Low-temperature magnetization dynamics of magnetic molecular solids in a swept field

The swept-field experiments on magnetic molecular solids such as Fe₈ are studied using Monte Carlo simulations, and a kinetic equation developed to understand collective magnetization phenomena in such solids, where the collective aspects arise from dipole–dipole interactions between different molecules. Because of these interactions, the classic Landau–Zener–Stückelberg theory proves inadequate, as does another widely used model constructed by Kayanuma. It is found that the simulations provide a quantitatively accurate account of the experiments. The kinetic equation provides a similarly accurate account except at very low sweep velocities, where it fails modestly. This failure is attributed to the neglect of short-range correlations between the dipolar magnetic fields seen by the molecular spins. The simulations and the kinetic equation both provide a good understanding of the distribution of these dipolar fields, although analytic expressions for the final magnetization remain elusive.     

First-passage-time approach to overbarrier relaxation of magnetization

We consider the irreversible dynamics of the magnetization vectorM in a single-domain particle. The dynamics is given by a stochastic phenomenological equation due to Gilbert. It contains a damping field proportional toM and a corresponding white noise field component. The probability distribution function satisfies a Fokker-Planck equation derived by Brown. We give the overbarrier decay rate out of a metastable minimum. First we rederive the well-known expression for for an axially symmetric model. We argue that this result is unphysical. For systems of general point symmetry of the magnetic anisotropy energy we give in both the low-damping and intermediate- to high-damping limits.     

Effect of inter-level relaxation and cavity length on double-state lasing performance of quantum dot lasers

Double-state lasing phenomena are easily observed in self-assembled quantum dot (QD) lasers. The effect of inter-level relaxation rate and cavity length on the double-state lasing performance of QD lasers is investigated on the basis of a rate equation model. Calculated results show that, for a certain cavity length, the ground state (GS) lasing threshold current increases almost linearly with the inter-level relaxation lifetime. However, as the relaxation rate becomes slower, the ratio of excited state (ES) lasing threshold current over the GS one decreases, showing an evident exponential behavior. A relatively feasible method to estimate the inter-level relaxation lifetime, which is difficult to measure directly, is provided. In addition, fast inter-level relaxation is favorable for the GS single-mode lasing, and leads to lower wetting layer (WL) carrier occupation probability and higher QD GS capture efficiency and external differential quantum efficiency. Besides, the double-state lasing effect strongly depends on the cavity length.     

Interfacial diffusion relaxation of internal stresses in solids

The relaxation of internal stresses due to interfacial diffusion in a two-phase solid is studied theoretically with the help of the onsageristic approach of irreversible thermodynamics. In this note we derive an expression for the rate at which internal stresses associated with misfit caused by bonding a flat surface of one material to a rough surface of another. The two phases are treated as isotropic clastic substances. It is assumed that the components of only of the solids are capable of leaving their positions of migrating along the interface. The driving force for this process is minimization of total energy-clastic plus interfacial energy. We show that the time constant for relaxing these stresses is proportional to the cube of the wavelength of the roughness.     

Low-temperature magnetization in nanofilms

The low-temperature magnetization of a film was analyzed by the use of exact Bose representation of spin operators that does not suffer from the presence of unphysical states. The magnetization of thin films has exponentially small temperature correctness, so that Dyson’s proof about exponentially small correction coming from two bosons at ideal lattice point cannot be used in film analyses. The main conclusions of this work are that magnetic lattice of a thin film is more rigid than the macroscopic lattice and that the autoreduction process (the three layer film divides into two layer subfilms) takes place in the film.     

Origin of the fast magnetization relaxation at low temperatures in HTS with strong pinning

The temperature T variation of the normalized magnetization relaxation rate S in high-temperature superconductors (HTS) with strong vortex pinning exhibits a maximum in the low-T range. This was reported for various HTS, and the origin of the faster relaxation at low T appearing in standard magnetization relaxation measurements was usually related to specific pinning properties of the investigated specimens. Since the observed behaviour seems to be characteristic to all HTS with enhanced pinning (generated by random and/or correlated disorder), we show that the S(T) maximum can be explained in terms of classic collective vortex creep. The influence of thermo-magnetic instabilities in the low-T range is also evidenced. The collective (elastic) creep regime is generated by the T dependent macroscopic currents induced in the sample during standard magnetization measurements.     

Effect of a dc magnetic field on the magnetization relaxation of uniaxial single-domain ferromagnetic particles driven by a strong ac magnetic field

The nonlinear ac stationary response of the magnetization of noninteracting uniaxial single-domain ferromagnetic particles acted on by superimposed dc and ac magnetic fields applied along the anisotropy axis is evaluated from the Fokker-Planck equation, expressed as an infinite hierarchy of recurrence equations for Fourier components of the relaxation functions governing longitudinal relaxation of the magnetization. The exact solution of this hierarchy comprises a matrix continued fraction, allowing one to evaluate the ac nonlinear response and reversal time of the magnetization. For weak ac fields, the results agree with perturbation theory. It is shown that the dc bias field changes substantially the magnetization dynamics leading to new nonlinear effects. In particular, it is demonstrated that for a nonzero bias field as the magnitude of the ac field increases the reversal time first increases and having attained its maximum at some critical value of the ac field, decreases exponentially.     

spin-lattice relaxation in cobalt-containing aluminophosphate molecular sieves

Phosphorus spin-lattice relaxation was studied in aluminophosphate molecular sieves containing various concentrations of either framework or non-framework cobalt. The behaviour of nuclear magnetisation in the presence of these paramagnetic centres was described successfully in the limit of no spin-diffusion. The diffusionless regime was strongly indicated with non-exponential magnetisation recovery and was therefore easy to recognise. According to the model, spin-lattice relaxation rates depend on the square of cobalt concentration. Measured relaxation rates agreed well with calculations if effective cobalt concentration was considered rather than the average one. The latter was obtained by bulk elemental analysis, while the former was extracted from cobalt concentration depth-profiles measured with Auger electron spectroscopy. These measurements indicated that in impregnated samples containing non-framework cobalt there could be much more cobalt near the crystal surface than within the crystal. Because high cobalt concentration can lead to an invisible phosphorus, only nuclei deep within the crystal contribute to the NMR signal. In such a case, the effective concentration is simply the concentration of cobalt far from the crystal surface. In our case, two impregnated samples with different bulk cobalt concentrations exhibited equal relaxation rates. Previously, such a case was misinterpreted as a case, in which nuclear spin-lattice relaxation was independent of cobalt concentration. AES measurements, however, revealed, that although average concentrations of the two samples were different by a factor of two, their effective concentrations were equal and thus in complete agreement with observed relaxation rates.     

High-temperature slow relaxation of the magnetization in Ni10 magnetic molecules

We investigate a family of molecular crystals containing noninteracting Ni10 magnetic molecules. We find slow relaxation of the magnetization below a temperature as high as 17 K and we show that this behavior is not associated with an anisotropy energy barrier. Ni10 has a characteristic magnetic energy spectrum structured in dense bands, the lowest of which makes the crystal opaque to phonons of energy below about 1 meV. We ascribe the nonequilibrium behavior to the resulting resonant trapping of these low-energy phonons. Trapping breaks up spin relaxation paths leading to a novel kind of slow magnetic dynamics which occurs in the lack of anisotropy, magnetic interactions and quenched disorder.     

Determination of the anisotropy constant and saturation magnetization of magnetic nanoparticles from magnetization relaxation curves

We have developed a new method for the determination of the anisotropy constant and saturation magnetization of magnetic nanoparticles. This method deals with the approximation of magnetization relaxation curves measured upon application and further fast switching off the dc magnetizing field. The relaxation process is registered in the time interval from 6 μs to several minutes by using a scanning high-T _C SQUID-microscope equipped with a specially designed electronic circuit composed of a fast solid-state switch and a low-inductance magnetizing coil. The algorithm for calculating the approximation data is based on the activation Néel–Arrhenius law and takes into account the size distribution of the nanoparticles and the angular distribution of their easy axes. The performance of the method is demonstrated on dilute (∼0.2 vol%) ensembles of near-spherical Fe₃O₄ nanoparticles with a mean size of 7.7 nm and a standard deviation of 45% as determined from transmission electron microscopy data.     

Spin-wave contributions to nuclear magnetic relaxation in magnetic metals

The longitudinal and transverse nuclear magnetic relaxation rates 1/T ₁(T) and 1/T ₂(T) are calculated for three- and two-dimensional (3D and 2D) metallic ferro- and antiferromagnets (FM and AFM) with localized magnetic moments in the spin-wave temperature region. The contribution of the one-magnon decay processes is strongly enhanced in comparison with the standard T-linear Korringa term, especially for the FM case. For the 3D AFM case this contribution diverges logarithmically, the divergence being cut at the magnon gap ω due to magnetic anisotropy, and for the 2D AFM case as ω^-1. The electron-magnon scattering processes yield T ²ln(T/ω) and T ²/ω^1/2-terms in 1/T ₁ for the 3D AFM and 2D FM cases, respectively. The two-magnon (“Raman”) contributions are investigated and demonstrated to be large in the 2D FM case. Peculiarities of the isotropic 2D limit (where the correlation length is very large) are analyzed. Received 29 November 1999 and Received in final form 6 June 2000     

Low-temperature phonoemissive tunneling rates in single molecule magnets

Tunneling between the two lowest energy levels of single molecule magnets with Ising type anisotropy, accompanied by the emission or absorption of phonons, is considered. Quantitatively accurate calculations of the rates for such tunneling are performed for a model Hamiltonian especially relevant to the best studied example, Fe₈. Two different methods are used: high-order perturbation theory in the spin–phonon interaction and the non-Ising-symmetric parts of the spin Hamiltonian, and a novel semiclassical approach based on spin-coherent-state-path-integral instantons. The methods are found to be in good quantitative agreement with other, and consistent with previous approaches to the problem. The implications of these results for magnetization of molecular solids of these molecules are discussed briefly.     

Integration of the boltzmann equation in the relaxation time approximation

We integrate by very simple means the Boltzmann equation in the relaxation time approximation. Our result improves on the solution previously found by Chambers, which does not take into account initial conditions.     

Measurement of spin-lattice relaxation times of C in organic solids

A transient nuclear Overhauser effect (NOE) makes measurements of the ¹³C spin-lattice relaxation times in organic solids complicated. Extended Solomon equations are applied in order to describe ¹³C spin-lattice relaxation with ¹H r.f. field irradiation. Spin-lattice relaxation under r.f. irradiation is shown to be generally a triple-exponential process, but it can be reduced to be single-exponential under stronger r.f. field irradiation as well as in the absence of ¹H initial magnetizations. Based on numerical calculations, the difference between spin-lattice relaxation curves obeying T₁^C < T₁^H and those obeying T₁^C < T₁^H is clearly indicated. The methyl group resonances in solid-state -valine are examined, and the experimental results agree well with the theoretical results.     

考虑激光下能级弛豫过程的调Q Nd∶YAG速率方程理论分析

本文比较了考虑与不考虑激光下能级弛豫过程的两种形式的调Q速率方程,并以二极管激光侧面泵浦电光调QNd∶YAG为例,分别采用两种形式的调Q速率方程,分析了调Q过程中上、下能级粒子数变化过程,计算了输出调Q激光脉冲波形、峰值功率以及能量,进行了比较分析,并解释了调Q“子脉冲”与拖尾现象     

考虑激光下能级弛豫过程的调Q Nd∶YAG 速率方程理论分析

本文比较了考虑与不考虑激光下能级弛豫过程的两种形式的调Q速率方程，并以二极管激光侧面泵浦电光调QNd∶ YAG为例，分别采用两种形式的调Q速率方程，分析了调Q过程中上、下能级粒子数变化过程，计算了输出调Q激光脉冲波形、峰值功率以及能量，进行了比较分析，并解释了调Q“子脉冲”与拖尾现象.     

用松弛法解薛定谔方程

求解定态薛定谔方程常常会涉及到常微分方程的本征值问题.目前解常微分方程本征值用的比较多的方法是以龙格-库塔方法为基础的打靶方法.打靶方法常用,但是计算时间长.当边界条件比较复杂或比较敏感的时候,用松弛法会有更好的效果.本文用松弛法解薛定谔方程,并和理论解进行比较.发现松弛法得到的数值解和理论解符合度很高,而且使用松弛法...     

Resonant tunnelling of the magnetization in molecular crystal of [（Mn1-xCrx）12O12 （CH3COO）16（H2O）4]·2CH3COOH·4H2O（x=0,0.03,0.04,0.05）

The quantum tunnelling of magnetization （QTM） in single crystals of the single molecule magnet （Mn1-xCrx）12- Ac （x=0, 0.03, 0.04, 0.05） has been investigated. In comparison with its parent Mnl2-Ac, a greater rate of magnetization relaxation and a lower effective potential-energy barrier have been observed in Cr-doping samples. This modulation of QTM due to the Cr-doping could be attributed to the small change of Sz due to the smaller spin of Cr itself and additional intrinsic but distributed transverse and longitudinal anisotropy raised by a subtle change of the local environment in the magnetic Mn12 core.     

Magnetocaloric features of complex molecular magnets: The (Cr7Ni)2Cu molecular magnet and beyond

We study the new kind of systems represented by the Cr₇Ni-M-Cr₇Ni (M=Cu⁺²) molecule, which is a promising molecular achievement from the perspective of molecular electronics. By using an effective quantum Hamiltonian, an exact calculation of the magnetic specific heat C_Mag and the magnetocaloric features, namely, the adiabatic change of the entropy ΔS_Mag and temperature ΔT_ad, respectively, are developed. A systematic simulation of the magnetocaloric properties is generated by modifying the effective exchange couplings into the molecular system. Extended discussion of calculated magnetocaloric features and its possible realization by experimental methods, are performed. In addition, comparisons with an exact numerical result and with a Van Vleck transformation, which has important application in similar micromagnetic structures with no exact analytical solution and larger Hilbert space, are presented. Moreover, an expression for the entangling-excitation frequencies of these systems is given as first application of our simplified solution to the effective molecular Hamiltonian.