Anisotropic FMR‐linewidth of triple‐domain Fe layers on hexagonal GaN(0001)

Büchmeier, M.; Bürgler, D. E.; Grünberg, P.; Schneider, Claus M.; Meijers, R.; Calarco, Raffaella; Raeder, C.; Farle, Michael

doi:10.1002/pssa.200563130

Cited by 9 publications

(2 citation statements)

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“…A number of papers have described, for example, the growth of iron on GaN. [1][2][3][4][5] Furthermore, there is great interest in general in the arrangement of atoms and atomic structures formed by depositing different elements onto the GaN(0001) surface. [6][7][8] Despite the high interest in Fe, its reported triple-domain structure on the GaN(0001) surface renders it less than ideal for achieving a homogeneous magnetic thin film on GaN(0001).…”

Section: Introductionmentioning

confidence: 99%

Manganese 3×3 and3×3-R30∘str

et al. 2013

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Manganese deposited on the N-polar face of wurtzite gallium nitride [GaN (0001)] results in two unique surface reconstructions, depending on the deposition temperature. At lower temperature (less than 105• C), it is found that a metastable 3 × 3 structure forms. Mild annealing of this Mn 3 × 3 structure leads to an irreversible phase transition to a different, much more stable• structure which can withstand hightemperature annealing. Scanning tunneling microscopy (STM) and reflection high-energy electron diffraction data are compared with results from first-principles theoretical calculations. Theory finds a lowest-energy model for the 3 × 3 structure consisting of Mn trimers bonded to the Ga adlayer atoms but not with N atoms. The lowest-energy model for the more stable √ 3 × √ 3-R30• structure involves Mn atoms substituting for Ga within the Ga adlayer and thus bonding with N atoms. Tersoff-Hamman simulations of the resulting lowest-energy structural models are found to be in very good agreement with the experimental STM images.

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Section: Introductionmentioning

confidence: 99%

Manganese 3×3 and3×3-R30∘str

et al. 2013

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“…It is worth noting that an angular dependence of magnetic losses (or effects associated with the same physics) has already been reported experimentally. [13][14][15][16][17][18] However, analytical and numerical approaches still have to be developed, especially for nanoscale structures where the magnetic resonances are strongly confined, and so, their spectra are discrete.…”

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Micromagnetic modeling of anisotropic damping in magnetic nanoelements

2013

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We report a numerical implementation of the Landau-Lifshitz-Baryakhtar theory that dictates that the micromagnetic relaxation term obeys the symmetry of the magnetic crystal, i.e., replacing the single intrinsic damping constant with a tensor of corresponding symmetry. The effect of anisotropic relaxation is studied in a thin saturated ferromagnetic disk and an ellipse with and without uniaxial magnetocrystalline anisotropy. We investigate the angular dependence of the linewidth of magnonic resonances with respect to the given structure of the relaxation tensor. The simulations suggest that the anisotropy of the magnonic linewidth is determined by two factors: the projection of the relaxation tensor onto the plane of precession and the ellipticity of the latter. 4 These terms are now widely used for the description of magnetic relaxations in magnetic thin films 5,6 and patterned magnetic media. 7 The microscopic mechanism behind the magnetic losses in metals has also been suggested, e.g., in Gilmore et al. 8 However, recent experimental data urge the development of new micromagnetic approaches to the description of magnetic losses, i.e., by introducing higher-order terms within the Gilbert approach, 9 inert relaxation, 10 and by generalizing the magnetization dynamics and relaxation within the framework of Onsager's kinetic equations.11 The latter approach shows that the relaxation part of the equation of precession should obey the crystallographic symmetry of the media, thereby replacing the single intrinsic damping constant with a tensor. The reason behind anisotropic relaxation in magnetic media is the symmetry of the spin-orbit and s-d interaction, 12 which couples the spins to the other subsystems (degrees of freedom), i.e., the lattice and the free electrons, respectively. It is worth noting that an angular dependence of magnetic losses (or effects associated with the same physics) has already been reported experimentally.13-18 However, analytical and numerical approaches still have to be developed, especially for nanoscale structures where the magnetic resonances are strongly confined, and so, their spectra are discrete.In this paper, we report on a numerical implementation of Baryakhtar's theory 11 within the mumax2 micromagnetic framework.19 Furthermore, we systematically investigate the influence of anisotropic relaxation on the angular dependence of ferromagnetic resonance (FMR) linewidths in a nanoscale magnetic disk and an ellipse.We start from the general Baryakhtar equation (LLBar),where M, γ LL , H are the magnetization vector, the positively defined gyromagnetic ratio, and the effective internal field, respectively. The first term in the equation defines the torque, while the second and third describe the local and nonlocal 20 relaxations, respectively.λ(M) andλ (e) (M) are the relaxation tensors of relativistic and exchange nature, respectively, and in general are functions of the magnetization vector. These tensors are in fact operators that describe how crystallographic and magnetic sym...

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