Search

Two well-known Hall-like effects are occurring in ferromagnets: the Anomalous Hall effect and the Planar Hall effect. The former is analogous to the classical Hall effect and is defined by the Onsager reciprocity relation of the second kind (antisymmetric conductivity matrix), while the latter is defined by the Onsager reciprocity relation of the first kind (symmetric conductivity matrix). The difference is fundamental, as it is based on time-invariance symmetry breaking at the microscopic scale. We study the Hall current generated in both cases, together with the power that can be extracted from the edges of Hall device. The expressions of the distribution of the electric currents, the distribution of electric carriers, and the power efficiencies (i.e. the power that can be injected into a load circuit) are derived at stationary regime from a variational method based on the second law of thermodynamics. It is shown that the distribution of the transverse Hall-current is identical in both cases but the longitudinal current and the power dissipated differ at the second order in the Hall angle., Comment: 12 pages, 3 Figures, synoptic presentation of the PHE vs AHE calculation

We analyze dispersion relations of magnons in ferromagnetic nanostructures with uniaxial anisotropy taking into account inertial terms, i.e. magnetic nutation. Inertial effects are parametrized by damping-independent parameter $\beta$, which allows for an unambiguous discrimination of inertial effects from Gilbert damping parameter $\alpha$. The analysis of magnon dispersion relation shows its two branches are modified by the inertial effect, albeit in different ways. The upper nutation branch starts at $\omega=1/ \beta$, the lower branch coincides with FMR in the long-wavelength limit and deviates from the zero-inertia parabolic dependence $\simeq\omega_{FMR}+Dk^2$ of the exchange magnon. Taking a realistic experimental geometry of magnetic thin films, nanowires and nanodiscs, magnon eigenfrequencies, eigenvectors and $Q$-factors are found to depend on the shape anisotropy. The possibility of phase-matched magneto-elastic excitation of nutation magnons is discussed and the condition was found to depend on $\beta$, exchange stiffness $D$ and the acoustic velocity.

The understanding of how spins move at pico- and femtosecond time scales is the goal of much of modern research in condensed matter physics, with implications for ultrafast and more energy-efficient data storage. However, the limited comprehension of the physics behind this phenomenon has hampered the possibility of realising a commercial technology based on it. Recently, it has been suggested that inertial effects should be considered in the full description of the spin dynamics at these ultrafast time scales, but a clear observation of such effects in ferromagnets is still lacking. Here, we report the first direct experimental evidence of inertial spin dynamics in ferromagnetic thin films in the form of a nutation of the magnetisation at a frequency of approximately 0.6 THz. This allows us to evince that the angular momentum relaxation time in ferromagnets is on the order of 10 ps., Comment: 10 pages, 4 figures, 1 table

The Kirchhoff-Helmholtz principle of least heat dissipation is applied in order to derive the stationary state of the spin-Hall effect. Spin-accumulation due to spin-orbit interaction, spin-flip relaxation, and electrostatic interaction due to charge accumulation are treated on an equal footing. A nonlinear differential equation is derived, that describes both surface and bulk currents and spin-dependent chemical potentials. It is shown that if the ratio of the spin-flip relaxation length over the Debye-Fermi length is small, the stationary state is defined by a linear spin-accumulation potential and zero pure spin-current., Comment: 10 pages, 1 figure

The characterization of the stationary states in the spin-Hall effect is discussed within the framework of the phenomenological two spin-channel model. It is shown that two different definitions of the stationary states can be applied in the spin-Hall effect, leading to two different types of state in the bulk: zero transverse spin-current or non-zero pure spin-current. This difference is due to the treatment of the region near the edges, in which electric charge accumulation occurs. The screening equations that describe the accumulation of electric charges due to spin-orbit coupling are derived. The spin-accumulation associated to spin-flip scattering and the spin-Hall accumulation due to spin-orbit coupling are two independent effects if we assume that the screening length is small with respect to the spin-diffusion length. The corresponding transport equations are discussed in terms of the Dyakonov-Perel equations., Comment: The work is a pedological presentation of the problem of the stationary states in the spin-Hall effect, in complement to a previously submitted article arXiv :1609.03916v1 [cond-mat.mes-hall] 2016, entitled "Conditions for the generation of spin and charge currents in spin-Hall devices" (Europhys. Lett. 118, 67005 (2017))

We investigate the out-of-equilibrium stationary states of spin-Hall devices on the basis of the least dissipation principle. We show that, for a bulk paramagnet with spin-orbit interaction, in the case of the Hall bar geometry the principle of minimum dissipated power prevents the generation of transverse spin and charge currents while in the case of the Corbino disk geometry, transverse currents can be produced. More generally, we show that electric charge accumulation prevents the stationary spin to charge current conversion., Comment: 2 figures

The Landau-Lifshitz-Gilbert (LLG) equation that describes the dynamics of a macroscopic magnetic moment finds its limit of validity at very short times. The reason for this limit is well understood in terms of separation of the characteristic time scales between slow degrees of freedom (the magnetization) and fast degrees of freedom. The fast degrees of freedom are introduced as the variation of the angular momentum responsible for the inertia. In order to study the effect of the fast degrees of freedom on the precession, we calculate the geometric phase of the magnetization (i.e. the Hannay angle) and the corresponding magnetic monopole. In the case of the pure precession (the slow manifold), a simple expression of the magnetic monopole is given as a function of the slowness parameter, i.e. as a function of the ratio of the slow over the fast characteristic times., Comment: 13 pages, 1 figure

We present a systematic construction of the probability-current operator,based on a momentum power expansion of effective Hamiltonians. The result is valid in the presence of a Rashba term and when a D'yakonov--Perel contribution is included. We propose practical tools for spin-orbit engineering of semiconductor heterostructures. We apply this formalism to a paradigmatic system, the interface between two semi-infinite media, on one side a free-electron-like material and on the other side a barrier material with spin-orbit interaction. We show that the usual boundary conditions, namely the continuity of the envelope function and of a velocity at the interface, according to the BenDaniel-Duke approach, comply with the conservation of the probability current only when first- (Rashba-like) and second-order (free-electron-like) terms are taken into account in the Hamiltonian. We revisit the boundary conditions and we prove that the envelope function may be discontinuous at the interface., Comment: 23 pages

We consider spin-dependent tunneling through a gallium arsenide barrier, a material which has no inversion symmetry. We are dealing with free electrons, with one effective mass and a spin-splitting in the barrier material. When we take into account both the spin-orbit interaction and the absence of the inversion symmetry, the evanescent states in the barrier are spin split and the tunneling process can become rather involved. Along some crystallographic directions, the incident wave experiences spin filtering during the tunneling. These results open stimulating perspectives for spin manipulation in tunnel devices.