Dipole-dipole Reservoir Research Articles

Stratonovich-Ito integration scheme in ultrafast spin caloritronics

The magnonic spin Seebeck effect is a key element of spin caloritronic, a field that exploits thermal effects for spintronic applications. Early studies were focused on investigating the steady-state nonequilibrium magnonic spin Seebeck current, and the underlying physics of the magnonic spin Seebeck effect is now relatively well established. However, the initial steps of the formation of the spin Seebeck current are in the scope of recent interest. To address this dynamical aspect theoretically we propose here a new approach to the time-resolved spin Seebeck effect. Our method exploits the supersymmetric theory of stochastics and Ito - Stratonovich integration scheme. We found that in the early step the spin Seebeck current has both nonzero transversal and longitudinal components. As the magnetization dynamics approaches the steady-state, the transversal components decay through dephasing over the dipole-dipole reservoir. The time scale for this process is typically in the sub-nanoseconds pointing thus to the potential of an ultrafast control of the dynamical spin Seebeck during its buildup.

Effect of interaction of electromagnetic fields with a resonant medium in epr when the saturating field is small compared with the local field

We propose a system of Bloch equations, modified to take into account the presence of a dipole-dipole reservoir (DDR), for the case when the saturating magnetic field is small compared with the local field. We take into account the transverse and longitudinal magnetizations in the equation for the DDR, in contrast to our previous papers in which we took into account only the longitudinal magnetization. Using the system obtained, we solve the problem of the interaction of three fields, where one is the saturating field, the second is the probe field, and the third is a combination field that is the result of the interaction of the first two fields in a resonant medium. We have studied the imaginary and real parts of the susceptibility of the system at the probe field frequency, both when the interacting waves have different frequencies and when they have matching frequencies (the degenerate case). We have compared the results with those we obtained previously. For the degenerate case, we consider the frequency dependence of the parametric coupling coefficient of the waves. We show that weak waves can be enhanced as they pass through a layer of a resonant absorbing medium.

Theoretical study of spin-temperature phenomena in EPR for the low-temperature approximation and steady-state conditions

Using the concept of spin temperature in EPR in the low-temperature approximation and under steady-state conditions, we examine the dependence of the reciprocal spin temperature of the Zeeman subsystem and the dipole-dipole reservoir on the reciprocal lattice temperature in the presence of a saturating field. We show that more significant cooling of the dipole-dipole reservoir and heating of the Zeeman subsystem can be achieved than in the case of the high-temperature approximation. In the presence of a probe field, we study the conditions for the absorption to go to zero at the frequency of this field, as a function of the intensity of the saturating field and the frequency difference between the two fields. We show that the intensity of the saturating field increases as the frequencies of the fields come closer together, and goes to infinity when they coincide. This qualitatively corresponds to what we have in the case of the high-temperature approximation. The intensity of the saturating field has a minimum in the dependence on detuning of the frequency of the saturating field when the frequency of the probe field is fixed, as in the case of the high-temperature approximation. We can use this dependence to estimate the relaxation parameters.

Determination of an Absorbed Radiation Dose by the EPR Method from the Concentration of the Centers Produced

A method to determine the absorbed radiation dose that is based on the spin-resonance dosimetry is suggested. It rests on the fact that under irradiation additional centers that absorb UHF radiation are generated in substance. This leads to a change in the time of longitudinal relaxation of a Zeeman subsystem and dipole-dipole reservoir as well as in the time of transverse relaxation because of the dipole-dipole interaction, which in turn causes a change in the shape of the line and in the saturation parameter. It is possible to determine the minimum absorbed dose at which the minimum deformation of the shape of the line is registered. A method is also suggested to determine an absorbed dose in the absence of absorbing centers in the substance before irradiation.

Dynamics of Spin Temperatures in EPR on Rapid Switching of the Frequency Detuning of a Saturating Field

In the framework of the spin temperature in EPR in the absence of interaction with the lattice, the time-dependent change in the spin temperatures of the Zeeman subsystem and dipole-dipole reservoir has been investigated theoretically in the high-temperature approximation. It is shown that amplification in the system can be obtained by switching the detuning of the saturating field frequency. The approach to the solution of the problem is based on the fact that during the process of switching and establishment of both temperatures the total energy of the Zeeman subsystem and of the dipole-dipole reservoir is preserved. It has been established that the values of absorption or amplification in the system depend on the frequency detunings of the saturating field. In the presence of a probe field, the possibility of determining the value of the local magnetic field related to the time of transverse relaxation of the system is demonstrated.

Interaction of two superhigh-frequency fields with the resonance system of electron spins

Within the framework of the concept of a spin temperature in a steady-state regime, the interaction with a resonance medium of two superhigh-frequency fields, one of which is saturating and the other of which is trial, is considered theoretically in the general case without using a high-temperature approximation. The case where the absorption of a resonance medium vanishes at the trial-field frequency is investigated in detail. This occurs with an intensity of the saturating field lower than in the case of a high-temperature approximation. This intensity is estimated in the second and third orders by the parameter ω0βz/2, where ω0 is the resonance frequency of the transition, βz=ħ/(kTz), Tz is the Zeeman-subsystem temperature, ħ is the Planck constant, and k is the Boltzmann constant. It is shown that the cooling of the dipole-dipole reservoir is more considerable than in the case of a high-temperature approximation.

Ultralow-temperature relaxation of far nuclei in solids via dipole reservoir of own nuclei of paramagnetic centers

Abragam et al. (Physica B81, 245 (1976)) proposed a relaxation mechanism for far nuclei via dipole–dipole reservoir (DDR) of own nuclei of paramagnetic centers which do not “freeze” at ultra low temperatures. In order to verify the possibility of such a process, they proved that the matrix elements of flip-flops of own nuclei are the electron matrix elements due to the mixing of electron and nuclear spin states as a result of superfine interaction. This is equivalent to an increase in heat capacity (“increase in weight”) of the DDR of own nuclei. Such a “heavier” DDR subsequently plays the role of a thermodynamic subsystem through which far nuclei relax to the lattice, a narrow bottleneck being observed on the second relaxation region. Since this mechanism can play a dominating role in low-temperature nuclear relaxation as well as in other processes, it is important to obtain the Hamiltonian of a “heavier” DDR in explicit form, to calculate its heat capacity, and to estimate the effective relaxation rate of far nuclei via DDR, which has been accomplished in the present publication.

Polarizing proton spins by electron-spin locking of photo-excited triplet state molecules

The transfer of the electron spin polarization from photo-excited triplet state molecules to proton spins has been studied in single crystals of fluorene doped with 2000 ppm acridine in three isotopically different forms. From spin-locking experiments it appears that the proton spins on the acridine guest molecules play a minor role in this process and that the evolution of the nuclear spin polarization is determined by the second moment of the dipolar interaction with the proton spins on neighbouring fluorene molecules. In contrast to recent reports we do not observe fast Rabi oscillations in the polarization transfer process. This is explained by the fact that the magnetic field in our experiments is large, resulting in a weak contact between the nuclear Zeeman reservoir and the electron dipole-dipole reservoir.

Spatial design of spin polarization in solids

Spatially designed non-equilibrium polarization arises due to the transfer of energy from the dipole-dipole reservoir to the Zeeman reservoir of localized magnetic moments in solids in the presence of non-uniform external magnetic fields. This statement is supported by the model calculations of spin dynamics in linear chains of spins.

Calculation of the average values of the Zeeman and dipole?dipole spin energies of a paramagnet at low temperatures

For average values of the Hamiltonians of the Zeeman energy and the dipole-dipole spin interaction energy, a series is obtained representing the expansion of these averages in powers of the inverse temperature of the dipole-dipole interaction reservoir. The average values of specific operators appearing in the series as coefficients of the series are calculated from the complete density matrix of the system. These coefficients essentially are the low-temperature moments of resonance absorption lines of the spin system.

Experiments on the 19F Dipole-Dipole Reservoir in Polytetrafluoroethylene

In polytetrafluoroethylene, we have cooled the dipolar reservoir of the fluorine nuclei. In a field of 2.5 Tesla the dipolar relaxation time is approximately 80 s at 3 K and 150 s at 1.8 K. The Zeeman reservoir relaxes in times 50 - 100 times longer. In the material used (a teflon powder produced by Aldrich-Chemie) the Zeeman relaxation time depends on contact to 3He at the surface, contrary to the dipolar relaxation time.

Role of the dipole reservoir in low-frequency absorption in paramagnetic systems with restricted spectral diffusion

The absorption of energy from the transverse low-frequency (LF) field by inhomogeneously broadened paramagnetic systems is studied theoretically taking into account the electronic dipole-dipole reservoir. The case of restricted spectral diffusion is studied. It is shown that LF absorption is associated with effective interactions of the type S/sup z/S/sup z/ and S/sup +/-/S/sup -/+/ and appears in second-order perturbation theory. The relative change in the magnetization of the spin system, owing to LF absorption in the presence of simultaneous interaction of a saturating microwave field with the system, is calculated. The dependence of the change in the magnetization on the parameters of the LF field and on the magnitude of the microwave detuning is analyzed. The theoretical results are in satisfactory agreement with the experimental results.

Cross‐relaxation of nuclear spins at low temperatures

AbstractA system of equations is derived for the evolution under action of cross‐relaxation (CR) of the dipole–dipole reservoir (DDR) and Zeeman subsystems, redefined taking into account the fact, that the part of secular dipole‐dipole interaction H′d, which causes homogeneous displacement of spin resonant frequencies at low temperatures (LT) must be subtracted from H′d. The case is considered, when the influence of the change of LT displacement due to CR on the energy, absorbed by DDR, is stronger, than that of the usual high‐temperature term. It is shown, that in this situation both, DDR and spins under CR acquire a negative temperature in spite of the fact, that the frequency of saturated spins is smaller than the frequency of spins under CR. This behaviour differs from the high‐temperature result.

A medium size polarised deuteron target

A frozen polarised deuteron target based on ethanediol with a high percentage of deuterium is described. Analytical expressions for the NMR spectrum correction for non-linearity of the Q-meter are obtained and a method for the determination of the asymmetry is developed. Experimental results confirm the thermal mixing theory for deuteron and proton spin systems with a dipole-dipole reservoir of electron spins.

Manifestation of dipole-dipole reservoir in systems with non-equidistant spectrum at saturation of quadrupolar transitions

The influence of the temperature change of dipole-dipole reservoir (DDR) of nuclear spins due to unrigorously resonance acoustic saturation of quadrupolar transitions on the NMR signals between the different eigenstates of a non-equidistant spectrum is studied.

Double nuclear magnetic resonance and crystal chemistry at the lattice positions of diamagnetic atoms, both structural, and foreign

Double nuclear magnetic resonance (DNMR) with Jeener's pulsed sequence on proton and fluorine frequencies was used to investigate the electric quadrupole interactions of (i) 23Na in Na2Cd(SO4)2·2H2O, B 2 0 =±218.5±1 kHz, B 2 2 =±98±5 kHz, (ii) of 23Na, which enter the crystal, CaF2: Na+ (0.07 wt. %) B 2 0 =±85.7±0.5 kHz, trigonal position, and (iii) 23Na which are near the foreign atom in NaF:Ca2+ (0.02 wt.%) B 2 0 =±86.7±0.5 kHz, tetragonal position. Some details of DNMR experiments are analyzed. The conditions for maximum transfer of a Zeeman energy to a dipole-dipole reservoir are described for multispin systems and some crystal hydrates. The angular dependence of the Hamiltonian containing the spherical tensor operators of second rank was obtained for all possible orientations of a local coordinate system relative to a laboratory system.

The nonresonant transfer of energy between impurities in solids

The nonequilibrium statistical operator method is used for theoretical investigation of nonresonant transfer of energy between impurities in solids in cases when energy migration between donors occurs during a time much less than the transfer time. Apart from subsystems of donors, acceptors and the vibrational quanta participating in the process under consideration (which may be intramolecular vibrations or phonons), we introduce the so-called dipole-dipole reservoir, which exerts an essential influence on the energy transfer kinetics. Various limiting cases are investigated. The saturation of donors by light pulses may lead to an avalanche-like increase of the number of vibrational quanta.

Consideration of the dipole-dipole reservoir in nonstationary double resonance

Manifestations of the dipole-dipole reservoir (DDR) of electron spins in nonstationary NNDOR and ENDOR are investigated, taking as an example the electron-nuclear spin system Cr 3+ − 53Cr− 27 Al in ruby. It is demonstrated, that a consistent consideration of the hyperfine structure of the EPR spectrum of the Cr 3+ ions explains the behaviour of the NMR signal of the 27Al nuclei, observed experimentally during saturation of NMR of the 53Cr nuclei. The ENDOR signals are calculated with allowance for the shift of the DDR temperature, and it is pointed out that the absorption signal of ENDOR can change its sign depending on nuclear detuning.

Dynamic nuclear polarization with an inhomogeneously broadened ESR line. II. Experiment

Results of proton dynamic nuclear polarization (DNP), nuclear spin-lattice relaxation, and ESR experiments in six YES: $^{168}\mathrm{Er}$ ($^{168}\mathrm{Er}$-doped yttrium ethyl sulphate) single crystals at 4.15 K and 9.1 GHz are reported here. This material approximates an inhomogeneously broadened (IHB) ESR line for certain crystal orientations relative to the applied magnetic field ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}}_{0}$. DNP peak enhancements ${E}_{\mathrm{ss}}^{\mathrm{peak}}\ensuremath{\approx}120$ are obtained for crystals 1-3 having $^{168}\mathrm{Er}$ dilutions of 0.2%-0.01% (mole%). The steady-state enhancement ${E}_{\mathrm{ss}}$ vs ${H}_{0}$ curves are proportional to the ESR absorption derivative at low powers (\ensuremath{\cong} 0.3 mW), but change shape in the wings of the ESR line at high microwave powers (\ensuremath{\cong} 300 mW). Essentially idential ${E}_{\mathrm{ss}}$ data are obtained for all three crystals. Extensive DNP pump time ${\ensuremath{\tau}}_{\mathrm{DNP}}$ and ESR data for crystals 2-4, as well as limited data for the other crystals, are also given. There is no ${E}_{\mathrm{ss}}$ or ${\ensuremath{\tau}}_{\mathrm{DNP}}$ evidence in these experiments (i) for the traditional strict-shell-of-influence model of IHB SE (solid effect) DNP, (ii) for non-negligible CE (cross effect) DNP processes, or (iii) for decreases in ${E}_{\mathrm{ss}}$ due to moderate spectral diffusion in an IHB ESR line, as proposed by Buishvili et al. The DNP and ESR data of crystals 1-3 have been fit by the least-squares technique to a muffin-tin model of IHB SE DNP which incorporates rapid nuclear spin diffusion. Moderate agreement with theory is obtained, especially if the data are interpreted with a three-spectral-region model for wide IHB ESR lines. These data have also been analyzed in terms of EDDR (electron dipole-dipole reservoir) DNP theory for an IHB ESR line with fast spectral diffusion throughout the line. There is qualitative and some quantitative agreement between this theory and the data. It is thus difficult to discriminate EDDR DNP theory from IHB SE DNP with the three-spectral-region model in these experiments. The only clearcut evidence for the latter is an order-of-magnitude theoretical calculation of the electron magnetic dipole-dipole contribution to the ESR intrinsic spin-packet width, which gives non-negligible spectral diffusion in the centers of the crystal 1 and 2 ESR lines, and negligible spectral diffusion in the wings of crystals 3 and (perhaps) 2. Conclusive evidence would require further experiments at $^{168}\mathrm{Er}$ dilutions lower than 0.01% and higher than 0.2%. Experiments are proposed for YES: $^{168}\mathrm{Er}$ to test further the three-spectral-region model, and to find high DNP by IHB SE with possible applications to polarized nuclear targets in other, more hydrogenous materials.

Dynamic nuclear polarization in samarium-doped lanthanum magnesium nitrate

We report theoretical and experimental investigations of the dynamic nuclear polarization (DNP) and nuclear spin-lattice relaxation of protons in single crystals of lanthanum magnesium nitrate (LMN) weakly doped (\ensuremath{\cong}0.1-1.1-mole%) with samarium ions (LMN:Sm) at 9.1 GHz and liquid-helium temperatures. Theoretical expressions for DNP and nuclear relaxation are given for a homogeneously broadened ESR line in the high-temperature limit. DNP effects due to the electron dipole-dipole reservoir (EDDR) are predicted for the case of well-resolved satellites. Our DNP experiments on LMN:Sm are in general agreement with the conventional theory, but no evidence for direct EDDR effects on DNP with well-resolved satellites is seen, despite suggestive nuclear-relaxation data. Various explanations for this disagreement are proposed. We suggest that these EDDR effects may be seen in crystals of \ensuremath{\cong}3-5-mole% LMN:Sm or in equivalent systems.