Low temperature MQ NMR dynamics in dipolar ordered state

We investigate analytically and numerically the Multiple Quantum (MQ) NMR dynamics in dipolar ordered spin systems of nuclear spins 1/2 at low temperatures. We consider two different methods of MQ NMR. One of them is based on the measurement of the dipolar energy. The other method uses an additional resonance (π/4)_y-pulse after the preparation period of the standard MQ NMR experiment in solids and allows one to measure the Zeeman energy. Both considered methods are sensitive to the contribution of remote spins in the interaction and to the spin system structure. The QS method is sensitive to the spin number in the molecule while the PS method gives very similar time dependencies of the intensities of MQ coherences for different spin numbers. It is shown that the use of the dipolar ordered initial state has the advantage of exciting the highest order MQ coherences in clusters of 4m identical spins, where m=1,2,3,…, that is impossible to do with the standard MQ method. MQ NMR methods based on the dipolar ordered initial states at low temperatures complement the standard NMR spectroscopy for better studying structures and dynamic processes in solids.     

The multiple quantum NMR dynamics in systems of equivalent spins with a dipolar ordered initial state

The multiple quantum (MQ) NMR dynamics in the system of equivalent spins with the dipolar ordered initial state is considered. The high symmetry of the Hamiltonian responsible for the MQ NMR dynamics (the MQ Hamiltonian) is used to develop analytic and numerical methods for the investigation of the MQ NMR dynamics in systems consisting of hundreds of spins from the “first principles.” We obtain the dependence of the intensities of the MQ NMR coherences on their orders (profiles of the MQ NMR coherences) for systems of 200–600 spins. It is shown that these profiles may be well approximated by exponential distribution functions. We also compare the MQ NMR dynamics in the systems of equivalent spins having two different initial states, the dipolar ordered state and the thermal equilibrium state in a strong external magnetic field.     

Determination of the spectral parameters of nuclear quadrupole resonance from nutation spectra of powdered samples

An analytical expression I(ω) is obtained for a normalized function of the shape of an idealized nuclear quandrupole resonance nutation line of a powdered sample for spins I=3/2 (η≠0). Calculations are made of the initial moments <ωⁿ> of the nutation spectrum of the powder in the form of functions of ω₀=γB₁ and the asymmetry parameter η of the electric field gradient tensor. A method is proposed for determining the spectral parameters η and eQq_zz from the experimentally measured values of <ω>, <ω²>, <ω⁴>, and ω_1/2 of the nuclear quadrupole resonance nutation spectrum of the powder. State University, Kaliningrad. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 3–8, July, 1997.     

Evolution of spin entanglement and an entanglement witness in multiple-quantum NMR experiments

We investigate the evolution of entanglement in multiple-quantum (MQ) NMR experiments in crystals with pairs of close nuclear 1/2-spins. The initial thermodynamic equilibrium state of the system in a strong external magnetic field evolves under the nonsecular part of the dipolar Hamiltonian. As a result, MQ coherences of the zeroth and plus/minus second orders appear. A simple condition for the emergence of entanglement is obtained. We show that the measure of the spin-pair entanglement—concurrence—coincides qualitatively with the intensity of MQ coherences of the plus/minus second order and, hence, the entanglement can be studied with MQ NMR methods. We introduce an entanglement witness using MQ NMR coherences of the plus/minus second order. The text was submitted by the authors in English.     

Dipolar Relaxation of Multiple Quantum NMR Coherences as a Model of Decoherence of Many-Qubit Coherent Clusters

Dipolar relaxation of multiple quantum (MQ) nuclear magnetic resonance (NMR) coherence is investigated on the evolution period of the MQ NMR experiment in chains of ¹⁹F nuclei in a single crystal of calcium fluorapatite. The dependence of the relaxation time of the MQ coherence of the second order on the size of the coherent spin cluster formed on the preparation period is obtained. The dipolar relaxation of MQ NMR coherences is considered as a model for the investigation of decoherence of quantum states of many-qubit spin clusters.     

NMR study of heterogeneity in pyridine-N-oxide...HCl crystal

An origin of narrow ¹H NMR signals in pyridine-N-oxide (PyO)...HCl crystal has been investigated by means of MAS, SPEDAS, NOESY and COSY techniques. Spectra of crystalline samples are compared with those of solid phase obtained from liquid PyO...HCl solutions (in acetonitile/H₂O) after the heterogeneous phase separation. It has been concluded that partially resolved peaks in ¹H NMR spectra of solids are related with heterogeneity of spin system and presence of different H-bond clusters of water molecules. NOESY spectra show no cross-peaks even at very long mixing time (500 ms). This indicates there is no exchange process between spins causing different peaks, and thus the corresponding molecular aggregates are captured in “islands of mobility8 without any channels sufficient for exchange. Appearance of MAS side bands as “pseudo8 cross-peaks in 2D NMR spectra using MAS/COSY technique is reported. In the case of accidental coincidence of spinning frequency (ω _MAS ) with spectral distances between some diagonal signals, intensive non-diagonal peaks are observed at the corresponding cross-positions. A misleading conclusion concerning spin coupling is easy to avoid using various ω _MAS . This work is dedicated to Professor Robert Blinc on the occasion of his 70^th birthday.     

27Al pulsed nuclear magnetic resonance study of CeAl2

The magnetic properties and the electronic structures of a rare-earth aluminum intermetallic compound CeAl₂ are investigated by magnetic susceptibility measurements and ²⁷Al pulsed nuclear magnetic resonance (NMR) techniques. The magnetic susceptibility is strongly temperature-dependent, following a Curie–Weiss law down to ∼12 K, and shows an antiferromagnetic transition at 4 K. The ²⁷Al NMR spectra show a typical powder pattern for a nuclear spin I of 5/2 with the second-order nuclear quadrupole interaction at high temperature and an additional large dipolar broadening between the 4f electron spins of cerium and the ²⁷Al nuclear spins at low temperature. The ²⁷Al NMR Knight shift follows the same temperature dependence as the magnetic susceptibility, suggesting that the ²⁷Al NMR Knight shift originates from the transferred hyperfine field of the Ce 4f electron spins with the hyperfine coupling constant of A = +5.7 kOe/μ_B. The spin-lattice relaxation rate 1/T₁ is roughly proportional to temperature, as with most non-magnetic metals at high temperature, and then strongly temperature-dependent, increasing rapidly with a peak near the antiferromagnetic transition temperature and decreasing at lower temperature. The temperature dependence of the Korringa ratio K, however, suggests that the antiferromagnetic spin fluctuation signature, which is an enhancement in the Korringa ratio, is washed out owing to the geometrical cancellation of Ce 4f fluctuations at the Al sites.     

Investigation of nuclear-spin couplings in the lithium fluorides as possible candidates for crystal nuclear magnetic resonance quantum computing devices

We have performed ⁷Li and ¹⁹F nuclear magnetic resonance (NMR) in two lithium fluorides BaLiF₃ and YLiF₄ to explore the possibility of a crystal NMR quantum computing device. We find that (1) both the absolute values and the angular dependences of the line widths can primarily be accounted for by the nuclear dipolar fields, and (2) the spin–lattice relaxation times are long enough for quantum computations. These characteristics indicate that these crystals can be possible candidates for quantum computing devices. We also find that, in the perovskite structures like BaLiF₃, magic angles are quite effective to diminish the nuclear dipole fields, which enables us to treat some nuclei as ‘isolated’. We propose using this feature to create low-dimensional nuclear-spin networks in the crystals. Received: 29 January 2001 / Accepted: 6 February 2001 / Published online: 3 April 2001     

Stacking fault defects in hep cobalt studied by PAC

A study was made of lattice defects in hep Co metal using the technique of perturbed γ-γ angular correlations. Lattice sites of¹¹¹Cd impurities were characterized by their nuclear magnetic dipole and electric quadrupole interaction frequencies, respectively ω_L and ω_O. The signal for defect-free substitutional Cd impurities was found to have collinear interactions at 77K, with ω_L=438 Mrad/s and ω_O=7 Mrad/s. Analysis of measurements after heavy deformation at 100 K and after annealings up to 700 K gave little evidence of thermal trapping of point defects. However, in all spectral measured after deformation, a highly stable defect site with ω_L=418 and ω_O Mrad/s, and showing collinear interactions, was also observed. It is attributed to a¹¹¹Cd probe in a stacking fault (SF). Assuming a random distribution of proble atoms and SF's, a SF density of 20% was estimated.     

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)     

Hyperfine Interactions of 181Ta in Zr2Ni Observed Using PAC Spectroscopy

We have measured nuclear electric–quadrupole interactions (EQI) at ¹⁸¹Ta impurities substituted as Hf atoms into the Zr site in Zr₂Ni. Using perturbed-angular-correlation (PAC) spectroscopy, we measured the EQI over temperatures ranging from 10 to 1200 K. Over the entire range of temperature, the Zr₂Ni crystal has a bct Al₂Cu structure that includes a single Zr site. The crystal field symmetry surrounding this site is rather low, giving rise to a highly asymmetric electric-field gradient tensor. At 10 K, the EQI is characterized by an angular frequency ω₀=601(3) Mrad s⁻¹, and an asymmetry parameter η=0.835(2). At 1200 K, ω₀ decreases to 516(3) Mrad s⁻¹, and η also decreases to 0.790(4). Although weak, the temperature dependence of ω₀ is consistent with a (1−BT ^3/2) power law, in which B=6×10⁻⁶ K^−3/2. The EQI also manifests a very narrow linewidth. We observed no evidence either for magnetic ordering or for structural phase transitions in the temperature range covered by this experiment. Moreover, the sharpness of the EQI indicates that the samples as prepared are remarkably free of strain and defects. These results indicate that the Zr₂Ni structure does not promote the formation of defects and that the power-law dependence of ω₀ on T is insensitive to the asymmetric nature of the crystal. This revised version was published online in September 2006 with corrections to the Cover Date.     

Nuclear matter properties in relativistic mean-field model with σ- ω coupling

The σ-ω coupling is introduced phenomenologically in the linear σ-ω model to study the nuclear matter properties. It is shown that not only the effective nucleon mass M^* but also the effective σ meson mass m _σ ^* and the effective ω meson mass m _ω ^* are nucleon-density-dependent. When the model parameters are fitted to the nuclear saturation point, with the nuclear radius constant r ₀ = 1.14 fm and volume energy a ₁ = 16.0 MeV, as well as to the effective nucleon mass M ^* = 0.85M, the model yields m _σ ^* = 1.09m _σ and m _ω ^* = 0.90m _ω at the saturation point, and the nuclear incompressibility K ₀ = 501 MeV. The lowest value of K₀ given by this model by adjusting the model parameters is around 227 MeV. Received: 23 March 2001 / Accepted: 8 June 2001     

Multiple Quantum Coherences (MQ) NMR and Entanglement Dynamics in the Mixed-Three-Spin XXX Heisenberg Model with Single-Ion Anisotropy

We analytically investigate Multiple Quantum (MQ) NMR dynamics in a mixed-three-spin (1/2,1,1/2) system with XXX Heisenberg model at the front of an external homogeneous magnetic field B. A single-ion anisotropy property ζ is considered for the spin-1. The intensities dependence of MQ NMR coherences on their orders (zeroth and second orders) for two pairs of spins (1,1/2) and (1/2,1/2) of the favorite tripartite system are obtained. It is also investigated dynamics of the pairwise quantum entanglement for the bipartite (sub)systems (1,1/2) and (1/2,1/2) permanently coupled by, respectively, coupling constants J₁ and J₂, by means of concurrence and fidelity. Then, some straightforward comparisons are done between these quantities and the intensities of MQ NMR coherences and ultimately some interesting results are reported. We also show that the time evolution of MQ coherences based on the reduced density matrix of the pair spins (1,1/2) is closely connected with the dynamics of the pairwise entanglement. Finally, we prove that one can introduce MQ coherence of the zeroth order corresponds to the pair spins (1,1/2) as an entanglement witness at some special time intervals.     

Quantum adiabatic polarons by translationally invariant perturbation theory

The translationally invariant diagrammatic quantum perturbation theory (TPT) is applied to the polaron problem on the 1D lattice, modeled through the Holstein Hamiltonian with the phonon frequency ω₀, the electron hopping t and the electron-phonon coupling constant g. The self-energy diagrams of the fourth-order in g are calculated exactly for an intermittently added electron, in addition to the previously known second-order term. The corresponding quadratic and quartic corrections to the polaron ground state energy become comparable at t/ω₀>1 for g/ω₀∼(t/ω₀) ^1/4 when the electron self-trapping and translation become adiabatic. The corresponding non adiabatic/adiabatic crossover occurs while the polaron width is large, i.e. the lattice coarsening negligible. This result is extended to the range (t/ω₀)^1/2>g/ω₀>(t/ω₀)^1/4>1 by considering the scaling properties of the high-order self-energy diagrams. It is shown that the polaron ground state energy, its width and the effective mass agree with the results found traditionally from the broken symmetry side, kinematic corrections included. The Landau self-trapping of the electron in the classic self-consistent, localized displacement potential, the restoration of the translational symmetry by the classic translational Goldstone mode and the quantization of the polaronic translational coordinate are thus all encompassed by a quantum theory which is translationally invariant from the outset. This represents the first example, open to various generalizations, of the capability of TPT to hold through the adiabatic symmetry breaking crossover. Plausible arguments are also given that TPT can describe the g/ω₀>(t/ω₀)^1/2 regime of the small polaron with adiabatic or non-adiabatic translation, i.e., that TPT can cover the whole g/ω₀, t/ω₀ parameter space of the Holstein Hamiltonian.     

C Chemical Shift and C–N Dipolar Coupling Tensors Determined by C Rotary Resonance Solid-State NMR

This work explores the utility of simple rotary resonance experiments for the determination of the magnitude and orientation of ¹³C chemical shift tensors relative to one or more ¹³C–¹⁴N internuclear axes from ¹³C magic-angle-spinning NMR experiments. The experiment relies on simultaneous recoupling of the anisotropic ¹³C chemical shift and ¹³C–¹⁴N dipole–dipole coupling interactions using 2D rotary resonance NMR with RF irradiation on the ¹³C spins only. The method is demonstrated by experiments and numerical simulations for the ¹³C^α spins in powder samples of -alanine and glycine with ¹³C in natural abundance. To investigate the potential of the experiment for determination of relative/absolute tensor orientations and backbone dihedral angles in peptides, the influence from long-range dipolar coupling to sequential ¹⁴N spins in a peptide chain (¹⁴N_i–¹³C^α_i–¹⁴N_i+1 and ¹⁴N_i+1–¹³C′_i–¹⁴N_i three-spin systems) as well as residual quadrupolar–dipolar coupling cross-terms is analyzed numerically.     

ωN final state interactions and ω-meson production from heavy-ion collisions

We calculate the elastic and inelastic ωN→ωN, →πN, →ρN, →ρπN, →ππN, →σN reactions within a boson exchange approximation where the ωρπ coupling constant and form factor are fixed by the reaction πN→ωN in comparison to the experimental data. We find rather large ωN cross sections at low relative momenta of the ω-meson which leads to a substantial broadening of the ω-meson width in nuclear matter. The implications of the ωN final state interactions are studied for ω production in ¹²C +¹²C, ⁴⁰Ca +⁴⁰Ca and ⁵⁸Ni +⁵⁸Ni reactions at about 2 · A GeV within the HSD transport approach; the drastic changes of the transverse mass spectra relative to a general m _T-scaling (for π⁰ and η mesons) might be controlled experimentally by the TAPS Collaboration. Received: 28 April 1999 / Revised version: 7 June 1999     

Isothermal depolarization currents in triglycine sulphate

5 s; the polarizing field was varied from 10 V/cm to 10 kV/cm, and the temperature between -190 °C and 25 °C. The results confirm that the depolarization current in TGS follows the formula I_d∼[(ω_pt)ⁿ+(ω_pt)^m]^-1, where n<1 and m>1. The values of the parameters n and m depend on both the electric field strength and the polarization time as well as on the temperature of the experiment. The loss peak frequency ω_p exhibits activation character: ω_p∼exp(-E/k_BT) with E=0.34 eV at temperatures directly below room temperature and E=0.013 eV in the range of liquid nitrogen temperatures. Received: 1 April 1997/Accepted: 7 April 1997     

Non-secular part of nuclear dipolar broadening detected by zero-field spin relaxation of positive muon

The zero-field spin relaxation function of μ⁺ observed in ZrH₂ has revealed that the second moment of the nuclear dipolar broadening is five times larger than the high-field value. This experiment clearly demonstrates the recovery of the non-secular part of dipolar interaction between unlike spins. A general expression of zero-field relaxation function is presented to account for a slow modulation of random fields on μ⁺ found at room temperature.     

A local moment approach to the gapped Anderson model

We develop a non-perturbative local moment approach (LMA) for the gapped Anderson impurity model (GAIM), in which a locally correlated orbital is coupled to a host with a gapped density of states. Two distinct phases arise, separated by a level-crossing quantum phase transition: a screened singlet phase, adiabatically connected to the non-interacting limit and as such a generalized Fermi liquid (GFL); and an incompletely screened, doubly degenerate local moment (LM) phase. On opening a gap (δ) in the host, the transition occurs at a critical gap δ_c, the GFL [LM] phase occurring for δ<δ_c [ δ>δ_c] . In agreement with numerical renormalization group (NRG) calculations, the critical δ_c = 0 at the particle-hole symmetric point of the model, where the LM phase arises immediately on opening the gap. In the generic case by contrast δ_c > 0, and the resultant LMA phase boundary is in good quantitative agreement with NRG results. Local single-particle dynamics are considered in some detail. The major difference between the two phases resides in bound states within the gap: the GFL phase is found to be characterised by one bound state only, while the LM phase contains two such states straddling the chemical potential. Particular emphasis is naturally given to the strongly correlated, Kondo regime of the model. Here, single-particle dynamics for both phases are found to exhibit universal scaling as a function of scaled frequency ω/ω_m ⁰ for fixed gaps δ/ω_m ⁰, where ω_m ⁰ is the characteristic Kondo scale for the gapless (metallic) AIM; at particle-hole symmetry in particular, the scaling spectra are obtained in closed form. For frequencies |ω|/ω_m ⁰ ≫δ/ω_m ⁰, the scaling spectra are found generally to reduce to those of the gapless, metallic Anderson model; such that for small gaps δ/ω_m ⁰≪ 1 in particular, the Kondo resonance that is the spectral hallmark of the usual metallic Anderson model persists more or less in its entirety in the GAIM.     

Dipolar Zeeman mixing in weak magnetic fields: An experiment with ice protons

The evolution of the longitudinal magnetization of nuclear spins in a cw high-frequency magnetic field has been measured using a SQUID magnetometer at liquid-helium temperatures in magnetic fields H ₀ of up to 57 Oe. The time T _m for thermal mixing of the Zeeman and dipolar systems has been found to range between 0.05 and 4×10² s. For T _m>1 s the function T _m(H ₀) is exponential. The proton NMR spectra near the fundamental and twice the Larmor frequency have been obtained. The shift in the resonance with respect to the Larmor frequency is close to the theoretical prediction. Zh. éksp. Teor. Fiz. 114, 1006–1017 (September 1998) Deceased.