Spin relaxation of quadrupole nuclei in paramagnetic and magnetically ordered insulators

The longitudinal and transverse spin relaxation through a (generally anisotropic) electron-nucleus interaction in paramagnetic and magnetically ordered insulators is theoretically studied for nuclei with a resolved quadrupole structure. Expressions are derived for the relaxation rates of both the transverse nuclear magnetization components when individual transitions are excited in the quadrupole structure and the total longitudinal nuclear magnetization component. These expressions are reduced to a form that contains the Fourier transforms of the time correlation functions only for the electron spins. Given the specific form of these correlation functions corresponding to different phase states of the electron spins and different origins of their fluctuations, the temperature dependences of the nuclear relaxation rates are ascertained in various cases, including those for dipole and isotropic hyperfine interactions. Calculations are performed for arbitrary electron and half-integer nuclear spins by taking into account the possible quadrupole splitting of the NMR spectrum without any restriction on the smallness of the ratio ?ω s/k_BT (ω_s is the resonance frequency of the electron spins). The derived expressions are compared with available experimental data on the longitudinal and transverse nuclear relaxation in colossal-magnetoresistance lanthanum manganites in the part of their phase diagram where the corresponding samples are either paramagnetic or magnetically ordered insulators and near the points of transition to an ordered state. Interpretations alternative to the existing ones are offered.     

Interaction of a nuclear spin with a soliton gas

We investigate the dynamics of a nuclear spin which is weakly coupled to a one-dimensional, thermalized, low-density gas of sine-Gordon solitons. Longitudinal (T₁) and transverse (T₂) relaxation times and the dynamic frequency shift are computed.     

Dynamics in quantum Ising chain driven by inhomogeneous transverse magnetization

We study the dynamics caused by transport of transverse magnetization in one dimensional transverse Ising chain at zero temperature. We observe that a class of initial states having product structure in fermionic momentum-space and satisfying certain criteria, produce spatial variation in transverse magnetization. Starting from such a state, we obtain the transverse magnetization analytically and then observe its dynamics in presence of a homogeneous constant field Γ. In contradiction with general expectation, whatever be the strength of the field, the magnetization of the system does not become homogeneous even after infinite time. At each site, the dynamics is associated with oscillations having two different timescales. The envelope of the larger timescale oscillation decays algebraically with an exponent which is invariant for all such special initial states. The frequency of this oscillation varies differently with external field in ordered and disordered phases. The local magnetization after infinite time also characterizes the quantum phase transition.     

Energy barrier distributions in magnetic systems from the Tln(t/τ0) scaling

A method based in the Tln(t/τ₀) scaling is proposed to obtain the energy barrier distribution of a randomly oriented assembly of magnetic entities. It essentially consists on performing the logarithmic time derivative of the master relaxation curve. The method has been applied to two small particle systems and the obtained distributions are in good agreement with the ones used to fit the master curves to the magnetization decay of a system following the Arrhenius law. The effect of the specific shape of the distribution functions on the low temperature behaviour of the relaxation rate and the possibility to erroneously attribute this behaviour to non-thermal processes is also discussed.     

Exploiting the flexibility of a family of models for taxation and redistribution

In this paper we present and discuss results of Monte Carlo numerical simulations of the two-dimensional Ising ferromagnet in contact with a heat bath that intrinsically has a thermal gradient. The extremes of the magnet are at temperatures T ₁?<?T _c ?<?T ₂, where T _c is the Onsager critical temperature. In this way one can observe a phase transition between an ordered phase (T?<?T _c ) and a disordered one (T?>?T _c ) by means of a single simulation. By starting the simulations with fully disordered initial configurations with magnetization m????0 corresponding to T?=???, which are then suddenly annealed to a preset thermal gradient, we study the short-time critical dynamic behavior of the system. Also, by setting a small initial magnetization m?=?m ₀, we study the critical initial increase of the order parameter. Furthermore, by starting the simulations from fully ordered configurations, which correspond to the ground state at T?=?0 and are subsequently quenched to a preset gradient, we study the critical relaxation dynamics of the system. Additionally, we perform stationary measurements (t??????) that are discussed in terms of the standard finite-size scaling theory. We conclude that our numerical simulation results of the Ising magnet in a thermal gradient, which are rationalized in terms of both dynamic and standard scaling arguments, are fully consistent with well established results obtained under equilibrium conditions.     

Saving transverse magnetization

A magnetization storage sequence, ALT-1 (alternating longitudinal and transverse components), is reported. The ALT-1 sequence is a hybrid of two types of storage sequences, the Carr–Purcell type and store-and-restore sequences. During incremental storage periods within the ALT-1 sequence, essentially half of the initially transverse magnetization is stored along the z-axis and the other half is prolonged by an echo-generating pulse. The portions of initial magnetization that are stored as longitudinal components or transverse components are alternated by a π/2 pulse during the cycle. Both transverse components of the initial magnetization are treated the same in the ALT-1 sequence and orientational (phase) information of the initial magnetization is kept during the storage period. The ALT-1 sequence can preserve magnetization more effectively than a published class of modified Carr–Purcell type sequences, because essentially half of the magnetization during incremental storage periods is not subjected to relaxation from T₂ effects.     

Characterization and Suppression Techniques for Degree of Radiation Damping in Inversion Recovery Measurements

Radiation damping is a phenomenon in which transverse nuclear magnetization couples with the current in a coil used in nuclear magnetic resonance experiments. This results in an additional magnetic field that increases the relaxation pathway for the magnetization, which then relaxes back to equilibrium more quickly. Radiation damping has been shown to affect longitudinal relaxation time (T₁) measurement in inversion recovery experiments. In this work, we demonstrate that the extent of radiation damping depends upon the T₁ of the sample. Radiation damping difference spectroscopy is used to characterize the severity of radiation damping, while gradient inversion recovery is used for radiation damping suppression in T₁ measurements. At field strength of 9.4 T, for the radiation damping characteristic time (T_rd) of 50 ms, these investigations show non-negligible radiation damping effects for T₁ values greater than T_rd, with severe distortions for T₁ longer than about 150 ms, showing reasonable agreement with the predicted T_rd. We also report a discrepancy between published expressions for the characteristic radiation damping time.     

Effects of off-resonance irradiation, cross-relaxation, and chemical exchange on steady-state magnetization and effective spin-lattice relaxation times

In the presence of an off-resonance radiofrequency field, recovery of longitudinal magnetization to a steady state is not purely monoexponential. Under reasonable conditions with zero initial magnetization, recovery is nearly exponential and an effective relaxation rate constant R_1eff = 1/T_1eff can be obtained. Exact and approximate formulas for R_1eff and steady-state magnetization are derived from the Bloch equations for spins undergoing cross-relaxation and chemical exchange between two sites in the presence of an off-resonance radiofrequency field. The relaxation formulas require that the magnetization of one spin is constant, but not necessarily zero, while the other spin relaxes. Extension to three sites with one radiofrequency field is explained. The special cases of off-resonance effects alone and with cross-relaxation or chemical exchange, cross-relaxation alone, and chemical exchange alone are compared. The inaccuracy in saturation transfer measurements of exchange rate constants by published formulas is discussed for the creatine kinase reaction.     

Zero‐field μ+SR study of the colossal magnetoresistance material La0.67Ca0.33MnO3

Zero‐field μ⁺SR and resistivity experiments on La_0.67Ca_0.33MnO₃ powder show that the ferromagnetic transition temperature (T_C=274\ K) and resistivity peak temperature coincide to within 1 K, about 10 K higher than T_C determined from the bulk magnetization. The sublattice magnetization \nu_μ(T) is well described for T ≤ T_C by (1-T/T_C)^β , where β =0.345 ± 0.015. Unusual relaxation dynamics suggest a wide distribution of Mn‐ion correlation times. These results are discussed in terms of the effects of polarons on the spin and charge dynamics. This revised version was published online in July 2006 with corrections to the Cover Date.     

What can we learn about critical magnetic phenomena from muon spin rotation experiments?

Measurements of the spin precession frequencies ω_μ and transvers relaxation rates Γ₂ of positive muons (μ⁺) magnetic phase of several iron-cobalt alloys and coabalt, and in amorphous Fe_o.91Zr_0.09 alloys are discussed with particular reference to the influence of critical phenomena on ω_μ and Γ₂. Although the temperature dependence ω_μ(T) is well described by scaling law ω_μ ∝ (T_c?T)^β′ where α′ varies strongly with the co concentration in the FeCo alloys, it is shown that the exponent α′ is not identical to the static scalling parameter β describing the critical behaviour of the spontaneous magnetization M. In paramagnetic iron we find Γ₂∝(T-T_c)^0.72, which is attributed to the effect of dynamical spin fluctuations on the μ⁺. Due to the apparent difference between the temperature dependence of ω_μ and that of M below T_c the frequency shifts observed in the paramagnetic regime are probably not directly proportional to the magnetic susceptibility. In amorphous Fe_0.91Zr_0.09 allosy frequency shifts and transverse relaxation rates are found up to nearly 2 T_c. Due to the shape of the Fe_0.91Zr_0.09 sample, demagnetization inhomogeneities certainly play an important rôle.     

The <Emphasis Type="Bold">±</Emphasis><Emphasis Type="Bold">J</Emphasis> spin glass in Migdal-Kadanoff approximation

We study the low-temperature phase of the three-dimensional ± J Ising spin glass in Migdal-Kadanoff approximation. At zero temperature, T = 0, the properties of the spin glass result from the ground-state degeneracy and can be elucidated using scaling arguments based on entropy. The approach to the asymptotic scaling regime is very slow, and the correct exponents are only visible beyond system sizes around 64. At T > 0, a crossover from the zero-temperature behaviour to the behaviour expected from the droplet picture occurs at length scales proportional to T ^-2/ds where d_s is the fractal dimension of a domain wall. Canonical droplet behaviour is not visible at any temperature for systems whose linear dimension is smaller than 16 lattice spacings, because the data are either affected by the zero-temperature behaviour or the critical point behaviour. Received 18 February 2001     

Critical nuclear relaxation in cobalt metal

Nuclear magnetic resonance of cobalt metal was investigated in the paramagnetic and ferromagnetic states and in the critical region below T_c. The Knight shift and spin lattice relaxation times were measured in the paramagnetic phase in the solid and liquid states from 1578 K to 1825 K. The resonant frequency, spin-lattice and spin-spin relaxation times were measured in the ferromagnetic phase from room temperature to 1385 K. The main part of (T₁T)^-1 results from fluctuating orbital moments in both phases except near T_c where this process forms the background for critical spin relaxation. The critical exponents for T^-1₁ and for the magnetization in the ferromagnetic state were found to be n' = 0.96 ± 0.07 and β = 0.308 ± 0.012, respectively.     

Aging effects in the nonequilibrium behavior of multilayer magnetic superstructures

A numerical Monte Carlo study of the nonequilibrium behavior of multilayer magnetic superstructures consisting of alternating magnetic and nonmagnetic nanolayers is performed. The calculated two-time autocorrelation function and the staggered magnetization of the structure at its evolution starting from various initial states are analyzed. The analysis reveals aging effects characterized by a slowing down of the relaxation and correlation characteristics in the system with the waiting time. It is shown that, in contrast to bulk magnetic systems, the aging effects in magnetic superstructures arise not only near the ferromagnetic ordering temperature T _c in the films but also within a wide temperature range at T ≤ T _c.     

Magnetization dynamics in isolated Ising chains

The Glauber dynamics of an Ising chain or ring is shown to be determined by two characteristic times: τ₁ for relaxation of the average magnetization per spin and τ₂ for dynamical spontaneous symmetry breaking. An analytical solution for magnetization dynamics in a finite chain with fixed spins at both ends is found by the method of images. This solution is then used to calculate the spin-spin correlation functions for rings and chains. At low temperatures, since τ₁ ? τ₂, there must exist a range of times when the chain is in one of two ordered states.     

Low temperature quantum diffusion of muonium in KCl

T ₁ spin relaxation of muonium in KCl has been studied at low temperatures (20 mK to 2 K), where the motion is believed to be band-like, i.e. the mean free path is longer than the lattice constant. The Celio model, based on the assumption of stochastic hopping of muonium, accurately describes the field dependence ofT ₁ at higher temperatures but fails below 4 K. The measuredT ₁ spin relaxation rates vary weakly with temperature below 2 K even thoughk _BT at the lowest temperature is well below the estimated muonium bandwidth obtained from the data at higher temperatures. This is taken as evidence that muonium is not completely thermalized on the time-scale of the muon lifetime due to the weak interaction with phonons at low temperatures.     

二维完全阻挫$lt;i$gt;XY$lt;/i$gt;模型的动力学指数

采用大规模动力学蒙特卡罗模拟方法,对二维完全阻挫XY模型的Kosterlitz-Thouless（KT）型相变展开数值研究.系统从有序初始态出发演化到高于KT相变的温度,以普适的动力学标度形式为基础,通过测量磁化和Binder累积量,得出动力学关联时间和平衡态空间关联长度,确定出更精确的动力学指数z.特别是建议并证实了一种在KT相变温度以上（T>T_KT）,独立判断动力学指数z的方法.模拟结果表明,动力学指数z≈2,这与在相变温度以下（T<T_KT）测量的结果一致. 关键词： 蒙特卡罗法 动力学指数 Kosterlitz-Thouless相变 XY模型')" href="#">二维完全阻挫XY模型     

Memory effects in superparamagnetic La<Subscript>0.6</Subscript>Pb<Subscript>0.4</Subscript>MnO<Subscript>3</Subscript> nanoparticles

Using different temperature and field protocols, the memory behaviors in the dc magnetization and magnetic relaxation are observed at temperature below blocking temperature T_B = 93 K in weakly interacting manganite La_0.6Pb_0.4MnO₃ nanoparticles. The results indicate that the magnetic dynamics of this nanoparticle system is strongly correlated with a wide distribution of particle relaxation times, which may arise from the particle weak interaction and distribution of the particle size.     

Erratum: “Magnetization dynamics in isolated Ising chains” [<Emphasis Type="Italic">JETP</Emphasis> 110, 360 (2010)]

The Glauber dynamics of an Ising chain or ring is shown to be determined by two characteristic times: τ₁ for relaxation of the average magnetization per spin and τ₂ for dynamical spontaneous symmetry breaking. An analytical solution for magnetization dynamics in a finite chain with fixed spins at both ends is found by the method of images. This solution is then used to calculate the spin-spin correlation functions for rings and chains. At low temperatures, since τ₁ ≫ τ₂, there must exist a range of times when the chain is in one of two ordered states.     

Ferromagnetic phase transitions in the magnetically heterogeneous solid solution system EuxLa1−xS

The ferromagnetic phase transitions of the solid solution system Eu_xLa_1-xS with Eu-concentrations x=0.85, 0.65 and 0.50 are analyzed by measurements of the initial permeability, the specific heat and the magnetization. For the sample with x=0.85 the spontaneous magnetization develops continuously between two temperatures T_c1 and T_c2. For the sample with x=0.65 a well defined magnetic ordering temperature exists. One observes strongly curved magnetization isotherms when plotting the magnetization data in form of modified Arrott plots. The M(H, T) data above the curved region show usual ferromagnetic scaling with the critical exponents β=0.5 and δ=4.7. These exponents fulfill the scaling relations with the exponents γ=2.1 and α≈-1 derived for the initial susceptibility and the magnetic specific heat. The sample with the concentration x=0.50 turns out to be not truely ferromagnetic. It is a spin glass with strong ferromagnetic short range order.     

Asymptotic dynamics,non-critical and critical fluctuations for a geometric long-range interacting model

We study the dynamics of geometric spin system on the torus with long-range interaction. As the number of particles goes to infinity, the process converges to a deterministic, dynamical magnetization field that satisfies an Euler equation (law of large numbers). Its stable steady states are related to the limits of the equilibrium measures (Gibbs states) of the finite particle system. A related equation holds for the magnetization densities, for which the property of propagation of chaos also is established. We prove a dynamical central limit theorem with an infinite-dimensional Ornstein-Uhlenbeck process as a limiting fluctuation process. At the critical temperature of a ferromagnetic phase transition, both a tighter quantity scaling and a time scaling is required to obtain convergence to a one-dimensional critical fluctuation process with constant magnetization fields, which has a non-Gaussian invariant distribution. Similarly, at the phase transition to an antiferromagnetic state with frequencyp ₀, the fluctuation process with critical scaling converges to a two-dimensional critical fluctuation process, which consists of fields with frequencyp ₀ and has a non-Gaussian invariant distribution on these fields. Finally, we compute the critical fluctuation process in the infinite particle limit at a triple point, where a ferromagnetic and an antiferromagnetic phase transition coincide.Work supported by Deutsche Forschungsgemeinschaft