The infrared spin-galvanic effect in semiconductor quantum wells

The spin-galvanic effect generated by homogeneous optical excitation with infrared circularly polarized radiation in quantum wells (QWs) is reviewed. The spin-galvanic current flow is driven by an asymmetric distribution of spin-polarized carriers in k-space of systems with lifted spin degeneracy due to k-linear terms in the Hamiltonian. Spin photocurrents provide methods to investigate the spin-splitting of the band structure and to make conclusion on the in-plane symmetry of QWs.     

High temperature spin wave dynamics of the uniaxial antiferromagnets

In the framework of the spin operators diagram technique the dynamical properties of the easy-axis type antiferromagnets at high temperatures are considered. The diagonalization procedure generalizing the Bogoliubov u-v transformation on the spin operators is presented. The spin wave (SW) spectrum allowing for the temperature and the magnetic field dependence of the sublattice magnetizations at T～T_～ is obtained. The SW relaxation frequencies due to the processes of SW scattering on the thermal spin fluctuations are calculated. The latter are in agreement with the data obtained on MnF₂ near the spin-flop transition¹⁰.     

EPR Study of Sc<Subscript>2</Subscript>SiO<Subscript>5</Subscript>:Nd<Superscript>143</Superscript> Isotopically Pure Impurity Crystals

The Sc₂SiO₅ single crystals doped with 0.001 at.% of the ¹⁴³Nd³⁺ ion were studied by continuous-wave and pulse electron paramagnetic resonance methods. The g-tensors and hyperfine structure tensors for two magnetically non-equivalent Nd ions were obtained. The spin–spin and spin–lattice relaxation times were measured at 9.82 GHz in the temperature range from 4 to 10 K. It was established that three relaxation processes contribute to the spin–lattice relaxation processes. There are one-phonon spin–phonon interaction, two-phonon Raman interaction and two-phonon Orbach–Aminov relaxation processes. It was established that spin–spin relaxation time is of the same magnitude for neodymium ion doped in Sc₂SiO₅ and in Y₂SiO₅.     

Low-energy electronic spin excitations between filling factors ν=1 and studied by optically detected nuclear magnetic resonance

We report measurements of the spin relaxation time (T_1n) for nuclei in the potential well confining a high-mobility two-dimensional electron system at a single GaAs–GaAlAs heterojunction. At low temperatures nuclear spin relaxation is dominated by electron–nuclear spin scattering: we find that T_1n displays sharp maxima at incompressible states throughout the hierarchy of the fractional quantum Hall effect. This behaviour is consistent with the existence of low-energy spin excitations only where the electron system is compressible. Our measurements also provide evidence for a gap in the spin excitation spectrum at .     

Two-magnon relaxation reversal in ferrite spheres

The reversal of two-magnon relaxation associated with linear scattering of oscillations of uniform magnetization precession from sample nonuniformities is studied theoretically and experimentally in ferrite spheres of yttrium iron garnet (YIG). Relaxation reversal is performed by parametric phase conjugation of dipole-exchange spin waves formed as a result of scattering of uniform precession from inhomogeneities. As a result of two-magnon backward scattering of dipole-exchange spin waves with a certain time delay, magnetization oscillations are renewed with an amplitude that could exceed the initial amplitude of uniform precession. The relaxation reversal is due to crystallographic anisotropy of the sample and is manifested most strongly when a YIG sphere is magnetized along the intermediate axis [110]. Experiments were carried out on YIG spheres of diameter 0.65–1.05 mm for a parallel pumping frequency ω _p /2π ≈ 9.4 GHz, which is about twice the uniform precession frequency. The maximal delay time for the restored signal of uniform precession was about 2 μs, while the maximal amplitude exceeded the initial uniform precession amplitude by a factor of about 5. The “latent” relaxation parameters of ferrites, e.g., the natural ferromagnetic resonance linewidth associated with many-particle processes and the linewidth associated with two-magnon scattering at bulk nonuniformities, are determined experimentally.     

Spin waves in the easy-plane ferromagnets

The modified version of the spin operator diagram technique is presented with regard to the dynamical properties of the easy-plane ferromagnets. The non-interacting spin wave (SW) spectrum and scattering amplitudes are obtained with the help of the spin Hamiltonian diagonalization procedure⁸). The SW relaxation frequencies due to the processes of the SW scattering on each other and on the longitudinal spin components thermal fluctuations are calculated.     

Spectral distribution of relaxation times in spin glasses

Recent neutron scattering measurements on spin glasses show that the dynamics of the spin systems can be best described in terms of wide spectral distribution of relaxation times evolving continuously with decreasing temperature but which is devoid of any critical behaviour, either speeding up or slowing down, at any finite temperature including the spin glass “freezing temperature T_sg”. It is argued that the latter temperature itself is dependent on the time constant of measurement for all spin glasses in general; the observed variation with frequency being less pronounced in some systems than others owing to some special characteristics of their spin dynamics such as, for example, the presence of parallel channels of rapid relaxation provided by the Korringa coupling in metallic spin glasses. The neutron scattering measurements presented here enable us to propose plausible forms for the density of relaxation times of the spin system and to show that the logarithmic frequency dependence of the freezing temperature observed in low frequency ac susceptibility measurements follows naturally from a uniform density of relaxation times at these frequencies.     

Theoretical model of spin transfer torque in multilayers

We present a model of spin transport in a Co/Cu(1 1 1)/Co pseudo-spin-valve (PSV) structure where current is flowing in the current perpendicular-to-plane (CPP) geometry. The model considers ballistic spin-dependent transmission at the two Co–Cu interfaces, as well as diffusive spin relaxation within the Cu spacer and free Co layer. In the latter, the spin relaxation process is composed of the usual longitudinal spin relaxation due to spin flip scattering, as well as transverse spin relaxation due to spin precession. The resulting spin transfer torque exerted on the moments within the free Co layer is composed of two contributions, the main contribution coming from “absorbed” spins in the interfacial regions. The second contribution arises from the relaxation of spin accumulation within the free Co layer. The calculated critical current density for switching is estimated to be approximately between 3.3×10⁷ and 1.1×10⁸ A/cm², which is in agreement with available experimental results.     

Why could electron spin resonance be observed in a heavy fermion Kondo lattice?

We develop a theoretical basis for understanding the spin relaxation processes in Kondo lattice systems with heavy fermions as experimentally observed by electron spin resonance (ESR). The Kondo effect leads to a common energy scale that regulates a logarithmic divergence of different spin kinetic coefficients and supports a collective spin motion of the Kondo ions with conduction electrons. We find that the relaxation rate of a collective spin mode is greatly reduced due to a mutual cancellation of all the divergent contributions even in the case of the strongly anisotropic Kondo interaction. The contribution to the ESR linewidth caused by the local magnetic field distribution is subject to motional narrowing supported by ferromagnetic correlations. The developed theoretical model successfully explains the ESR data of YbRh₂Si₂ in terms of their dependence on temperature and magnetic field.     

In-plane electric current is induced by tunneling of spin-polarized carriers

It has been shown that tunneling of spin-polarized electrons through a semiconductor barrier is accompanied by generation of an electric current in the plane of the interfaces. The direction of this interface current is determined by the spin orientation of the electrons and symmetry properties of the barrier; in particular, the current reverses its direction if the spin orientation changes the sign. Microscopic origin of such a "tunneling spin-galvanic" effect is the spin-orbit coupling-induced dependence of the barrier transparency on the spin orientation and the wave vector of electrons.     

Hebel-Slichter peak and superconducting energy gap in Rb3C60 observed by muon spin relaxation

Muon spin relaxation has been observed in both the normal and superconducting states of Rb₃C₆₀ (T _c=29.3K). The field dependence of theT ₁ spin relaxation rate is due to muonium undergoing spin-exchange scattering with conduction electrons, making this the first observation of muonium in a metal. The temperature dependence ofT ₁ ^–1 shows a Hebel-Slichter coherence peak just belowT _c which is not seen in¹³C spin relaxation. The peak can be fit assuming spin relaxation due to interaction with the quasiparticle excitations of a BCS superconductor provided the density of states is broadened relative to that of BCS. Such fits yield a value for the zero temperature energy gap, ₀/k _B , of 53(4)K, consistent with weak-coupling BCS.     

Raman scattering from spin fluctuations and phonons in the heavy-fermion superconductor UPt3

Quasielastic scattering from spin fluctuations has been observed in UPt₃ by Raman spectroscopy. The experiments for wave vectors q≈0 show a nearly temperature independent linewidth for 5 K ⩽ T ⩽ 300 K Complementary to neutron scattering results this establishes the q independence of the spin relaxation rate, indicating the localized nature of the spin fluctuations. A Raman-active phonon near 79 cm^-1 (10 meV) shows a drastic increase in line-width with decreasing temperature, demonstrating strong electron-phonon coupling.     

Dynamics of the one dimensional ideal spin glass

The dynamical susceptibility and relaxational behaviour of the one dimensional ideal spin glass obeying Glauber's model is considered. The dynamics can be found exactly as they are related by a transformation to the dynamics of the Ising model. The susceptibility does not show simple relaxational behaviour, rather it can be scaled by two relaxation timesτ ₁ andτ ₂ , with dynamical exponentsz ₁=2 andz ₂=1, which are just the arithmetic and geometric means of the related ferromagnetic and antiferromagnetic relaxation times. The critical slowing down at lower temperatures will result in an increasingly nearly elastic contribution to diffuse magnetic neutron scattering, while at higher temperatures the susceptibility is dominated by independent spin relaxation.     

Spin relaxation rates of Kondo systems measured by diffuse neutron scattering

A method for the direct measurement of spin relaxation rates of dilute magnetic systems by diffuse scattering of unpolarized neutrons is discussed. The magnetic scattering from the single magnetic impurities results from a difference measurement of doped and undoped sample. To discriminate against the large background from nonmagnetic scattering the choice of special energy windows is necessary for the detection of the magnetic scattering.Neutron scattering experiments were performed on the Kondo system CuFe for concentrations between 600 and 4800 at. ppm Fe and in the temperature range 15 K to 300 K. The measured absolute values and the temperature dependence of the spin relaxation rates, which have been measured for the first time in this experiment, are found to agree well with theoretical calculations by Götze and Schlottmann. This supports the explanation of the Kondo effect as a dynamical phenomenon and is contradictory to the static picture of a quasiparticle as proposed by Heeger.     

Anelastic relaxation and around the critical Sr content x = 0.02

Anelastic relaxation and ¹³⁹LaNQR relaxation rates in La_2–xSr_xCuO₄ for Sr content around 2 and 3 percent are discussed in terms of spin and lattice excitations and of the related ordering processes. It is argued how the phase diagram of La_2–xSr_xCuO₄ at the boundary between the antiferromagnetic (AF) and the spin-glass phase (x = 0.02) could be more complicate than previously thought, with a transition to a quasi-long range ordered state at K, as indicated by neutron scattering data. On the other hand, the ¹³⁹LaNQR spectra are compatible with a transition to an AF phase around K, in agreement with the phase diagram commonly accepted in literature. In this case the peaks in NQR and anelastic relaxation rates around 150 K and 80 K respectively in La_1.98Sr_0.02CuO₄, yield the first evidence of freezing process involving simultaneously lattice and spin excitations, possibly corresponding to motion of charged stripes. Received 18 May 2000 and Received in final form 11 July 2000     

Recombination mechanism of the spin-galvanic effect

The mechanism responsible for the spin-galvanic effect is considered. According to this mechanism, the current is generated as a result of the difference between the rates of spontaneous radiative transitions of charge carriers with oppositely directed spins. This difference arises when a spatially uniform nonequilibrium spin orientation of thermalized electrons (holes) is provided by any known method.     

μ+ SR studies on pure MnF2 and site-diluted (Mn0.5Zn0.5)F2SR studies on pure MnF2 and site-diluted (Mn0.5Zn0.5)F2

Positive muon spin rotation and relaxation measurements have been carried out on the antiferromagnets, pure MnF₂ and site-diluted (Mn_0.5Zn_0.5)F₂, above and below the Néel temperature T_N using single-crystal specimens. Two different muon signals have been found in the pure MnF₂; with the precession frequency υ_A for the site A and υ_B for the site B measured in zero external magnetic field at T=5 K. We propose a picture that the signal from the A site represents the “muonium” state, and discuss the characteristic features of muonium in magnetic materials. The spin relaxation rate 1/T₁, measured in zero external field, decreases rapidly with decreasing temperature below T_N. The mechanism of the spin relaxation above T_N is explained by the exchange fluctuations of the Mn moments, while below T_N by the Raman scattering of spin waves. At the same normalized temperature T/T_N, 1/T₁ observed in the diluted (Mn_0.5Zn_0.5)F₂ is significantly larger than that in the pure MnF₂ below T_N. The difference between the pure and diluted systems is related to the large spectral weight of low-energy magnons in (Mn_0.5Zn_0.5)F₂ found by neutron scattering.     

Edge spin accumulation in a ballistic regime

We consider a mesoscopic ballistic structure with Rashba spin-orbit splitting of the electron spectrum. The ballistic region is attached to the leads with a voltage applied between them. We calculate the edge spin density which appears in the presence of a charge current through the structure due to the difference in populations of electrons coming from different leads. Combined effect of the boundary scattering and spin precession leads to oscillations of the edge polarization with the envelope function decaying as a power law of the distance from the boundary. The problem is solved with the use of scattering states. The simplicity of the method allows us gain an insight into the underlying physics. We clarify the role of the unitarity of scattering for the problem of edge spin accumulation. In case of a straight boundary it leads to exact cancellation of all long-wave oscillations of the spin density. As a result, only the Friedel-like spin density oscillations with the momentum 2k _F survive. However, this appears to be rather exceptional case. In general, the smooth spin oscillations with the spin precession length recover, as it happens, e.g., for the wiggly boundary. We demonstrate also, that there is no relation between the spin current in the bulk, which is zero in the considered case, and the edge spin accumulation.     

Nuclear magnetic relaxation induced by the relaxation of electron spins

A physical mechanism responsible for the relaxation of nuclear spins coupled by the hyperfine interaction to relaxed electron spins in materials with spin ordering is proposed. The rate of such induced nuclear spin relaxation is proportional to the dynamic shift of the nuclear magnetic resonance (NMR) frequency. Therefore, its maximum effect on the NMR signal should be expected in the case of nuclear spin waves existing in the system. Our estimates demonstrate that the induced relaxation can be much more efficient than that occurring due to the Bloch mechanism. Moreover, there is a qualitative difference between the induced and Bloch relaxations. The dynamics of nuclear spin sublattices under conditions of the induced relaxation is reduced to the rotation of m₁ and m₂ vectors without any changes in their lengths (m ₁ ² (t) = m ₂ ² (t) = m ₀ ² (t)= const). This means that the excitation of NMR signals by the resonant magnetic field does not change the temperature T _n of the nuclear spin system. This is a manifestation of the qualitative difference between the induced and Bloch relaxations. Indeed, for the latter, the increase in T _n accompanying the saturation of NMR signals is the dominant effect.     

Rare earth paramagnetism,as studied by μSR

Some recent result of muon spin relaxation measurements in rare earth metals and intermetallic compounds are reviewed. Special emphasis is put on measurements that relate to the properties of correlated regions of spins existing relatively far above the ordering temperature in the rare earth ions. As far as comparable data from paramagnetic neutron scattering exist, they will be discussed in the same framework. For each temperature the correlated regions (or short-lived magnetic clusters) are characterized by their size, possible anisotropy with respect to the crystalline axes and their lifetime. The actual form of the interaction between the rare earth spins themselves and with the crystal fields determine the temperature dependence of these properties; a strong dipole interaction can, for instance, be expected to change the critical behaviour nearT _c . Much of the time will be devoted to experiments on Gd-metal where there are experimental indications that several interesting phenomena occur: (1) a strong effect of a cross-over from a non-conserved dynamics (dipolar) regime to a conserved (exchange dominated) regime some 10 K aboveT _c , (2) an anisotropy of the magnetic clusters with respect to the hexagonalc-axis, and (3), a persistence of spin correlations far aboveT _c . Some attempts to correlate the rare earth spin relaxation times measured in this region with cluster lifetimes deduced from neutron scattering will be reviewed, as well as a model for understanding these lifetimes in terms of temperature dependent cluster wall motion, which is determined by exchange and magnetic anisotropy parameters. Effects of possible quantum correlations originating from the “spin system+bath” interaction will be mentioned.