ENDOR amplitudes of triplet state molecules: I. Electric-circuit analogy treatment

ENDOR spectra of triplet state molecules have a chacteristic line from degenerate NMR transitions within the zero level (ZL) electron spin manifoldM _S=0. The ZL line, observed at the free nuclear Larmor frequency, dominates spectra when the number of nuclei is large. This line was found to be substantially reduced in intensity at low temperature. The strong variation of the ZL line intensity is analyzed within the frame of an electric-circuit analogy modeling. The result is as follows: At low temperature the electron and nuclear spin-lattice relaxation rates become small, and the nuclear-nuclear spin flip-flop transitions between degenerate substates,M _I=const within the ZL manifold, become relatively strong to compete for population redistribution. This reduces the population differences between nuclear sublevels. Additional NMR irradiation can thus do very little to reduce these differences even more, and the ENDOR effect becomes suppressed. A certain enhancement of the relaxationally suppressed ZL line occurring at increased EPR saturation is explained by the coherent action of the microwave field on the selected substate within the ZL manifold that shifts its energy out of the other degenerate states thereby closing the flip-flop relaxation channel.     

ENDOR amplitudes of triplet state molecules: II. Orientational dependence of the νp frequency line and S-T0 mixing

The specific ENDOR line at the free Larmor frequency ν_p in the low temperature spectra of triplet state molecules is caused by degenerate NMR transitions within theM _s=0 zero-level (ZL) electron spin manifold. This ZL line was found to be orientationally dependent for the diradical complex Zn(3,6-di-tert-butyl-o-semiquinone)₂Zn(DBSQ)₂: the ZL line dominates the ENDOR spectrum if it is detected at the perpendicular canonical components of the EPR spectrum, and vanishes if the complex is oriented with its ZFSz-axis parallel to the direction of the magnetic field, i.e., if detected at the parallel canonical EPR components. This effect is shown to result from the interaction between nuclear spin substates of the S and T₀ manifolds, their levels being close to each other for the Zn(DBSQ)₂ complex. Such an interaction mixes the states and shifts energy levels. Consequently, it cancels the degeneracy of the nuclear substates within the ZL manifold and reduces the rate of nuclear flip-flop relaxation. This specific relaxation mechanism has been shown to substantially affect the amplitude of the ZL line (Doubinskii A.A., Lebedev Ya.S., Möbius K.: Appl. Magn. Reson.13, 439 (1997)). The nuclear flip-flop relaxation effect is expected to be orientationally dependent since the S-T_o separation depends upon the orientation of the diradical with respect to the external magnetic field.     

Spin relaxation of quadrupole nuclei in paramagnetic and magnetically ordered insulators

The longitudinal and transverse spin relaxation through a (generally anisotropic) electron-nucleus interaction in paramagnetic and magnetically ordered insulators is theoretically studied for nuclei with a resolved quadrupole structure. Expressions are derived for the relaxation rates of both the transverse nuclear magnetization components when individual transitions are excited in the quadrupole structure and the total longitudinal nuclear magnetization component. These expressions are reduced to a form that contains the Fourier transforms of the time correlation functions only for the electron spins. Given the specific form of these correlation functions corresponding to different phase states of the electron spins and different origins of their fluctuations, the temperature dependences of the nuclear relaxation rates are ascertained in various cases, including those for dipole and isotropic hyperfine interactions. Calculations are performed for arbitrary electron and half-integer nuclear spins by taking into account the possible quadrupole splitting of the NMR spectrum without any restriction on the smallness of the ratio ?ω s/k_BT (ω_s is the resonance frequency of the electron spins). The derived expressions are compared with available experimental data on the longitudinal and transverse nuclear relaxation in colossal-magnetoresistance lanthanum manganites in the part of their phase diagram where the corresponding samples are either paramagnetic or magnetically ordered insulators and near the points of transition to an ordered state. Interpretations alternative to the existing ones are offered.     

Korringa relaxation time of magnetic ion system near a two-dimensional electron gas

Spin relaxation of Mn ions in a (Cd,Mn)Te quantum well with quasi-two-dimensional carriers (Q2DEG) is investigated. The mechanism of energy transfer is spin-flip scattering of Mn spin with electrons making transitions between spin subbands accompanied by a change in the Mn spin. A calculation of the spin-flip scattering rate shows that the Mn spin relaxation rate is proportional to the coupling constant squared, the density of states squared, and the electron temperature, the so called Korringa relaxation rate. It was found that for small Mn ion concentration, the relaxation time ≈10−7-10−6s is in a good agreement with experimental results. Moreover, the relaxation rate scales with L⁻², L being the well width, and it can be enhanced over its value in bulk.     

Nuclear spin conversion in diatomic molecules

A mechanism of the internal interaction in dimers that mixes different nuclear spin modifications has been proposed. It has been shown that the intramolecular current associated with transitions between electronic terms of different parities can generate different magnetic fields on nuclei, leading to transitions between spin modifications and to the corresponding changes in rotational states. In the framework of the known quantum relaxation process, this interaction initiates irreversible conversion of nuclear spin modifications. The estimated conversion rate for nitrogen at atmospheric pressure is quite high (10^?3–10^?5 s^?1).     

Longitudinal muon spin relaxation in muonium-like systems

Nuclear spin-lattice relaxation in paramagnetic systems is treated using the classic expression for transition probability between the coupled electron and nuclear spin states. The rate equations governing the incoherent occupancies of these states are solved analytically (where possible) and numerically (where not) to construct the relaxation function for the nuclear spin. The method is illustrated for muonium, and the muonium-substituted molecular radicals, for the case of perturbation due to fluctuation of the local field,i.e. modulation of the interaction with a third spin. A slight departure from single exponential behaviour is demonstrated for slow fluctuations.     

Long-lived states in solution NMR: theoretical examples in three- and four-spin systems

Long-lived spin states have been observed in a variety of systems. Although the dynamics underlying the long lifetimes of these states are well understood in the case of two-spin systems, the corresponding dynamics in systems containing more spins appear to be more complex. Recently it has been shown that a selection rule for transitions mediated by intramolecular dipolar relaxation may play a role in determining the lifetimes of long-lived states in systems containing arbitrary numbers of spins. Here we present a theory of long-lived states in systems containing three and four spins and demonstrate how it can be used to identify states that have little or no intramolecular dipolar relaxation.     

Theoretical Study of Dipolar Relaxation of Coupled Nuclear Spins at Variable Magnetic Field

A theoretical study was made of magnetic field-dependent dipolar relaxation in two- and three-spin systems. The results for the nuclear magnetic relaxation dispersion (NMRD) curves were compared with those for the simpler model of fluctuating local fields. For both models it was found that at low fields spins tend to relax with a common T ₁-relaxation time. Sharp features in the NMRD curves coming from nuclear spin level anti-crossings are also predicted by both models. However, the simple model fails to describe the behavior of so-called long-lived spin states (LLS). We have studied the LLS as function of magnetic field and molecular geometry and simulated experimental results for the LLS in histidine amino acid obtained at the laboratory of Prof. H.-M. Vieth (Free University Berlin, Germany). In addition, we described polarization transfer in a three-spin system where two spins are protons, which are initially hyperpolarized by para-hydrogen induced polarization (PHIP), while the third spin is a spin ½ hetero-nucleus, which acquires polarization in the course of cross-relaxation.     

The role of the nuclear spin in optical pumping withD 2-light

Optical pumping withD ₂-light provides an excellent means for studying collisional relaxation in the excited² P _3/2-state of alkali atoms. Collisional relaxation of orientations in that state very sensitively affects the spin orientation in the ground state. All these orientations may be easily created by absorption of σ⁺- or σ{?{-light. At a certain strength of the relaxation realized by a certain buffer gas pressure, the spin orientation in the ground state even vanishes, providedD ₂-light is used for excitation. The condition for this situation is derived from the set of rate equations which governs the evolution of all the orientations involved. These conditions very markedly depend on the nuclear spin valueI. The validity of this dependence has been checked by magnetic decoupling of the nuclear spin and observing the associated shift of the pressure for vanishing spin orientation.     

Magnetic relaxation in spinel Mo-ferrite and Ti substituted Mo-ferrite

A compensation temperature of 138 K was observed in the temperature-dependent magnetization curves of MoFe₂O₄. Relatively slow magnetization relaxation characterized the transitions between different spin states (compensated and uncompensated). Large magnetic after effect was found in time-dependent magnetization curves after heating or cooling from different characteristic temperatures for different spin states. The magnetic relaxation was nearly independent on magnetic field, supporting the presence of spin states and no involvement of domain structure. For the Ti substituted Mo_0.6Ti_0.4Fe₂O₄ sample, there were a compensation at ∼ 100 K and a maximum of magnetization at ∼ 175 K. Similar results of anomalous magnetic relaxation was observed in Ti substituted Mo-ferrite (Mo_0.6Ti_0.4Fe₂O₄). If the Mo_0.6Ti_0.4Fe₂O₄ sample was heated from 100 K to 235 K, the time-dependent magnetization curve could be considered as a combination of two magnetic relaxation processes. However, if the sample was heated from 100 K to 295 K, the time- dependent magnetization curve became complex. Received 30 October 2001 and Received in final form 21 January 2002     

Majorana flipping of quarkonium spin states in transient magnetic field

We demonstrate that spin flipping transitions occur between various quarkonium spin states due to transient magnetic field produced in non central heavy ion collisions (HICs). The inhomogeneous nature of the magnetic field results in non adiabatic evolution of (spin)states of quarkonia moving inside the transient magnetic environment. Our calculations explicitly show that the consideration of azimuthal inhomogeneity gives rise to dynamical mixing between different spin states owing to Majorana spin flipping. Notably, this effect of non-adiabaticity is novel and distinct from previously predicted mixing of the singlet and one of the triplet states of quarkonia in the presence of a static and homogeneous magnetic field.     

Nuclear spin-lattice relaxation of protons in low-dimensional Ising-like system: [(CH3)3NH]CoCl3 · 2H2O

The nuclear spin-lattice relaxation times of protons in a low-dimensional Ising-like system [(CH₃)₃NH]CoCl₃ · 2H₂O were measured from 1.2 to 4.2 K in zero field and in an external magnetic field applied along the spin easy-axis. The calculation for the two-magnon Raman process was carried out with respect to a ferromagnetic layer of the bc-plane. By taking the gap energy to be 14.0 K, the best fit of the theoretical curves with the data was obtained from 1.2 K to about 2.0 K. The experimental results at high temperatures deviate seriously from the prediction of this process, which is discussed in terms of a tentative model for the nuclear relaxation process associated with magnon bound states.     

High-Field Phenomena of Qubits

Electron and nuclear spins are very promising candidates to serve as quantum bits (qubits) for proposed quantum computers, as the spin degrees of freedom are relatively isolated from their surroundings and can be coherently manipulated, e.g., through pulsed electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR). For solid-state spin systems, impurities in crystals based on carbon and silicon in various forms have been suggested as qubits, and very long relaxation rates have been observed in such systems. We have investigated a variety of these systems at high magnetic fields in our multifrequency pulsed EPR/ENDOR (electron nuclear double resonance) spectrometer. A high magnetic field leads to large electron spin polarizations at helium temperatures, giving rise to various phenomena that are of interest with respect to quantum computing. For example, it allows the initialization of both the electron spin as well as hyperfine-coupled nuclear spins in a well-defined state by combining millimeter and radio-frequency radiation. It can increase the T ₂ relaxation times by eliminating decoherence due to dipolar interaction and lead to new mechanisms for the coherent electrical readout of electron spins. We will show some examples of these and other effects in Si:P, SiC:N and nitrogen-related centers in diamond.     

Nuclear spin relaxation in free radicals as revealed in a stimulated electron spin echo experiment

Electron spin echo envelope modulation (ESEEM) in a three-pulse stimulated echo experiment, when the time interval between the first and second pulses τ is varied, is attributed to a spontaneous change of the electron spin Larmor frequency in the time intervalT between the second and third pulses, due to the longitudinal relaxation of nearby nuclei. It is observed for nitroxide radicals in glassy matrices in the temperature range of 130–240 K. Nuclear relaxation is assumed to arise from fluctuation of the proton hyperfine interaction, due to fast rotation of the methyl groups. This contribution to ESEEM and the conventional one that is induced by the simultaneous excitation of allowed and forbidden electron spin transitions were found to be multiplicative. As the latter does not depend on the timeT, both contributions can be easily separated. The rate of nuclear spin relaxation was determined, and correlation time of methyl group rotation was estimated by Redfield theory of spin relaxation. Arrhenius parameters of this motion were estimated on the basis of these data and those at 77 and 90 K, where the previously developed approach was used (L.V. Kulik, I.A. Grigor’ev, E.S. Salnikov, S.A. Dzuba, Yu.D. Tsvetkov, J. Phys. Chem. A 106, 12066–12071, 2003).     

The mesoscopic chiral metal-insulator transition

Sharp localization transitions of chiral edge states in disordered quantum wires subject to a strong magnetic field are shown to be driven by crossovers from two-to one-dimensional localization of bulk states. As a result, the two-terminal conductance is found to exhibit discontinuous transitions at zero temperature between exactly integer plateau values and zero, reminiscent of first-order phase transitions. We discuss the corresponding phase diagram. The spin of the electrons is shown to result in a multitude of phases when the spin degeneracy is raised by the Zeeman energy. The width of conductance plateaus is found to depend sensitively on the spin flip rate 1/τ_s.     

Probing the paramagnetic interactions between the unpaired electronic spins of carbon atoms and the nuclear spins of hydrogen molecules with Raman spectroscopy

Carbon materials typically have a high density of unpaired electronic spins but the exact nature of the defect sites that give rise to their magnetic properties are not yet well understood. In this work, the paramagnetic interactions between the unpaired electronic spins of carbon atoms and the nuclear spins of hydrogen molecules were probed with Raman spectroscopy by monitoring the relative population of H₂ rotational states. For H₂, the symmetries of nuclear spin and rotational wave functions are correlated. Because of the weak interactions between H₂ nuclear spins, the transitions between odd and even rotational states are normally hindered. The magnetic field generated by unpaired electronic spins relaxes the selection rules and promotes transitions between H₂ rotational levels of different symmetry. This affects the rotational levels' relaxation kinetics toward equilibrium and makes H₂ molecules useful to study unpaired electrons in paramagnetic materials. It is suggested that simultaneous electron paramagnetic resonance and Raman measurements on carbon materials interacting with hydrogen molecules could result in a better understanding of the nature of paramagnetic defects in carbon materials, which could have a substantial impact on Li‐ion batteries or for understanding the graphene electronic properties. Copyright © 2011 John Wiley & Sons, Ltd.     

ESR study of exchange coupled pairs in copper diethyldithiocarbamate—explanation of the low temperature hyperfine anomaly

A study of the hyperfine interaction in the ESR of Cu-Cu pairs in single crystals of copper diethyldithiocarbamate as a function of temperature has shown distinct differences in the hyperfine structure in the two fine structure transitions at 20 K, the spectrum not having the same hyperfine intensity pattern in the low field fine structure transition in contrast to that of the high field transition. The details of the structure of both the fine structure transitions in the 20 K spectrum have now been explained by recognizing the fact that the mixing of the nuclear spin states caused by the anisotropic hyperfine interaction affects the electron spin states | + 1 > and | −> differently. This has incidentally led to a determination of the sign ofD confirming the earlier model. The anomalous hyperfine structure is found to become symmetric at 77 K and 300 K. It is proposed that the reason for this lies in the dynamics of spin-lattice interaction which limits the lifetime of the spin states in each of the electronic levels | − 1 >, | 0 > and | + 1 > The estimate of spin-lattice relaxation time agrees with those indicated from other studies. The model proposed here for the hyperfine interaction of pairs in the electronic triplet state is of general validity.     

Foreign gas broadening of an IR absorption line of formaldehyde

The theory of nuclear spin state relaxation of symmetrical molecules like formaldehyde contains a collision time t_c that is interpreted as time between rotationally inelastic molecular collisions. This time traditionally is determined from measurements of pressure broadening of spectral lines. In order to test whether these collision times, which determine spin relaxation rate constants and line broadening coefficients, respectively, are the same or at least related to another, we have performed systematic measurements of the broadening of an IR line of formaldehyde by other gases of different pressures.     

Effective field and the Bloch-Siegert shift at bichromatic excitation of multiphoton EPR

The dynamics of multiphoton transitions in a two-level spin system excited by transverse microwave and longitudinal RF fields with the frequencies ω_mw and ω_rf, respectively, is analyzed. The effective time-independent Hamiltonian describing the “dressed” spin states of the “spin + bichromatic field” system is obtained by using the Krylov-Bogoliubov-Mitropolsky averaging method. The direct detection of the time behavior of the spin system by the method of nonstationary nutations makes it possible to identify the multiphoton transitions for resonances ω₀ = ω_mw + rω_rf (ω₀ is the central frequency of the EPR line, r = 1, 2), to measure the amplitudes of the effective fields of these transitions, and to determine the features generated by the inhomogeneous broadening of the EPR line. It is shown that the Bloch-Siegert shifts for multiphoton resonances at the inhomogeneous broadening of spectral lines reduce only the nutation amplitude but do not change their frequencies.     

Hyperfine anomaly arising from the nuclear spin-forbidden transition,and absolute sign determination of the zero-field splitting constant

It has been found in the triplet E.S.R. spectra of radical pairs in irradiated potassium deuterium fumarate that the hyperfine structure of the two transitions, M _s = 1?0 and M _s = 0?+1, are entirely different. This anomaly has been interpreted in terms of the forbidden transition arising from the mixing of the nuclear spin states by the anisotropic hyperfine interaction. The theory has been developed for multiplet electron spin systems and includes the nuclear Zeeman interaction which is often neglected. The theoretical predictions are in good agreement with the observed separations and intensities of the anomalous hyperfine lines. In addition, it has been found that since the forbidden lines of the electron spin multiplet system with S ≥ 1 appear strongly only in transitions which include some specific electronic spin states, the anomalous features of the spectra make it possible to determine the absolute sign of the zero-field or hyperfine splitting constant, if the sign for one of them is known. Using this principle, attempts have been made to determine the absolute sign of the zero-field splitting constant for a number of triplet E.S.R. spectra which exhibit a hyperfine anomaly arising from the proposed mechanism.