an illustration, we present spin-wave spectra and dispersions for the elementary ferromagnets Fe, Co, and Ni as well as their alloys Fe. Co and Fe. Pd calculated with our scheme. The results are in good agreement with available experimental data. Average V and W for 3 d elements • Stoner excitations Magnetic excitations Kernel (K) Non-interacting response (R=K) (Single-particle excitations) Local-moment systems Interacting response (R=K+KTK) bcc Cr Screened Coulomb potential (W) Spin waves Stoner excitations Spin waves Approximation: Local static Coulomb potential in RPA Spin-wave dispersion and spin-wave lifetimes in bcc Fe, fcc Co and Ni Projection onto mixed product basis Green Function Method Dynamical spin susceptibility (Magnetic response function [1, 4]) Magnetic excitations are related to the imaginary part of the dynamical spin susceptibility (or magnetic response function) Implementation within FLAPW FLEUR (DFT-LDA) Wannier 90 § DS: Dynamical Susceptibility § FT: Force Theorem § : HWHM ~ magnon lifetime § Expt: Fe: Ref. [8], Co: Ref. [9], Ni: Ref. [10] Spex (GW) The magnetic response function Rij can be written as a functional derivative of the spin density with respect to external magnetic field Our calculations predict a double branch in spin-wave dispersion of fcc Ni in [100] and [111] directions in the Brillion zone in agreement with previous studies [11]. Spin waves in L 10 -type magnetic multilayers Fe. Co Pauli spin matrices Energy (me. V) Green function Fe. Pd Applications: Fe, Co, Ni Coulomb potential in Wannier basis for collinear ferromagnets Convergence of average V, W and for FM (NM) bcc Fe [1] Ladder approximation · We have developed a computational method to study magnetic excitations in ferromagnetic materials within the framework of many-body perturbation theory using Wannier functions. · The developed scheme has been applied to 3 d transition metals and their alloys. · In contrast to previous implementations [11], the matrix elements of the screened Coulomb potential are calculated from first principles. · The calculated spin-wave dispersion of bcc Fe, fcc Co and fcc Ni is in agreement with available experimental data as well as previous studies. On-site direct and exchange Coulomb matrix elements for FM (NM) bcc Fe [1] Non-interacting response T-matrix Conclusions Interacting response Acknowledgments We acknowledge helpful discussions with F. Freimuth, M. Niesert, A. Gierlich, G. Bihlmayer, Y. Mokrousov, T. Miyake and F. Aryasetiawan. References [1] E. Sasioglu, et al. , Phys. Rev. B 81, 054434 (2010). [2] C. Friedrich, S. Blügel, and A. Schindlmayr, Phys. Rev. B 81, 125102 (2010). [3] F. Freimuth, et al. , Phys. Rev. B 78, 035120 (2008). [4] F. Aryasetiawan and K. Karlsson, Phys. Rev. B 60, 7419 (1999). [5] N. Marzari and D. Vanderbilt, Phys. Rev. B 56, 12847 (1997). [6] I. Souza, N. Marzari and D. Vanderbilt, Phys. Rev. B 65, 035109 (2002). [7] T. Miyake and F. Aryasetiawan, Phys. Rev. B 77, 085122 (2008). [8] J. W. Lynn, Phys. Rev. B 11, 2624 (1975). [9] T. Balashov, Ph. D Thesis, Universität-Halle-Wittenberg, 2008. [10] H. A. Mook et al. , Phys. Rev. Lett. 54, 227 (1985). [11] K. Karlsson and F. Aryasetiawan, Phys. Rev. B 62, 3006 (2000).
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