NMR spectra under skin-effect conditions at ultralow temperatures

An investigation based on the coupled Maxwell-Bloch equations for a system of equivalent exchange-coupled spins is performed in order to explain a number of features of NMR spectra obtained in metals by Fourier-transforming of the free-induction decay at ultralow temperatures. Small angles of tilting of the nuclear magnetization by the exciting rf field are considered. It is shown that the free precession inherits the nonuniformity in the distribution of the rf field and the magnetization produced at the excitation stage inside the sample on account of the skin effect. As a result, the NMR spectrum is found to consist of a set of peaks—signals due to standing spin waves. However, such a spectrum can be observed only when the detuning of the exciting rf field is sufficiently large relative to the Larmor frequency of the spins. Otherwise, the rf field does not penetrate into the sample because of strong absorption by the spins. If the detuning is large, the dispersion signal and part of the NMR absorption signal are proportional to the equilibrium magnetization to the power 3/2. Such behavior is expected at low temperatures so that the coupling of the magnetization with the rf field is strong. The results obtained qualitatively explain the experimentally observed characteristics of the NMR spectra: the presence of kinks and structure of the NMR lines, the dependence of the shape and intensity of the spectrum on the detuning of the exciting rf field, and the nonlinear dependence of the nuclear susceptibility on the reciprocal of the sample temperature. Zh. éksp. Teor. Fiz. 114, 1836–1847 (November 1998)     

Temperature dependence of superradiance intensity

Using the idea of exchange interaction in a system of two-level atoms participating in a superradiance process, we derive from first principles the superradiance Hamiltonian of such a system, which is found to be analogous to the Heisenberg Hamiltonian. We consistently calculate the coupling constant of the interaction that leads to the emergence of a superradiance state in the system. We also predict the existence of isospin excitations in the superradiance state, whose presence reduces the intensity of the corresponding superradiance pulse. Finally, we calculate the temperature dependence of the intensity of the superradiance pulse and find it be analogous to the Bloch T ^3/2-law for spin systems. Zh. éksp. Teor. Fiz. 116, 1148–1160 (October 1999)     

Effect of rf field on spin diffusion

A study was made of the effect of an rf field on spin diffusion. The interaction of spins with the rf field is described quantum mechanically. It is shown that the effect of the rf field on the system of spins can, in some approximation, be interpreted as the effect of a change in the Larmor frequency of the spin and a decrease in the magnitude of the dipole-dipole interaction between spins. These conclusions were obtained on the basis of a unitary transformation which eliminates the explicit form of the spin-photon interaction operator in the Hamiltonian of the system considered. An expression is derived for the spin-diffusion coefficient under saturation. The presence of the rf field results in a decrease in the diffusion coefficient.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 7–11, September, 1979.     

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.     

Vector model of electron spin echo envelope modulation due to nuclear hyperfine and zeeman interactions

The transverse electron spin magnetization of a paramagnetic center with effective spinS=1/2 interacting with nonquadrupolar nuclei may be presented as a function of pairs of nuclei magnetization vectors which precess around the effective magnetic field directions. Each vector of the pair starts its precession perpendicular to both effective fields. The free induction decay (FID) signal is proportional to the scalar product of the vectors for nuclear spinI=1/2. The electron spin echo (ESE) signal can be described with two pairs of magnetization vectors. The ESE shape is not equal to two back-to-back FID signals except in the absence of ESE envelope modulation. A recursion relation is obtained which allows calculation of ESE signals for larger nuclear spins in the absence of nuclear quadrupole interaction. This relation can be used to calculate the time course of the ESE signal for arbitrary nuclear spins as a function of the nuclear magnetization vectors. While this formalism allows quantitative calculation of modulation from nuclei, it also provides a qualitative means of visualizing the modulation based on simple magnetization vectors.     

One-Step Implementation of Single Spin Measurement in Spin Star Network

We present an efficient one-step scheme for a single spin measurement based on nuclear magnetic resonance （NMR） techniques. This scheme considerably reduces the time of operation using a spin star network where a target spin and an ancillary spin are coupled to a ring of N spins. As opposed to the proposal in [Phys. Rev. Lett. 97 （2006） 100501] using a cubic lattice crystal to achieve a cubic speedup, the distinct advantage of this scheme is that under ideal conditions it requires the application of only one step to create a system of N correlated spins. In the process of single spin measurement, the total macroscopic magnetization, the individual magnetization and the transfer fidelity are calculated analytically as simple cosine functions of time and the amplitude of irradiation.     

Monte Carlo evidence of non-equilibrium effects for ising model in a random field

Simulating an Ising model, up to sizes 150×150×150 in three and 225×225 in two dimensions, in a random field of strength ±H, we find a magnetization slowly decreasing with time if initially all spins are parallel. This decay is extremely slow for small random fields, so that a stable magnetization cannot be excluded. Below some freezing temperature, the system remains a single domain, with a finite magnetization in both two and three dimensions. If instead the system is cooled down in a constant random field, from temperatures above to temperatures below this freezing transition, then at the lower temperature the magnetization increases with time; this increase is very slow for large systems, with similar results in two and three dimensions.     

Critical droplets and metastability for a Glauber dynamics at very low temperatures

We consider the metastable behavior in the so-called pathwise approach of a ferromagnetic spin system with a Glauber dynamics in a finite two dimensional torus under a positive magnetic field in the limit as the temperature goes to zero. First we consider the evolution starting from a single rectangular droplet of spins +1 in a sea of spins −1. We show that small droplets are likely to disappear while large droplets are likely to grow; the threshold between the two cases being sharply defined and depending only on the external field. This result is used to prove that starting from the configuration with all spins down (−1) the pattern of evolution leading to the more stable configuration with all spins up (+1) approaches, as the temperature vanishes, a metastable behavior: the system stays close to −1 for an unpredictable time until a critical square droplet of a precise size is eventually formed and nucleates the decay to +1 in a relatively short time. The asymptotic magnitude of the total decay time is shown to be related to the height of an energy barrier, as expected from heuristic and mean field studies of metastability. Partially supported by CNPq. Part of this work was done while RHS was visiting Rome, supported by an agreement between CNPq and CNR     

Investigation of a gap in the AFMR spectrum in the quasi-one-dimensional hexagonal antiferromagnet CsMnBr3

The low-frequency part of the magnetic resonance spectrum of the hexagonal six-sublattice quasi-one-dimensional antiferromagnet CsMnBr₃ at temperatures which are low compared with T _N =8.3 K is investigated experimentally. A temperature-dependent gap Δ(T) is found in the spectrum ω _e (H) of the lower AFMR branch; this gap is due to the hyperfine interaction of the nuclear spins with the electronic spins of the (⁵⁵Mn)²⁺ ions. The spectrum of the low-lying resonance frequencies of such a system is calculated taking this interaction into acount in the approximation of fluctuationless spin hydrodynamics for the electronic branch of the oscillations. The computational results are in good qualitative and satisfactory quantitative agreement with experiment. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 6, 433–437 (25 September 1996)     

Potential of electron paramagnetic resonance to study Einstein-Podolsky-Rosen-Bohm pairs

The potential of electron paramagnetic resonance (EPR) methods to study the correlation of the states of two noninteracting spins prepared in the singlet state (Einstein-Podolsky-Rosen-Bohm [EPRB] pairs) is discussed. EPR methods with a selective excitation of spins in the EPRB pairs allow one, in principle, to reveal this correlation of spin states if single-spin measurements are performed. However, it is illustrated that the conventional ensemble EPR experiments, when the average values of projections of the spin moments are observables, fail in studying the correlation of spins in EPRB pairs. An exploitation of the EPR phenomenon to study the correlation of spins for ensembles of EPRB pairs needs some modifications of the experimental approach: either the indirect detection of EPR signals (new observables) should be used or the EPRB pairs should be transferred to another state when the spin-spin interaction becomes essential, while EPR observables manifest the spin correlation in the precursor EPRB pair state. In this respect it appears that in spin chemistry many results were already obtained which demonstrate that it is a reality that two spins might occupy the “entangled” (correlated) state, when there is no interaction between them. The results obtained in spin chemistry confirm the quantum mechanical predictions for spin-correlated pairs of spins which can be considered as a realization of EPRB pairs.     

Dynamics of collective decoherence and thermalization

We analyze the dynamics of N interacting spins (quantum register) collectively coupled to a thermal environment. Each spin experiences the same environment interaction, consisting of an energy conserving and an energy exchange part.We find the decay rates of the reduced density matrix elements in the energy basis. We show that if the spins do not interact among each other, then the fastest decay rates of off-diagonal matrix elements induced by the energy conserving interaction is of order N², while that one induced by the energy exchange interaction is of the order N only. Moreover, the diagonal matrix elements approach their limiting values at a rate independent of N. For a general spin system the decay rates depend in a rather complicated (but explicit) way on the size N and the interaction between the spins.Our method is based on a dynamical quantum resonance theory valid for small, fixed values of the couplings. We do not make Markov-, Born- or weak coupling (van Hove) approximations.     

Decay of rabi oscillations induced by magnetic dipole interactions in dilute paramagnetic solids

Decay of Rabi oscillations of equivalent spins diluted in diamagnetic solid matrix and coupled by magnetic dipole interactions is theoretically studied. It is shown that these interactions result in random shifts of spin transient nutation frequencies and thus lead to the decay of the transient signal. Averaging over random spatial distribution of spins within the solid and over their spectral positions within magnetic resonance line, we obtain analytical expressions for the decay of Rabi oscillations. The rate of the decay in the case when the half-width of magnetic resonance line exceeds Rabi frequency is found to depend on the intensity of resonant microwave field and on the spin concentration. The results are compared with the literature data for E′₁ centers in glassy silica and [AlO₄]⁰ centers in quartz.     

Electron paramagnetic resonance study of the nuclear spin dynamics in an AlAs quantum well

The nuclear spin dynamics in an asymmetrically doped 16-nm AlAs quantum well grown along the [001] direction has been studied experimentally using the time decay of the Overhauser shift of paramagnetic resonance of conduction electrons. The nonzero spin polarization of nuclei causing the initial observed Overhauser shift is due the relaxation of the nonequilibrium spin polarization of electrons into the nuclear subsystem near electron paramagnetic resonance owing to the hyperfine interaction. The measured relaxation time of nuclear spins near the unity filling factor is (530 ± 30) min at the temperature T = 0.5 K. This value exceeds the characteristic spin relaxation times of nuclei in GaAs/AlGaAs heterostructures by more than an order of magnitude. This fact indicates the decrease in the strength of the hyperfine interaction in the AlAs quantum well in comparison with GaAs/AlGaAs heterostructures.     

Two-photon nutation excited in a two-level spin system by microwave and RF fields

Two-photon transient nutation is observed in a two-level spin system (E′₁ centers in crystalline quartz) using a transverse microwave field and a linearly polarized rf field oriented along a static magnetic field in the electron paramagnetic resonance. Nutation is excited when the sum of the energies of a microwave photon and a rf photon is equal to the energy difference between two spin states. The two-photon nature of nutation is confirmed by measuring its frequency as a function of the amplitude and frequency of the rf field as well as the amplitude of the microwave field. The amplitude of the effective field of two-photon transitions is measured. It is shown that the decay rate of two-photon nutation is close to the decay rate for one-photon nutation and is determined by the spin-spin interaction between E′₁ centers.     

Electric field induced nuclear spin resonance mediated by oscillating electron spin domains in GaAs-based semiconductors

We demonstrate an alternative nuclear spin resonance using a radio frequency (rf) electric field [nuclear electric resonance (NER)] instead of a magnetic field. The NER is based on the electronic control of electron spins forming a domain structure. The rf electric field applied to a gate excites spatial oscillations of the domain walls and thus temporal oscillations of the hyperfine field to nuclear spins. The rf power and burst duration dependence of the NER spectrum provides insight into the interplay between nuclear spins and the oscillating domain walls.     

Effect of the nuclear hyperfine field on the 2D electron conductivity in the quantum Hall regime

The effect of the nuclear hyperfine interaction on the dc conductivity of 2D electrons under quantum Hall effect conditions at filling factor ν=1 is observed for the first time. The local hyperfine field enhanced by dynamic nuclear polarization is monitored via the Overhauser shift of the 2D conduction electron spin resonance in AlGaAs/GaAs multiquantum-well samples. The experimentally observed change in the dc conductivity resulting from dynamic nuclear polarization is in agreement with a thermal activation model incorporating the Zeeman energy change due to the hyperfine interaction. The relaxation decay time of the dc conductivity is, within experimental error, the same as the relaxation time of the nuclear spin polarization determined from the Overhauser shift. These findings unequivocally establish the nuclear spin origins of the observed conductivity change. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 1, 58–63 (10 January 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Spin bath decoherence of quantum entanglement

We study an analytically solvable model for decoherence of a two spin system embedded in a large spin environment. As a measure of entanglement, we evaluate the concurrence for the Bell states (Einstein-Podolsky-Rosen pairs). We find that while for two separate spin baths all four Bell states lose their coherence with the same time dependence, for a common spin bath, two of the states decay faster than the others. We explain this difference by the relative orientation of the individual spins in the pair. We also examine how the Bell inequality is violated in the coherent regime. Both for one bath and two bath cases, we find that while two of the Bell states always obey the inequality, the other two violate the inequality at early times.     

Two-dimensional magnetic ordering in a multilayer structure

The effect of confinement from one, two or from all three directions on magnetic ordering has remained an active field of research for almost 100 years. The role of dipolar interactions and anistropy are important to obtain, the otherwise forbidden, ferromagnetic ordering at finite temperature for ions arranged in two-dimensional (2D) arrays (monlayers). We have demonstrated that conventional low-temperature magnetometry and polarized neutron scattering measurements can be performed to study short-range ferromagnetic ordering of in-plane spins in 2D systems using a multilayer stack of non-interacting monolayers of gadolinium ions formed by Langmuir-Blodgett (LB) technique. The spontaneous magnetization could not be detected in the heterogeneous magnetic phase observed here and the saturation value of the net magnetization was found to depend on the sample temperature and applied magnetic field. The net magnetization rises exponentially with lowering temperature and then reaches saturation following a T ln(βT) dependence. The T ln (βT) dependence of magnetization has been predicted from spinwave theory of 2D in-plane spin system with ferromagnetic interaction. The experimental findings reported here could be explained by extending this theory to a temperature domain of βT<1.     

Latent paramagnetism in CsFeCl3

It is shown that latent paramagnetism can occur in a lattice having a hexagonal arrangement of magnetic spins. This state is characterized by the fact that the effective exchange interaction on the two sublattices vanishes and the corresponding ions become paramagnetic. The appearance of such a state explains the nonequidistant spacing of the jumps in the magnetization in CsFeCl₃. Fiz. Tverd. Tela (St. Petersburg) 41, 645–646 (April 1999)