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.     

Energy barrier distributions for magnetic nanoparticles with competing cubic and uniaxial anisotropies

We report in this study the effect of the competition between cubic and uniaxial anisotropies on the magnetic properties of magnetic nanoparticles. We have employed Monte Carlo simulations in our calculations and we have seen that the observed behavior is very different for the cases where easy uniaxial axes are completely random oriented or parallel to an external magnetic field. We have also calculated the effective energy barrier distribution probed during the isothermal magnetic relaxation and a two peak structure is observed only for a random orientation of uniaxial axes.     

New exact approach to models of diffusion in one-dimensional random systems and optimal network kinetics in spin glass models

It is shown that in one-dimensional stochastic models with gaussian random energy levels along a quantum reaction coordinate the dominant, rate-determining time-scale does not follow the conventional Arrhenius law, but rather has a much stronger temperature dependence, of the form τ ～ exp[(B/k_BT)²], where B is proportional to the width of the energy distribution. The new activation law can be ascribed to the large number of energy barriers of varying heights which exist in the random structure, as distinct from the conventional case of a single barrier, leading to the Arrhenius form τ ～ T^p × exp(A/k_BT). In systems with random structure and configuration space which are not strictly one-dimensional it is discussed if the thermal energy bias of detailed balance may lead to a kinetics that is essentially restricted to an energetically optimal network at low temperatures, thus leading to an essentially one-dimensional diffusion. Several recent studies of spin glass models appear to support the relevance of this principle, and include the observation of the new activation law in Monte Carlo experiments.     

Features of low-frequency spin dynamics in manganite LaMnO3 according to 139La NMR data

The spin-lattice and spin-spin relaxation times of ¹³⁹La are measured in manganite LaMnO₃. Analysis of the frequency dependence of the spin-lattice relaxation rate in the paramagnetic temperature range shows that this quantity is determined by magnetic fluctuations. The magnitude of the fluctuating field is estimated. It is shown that the correlation time for spin fluctuations varies with temperature in accordance with the Arrhenius law. The high value of the spin-spin relaxation rate in the paramagnetic region can be due to strong anisotropy of fluctuating magnetic fields at La nuclei.     

Rotating frame analog of spin-locking and spin-lattice relaxation in the doubly rotating frame

The present paper reports the achievement of the rotating-frame analog of spin-locking and its application to the precise measurements of the spin-lattice relaxation time T(1DR) in the doubly rotating frame. After the magnetization is aligned along the resonant RF field H(1), a pulse sequence of a low-frequency oscillating magnetic field at exact resonance is applied perpendicular to H(1). We have overcome several technical difficulties arising from the fact that the rotating-wave approximation is not valid for the low-frequency field. We have theoretically derived an expression of T(-1)(1DR) due to fluctuating magnetic dipole interactions in the weak collision case and found an important relation among the spin-lattice relaxation rates T(-1)(1), T(-1)(1rho), and T(-1)(1DR). This relation can be used to ascertain whether the relaxation is only due to the fluctuating magnetic dipole interactions between like spins. The experiment was carried out on (1)H nuclei in tetramethylammonium iodide (CH(3))(4)NI and the temperature dependence of T(-1)(1DR) was measured together with that of T(-1)(1) and T(-1)(1rho). The activation energies and the preexponential factors of Arrhenius expressions of the correlation times are newly determined.     

Dielectric relaxation in nanopillar NiFe–silicon structures in high magnetic fields

We explore the dielectric relaxation properties of NiFe nanowires in a nanoporous silicon template. Dielectric data of the NiFe–silicon structure show a strong relaxation resonance near 30 K. This system shows Arrhenius type of behavior in the temperature dependence of dissipation peaks vs. frequency. We report magnetic field dependence of dipolar relaxation rate and the appearance of structure in the dielectric spectrum related to multiple relaxation rates. A magnetic field affects both the exponential prefactor in the Arrhenius formula and the activation energy. From this field dependence we derive a simple exponential field dependence for the prefactor and linear field approximation for the activation energy which describes the data. We find a significant angular dependence of the dielectric relaxation spectrum for regular silicon and nanostructured silicon vs. magnetic field direction, and describe a simple sum rule that describes this dependence. We find that although similar behavior is observed in both template and nanostructured materials, the NiFe–silicon shows a more complex, magnetic field dependent relaxation spectrum.     

Non-Arrhenius relaxation of the Heisenberg model with dipolar and anisotropic interactions

The dynamical properties of a 2D Heisenberg model with dipolar interactions and perpendicular anisotropy are studied using Monte Carlo simulations in two different ordered regions of the equilibrium phase diagram. We find a temperature defining a dynamical transition below which the relaxation suddenly slows down and the system apart from the typical Arrhenius relaxation to a Vogel-Fulcher-Tamann law. This anomalous behavior is observed in the scaling of the magnetic relaxation and may eventually lead to a freezing of the system. Through the analysis of the domain structures we explain this behavior in terms of the domains dynamics. Moreover, we calculate the energy barriers distribution obtained from the data of the magnetic viscosity. Its shape supports our comprehension of both, the Vogel-Fulcher-Tamann dynamical slowing down and the freezing mechanism.     

1H nutation experiments under low-amplitude radiofrequency fields. Quantitative analysis of a complex NMR signal arising from water in clays and including a Pake doublet

It is shown theoretically and experimentally that, under weak radiofrequency (RF) field conditions, nutation frequency depends on relaxation times. The Fourier transform of a nutation curve, which is obtained by plotting signal amplitude as a function of RF field application time, yields separate bands corresponding to the components of an unresolved composite signal. This can be effectively achieved provided that these components possess different relaxation characteristics. Using proton nuclear magnetic resonance, this new method is applied to the study of water in clays and leads to the proportion of different types of water. The case where one water species appears in the form of a Pake doublet is considered.     

Exchange anisotropy in Co/NiO bilayers: time-dependent effects

The time dependence of the exchange anisotropy was studied in Co/NiO bilayers. In order to only observe the relaxation phenomena inside the antiferromagnetic (AF) layer and to eliminate the dynamic behaviour inside the ferromagnetic (F) layer, we have developed an experimental method where a small a.c. magnetic field is applied perpendicular to the main anisotropy axis. All data are obtained by magneto-optical (m.o.) experiments. We observe a logarithmic time dependence of Hud, the exchange unidirectional anisotropy. We prove that the key parameter for the rate of relaxation is the anisotropy of the AF layer which depends strongly of the preparation method. We use the random field model as proposed by Malozemoff and suppose a breakdown of the AF interface into regular domains of size close to the crystallite size (10 nm width). If we further develop a Fulcomer and Charap relaxation model, we can propose from the distribution of relaxation times an analysis in terms of a spread of AF anisotropy energies. High magnetic pulsed field experiments (55 T) complete the experimental study and the results are analysed assuming that the Zeeman energy balances the anisotropy energy of the AF domains and switches them into the opposite direction.     

Nonlinear dielectric susceptibility of dipole impurities dissolved in the lattice of quantum paraelectrics

A general relation is derived for calculating the nonlinear dielectric susceptibility of a system placed in an external ac magnetic field, which consists of tunneling and interacting dipole impurities described by the Hamiltonian of the transverse Ising model and a lattice of ions whose dynamics is specified in the soft-mode model with the possible ferroelectric phase transition suppressed by zero-point quantum oscillations. It is shown that the relaxation peaks in the dielectric response can be enhanced several times through relaxator interaction with the soft mode. A general expression is obtained to describe the deviation from the Arrhenius law in this case. The results of this work can be employed for interpretation of recent experiments that revealed a strong effect of isovalent impurities at extremely low concentrations on the macroscopic properties of incipient ferroelectrics.     

Dielectric relaxation and ac conductivity of double perovskite oxide Ho2ZnZrO6

Double perovskite oxide holmium zinc zirconate Ho₂ZnZrO₆ (HZZ) is synthesized by solid state reaction technique under a calcination temperature of 1100 °C. The crystal structure has been determined by powder X-ray diffraction, which shows monoclinic phase at room temperature. The variation of dielectric constant (ε′) and loss tangent (tan δ) with frequency is carried out assuming a distribution of relaxation times. The frequency corresponding to loss tangent peak is found to obey an Arrhenius law with activation energy of 89.7 meV. The frequency-dependant electrical data are analyzed in the framework of conductivity and electric modulus formalisms. Both these formalisms show qualitative similarities in relaxation times. The scaling behaviour of imaginary electric modulus shows the temperature-independent nature of the distribution of relaxation times. Nyquist plots are drawn to identify an equivalent circuit and to know the bulk and interface contributions.     

Magnetic properties of nanoscale crystalline maghemite obtained by a new synthetic route

In this work we describe the synthesis and characterization of maghemite nanoparticles obtained by a new synthetic route. The material was synthesized using triethylamine as a coprecipitation agent in the presence of the organic ligand N,N′-bis(3,5-di-tert-butyl-catechol)-2,4-diaminotoluene (LCH₃). Mössbauer spectrum at 4 K shows typical hyperfine parameters of maghemite and Transmission Electron Microscopy images reveal that the nanoparticles have a mean diameter of 3.9 nm and a narrow size distribution. AC magnetic susceptibility in zero field presents an Arrhenius behavior with unreasonable relaxation parameters due to the strong influence of dipolar interaction. In contrast when the measurements are performed in a 1 kOe field, the effect of dipolar interactions becomes negligible and the obtained parameters are in good agreement with the static magnetic properties. The dynamic energy barrier obtained from the AC susceptibility results is larger than the expected from the average size observed by HRTEM results, evidencing the strong influence of the surface contribution to the anisotropy.     

Low-temperature behavior of a one-dimensional random Ising model

The random Ising chain is a very simple model with a large number of metastable states. Simple analytical calculation of the relaxation of energy and magnetization is presented. The effect of a nonzero magnetic field is discussed qualitatively. The slow relaxation in this simple model resembles that observed in spin glasses. A weak magnetic field can produce rather strong effects. The magnetization is shown to be a nonanalytic function of the field. The field also greatly alters the metastability characteristics.     

Diffusion and relaxation effects in general stray field NMR experiments

We analyze the evolution of magnetization following any series of radiofrequency pulses in strongly inhomogeneous fields, with particular attention to diffusion and relaxation effects. When the inhomogeneity of the static magnetic field approaches or exceeds the strength of the RF field, the magnetization has contributions from different coherence pathways. The diffusion or relaxation induced decay of the signal amplitude is in general nonexponential, even if the sample has single relaxation times T(1), T(2) and a single diffusion coefficient D. In addition, the shape of the echo depends on diffusion and relaxation. It is possible to separate contributions from different coherence pathways by phase cycling of the RF pulses. The general analysis is tested on stray field measurements using two different pulse sequences. We find excellent agreement between measurements and calculations. The inversion recovery sequence is used to study the relaxation effects. We demonstrate two different approaches of data analysis to extract the relaxation time T(1). Finite pulse width effects on the timing of the echo formation are also studied. Diffusion effects are analyzed using the Carr--Purcell--Meiboom--Gill sequence. In a stray field of a constant gradient g, we find that unrestricted diffusion leads to nonexponential signal decay versus echo number N, but within experimental error the diffusion attenuation is still only a function of g(2)Dt(3)(E)N, where t(E) is the echo spacing.     

Magnetic relaxation in a random system of interacting rodlike nanoparticles

It is shown in the framework of the generalized mean-field approximation taking into account spatial fluctuations of the local magnetic field that the collective effect of dipole interaction in a random 3D system of identical (rodlike) magnetic nanoparticles with parallel easy magnetization axes shifts the relaxation magnetization curves towards shorter times (i.e., accelerates the relaxation process). In addition, the course of this process depends (via the demagnetizing field) on the sample shape. The interaction between nanograins affects the magnetization relaxation of a random 2D system only when the magnetic moments of the grains are perpendicular to the plane of the system.     

Transient response of hot electrons in narrow-gap semiconductors at low temperatures in the presence of a longitudinal quantizing magnetic field

Transient response of hot electrons in narrow-gap semiconductors to a step electric field in the presence of a longitudinal quantizing magnetic field has been studied at low temperatures using displaced Maxwellian distribution. The energy and momentum balance equations are used assuming acoustic phonon scattering via deformation potential responsible for the energy relaxation and elastic acoustic phonon scattering together with ionized impurity scattering for momentum relaxation. The calculations for the variation of drift velocity and electron temperature as functions of time are made for n-Hg_0.8Cd_0.2 Te in the extreme quantum limit at 1.5 K and 4.2 K. The momentum and energy relaxation times are found to be of the same order of magnitudes as with the experimental values. The magnetic field and lattice temperature dependences of the relaxation rates have been investigated.One of the authors, Suchandra Bhaumik, acknowledges the Council of Scientific and Industrial Research (New Delhi) for financial support.     

磁性纳米颗粒系统偶极相互作用的Monte Carlo研究

采用局域Monte Carlo方法模拟不同易轴分布的简单立方排列单分散单畴Fe纳米颗粒系统的ZFC-FC曲线及磁滞回线.结果表明：随着偶极相互作用的增强，系统的阻塞温度T_B逐渐增大，且ZFC曲线的峰变宽.说明偶极相互作用使得系统的有效能垒提高，分布宽度增加.研究FC曲线磁化强度的倒数与温度关系，发现偶极相互作用系统中存在反铁磁有序.系统的阻塞态及超顺磁态的磁滞回线表明，极低低温下，随着偶极相互作用的增强，系统的矫顽力和剩磁减小，偶极相互作用阻碍系统的磁化；系统处于超顺磁态，各向异性作用及偶极相互作用使得系统的磁化曲线偏离Langevin曲线且偶极相互作用展现出退磁相互作用效应.偶极相互作用增强，系统磁化曲线与Langevin曲线偏差量的最大值向低场移动.在偶极相互作用下，易轴与外场夹角为45°的磁性纳米颗粒系统的平均有效能垒和有效能垒分布宽度较易轴随机分布系统的大.     

On the determination of the energy of activation of relaxation transitions in polymers by differential scanning calorimetry

The determination of the energy of activation (barrier height) of elementary events involved in relaxation (fluctuation) transitions in polymers from the temperature dependence of the specific heat is discussed. The dependence is derived by the method of differential scanning calorimetry. It is emphasized that the correct determination of the energy of activation must include the temperature variation of the barrier. The deviation of the preexponential in the Arrhenius temperature dependence from the value predicted theoretically demonstrates that the barrier does depend on temperature. Experimental data from which the realistic energy of activation of the α relaxation in polymers can be found are given.     

Determination of the two dimensional distribution of the attempt relaxation times and activation energies from temperature dependence of dielectric dispersion

We present a method for numerical calculation of two dimensional distributions of the attempt relaxation times and activation energies from the temperature dependence of the experimental dielectric permittivity dispersion. We introduce empirical attempts to account for broad and/or asymmetric dispersions with the idea of using a weighted collection of Debye relaxation times. Then we present a modification of the aforementioned idea including attempt relaxation time and activation energy using the Arrhenius law, which significantly complicates the computation of the aforementioned distribution. Incorporating the activation energy and the attempt relaxation time into the equation transforms the discretized matrix equations into tensor equations. We rework the tensor equations into simpler matrix equations, thus permitting us to solve the presented discretized integral equation by using existing Least Distance Problem solving methods. Also, we present a regularization method and a way to choose the regularization parameter based on a best fit criterion. In the end we discuss the method showing some simulated results and experimental results. We then point out some problems involved in the calculations and propose methods to reduce their significance.