We study how the stability of the fractional quantum Hall effect (FQHE) is influenced by the geometry of band structure in lattice Chern insulators. We consider the Hofstadter model, which converges to continuum Landau levels in the limit of small flux per plaquette. This gives us a degree of analytic control not possible in generic lattice models, and we are able to obtain analytic expressions for the relevant geometric criteria. These may be differentiated by whether they converge exponentially or polynomially to the continuum limit. We demonstrate that the latter criteria play a dominant role in predicting the physics of interacting particles in Hofstadter bands in this low flux density regime. In particular, we show that the many-body gap depends monotonically on a band-geometric criterion related to the trace of the Fubini-Study metric.

The spin relaxation induced by the Elliott-Yafet mechanism and the extrinsic spin Hall conductivity due to the skew-scattering are investigated in 5d transition-metal ultrathin films with self-adatom impurities as scatterers. The values of the Elliott-Yafet parameter and of the spin-flip relaxation rate reveal a correlation with each other that is in agreement with the Elliott approximation. At 10-layer thickness, the spin-flip relaxation time in 5d transition-metal films is quantitatively reported about few hundred nanoseconds at atomic percent which is one and two orders of magnitude shorter than that in Au and Cu thin films, respectively. The anisotropy effect of the Elliott-Yafet parameter and of the spin-flip relaxation rate with respect to the direction of the spin-quantization axis in relation to the crystallographic axes is also analyzed. We find that the anisotropy of the spin-flip relaxation rate is enhanced due to the Rashba surface states on the Fermi surface, reaching values as high as 97% in 10-layer Hf(0001) film or 71% in 10-layer W(110) film. Finally, the spin Hall conductivity as well as the spin Hall angle due to the skew-scattering off self-adatom impurities are calculated using the Boltzmann approach. Our calculations employ a relativistic version of the first-principles full-potential Korringa-Kohn-Rostoker Green function method.

Using first-principles methods based on density-functional theory, we investigate the spin relaxation in W(001) ultrathin films. Within the framework of the Elliott-Yafet theory, we calculate the spin mixing of the Bloch states and we explicitly consider spin-flip scattering off self-adatoms. At small film thicknesses, we find an oscillatory behavior of the spin-mixing parameter and relaxation rate as a function of the film thickness, which we trace back to surface-state properties. We also analyze the Rashba effect experienced by the surface states and discuss its influence on the spin relaxation. Finally, we calculate the anisotropy of the spin-relaxation rate with respect to the polarization direction of the excited spin population relative to the crystallographic axes of the film. We find that the spin-relaxation rate can increase by as much as 27% when the spin polarization is directed out of plane, compared to the case when it is in plane. Our calculations are based on the multiple-scattering formalism of the Korringa-Kohn-Rostoker Green-function method.

We analyze the spontaneous magnetization reversal of supported monoatomic chains of finite length due to thermal fluctuations via atomistic spin-dynamics simulations. Our approach is based on the integration of the Landau-Lifshitz equation of motion of a classical spin Hamiltonian at the presence of stochastic forces. The associated magnetization lifetime is found to obey an Arrhenius law with an activation barrier equal to the domain wall energy in the chain. For chains longer than one domain-wall width, the reversal is initiated by nucleation of a reversed magnetization domain primarily at the chain edge followed by a subsequent propagation of the domain wall to the other edge in a random-walk fashion. This results in a linear dependence of the lifetime on the chain length, if the magnetization correlation length is not exceeded. We studied chains of uniaxial and tri-axial anisotropy and found that a tri-axial anisotropy leads to a reduction of the magnetization lifetime due to a higher reversal attempt rate, even though the activation barrier is not changed.

Spin dephasing by the Dyakonov-Perel mechanism in metallic films deposited on insulating substrates is revealed, and quantitatively examined by means of density functional calculations combined with a kinetic equation. The surface-to-substrate asymmetry, probed by the metal wave functions in thin films, is found to produce strong spin-orbit fields and a fast Larmor precession, giving a dominant contribution to spin decay over the Elliott-Yafet spin relaxation up to a thickness of 70 nm. The spin dephasing is oscillatory in time with a rapid (subpicosecond) initial decay. However, parts of the Fermi surface act as spin traps, causing a persistent tail signal lasting 1000 times longer than the initial decay time. It is also found that the decay depends on the direction of the initial spin polarization, resulting in a spin-dephasing anisotropy of 200% in the examined cases. DOI: 10.1103/PhysRevB.94.180406 In spintronics experiments, spins are often excited in, or transported through, nonmagnetic metallic thin film media [1]. Typical examples are Cu, Au, or Pt, used in spin-current creation or detection via the spin Hall effect [2][3][4][5] or spin Nernst effect [6,7]. Paramount for the spin-transport properties of a medium is the characteristic time T after which the outof-equilibrium spin population that was created in the medium is lost by relaxation or dephasing [8,9]. The microscopic mechanisms leading to spin reduction depend on the material properties, and it is commonly accepted that the Elliott-Yafet (EY) mechanism [10,11] is dominant in metals [12][13][14][15], since they show space-inversion symmetry [16]. However, any substrate on which the film is deposited breaks the inversion symmetry; if the film is thin enough (thinner than the electron phase relaxation length), the resulting asymmetry is felt by the metallic states extending over the film thickness, even though the substrate and surface potential are screened in the film interior. In this case, as we argue in this Rapid Communication, the band structure changes throughout the film and the Dyakonov-Perel (DP) mechanism [17] for spin dephasing is activated and becomes the dominant cause of spin reduction. The DP mechanism (that we briefly describe below) is known to be important in III-V or II-VI semiconductors or semiconductor heterostructures due to their inversion asymmetry [18,19], but, to our knowledge, it has been largely overlooked so far in the important case of supported films or metallic bilayers, which show manifestly no inversion symmetry. Only recently, data from spin-pumping [20] and weak antilocalization [21] experiments in ultrathin films were found to fit the DP and not the EY mechanism.Characteristic of systems with spin-orbit coupling and timereversal symmetry but broken inversion symmetry is the lifting of conjugation degeneracy [11] at each crystal momentum k and energy E k of the band structure. The resulting pair of states where σ is the vector of Pauli matrices and the vector quantity k is called the spin-orbit field (SOF) ...