On the critical dynamics of disordered spin systems

The dynamic critical behaviour of spin systems with quenched impurities, and of amorphous spin systems as characterized by the additional presence of random anisotropy directions, is studied by renormalization group methods to second order in=4–d. For the Halperin-Hohenberg-Ma model with purely relaxational dynamics it is concluded that in three dimensions (d=3) the critical slowing down should be enhanced by impurities for systems with Ising type statics, whereas there is no change forXY- and Heisenberg systems. For amorphous systems, however, the critical dynamics should change also in theXY- and Heisenberg cases. Furthermore, it is concluded that additional conserved, but noncritical modes become always statically decoupled from the order parameter for systems with impurities, but not for amorphous systems. Thus, for the impure system, the energy density mode and the asymmetric models of Halperin, Hohenberg and Siggia are ruled out. But the effects of dynamic coupling remain: Especially, the relationz=d/2 for the dynamic exponent of planar and isotropic antiferromagnets is modified for impure or amorphous systems.     

Off equilibrium dynamics in disordered quantum spin chain

We study the non-equilibrium time evolution of the average transverse magnetisation and end-to-end correlation functions of the random Ising quantum chain. Starting with fully magnetised states, either in the x or z direction, we compute numerically the average quantities. They show similar behaviour to the homogeneous chain, that is an algebraic decay in time toward a stationary state. During the time evolution, the spatial correlations, measured from one end to the other of the chain, are building up and finally at long time they reach a size-dependent constant depending on the distance from criticality. Analytical arguments are given which support the numerical results. Received 11 July 2002 / Received in final form 9 September 2002 Published online 29 October 2002     

NMR study of spin dynamics in disordered Heisenberg paramagnets

The spin dynamics in the disordered paramagnets KMg_1?xMn_xF₃ and Zn_1?xMn_xF₂ were investigated using the F¹⁹ NMR. Linewidths and relaxation rates of those distinct classes of F¹⁹ nuclei that have different numbers of nearest neighbor magnetic ions were obtained as a function of concentration x. The particular importance of the isolated magnetic ion to the low frequency spectral density was established.     

Charge current driven by spin dynamics in disordered Rashba spin-orbit system

Pumping of charge current by spin dynamics in the presence of the Rashba spin-orbit interaction is theoretically studied. Considering a disordered electron, the exchange coupling and spin-orbit interactions are treated perturbatively. It is found that the dominant current induced by spin dynamics is interpreted as a consequence of the conversion from spin current via the inverse spin Hall effect. We also find that the current has an additional component from a fictitious conservative field. The results are applied to the case of a moving domain wall.     

Low frequency dynamics of disordered XY spin chains and pinned density waves: from localized spin waves to soliton tunneling

A long-standing problem of the low-energy dynamics of a disordered XY spin chain is reexamined. The case of a rigid chain is studied, where the quantum effects can be treated quasiclassically. It is shown that, as the frequency decreases, the relevant excitations change from localized spin waves to two-level systems to soliton-antisoliton pairs. The linear-response correlation functions are calculated. The results apply to other periodic glassy systems such as pinned density waves, planar vortex lattices, stripes, and disordered Luttinger liquids.     

From spin flip excitations to the spin susceptibility enhancement of a two-dimensional electron gas

The g-factor enhancement of the spin-polarized two-dimensional electron gas was measured directly over a wide range of spin polarizations, using spin flip resonant Raman scattering spectroscopy on two-dimensional electron gases embedded in Cd(1-x)Mn(x)Te semimagnetic quantum wells. At zero Raman transferred momentum, the single-particle spin flip excitation, energy Z*, coexists in the Raman spectrum with the spin flip wave of energy Z, the bare giant Zeeman splitting. We compare the measured g-factor enhancement with recent spin-susceptibility enhancement theories and deduce the spin-polarization dependence of the mass renormalization.     

Effects of spin interactions in disordered electronic systems: Loop expansions and exact relations among local gauge invariant models

Spindependent ensembles for disordered electronic systems are examined in the region of extended states. We derive relations between spindependent and previously studied spinless ensembles. We prove that these relations are valid in all orders of a graph theory, on the basis of which we propose them to be exact. These exact relations and supplementary two loop order calculations in 2+ dimensions are used to reveal the existence of universality classes for the critical behaviour at the mobility edges. The mobility edge behaviour of a spindependent ensemble with real (random) hopping agrees with that of the spinless phase invariant ensemble except for a crossover to the real matrix ensemble in the limit of vanishing spinflip amplitudes. Anomalous properties in the band center are also discussed. We derive a transformation which maps arbitrary correlation functions of a complex spindependent ensemble into those of the real matrix ensemble. This relation implies the absence of a mobility edge for the complex spindependent ensemble within the validity region of the theory.     

Slow relaxation experiments in disordered charge and spin density waves: collective dynamics of randomly distributed solitons

We show that the dynamics of disordered charge density waves (CDWs) and spin density waves (SDWs) is a collective phenomenon. The very low temperature specific heat relaxation experiments are characterized by: (i) “interrupted” ageing (meaning that there is a maximal relaxation time); and (ii) a broad power-law spectrum of relaxation times which is the signature of a collective phenomenon. We propose a random energy model that can reproduce these two observations and from which it is possible to obtain an estimate of the glass cross-over temperature (typically T _g≃ 100-200 mK). The broad relaxation time spectrum can also be obtained from the solutions of two microscopic models involving randomly distributed solitons. The collective behavior is similar to domain growth dynamics in the presence of disorder and can be described by the dynamical renormalization group that was proposed recently for the one dimensional random field Ising model [D.S. Fisher, P. Le Doussal, C. Monthus, Phys. Rev. Lett. 80, 3539 (1998)]. The typical relaxation time scales like ∼τexp(T _g/T). The glass cross-over temperature T_g related to correlations among solitons is equal to the average energy barrier and scales like T _g∼ 2xξΔ. x is the concentration of defects, ξ the correlation length of the CDW or SDW and Δ the charge or spin gap. Received 12 December 2001     

Block spin techniques applied to the ising model

A detailed study of the critical behaviour of the Ising model in 1+1 and 2+1 dimensions is made using an approximate real space renormalization transformation which involves block spins. The critical indices α, β, η, and ν are calculated and compared with previous results, as is the critical couplingy _c. The method is shown to respect one of the scaling relations, and in 1+1D some exact results are reproduced (y _c=1, ν=1).     

A unique approach to accurately measure thickness in thick multilayers

X‐ray optics called multilayer Laue lenses (MLLs) provide a promising path to focusing hard X‐rays with high focusing efficiency at a resolution between 5 nm and 20 nm. MLLs consist of thousands of depth‐graded thin layers. The thickness of each layer obeys the linear zone plate law. X‐ray beamline tests have been performed on magnetron sputter‐deposited WSi₂/Si MLLs at the Advanced Photon Source/Center for Nanoscale Materials 26‐ID nanoprobe beamline. However, it is still very challenging to accurately grow each layer at the designed thickness during deposition; errors introduced during thickness measurements of thousands of layers lead to inaccurate MLL structures. Here, a new metrology approach that can accurately measure thickness by introducing regular marks on the cross section of thousands of layers using a focused ion beam is reported. This new measurement method is compared with a previous method. More accurate results are obtained using the new measurement approach.     

How to measure the phase diffusion dynamics in the micromaser

We propose a realistic scheme for measuring the micromaser linewidth by monitoring the phase diffusion dynamics of the cavity field. Our strategy consists of exciting an initial coherent state with the same photon number distribution as the micromaser steady-state field, singling out a purely diffusive process in the system dynamics. After the injection of a counterfield, measurements of the population statistics of a probe atom allow us to derive the micromaser linewidth in all ranges of the relevant parameters, establishing experimentally the distinctive features of the micromaser spectrum due to the discreteness of the electromagnetic field.     

On the dynamics of excitations in disordered systems

A new, time-local (TL) reduced equation of motion for the probability distribution of excitations in a disordered system is developed. ToO(k²) the TL equation results in a Gaussian spatial probability distribution, i.e, P(r, t) = [(2)^1/2]^–dexp(-r²/2²), where = (t) is a correlation length, andr = ¦r¦. The corresponding distribution derived from the Hahn-Zwanzig (HZ) equation is more complicated and assumes the asymptotic (r ) form: P(r, s)(s ^d )^–1exp(–r/) · (r/)^(1-d)/2 where = (s),d is the space dimensionality, ands is the Laplace transform variable conjugate tot. The HZ distribution generalizes the scaling form suggested by Alexanderet al. ford= 1. In the Markov limit (t)t, (s)1/s, and the two distributions are identical (ordinary diffusion).     

Uniqueness of the translationally invariant ground state in quantum spin systems

We introduce a class of quantum spin systems on ^d. We show that the translationally invariant ground state is unique for this system if it is in a strong external field.Supported by the Science and Engineering Research Council