On the influence of heat transport on low- frequency paramagnetic spin—Lattice relaxation experiments (original) (raw)
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Spin-spin relaxation in magnetically dilute crystals
2015
Magnetic resonance is examined in paramagnetic systems with a small concentration of spins. The free induction signal (FIS) and resonance line shape function (LSF) are calculated. The theory is based on the introduction of an auxiliary system where one spin does not have a flip-flop interaction with the surroundings. The FIS is calculated for this spin using the Anderson-Weiss-Kubo theory and its memory function is used to construct the memory of the main system. The needed numerical coefficients are obtained from expansions of the FIS in terms of the concentration. Here the polarization transport in magnetically dilute systems is taken into account for the first time. This is shown to lead to significant slowing down of the decay in the FIS for times longer than the phase relaxation time. Existing experimental data are compared with theoretical models. Satisfactory agreement is obtained for the description of the central part of the LSF after an additional experimentally observed broadening is introduced in the theory. Data on the amplitude and position of the sideband peaks from the different experiments are not in good agreement with one another or with the theory.
Spin-lattice relaxation in potassium chromium alum
Physica B+C, 1978
A comparison is made between the results of low-frequency relaxation measurements on potassium chromium alum placed in liquid helium and in vacuum, respectively. It is found that only a part of the lattice oscillations is involved in the spin-lattice relaxation process. The spin-lattice relaxation time was found after correcting the time constants of the vacuum measurements by experimental shortening factors. The differences between the spin-lattice relaxation time and the time constants from the liquid-helium measurements can be explained for the greater part by the finite thermal conductivity of the liquid helium.
Journal of Magnetic Resonance (1969), 1980
A model involving two coupled thermodynamic reservoirs is used to describe the homogeneous saturation behavior of an inhomogeneous system of strongly coupled spins in interaction with a microwave field and a lattice. A semiclassical treatment in the rotating frame, in the weak-and strong-saturation limits, leads to expressions for the slow-passage dispersion, absorption, and first derivative, which can be cast into analytic forms as functions of a small number of specific parameters. This allows the determination of spin-spin and spin-lattice relaxation rates from extremum-saturation curves and unsaturated-line profiles. An algorithm is also proposed to deal with the intermediate-saturation range.
Temperature-Independent Spin-Lattice Relaxation Time in Metals at Very Low Temperatures
Physical Review B, 1972
The formalism of nuclear spin-lattice relaxation at low temperatures is developed, leading to a new relaxation time Tμ and a straightforward method of interpreting very-low-temperature relaxation data. Data for 60Co in Fe, Ni, and Co hosts and for 56Co in Fe are summarized. The use of NMR in oriented nuclei for determining relaxation times is discussed, and some comments are made on the role of frequency modulation in NMR experiments with oriented nuclei.
Thermodynamics of Spin Systems in Solids
Physical Review, 1964
Quasiequilibrium states of the spin system in a solid are described in terms of one "Zeeman" temperature for each spin species plus one "dipole-dipole" temperature, TD. Energy and entropy are calculated and used to predict the steady state of processes such as cross relaxation. It is predicted and demonstrated by an experiment on the nuclear spins in LiF that the state of the "dipole-dipole" system has a strong influence on such steady states. Continuous wave (cw) and pulse spectroscopy are discussed for systems with low TD. Techniques are proposed (and have been used) to measure TD and one Zeeman temperature simultaneously, using coherent pulse instrumentation, and for preparing a state of low TD in a large magnetic field by complete adiabatic demagnetization followed by sudden magnetization. A density matrix formalism is proposed for the description of quasiequilibrium situations in the case of "spins" with unequally spaced energy levels. Finally the influence of the "nonsecular" part of the spin-spin Hamiltonian on the quasiequilibrium states is estimated by a perturbation calculation, and the resulting description includes the cases of low-or zero-magnetic field and partly or completely overlapping absorption lines.
Journal of Magnetism and Magnetic Materials, 2000
The purpose of the present work is a quantitative study of the spin time relaxation within superweak ferrimagnetic materials exhibiting a paramagnetic}ferrimagnetic transition, when the temperature is changed from an initial value ¹ to a "nal one ¹ very close to the critical temperature ¹ . From a magnetic point of view, the material under investigation is considered to be made of two strongly coupled paramagnetic sublattices of respective moments and . Calculations are made within a Landau mean-"eld theory, whose free energy involves, in addition to quadratic and quartic terms in both moments and , a lowest-order coupling } C , where C(0 stands for the coupling constant measuring the interaction between the two sublattices. We "rst determine the time dependence of the shifts of the order parameters and from the equilibrium state. We "nd that this time dependence is completely controlled by two kinds of relaxation times and . The former is a long time and the second a short one, and they are associated, respectively, with long and local wavelength #uctuations. We "nd that, only the "rst relaxation time is relevant for physics, since it drives the system to undergo a phase transition. Spatial #uctuations are also taken into account. In this case, we "nd an explicit expression of the relaxation times, which are functions of temperature ¹, coupling constant C and wave vector q. We "nd that the critical mode is that given by the zero scattering-angle limit, i.e. q"0. Finally, we emphasize that the appearance of these two relaxation times is in good agreement with results reported in recent experimental work dealt with the Curie}Weiss paramagnet compound Li V Ni \V O , where the composition x is very close to 1.
The orientation dependence of spin-lattice relaxation times in single crystals
Journal of magnetic resonance, 1983
The orientation dependence of T;' and r;i for single crystals is discussed in terms of the second moment tensor formalism applied to dipolar solids. It is shown that for long correlation times, T;' is a linear function of the maximum possible second moment reduction that may be caused by the motion responsible for the relaxation. Similarly, r;d in the vicinity of the Y&' maximum is proportional to the same second moment reduction. For short correlation times the symmetry restrictions on the orientation dependence of T;' are discussed and are found to differ from the restrictions on the second moment tensor for some crystal symmetries. The nonexponentiality of the relaxation for polycrystalline samples, resulting from anisotropy of the relaxation rates for single crystals is discussed.
NMR proton spin dynamics in thermotropic liquid crystals subject to multipulse excitation
Physical Review E, 2003
Previous experiments of NMR spin-lattice relaxation times as a function of the Larmor frequency, as measured with the field-cycling technique ͑FC͒, were shown to be very useful to disentangle the various molecular motions, both local and collective, that dominate the relaxation in different time scales in liquid crystals. However, there are many examples where the known theoretical models that represent the molecular relaxation mechanisms cannot be fitted to the experimental trend in the region of low fields, making it difficult to obtain reliable values for the spectral densities involved, especially for the cooperative motions which dominate at low frequencies. In some cases, these anomalies are loosely ascribed to ''local-field'' effects but, to our knowledge, there is not a detailed explanation about the origin of these problems nor the range of frequencies where they should be expected. With the aim of isolating the dipolar effects from the influence of molecular dynamics, and taking into account the previous results in solids, in this work we investigate the response of the proton spin system of thermotropic liquid crystals 4-pentyl-4Ј-cyanobiphenyl ͑5CB͒ and 4-octyl-4Ј-cyanobiphenyl ͑8CB͒ in nematic and smectic A phases, due to the NMR multipulse sequence 90 y ؠ-(x-) N. The nuclear magnetization presents an early transient period characterized by strong oscillations, after which a quasistationary state is attained. Subsequently, this state relaxes towards internal equilibrium over a time much longer than the transverse relaxation time T 2. As occurs in solids, the decay time of the quasistationary state T 2e presents a minimum when the pulse width x and the offset of the radiofrequency are set to satisfy resonance conditions ͑spin-lock͒. When measured as a function of the pulse spacing in ''onresonance'' experiments, T 2e shows the behavior expected for cross relaxation between the effective Zeeman and dipolar reservoirs, in accordance with the thermodynamic theory previously developed for solids. Particularly, for values of comparable with T 2 , the relaxation rate follows a power law T 2e ϰ Ϫ2 , in all the observed cases, for the resonance conditions x ϭ/3 and equivalent frequency e ϭ/3. When is similar to or greater than typical dipolar periods, the relaxation rate becomes constant and for much shorter than T 2 , the thermodynamic reservoirs get decoupled. These experiments confirm that the thermodynamic picture is valid also in liquid crystals and the cross relaxation between the reservoirs can be detected without interference with spin-lattice relaxation effects. Accordingly, this technique can be used to estimate the frequency range, where cross-relaxation effects can be expected when Zeeman and dipolar reservoirs are put in thermal contact with each other and with the lattice, as in FC experiments. In particular, the present results allow us to associate the anomalies observed in low-field spin-lattice relaxation with nonadiabatic energy exchange between the reservoirs.
Spin-lattice relaxation of individual solid-state spins
Physical Review B, 2018
Understanding the effect of vibrations on the relaxation process of individual spins is crucial for implementing nano systems for quantum information and quantum metrology applications. In this work, we present a theoretical microscopic model to describe the spin-lattice relaxation of individual electronic spins associated to negatively charged nitrogen-vacancy centers in diamond, although our results can be extended to other spin-boson systems. Starting from a general spin-lattice interaction Hamiltonian, we provide a detailed description and solution of the quantum master equation of an electronic spin-one system coupled to a phononic bath in thermal equilibrium. Special attention is given to the dynamics of one-phonon processes below 1 K where our results agree with recent experimental findings and analytically describe the temperature and magnetic-field scaling. At higher temperatures, linear and second-order terms in the interaction Hamiltonian are considered and the temperature scaling is discussed for acoustic and quasi-localized phonons when appropriate. Our results, in addition to confirming a T 5 temperature dependence of the longitudinal relaxation rate at higher temperatures, in agreement with experimental observations, provide a theoretical background for modeling the spin-lattice relaxation at a wide range of temperatures where different temperature scalings might be expected.