### Abstract

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 Cu(001) and Au(001) surfaces and for a Co monolayer on Cu(001). 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.

Original language | English |
---|---|

Article number | 104436 |

Pages (from-to) | 1044361-10443611 |

Number of pages | 9399251 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 68 |

Issue number | 10 |

Publication status | Published - Sep 2003 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*68*(10), 1044361-10443611. [104436].

**First-principles relativistic study of spin waves in thin magnetic films.** / Udvardi, L.; Szunyogh, L.; Palotás, K.; Weinberger, P.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 68, no. 10, 104436, pp. 1044361-10443611.

}

TY - JOUR

T1 - First-principles relativistic study of spin waves in thin magnetic films

AU - Udvardi, L.

AU - Szunyogh, L.

AU - Palotás, K.

AU - Weinberger, P.

PY - 2003/9

Y1 - 2003/9

N2 - 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 Cu(001) and Au(001) surfaces and for a Co monolayer on Cu(001). 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.

AB - 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 Cu(001) and Au(001) surfaces and for a Co monolayer on Cu(001). 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.

UR - http://www.scopus.com/inward/record.url?scp=0142184885&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0142184885&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0142184885

VL - 68

SP - 1044361

EP - 10443611

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 10

M1 - 104436

ER -