The Hall effect occurring in a Hall bar is revisited on the basis on non-equilibrium thermodynamics principles. Following the approach developed in a previous work (Creff et al. J. Appl. Phys 2020), the stationary state is defined by the minimum power dissipation principle, and the well-known results about the charge accumulation at the lateral edges and the corresponding Hall voltage are recovered. Beyond, the effect of a sizable current leakage occurring at the edges is investigated. An analytical expression of this output current - proportional to the magnetic field and the leakage resistance - is derived.
We investigate the compatibility of the concept of "charge to spin current conversion" with the second law of thermodynamics in the context of the spin-Hall effect (SHE).
This investigation is performed in the framework of the two spin channel model of the SHE.
It is first shown that the spin-accumulation due to spin-flip scattering at the interface is independent of the We investigate the compatibility of the electric charge to spin current conversion with the second law of the thermodynamics in the spin-Hall effect (SHE).
This investigation is performed in the framework of the two spin channel model of the SHE.
It is first shown that the spin-accumulation due to spin-flip scattering at the interface is independent of the spin-accumulation due to SHE, if the spin-flip scattering length is much larger than the electrostatic screening length [1].
A variational technique based on the least dissipation principle is then applied. 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 to occur inside the device [2].
[1] J.-E. Wegrowe, "Stationary state and screening equations in spin-Hall effect", arXiv:1701.0601 (2017)
[2] J.-E. Wegrowe, R. V. Benda, and J. M. Rubi, Conditions for the generation of sin current in spin-Hall devices, arXiv :1609.03916v1 [cond-mat.mes-hall] 2016.
We measured transverse magneto-thermoelectric voltage on devices made of a Permalloy (Py) line and a transverse
electrode made of platinum (Pt), copper (Cu) or bismuth (Bi). We show that the angular dependence of the voltage is the
same for Pt and Cu but different with a Bi electrode. We interpret the angular dependence with Pt and Cu electrode as
anomalous and planar Nernst and Righi-Leduc effect on Py. The results obtained with a Bi electrode can be explained as
the Nernst effect of the electrode itself which overwhelms the signal coming from the Py.
The change of magnetization (i.e. using the inverse magnetostriction effect) allows to investigate at the nanoscale the effects of thermoelastic and piezoelectric strain of an active track-etched β-PVDF polymer matrix on an electrodeposited single-contacted Ni nanowire (NW). The magnetization state is measured locally by anisotropic magnetoresitance (AMR). The ferromagnetic NW plays thus the role of a mechanical probe that allows the effects of mechanical strain to be characterized and described qualitatively and quantitatively. Due to the inverse magnetostriction, a quasi-disappearance of the AMR signal for a variation of the order of ΔT ≈ 10 K has been evidenced. The coplanarity of the vectors between the magnetization and the magnetic field is broken. A way of studying the effect of the geometry on such a system, is to fabricate oriented polymer templates. Track-etched polymer membranes were thus irradiated at various angles (α_{irrad}) leading, after electrodeposition, to embedded Ni NWs of different orientations. With cylindrical Ni NW oriented normally to the template surface, the induced stress field in a single Ni NW was found 1000 time higher than the bulk stress field (due to thermal expansion measured on the PVDF). This amplification results in three nanoscopic effects: (1) a stress mismatch between the Ni NW and the membrane, (2) a non-negligible role of the surface tension on Ni NW Young modulus, and (3) the possibility of non-linear stress-strain law. When the Ni NWs are tilted from the polymer template surface normality, the induced stress field is reduced and the amplification phenomenon is less important.
It is well known that the Landau-Lifshitz-Gilbert (LLG) equation for a macroscopic magnetic
moment find its limit of validity at very short time scales or equivalently at very high
frequencies. The reason for this limit of validity is well understood in terms of separation of the
characteristic times between slow (the magnetization) and fast (the environment) degrees of
freedom, as pointed-out in the stochastic derivation of the LLG equation first proposed by W. F.
Brown in 1963. Indeed, the ferromagnetic moment is a slow collective variable, but fast degrees
of freedom are also playing a role in the dynamics, and especially the variation of the angular
momentum responsible for inertia. In the last couple of years, the generalization of the LLG
equation with inertia (ILLG) has been derived by different means (see list of references). The
signature of the inertial regime of the magnetization is the nutation that can be measured by
resonance experiments (but it has not been observed up to know). We developed an approach in
terms of geometrical phase (defining the corresponding Hannay angle, which is the classical
analog to the quantum Berry phase: see references), that has recently been used with success to
analogous problems. We calculated the Hannay angle for the precession of the magnetization in
the case of the inertial effect, and the corresponding magnetic monopole. This analysis allows the
slow vs. fast variable expansion to be calculated in the specific case of pure precession.
The anisotropic properties of thermal transport in insulating or conducting ferromagnets are derived on the basis of the Onsager reciprocity relations applied to a magnetic system. It is shown that the angular dependence of the temperature gradient takes the same form as that of the anisotropic magnetoresistance, including anomalous and planar Hall contributions [1].
The experimental study [2] shows that the voltage measured between the extremities of the non-magnetic electrode in thermal contact to the Py or YIG ferromagnetic layers follows the predicted angular dependence. Furthermore, the sign and the amplitude of the magneto-voltaic signal measured is in agreement with the thermocouples calculated from the corresponding Seebeck coefficients, for the three different electrodes used in the study (Pt, Cu, Bi).
Based on a proper definition of the current operators for non-quadratic Hamiltonians, we derive the expression for the transport current which involves the derivative of the imaginary part of the free-electron current, highlighting peculiarities of the extra terms. The expression of the probability current, when Spin-Orbit Interaction (SOI) is taken into account, requires a reformulation of the boudary conditions. This is especially important for tunnel heterojunctions made of non-centrosymmetric semiconductors. Therefore, we consider a model case: tunneling of conduction electrons through a [110]-oriented GaAs barrier. The new boundary conditions are reduced to two set of equations: the first one expresses the discontinuity of the envelope function at the interface while the other one expresses the discontinuity of the derivative of the envelope function.
Thermokinetic considerations are appled to the case of a generic spintronic device in which a magneto-voltaic response is measured, in the absence of electric current, on an electrode placed perpendicular to a ferromagnetic layer (see Fig. 1). The magnetovoltaic signal is a response to a power excitation, that is related to the ferromagnetic degrees of freedom. This excitation can be performed by ferromagnetic resonance (electromagnetic excitations), by a temperature gradient, by magnetomechanical coupling or by magneto optic coupling (see these proceedings). The description of this generic device allows the so-called spin-Seebeck effects and spin-pumping effects^{17-16} to be addressed.
We propose a novel set of boundary conditions, based on the continuity of a generalized velocity and on the continuity of the probability current at the interface of heterojunctions, which is well suited to construct the solution of the tunneling problem when spin-orbit interaction is taken into account. We illustrate this procedure in a model case: tunneling of conduction electrons through a [110]-oriented GaAs barrier. In that case, the new boundary conditions reduce to two set of equations: the first one expresses the discontinuity of the envelope function at the interface while the other one is close to the standard condition on the derivative of the envelope function.
In order to understand some new spintronics experiments of spin-dependent voltage for which the electric conduction does not play a role, a model of two spin-conduction channel is proposed in which the ferromagnets (either electric conductors or insulators) are defined by an ensemble of non equilibrium heat carriers composed of a populations of heat carriers of spin up, and heat carriers of spin down. It is shown that a temperature gradient generates locally a spin-accumulation. The diffu sion equation of this thermal spin-accumulation is straightforwardly derived from the corresponding transport equations and conservation equations. The principle of the detection is described in terms of Spin-Nernst effect.
Proc. SPIE. 8268, Quantum Sensing and Nanophotonic Devices IX
KEYWORDS: Scattering, Crystals, Interfaces, Gallium arsenide, Nanophotonics, Electron transport, Heterojunctions, Group III-V semiconductors, Systems modeling, Current controlled current source
New boundary conditions are derived for tunnel-heterojunctions, where the effective Hamiltonian is a generic
power of the momentum-operator. A novel expression of probability-current operator, which can be also applied
in presence of the D'yakonov-Perel (DP) Hamiltonian, has to be used. We test our technique on the interface
between two semi-infinite media, with on one side a free-electron-like material and on the other side the [110]-
oriented GaAs barrier.
KEYWORDS: Ferromagnetics, Particles, Magnetism, Physics, Picosecond phenomena, Neodymium, Electroluminescent displays, Spintronics, Magnetic semiconductors, Picture Archiving and Communication System
The intimate relation between the angular momentum and the magnetization - expressed through
the gyromagnetic relation - is well known and is easy to evidenced at the macroscopic scale with
magnetomechanical measurements. On the other hand, the conservation of the angular momentum
find also a simple illustration in the behavior of a spinning top. Accordingly, the dynamics of a
single domain ferromagnet should follow the same laws as a symmetrical spinning top. Paradoxically,
this is not true since the equations that govern the dynamics of the magnetization do not contain inertial terms. We investigate under what conditions the inertial terms that are initially present in the conservation laws disappear, in order to lead to the well-known expressions of the Landau-Lifshitz-Gilbert equation
We propose a procedure, based on momentum power series expansion Hamiltonian of nth general order, to
obtain a coherent expression of the probability current operator that is valid also when Spin-Orbit Interaction
(SOI) terms are included. We prove that we recover the standard definition when the free electron-like term
is included in the Hamiltonian, but when taking into account higher order Spin-Orbit Interaction (SOI) terms,
a more general definition of the probability current operator is mandatory, due to its different symmetrization,
compared to the Hermitian velocity operator expression.
In non-centrosymmetric semiconductors with zinc-blende structure grown along the [110] crystallographic direction,
electrons with up and down spins undergo different quantum phase shifts upon tunneling, which can be
wieved as resulting from spin precession around a complex magnetic field. There is no spin filtering but a pure
spin dephasing. The phase shift of the transmitted wave is proportional to the overall barrier-material thickness.
We show that a device incorporating a number of resonant tunnel barriers constitutes an efficient quantum-phase
shifter.
We present the last developments of the
approach of spin-transfer in terms of mesoscopic non-equilibrium
thermodynamics. The modification of the ferromagnetic
states due to the presence of a spin-accumulation process is investigated. The spin accumulation (also responsible for
giant magnetoresistance) is generated by an electric current at the interfaces with a
ferromagnetic nanostructure. The dynamical coupling that links the
ferromagnetic degree of freedom to the spin of the conduction electrons is
investigated with taking into account longitudinal and transverse spin
accumulation. It seems that the coupling with the transverse spin-accumulation
may be equivalent to the usual spin-transfer-torque mechanisms deduced from
microscopic transmission- reflection coefficients at the interface. In
contrast, the coupling with the longitudinal spin-
accumulation generates fluctuations and seems to play important
role in the activation process at larger time
scales only.
The aim of this paper is to demonstrate the relevance of the
a non-equilibrium stochastic approach in the context of spin-transfer
mechanism. Spin-transfer is the generic name for the effect of
magnetization reversal (or magnetic excitation) produced by the
injection of a spin-polarized current in a ferromagnetic layer.
Deterministic vs. stochastic approaches are first defined in the
context of the Landau-Lifshitz Gilbert equation of the magnetization.
We then present a model based on non-equilibrium
thermodynamics in which the spin-accumulation at the interface appears
as a diffusion term in the Landau-Lifshitz equation. The expression of
the critical current I_{c} is derived from this diffusive process and
compared to the experimental results. Due to the definition of the
critical current in terms of activation process, the phenomenological
expression of I_{c} is identical to that derived in the
deterministic case, after introducing an "efficiency parameter". Only
the specific form of this efficiency parameter allows one to discriminate
between the different models. The direct link to the integral of the
magnetoresistance of the junction derived here allows some
highly specific behaviour to be predicted.
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: Depending on the crystallographic direction, the incident wave experiences spin filtering during the tunneling or a spin precession around an effective magnetic field. These results open stimulating perspectives for spin manipulation in tunnel devices.
In a crystal without inversion center, when the spin-orbit interaction is taken into account, it has been shown that the evanescent branches inside the forbidden band gap correspond to complex wave vectors. Here, we discuss possible tunneling phenomena associated with complex wave vectors. We demonstrate that in a case where the wave vector has orthogonal real and imaginary components, an almost standard tunneling process can be restored under crude approximations, analoguous to off-normal tunneling through a potential barrier. Any more accurate analysis is an open problem. In one-dimensional tunneling with a complex wave vector, no solution can be calculated under simple hypotheses.
Spin injection in metallic normal/ferromagnetic junctions is investigated taking into account the anisotropic magnetoresistance occurring in the ferromagnetic layer. On the basis of a generalized two-channel model, it is shown that there is an interface resistance contribution due to anisotropic scattering, besides spin accumulation and giant magnetoresistance. The corresponding expression of the thermoelectric power is derived and compared with the expression accounting for the thermoelectric power produced by the giant magnetoresistance. The results of this study show that, while the giant magnetoresistance and the corresponding thermoelectric power indicate the role of spin-flip scattering, the observed anisotropic magneto-thermoelectric power might be the fingerprint of interband s-d relaxation mechanisms.
We present here, a novel approach for the membrane-based synthesis, also called template synthesis of arrays of nanomaterials with monodispersed geometrical features. The basic principle is to grow or generate the desired material inside the pores of a nanoporous alumina membrane. The pores of are synthesised parallel to the surface of the substrate by performing the anodic oxidation of an aluminium thin film laterally, i.e. parallel to the surface of the substrate, instead of perpendicular as usually done. We obtain highly regular and ordered pore arrays, with a minimum pore size in the range of ~3 to 4 nm, which to the best of our knowledge is the smallest reported to date for anodic alumina membranes. After anodic oxidation, the pores of the lateral alumina membranes have been electrochemically “filled” with Te nanowires. Such porous alumina structures may allow to control the in-plane organisation of arrays of template-grown nanowires and carbon nanotubes for reproducible device fabrication.
Experiments of spin injection, from a normal metal to a ferromagnet, show that the magnetization of the ferromagnet can be switched with high current pulses, without the need of a magnetic field. In order to describe the experimental observations, two different kinds of electronic populations are defined for the transport: the spin polarized current inside the normal metal (paramagnetic spin-polarized current) and the spin-polarized current inside the ferromagnet (ferromagnetic spin polarization). The redistribution of the electronic populations is then investigated in the framework of a four-channel approach (up and down spin polarization for paramagnetic and ferromagnetic currents). This mechanism couples the electronic transport (Boltzmann equations to the dynamics of the magnetization (Landau-Lifshitz-Gilbert equation), and leads to define a magnetic temperature which depends on the current injection.
Experiments of spin injection on magnetic nanostructures show that the magnetization can be switched with high current pulses, and without the need of a magnetic field. The mechanism responsible for this effect is still not known, but some experiments show that it is related to fluctuations and noise in magnetic systems. The response of a magnetic nanostructure shows typical processes of activation out of a metastable state and two level fluctuations. An effective temperature is measured is measured through the effective barrier variation. The effective temperature depends on the magnetic configuration and to the current direction. This approach leads to conclude that the transfer of energy is due to a transfer of spin from the current to the magnetization. A new mechanism is proposed as a consequence of the s-d relaxation at the interface in 3d ferromagnets. This mechanism couples the electronic transport (Boltzmann equations) to the dynamics of the magnetization (Landau-Lifshitz-Gilbert equation).
The usual charge carrier exploited in all electronic devices is
the electron (and hole) and possesses hence, associated with its inertial masse, a spin degree of freedom. Manipulating spin-polarized electric current is the role devoted to Spintronics. Investigating the current induced magnetization switching (CIMS), consists in measuring the dynamics of the magnetization due to
spin-polarized current injection. It is shown that two different mechanisms are operating. One can be described with a current dependent torque, and the other one is attributed to longitudinal spin-transfer.
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