Dipolar-coupled Spins Research Articles

Relaxation of Multiple-Quantum Coherences in Dipolar Coupled 1H Spin Pairs in Gypsum

Relaxation of Multiple-Quantum Coherences in Dipolar Coupled 1H Spin Pairs in Gypsum

Intrinsic decoherence dynamics and dense coding in dipolar spin system

The quantum decoherence is an ineluctable process when a quantum system interacts with its surrounding environment. Milburn’s dynamical master equation, as a modified shape of the Schrödinger equation, is typically used to study the effects decoherence even without intervention of environment. We studied the temporal evolution of non-local correlations in a dipolar-coupled spin system under the influence of intrinsic decoherence. Primarily, the generation in correlations of Einstein–Podolsky–Rosen steering, measurement-induced non-locality and entanglement in an uncorrelated initial system state were studied. Also, the effect of the intrinsic decoherence on the quality of the dense coding capacity dynamics for the dipolar-coupled spin system was examined. Our results highlight that the initial system’s role in defining the quantum correlations’ robustness, and we also brought out the impacts of system’s parameters on the non-local correlations and the efficiency of dense coding process.

Partial lifting of degeneracy in the J1−J2−J3 Ising antiferromagnet on the kagome lattice

Motivated by dipolar-coupled artificial spin systems, we present a theoretical study of the classical $J_1-J_2-J_3$ Ising antiferromagnet on the kagome lattice. We establish the ground-state phase diagram of this model for $J_1 > |J_2|, |J_3|$ based on exact results for the ground-state energies. When all the couplings are antiferromagnetic, the model has three macroscopically degenerate ground-state phases, and using tensor networks, we can calculate the entropies of these phases and of their boundaries very accurately. In two cases, the entropy appears to be a fraction of that of the triangular lattice Ising antiferromagnet, and we provide analytical arguments to support this observation. We also notice that, surprisingly enough, the dipolar ground state is not a ground state of the truncated model, but of the model with smaller $J_3$ interactions, an indication of a very strong competition between low-energy states in this model.

Entropic Uncertainty for Two Coupled Dipole Spins Using Quantum Memory under the Dzyaloshinskii-Moriya Interaction.

In the thermodynamic equilibrium of dipolar-coupled spin systems under the influence of a Dzyaloshinskii–Moriya (D–M) interaction along the z-axis, the current study explores the quantum-memory-assisted entropic uncertainty relation (QMA-EUR), entropy mixedness and the concurrence two-spin entanglement. Quantum entanglement is reduced at increased temperature values, but inflation uncertainty and mixedness are enhanced. The considered quantum effects are stabilized to their stationary values at high temperatures. The two-spin entanglement is entirely repressed if the D–M interaction is disregarded, and the entropic uncertainty and entropy mixedness reach their maximum values for equal coupling rates. Rather than the concurrence, the entropy mixedness can be a proper indicator of the nature of the entropic uncertainty. The effect of model parameters (D–M coupling and dipole–dipole spin) on the quantum dynamic effects in thermal environment temperature is explored. The results reveal that the model parameters cause significant variations in the predicted QMA-EUR.

Floquet Dynamics in a One-Dimensional Chain in the Multipulse Spin Locking of Nuclear Magnetic Resonance

The dynamics of a one-dimensional chain that consists of 10–14 dipolar-coupled nuclear spins, is placed in an external magnetic field, and is irradiated by a periodic sequence of resonant π/n pulses (n is a natural number) with the same time delay 2τ between them has been studied. The numerical calculation has shown that thermodynamic equilibrium, which is determined by the common temperature of the Zeeman and dipole reservoirs, is established in the spin system at the average pulse field π/(2nτ) ∼ ωloc (where ωloc is the dipole frequency and n > 2) and times t ∼ ω loc −1 . The relaxation of the magnetization in the system irradiated by (π/2)x pulses at π/4τ ≫ πlocis due to a four-spin resonant process, and the relaxation rate is proportional to τ4.

The origin of negative cross-peaks in proton-spin diffusion spectrum of fully protonated solids at fast MAS: Coherent or incoherent effect?

Spin-diffusion (SD) is amongst the first methods proposed to spatially transfer polarization between dipolar-coupled nuclear spins. Lab-frame SD has proved particularly useful in structural characterization of a large variety of molecules. During SD, the rate of magnetization transfer between the two nuclei depends on the square of the dipolar coupling and the zero-quantum lineshape of the two spins. The relative sign of the diagonal and cross-peaks is determined by the spin part of the dipolar Hamiltonian. Practically, SD experiments are used in two ways: (a) SD transfer amongst only the protons (known as proton spin-diffusion or PSD) and b) SD amongst rare nuclei, coupled to a strong proton bath, known as proton driven spin-diffusion (PDSD). It is well established that the diagonal and cross-peaks have the same sign during SD based polarization transfer. 2D PSD experiments recorded on Histidine.HCl.H2O sample at fast magic angle spinning (MAS) show that some of the cross-peaks in the 2D spectrum are negative with respect to the diagonal peaks. Cross-relaxation due to stochastic motion is generally believed to give rise to such negative peaks. Herein, we use theoretical calculations, numerical simulations and experiments to show that the origin of the negative cross-peaks in PSD spectrum is due to coherent interactions. The origin of negative peaks can be specifically ascribed to a four spin, double-flip-double flop term, in the third-order Hamiltonian. These terms become the dominant terms at fast spinning when additional — conditions are satisfied.

Pulse control protocols for preserving coherence in dipolar-coupled nuclear spin baths

Coherence of solid state spin qubits is limited by decoherence and random fluctuations in the spin bath environment. Here we develop spin bath control sequences which simultaneously suppress the fluctuations arising from intrabath interactions and inhomogeneity. Experiments on neutral self-assembled quantum dots yield up to a five-fold increase in coherence of a bare nuclear spin bath. Numerical simulations agree with experiments and reveal emergent thermodynamic behaviour where fluctuations are ultimately caused by irreversible conversion of coherence into many-body quantum entanglement. Simulations show that for homogeneous spin baths our sequences are efficient with non-ideal control pulses, while inhomogeneous bath coherence is inherently limited even under ideal-pulse control, especially for strongly correlated spin-9/2 baths. These results highlight the limitations of self-assembled quantum dots and advantages of strain-free dots, where our sequences can be used to control the fluctuations of a homogeneous nuclear spin bath and potentially improve electron spin qubit coherence.

A DNP-hyperpolarized solid-state water NMR MASER: observation and qualitative analysis.

We present observations of an NMR MASER (microwave amplification by stimulated emission of radiation) of hyperpolarized 1H nuclei by dynamic nuclear polarization (DNP) at 1.2 K and in a magnetic field of 6.7 T. The sustained maser pulses originate from the interplay between radiation damping (RD) due to the large 1H magnetization, and the remagnetization to a negative value by the DNP process. NMR signals lasting for several tens of seconds are thus observed on an ensemble of dipolar-coupled nuclear spins. Magnetization dynamics are analyzed in terms of the combined Bloch-Maxwell and Provotorov (BMP) equations for RD and DNP. Insight into the long time evolution of the magnetization is provided by a theoretical analysis of this nonlinear dynamical system, and by fitting the NMR signal to a simplified version of the BMP equations.

Collective magnetism in an artificial 2D XY spin system

Two-dimensional magnetic systems with continuous spin degrees of freedom exhibit a rich spectrum of thermal behaviour due to the strong competition between fluctuations and correlations. When such systems incorporate coupling via the anisotropic dipolar interaction, a discrete symmetry emerges, which can be spontaneously broken leading to a low-temperature ordered phase. However, the experimental realisation of such two-dimensional spin systems in crystalline materials is difficult since the dipolar coupling is usually much weaker than the exchange interaction. Here we realise two-dimensional magnetostatically coupled XY spin systems with nanoscale thermally active magnetic discs placed on square lattices. Using low-energy muon-spin relaxation and soft X-ray scattering, we observe correlated dynamics at the critical temperature and the emergence of static long-range order at low temperatures, which is compatible with theoretical predictions for dipolar-coupled XY spin systems. Furthermore, by modifying the sample design, we demonstrate the possibility to tune the collective magnetic behaviour in thermally active artificial spin systems with continuous degrees of freedom.

Saturation capability of short phase modulated pulses facilitates the measurement of longitudinal relaxation times of quadrupolar nuclei

The ability of various pulse types, which are commonly applied for distance measurements, to saturate or invert quadrupolar spin polarization has been compared by observing their effect on magnetization recovery curves under magic-angle spinning. A selective central transition inversion pulse yields a bi-exponential recovery for a diamagnetic sample with a spin-3/2, consistent with the existence of two processes: the fluctuations of the electric field gradients with identical single (W1) and double (W2) quantum quadrupolar-driven relaxation rates, and spin exchange between the central transition of one spin and satellite transitions of a dipolar-coupled similar spin. Using a phase modulated pulse, developed for distance measurements in quadrupolar spins (Nimerovsky et al., JMR 244, 2014, 107–113) and suggested for achieving the complete saturation of all quadrupolar spin energy levels, a mono-exponential relaxation model fits the data, compatible with elimination of the spin exchange processes. Other pulses such as an adiabatic pulse lasting one-third of a rotor period, and a two-rotor-period long continuous-wave pulse, both used for distance measurements under special experimental conditions, yield good fits to bi-exponential functions with varying coefficients and time constants due to variations in initial conditions. Those values are a measure of the extent of saturation obtained from these pulses. An empirical fit of the recovery curves to a stretched exponential function can provide general recovery times. A stretching parameter very close to unity, as obtained for a phase modulated pulse but not for other cases, suggests that in this case recovery times and longitudinal relaxation times are similar. The results are experimentally demonstrated for compounds containing 11B (spin-3/2) and 51V (spin-7/2). We propose that accurate spin lattice relaxation rates can be measured by a short phase modulated pulse (<1–2ms), similarly to the "true T1" measured by saturation with an asynchronous pulse train (Yesinowski, JMR 252, 2015, 135–144).

Bis-Gadolinium Complexes for Solid Effect and Cross Effect Dynamic Nuclear Polarization.

High-spin complexes act as polarizing agents (PAs) for dynamic nuclear polarization (DNP) in solid-state NMR spectroscopy and feature promising aspects towards biomolecular DNP. We present a study on bis(Gd-chelate)s which enable cross effect (CE) DNP owing to spatial confinement of two dipolar-coupled electron spins. Their well-defined Gd⋅⋅⋅Gd distances in the range of 1.2-3.4 nm allowed us to elucidate the Gd⋅⋅⋅Gd distance dependence of the DNP mechanism and NMR signal enhancement. We found that Gd⋅⋅⋅Gd distances above 2.1 nm result in solid effect DNP while distances between 1.2 and 2.1 nm enable CE for 1 H, 13 C, and 15 N nuclear spins. We compare 263 GHz electron paramagnetic resonance (EPR) spectra with the obtained DNP field profiles and discuss possible CE matching conditions within the high-spin system and the influence of dipolar broadening of the EPR signal. Our findings foster the understanding of the CE mechanism and the design of high-spin PAs for specific applications of DNP.

Theory of solid effect and cross effect dynamic nuclear polarization with half-integer high-spin metal polarizing agents in rotating solids.

Dynamic nuclear polarization (DNP) is a powerful method to enhance sensitivity especially of solid-state magic-angle spinning (MAS) NMR by up to several orders of magnitude. The increased interest both from a practical as well as theoretical viewpoint has spawned several fields of active research such as the development of new polarizing agents with improved or unique properties and description of the underlying DNP mechanisms such as solid effect (SE) and cross effect (CE). Even though a novel class of unique polarizing agents based on high-spin metal ions such as Gd(iii) and Mn(ii) has already been utilized for MAS DNP a theoretical description of the involved DNP mechanism is still incomplete. Here, we review several aspects of DNP-relevant electron-paramagnetic resonance (EPR) properties of the general class of these half-integer high-spin metal ions with isotropic Zeeman interaction but significant zero-field splitting (ZFS). While the SE can be relatively easily described similar to that of a S = 1/2 system and is assumed to be effective only for polarizing agents featuring a narrow central EPR transitions (i.e., mS = -1/2 → +1/2) with respect to the nuclear Larmor frequency, the CE between two high-spin ions requires a more detailed theoretical investigation due to a multitude of possible transitions and matching conditions. This is especially interesting in light of recent understanding of CE being induced by MAS-driven level anti-crossings (LACs) between dipolar-coupled electron spins. We discuss the requirements of such CE-enabling LACs to occur due to anisotropy of ZFS, the expected adiabaticity, and the resulting possibilities of high-spin metal ion pairs to act as polarizing agents for DNP. This theoretical description serves as a framework for a detailed experimental study published directly following this work.

“Pseudo solid” nuclear spin echo study of poly(ethylene oxide) grafted on silica. Comparison with magic‐angle spinning technique results

AbstractThe polymer/solid interface of Poly (ethylene oxide) (PEO) grafted on silica is studied by 1H NMR. For grafted polymers, the dipolar interaction is an important factor in the spin–spin relaxation process. For this purpose, the part of the dipolar interaction that is not averaged to zero by the motion is used. The “pseudo solid” spin echo can indeed give an estimation of the nonzero average dipolar interactions. The appropriate pulse sequence permits a standard measurement of the average dipolar spin coupling involved in the transverse magnetization relaxation. The influence of some major parameters such as molecular weights of the chains, grafting ratios, and temperatures on the relaxation and ultimately on the concentration is followed by “pseudo solid” spin echo. The magic‐angle spinning technique is also used. The sample rotation confirms by the narrowing of the central line and the appearance of side bands, the existence of a residual dipolar interaction which reveals the concentration of high monomer units at the surface. The study of the side bands permits to calculate the second moment as a function of temperature. A fair agreement is obtained by these two independent techniques: pseudo solid echo and magic‐angle spinning.

QUANTUM SIMULATION. Localization-delocalization transition in the dynamics of dipolar-coupled nuclear spins.

Nonequilibrium dynamics of many-body systems are important in many scientific fields. Here, we report the experimental observation of a phase transition of the quantum coherent dynamics of a three-dimensional many-spin system with dipolar interactions. Using nuclear magnetic resonance (NMR) on a solid-state system of spins at room-temperature, we quench the interaction Hamiltonian to drive the evolution of the system. Depending on the quench strength, we then observe either localized or extended dynamics of the system coherence. We extract the critical exponents for the localized cluster size of correlated spins and diffusion coefficient around the phase transition separating the localized from the delocalized dynamical regime. These results show that NMR techniques are well suited to studying the nonequilibrium dynamics of complex many-body systems.

Floquet–Magnus expansion for general N-coupled spins systems in magic-angle spinning nuclear magnetic resonance spectra

In this paper we present a theoretical perturbative approach for describing the NMR spectrum of strongly dipolar-coupled spin systems under fast magic-angle spinning. Our treatment is based on two approaches: the Floquet approach and the Floquet–Magnus expansion. The Floquet approach is well known in the NMR community as a perturbative approach to get analytical approximations. Numerical procedures are based on step-by-step numerical integration of the corresponding differential equations. The Floquet–Magnus expansion is a perturbative approach of the Floquet theory. Furthermore, we address the “γ-encoding” effect using the Floquet–Magnus expansion approach. We show that the average over “γ” angle can be performed for any Hamiltonian with γ symmetry.

Entanglement under equilibrium establishing in spin systems subjected to radiofrequency field

We study the entanglement evolution in a dipolar-coupled spin system irradiated by a radiofrequency (RF) field in quasi-equilibrium state characterized by a two-temperature density matrix. Process of the establishment of equilibrium is in the equalization of these temperatures. The method of the nonequilibrium statistical operator in a rotating frame is used to describe the evolution of the spin system. It is shown that the equilibrium establishment has nonexponential character, and the time needed for this establishment depends strongly on the RF field strength. Particularly, the weak RF irradiation increases the lifetime of entanglement. Temporal and temperature dependencies of the concurrence of spin pairs are obtained and discussed. It is shown that application of RF field increases the time of the equilibrium establishment (up to order of 1,000 times) and lifetime of the existence of entangled states (up to order of 1,000 times). Thus, with the help of RF irradiation, we can govern the relaxation process and control entanglement in the system. The obtained results can be used for analysis of more complex spin systems because dipole---dipole interaction decreases proportionally to inverse third power of the distance between the spins, and influence of far way spins can be negligible.

Magnetic ordering and charge dynamics in κ-(BEDT-TTF)2Cu[N(CN)2]Cl

The Mott insulator κ-(BEDT-TTF)2Cu[N(CN)2]Cl consists of molecular dimers arranged on an anisotropic triangular lattice. At low temperatures a pronounced dielectric anomaly is observed, and eventually a canted antiferromagnetic ground state forms. Optical spectroscopy clearly rules out charge imbalance and the existence of quantum electric dipoles with a dipolar-spin coupling. Here we suggest a novel form of spin–charge coupling where the prominent in-plane dielectric response in κ-(BEDT-TTF)2Cu[N(CN)2]Cl is explained by short-range discommensurations of the antiferromagnetic phase in the temperature range 30 K < T < 50 K, and by relaxation of charged domain walls in the ferromagnetic structure at lower temperatures.

Communication: Long-lived states of nuclear spins in solids

We report an observation of extremely long-lived spin states in systems of dipolar-coupled nuclear spins in solids. The "suspended echo" experiment uses a simple stimulated echo pulse sequence and creates non-equilibrium states which live many orders of magnitude longer than the characteristic time of spin-spin dynamics T2. Large amounts of information can be encoded in such long-lived states and subsequently retrieved by an application of a single "reading" pulse.

Quantum discord in spin systems with dipole–dipole interaction

The behavior of total quantum correlations (discord) in dimers consisting of dipolar-coupled spins 1/2 are studied. We found that the discord $$Q=0$$ at absolute zero temperature. As the temperature $$T$$ increases, the quantum correlations in the system increase at first from zero to its maximum and then decrease to zero according to the asymptotic law $$T^{-2}$$ . It is also shown that in absence of external magnetic field $$B$$ , the classical correlations $$C$$ at $$T\rightarrow 0$$ are, vice versa, maximal. Our calculations predict that in crystalline gypsum $$\hbox {CaSO}_{4}\cdot \hbox {2H}_{2}{\hbox {O}}$$ the value of natural $$(B=0)$$ quantum discord between nuclear spins of hydrogen atoms is maximal at the temperature of 0.644 $$\upmu $$ K, and for 1,2-dichloroethane $$\hbox {H}_{2}$$ ClC– $$\hbox {CH}_{2}{\hbox {Cl}}$$ the discord achieves the largest value at $$T=0.517~\upmu $$ K. In both cases, the discord equals $$Q\approx 0.083$$ bit/dimer what is $$8.3\,\%$$ of its upper limit in two-qubit systems. We estimate also that for gypsum at room temperature $$Q\sim 10^{-18}$$ bit/dimer, and for 1,2-dichloroethane at $$T=90$$ K the discord is $$Q\sim 10^{-17}$$ bit per a dimer.

Transient Nutations in Magnetically Diluted Solids: An Account of the Spin Flip-Flop Transitions

Transient nutations of the dipolar-coupled spins in solids are studied theoretically. The spins have either electronic (paramagnetic ions or defects in crystals) or nuclear origin and are subjected to the external resonant magnetic field that continually drives the total magnetization. For an ensemble of spins that have equal resonance frequencies, the flip-flop transitions are possible. The existing microscopic model of the magnetic relaxation in transient regime is modified in order to obtain the decay rate of the transient nutations in this particular case.