Electron Spin Exchange Research Articles

Anisotropic muonium atoms: Energy levels and electron spin exchange

The time evolution of the muon spin in fully anisotropic muonium $(\mathrm{Mu}={\ensuremath{\mu}}^{+}{+e}^{\ensuremath{-}})$ in the presence of Heisenberg spin exchange has been investigated theoretically. First, the energy levels of anisotropic Mu as a function of field are investigated analytically with a particular emphasis on the crossing and avoidance of energy levels at certain magnetic fields, which have important consequences in muon spin dynamics. Second, the knowledge of the energy levels is applied to investigate the muon spin depolarization due to electron spin exchange with spin-$\frac{1}{2}$ paramagnetic species, where the muon spin depolarization rate and the precession amplitude observed by the muon-spin-rotation (\ensuremath{\mu}SR) technique are explicitly expressed solely in terms of the matrix that diagonalizes the anisotropic Mu hyperfine Hamiltonian. The treatment presented here represents a special systematic and practical method that allows one to investigate the time evolution of the muon spin in anisotropic Mu in the presence of electron spin exchange. Several concrete examples are discussed in detail, including those in which all the \ensuremath{\mu}SR observables can be obtained analytically. The method developed in this work is used to explain the relaxation rate maximum in anisotropic Mu in semiconductors observed at the longitudinal fields at which two of the Mu energy levels avoid each other due to a strong level mixing or avoidance, where the present formalism takes the tensor nature of the anisotropic hyperfine interaction fully into account without invoking the convenient but not necessarily correct notion of an effective magnetic field in an anisotropic Mu. Also discussed is the possibility of observing additional relaxation maximum at a low-avoidance field, where the effective magnetic-field approximation completely breaks down. Observation of such a maximum will provide valuable information on the parameters characterizing the anisotropic Mu in question. The formalism presented here can also be applied to anisotropic positronium on surfaces, anisotropic Mu undergoing both charge exchange and spin exchange, and fast spin exchange.

Conformational dynamics of some short-chain biradicals in solutions

Intramolecular electron spin exchange, as a function of temperature and the solvent nature, has been studied by X-band electron paramagnetic resonance (EPR) spectroscopy in five short-chain flexible nitroxide biradicals. Certain thermodynamic parameters of the conformational rearrangements were calculated from the EPR spectra. The process of spin exchange in short flexible biradicals has some peculiarities in comparison with that in long-chain molecules.

Estimation of the charge carrier localization length from Gaussian fluctuations in the magneto-thermopower ofLa0.6Y0.1Ca0.3MnO3

The magneto-thermoelectric power (TEP) $\Delta S(T,H)$ of perovskite type manganise oxide $La_{0.6}Y_{0.1}Ca_{0.3}MnO_3$ is found to exhibit a sharp peak at some temperature $T^{*}=170K$. By approximating the true shape of the measured magneto-TEP in the vicinity of $T^{*}$ by a linear triangle of the form $\Delta S(T,H)\simeq S_p(H)\pm B^{\pm}(H)(T^{*}-T)$, we observe that $B ^{-}(H)\simeq 2B ^{+}(H)$. We adopt the electron localization scenario and introduce a Ginzburg-Landau (GL) type theory which incorporates the two concurrent phase transitions, viz., the paramagnetic-ferromagnetic transition at the Curie point $T_C$ and the "metal-insulator" (M-I) transition at $T_{MI}$. The latter is characterized by the divergence of the field-dependent charge carrier localization length $\xi (T,H)$ at some characteristic field $H_0$. Calculating the average and fluctuation contributions to the total magnetization and the transport entropy related magneto-TEP $\Delta S(T,H)$ within the GL theory, we obtain a simple relationship between $T^{*}$ and the above two critical temperatures ($T_{C}$ and $T_{MI}$). The observed slope ratio $B ^{-}(H)/B ^{+}(H)$ is found to be governed by the competition between the electron-spin exchange $JS$ and the induced magnetic energy $M_sH_0$. The comparison of our data with the model predictions produce $T_{C}=195K$, $JS=40meV$, $M_0=0.4M_s$, $\xi_0=10\AA$, and $n_e/n_i=2/3$ for the estimates of the Curie temperature, the exchange coupling constant, the critical magnetization, the localization length, and the free-to-localized carrier number density ratio, respectively.

Quantum dynamical studies of H 3

The Electron nuclear dynamics theory is used to study various processes involving the disintegration of an H 3 unit from an initial state of equilateral geometry that is associated with a degeneracy of the electronic system. The electronic wavefunction is initially defined as representation of either of the D 3h doublet components; the corresponding dynamical features are considered in terms of nuclear trajectories for both cases. Disintegration out of a rotating state is shown to yield periodic electronic spin exchange between two bonding H atoms, which is interpreted as a signature of non-adiabatic behavior. Possible applications of this phenomenon in the study of molecular dissociation are discussed.

Intramolecular electron transfer and spin exchange in molecules with two electrophoric moieties. Bis(2,4,6-triphenylpyridinium)-1,ω-alkanes

Intramolecular electron transfer and spin exchange in molecules with two electrophoric moieties. Bis(2,4,6-triphenylpyridinium)-1,ω-alkanes

Electron nuclear dynamics studies of H3 and H3+

The electron nuclear dynamics (END) theory is used to study various processes involving the disintegration of a H3 and the pseudorotation of the H 3 + ion. The former system is prepared in an initial state of equilateral geometry which is associated with a degeneracy of the electronic system. The electronic wave function is initially defined as a representation of either of the D3h doublet components; the corresponding dynamical features are considered in terms of nuclear trajectories for both cases. Disintegration out of a rotating state is shown to yield periodic electronic spin exchange between two bonding H atoms, which is interpreted as a signature of nonadiabatic behavior. Possible applications of this phenomenon in the study of molecular dissociation is discussed. The bound system H 3 + is explored under the aspect of pseudorotational motion. Different dynamic regimes are explored; it is shown that the limiting case of circular pseudorotation can be approximated through the choice of an initial nuclear distortion momentum of magnitude P≈1.7 au. For sizably smaller momenta, the motion is dominated by one distortion mode only; for larger momenta, pseudoprecession results. These dynamic phenomena find their electronic counterparts in cyclical charge waves excited in the electronic system. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 367–383, 1999

Manifestation of spin exchange relaxation in microwave field induced magnetic field effects on recombination of confined radical pairs

Within the simple exponential kinetic model, possible manifestations of the strong electron spin exchange interaction (ESEI) and relaxation (ESER) in microwave field induced magnetic field effects on recombination of confined radical pairs are analysed theoretically. It is shown that not only ESEI but also ESER strongly affects the spectra of reaction yield detected magnetic resonance, stimulated nuclear polarisation and EPR leading to broadening and change of line shape.

Fast Muonium Reactions in Solution: An Electron Spin Exchange Interaction with Cr(NCS)63- in Water and Reaction with Iodine in Organic Solvents

Two reactions of muonium atoms close to the diffusion-controlled limit were analyzed as a function of solute size and solvent viscosity. With Cr(NCS)63- as solute in water, the reaction is an electron spin-conversion process, and the observed rate is taken to be half of the actual encounter rate, because of the quantum mechanical statistical factor and the occurrence of multiple collisions due to the solvent cage effect. The encounter rate deduced is 6.2 × 1010 M-1 s-1, which implies a large cross section for the Cr complex. In a second series of experiments, the rate of reaction of muonium with I2 was compared in water, methanol and n-heptane. The bimolecular rate constants determined are (1.7 ± 0.3), (7.0 ± 1.2), and (57 ± 22) × 1010 M-1 s-1, respectively, in these three solvents. This ∼30-fold change in rate is not matched by the change in the inverse of the solvents' viscosities, which changed overall by a factor of only 2.4. It looks as if quantum tunneling dominates over classical diffusion in less polar media where muonium is unencumbered by solvent clathration.

On the mechanism of multiplet CIDEP in radical ion pairs

It is shown that multiplet chemically induced dynamic electron polarization (CIDEP) in radical ion pairs is unlikely to be caused by electron spin exchange ( J>0), unless the rate of electron transfer is slowed down either by exciplex formation or by a low Franck-Condon factor. In radical ion pairs for which the electron transfer is efficient, the electron tunnels prior to the spin exchange, and the multiplet CIDEP is due to dipole-dipole interactions of electron spins. The corresponding polarization factor is of the order of several Boltzmann units. In appearance, such a polarization is similar to the usual exchange-induced multiplet CIDEP at J. It is concluded that the long-range dipole-dipole interaction caused a ‘ J>0’ multiplet CIDEP in all the pairs that involved a solvated electron as a partner.

Positronium spin exchange with spin 1/2 paramagnetic species

Electron spin exchange of positronium (Ps = e+e−) with spin 1/2 paramagnetic species was investigated. First, the concept of spin flip (nonflip) collisions is examined in the light of the difference in phase shifts between electron spin singlet and triplet encounters. Then, the effects of spin exchange on positron spin dynamics and on Ps lifetimes are discussed and results are compared to muon (electron) spin dynamics in the muon spin rotation (electron spin resonance) techniques.

Effects of electron-spin exchange interaction on the electronic state of the onedimensional spin-electron-phonon system

A one-dimensional spin-electron-phonon model is proposed for the discovery of new compounds composed of strongly correlated electrons. The total energies and the energy gaps at half filling and less-than half-filling have been computed within a mean-field theory and a periodic boundary condition. As the value of the antiferromagnetic (AF) exchange interaction between nearest-neighbor itinerant-electron spin and localized spin is increased, the energy gaps of 0 and two holes increase and the binding energy of two holes increases. This system with two holes formates a bound state. It turns out that the AF exchange interaction between itinerant-electron spin and localized spin plays the important role in the electronic state of this system.

Electron spin exchange with O2: Effects on the muon spin rotation, the electron spin resonance, and the positronium lifetime.

Electron spin exchange with spin one paramagnetic species has been investigated with particular emphasis on the cases of hydrogen (H={ital p}{sup +}{ital e}{sup {minus}}), Mu (Mu={mu}{sup +}{ital e}{sup {minus}}), positronium (Ps={ital e}{sup +}{ital e}{sup {minus}}) colliding with O{sub 2}. The effects of spin exchange on electron spin relaxation (ESR), muon spin relaxation ({mu}SR), and positronium lifetime measurements are described in terms of the difference in phase shifts between quartet and doublet encounters ({Delta}), which will allow one to interpret ESR, {mu}SR, and positron data in a unified way and help one to understand isotope mass effects not only in spin exchange but also in chemical reactions, which often compete with spin exchange. For instance, the ESR and {mu}SR relaxation rates in high transverse fields are expressed, in terms of the rate of collisions {lambda}, as {lambda}{sup {ital e}}{sub {ital T}}=(32/27){lambda} sin{sup 2}({Delta}/2) and {lambda}{sub {ital T}}{sup {mu}}=(16/27){lambda} sin{sup 2}({Delta}/2), respectively, and the so-called statistical factors, such as (32/27) and (16/27), are strong functions of the magnitude and direction of the applied field.

Dynamic behaviour of a nitroxide biradical undergoing multiple internal motions: An ESR and 13C NMR relaxation study

AbstractThe ESR spectra of the bis(2,2,6,6‐tetramethyl‐4‐piperidinol‐1‐oxyl) adipate biradical at several temperatures in ethanol solution were simulated, taking into account all allowed conformers corresponding to the rotational isomerism model. The probabilities of these conformers, not accessible by ESR, were derived from 13C spin relaxation measurement on the diamagnetic reduced form of the biradical. The least‐squares fits of ESR spectra provided the temperature dependence of the rates of internal motions and of the tumbling correlation time of the biradical and also an estimate of the electron spin exchange parameters.

Intramolecular Long Range Electronic Spin Exchange Coupling in Diradicals: A New Magnetic Coupling Unit

Abstract A phenyl diethynyl bridge is used as a magnetic coupling unit (MCU) between two iminonitroxide π-radicals. The ethynyl moiety is attached to the central phenyl ring either in the para or in the meta position. The magnetic properties of the resulting bis-imino nitroxide diradicals (p-BIN and m-BIN) are investigated both at the molecular scale and in the condensed phases. An intramolecular through bond spin coupling is observed at an unusual long distance (about 20 ÅS) in both derivatives. However, the ground state is found to be a singlet spin state in both compounds. The results suggest an interplay between the spin polarization and the spin delocalization (π-conjugation). An intermolecular weak antiferromagnetic spin coupling is occuring in both compounds.

Investigation of muon-state dynamics in silicon by longitudinal field-quenching and radio-frequency μ+ spin resonance

The two paramagnetic muon states-normal and anomalous muonium-and the diamagnetic muon states have been investigated in different monocrystalline silicon samples (intrinsic, boron-, phosphorus-, or arsenic-doped, float-zone or Czochralski-grown) between 6K and 800K by means of longitudinal field-quenching (LFQ) and radio-frequency μ + spin resonance (RFμSR). The LFQ data can be described consistently by coupled equations of motion for the muonium spin systems if spin exchange processes as well as transitions between different muon states are taken into account. It is shown that the initial formation probabilities of the different muon states, the ionization rate of the anomalous muonium, and the electron spin exchange rates depend strongly on the charge carrier densities. These results are in agreement with the RFμSR data obtained on the same samples if the different time scales of RFμSR and LFQ experiments are taken into account. At temperatures above 300 K both RFμSR and longitudinal relaxation results appear to indicate reversible ionization of normal muonium.

The study of the electron spin exchange efficiency in liquid solutions of radicals at various EPR frequencies

The electron spin exchange efficiency in toluene solutions of stable nitroxide radicals at different EPR frequencies has been studied. The experimental results are in good agreement with the theory. The spin exchange constantsKe measured at X-band and 2-mm band coincide. TheKe values measured from the exchange broadening of the EPR lines do not depend on the value of the nitrogen nuclear spinIN

Effect of mass on particle diffusion in liquids studied by electron spin exchange and chemical reaction of muonium with oxygen in aqueous solution

The dephasing rate constant of the muon precession signal of the light hydrogen isotope muonium (Mu) in the presence of oxygen in liquid water is (1.8 ± 0.1)× 1010 l mol–1 s–1 at 297 K. (90 ± 17)% of this is ascribed to electron spin exchange interaction, leaving no measurable amount for chemical reaction. Based on a spin statistical analysis, the diffusion-limited rate constant of Mu encounters with O2 is determined to be (5.7 ± 0.5)× 1010 l mol–1 s–1 for Mu at 297 K, which is a factor of 1.78 higher than the value deduced from literature data for H. From this we conclude that the ratio of diffusion coefficients, DMu/DH, is 2.0 ± 0.2 and DMu=(14 ± 4)× 10–9 m2 s–1. This reveals an unprecedented mass effect which by comparison with literature values appears, in clear contradiction to Stokes–Einstein behaviour, to scale approximately with the inverse cube root of the mass of the diffusing particle. The behaviour is discussed by comparison with literature values for the diffusion of noble gases.

Electron Spin Exchange Reactions of Muonium Atoms with Chromium(III) Complexes: Contrasts with Positronium

Electron Spin Exchange Reactions of Muonium Atoms with Chromium(III) Complexes: Contrasts with Positronium

Muonium spin exchange in spin-polarized media: Spin-flip and -nonflip collisions.

The transverse relaxation of the muon spin in muonium due to electron spin exchange with a polarized spin-1/2 medium is investigated. Stochastic calculations, which assume that spin exchange is a Poisson process, are carried out for the case where the electron spin polarization of the medium is on the same axis as the applied field. Two precession signals of muonium observed in intermediate fields (B>30 G) are shown to have different relaxation rates which depend on the polarization of the medium. Furthermore, the precession frequencies are shifted by an amount which depends on the spin-nonflip rate. From the two relaxation rates and the frequency shift in intermediate fields, one can determine (i) the encounter rate of muonium and the paramagnetic species, (ii) the polarization of the medium, and most importantly (iii) the quantum-mechanical phase shift (and its sign) associated with the potential energy difference between electron singlet and triplet encounters. Effects of spin-nonflip collisions on spin dynamics are discussed for non-Poisson as well as Poisson processes. In unpolarized media, the time evolution of the muon spin in muonium is not influenced by spin-nonflip collisions, if the collision process is Poissonian. This seemingly obvious statement is not true anymore in non-Poissonian processes, i.e., it is necessary to specify both spin-flip and spin-nonflip rates to fully characterize spin dynamics.

Molecular and crystal structure of 9-[α-(9H-fluoren-9-ylidene)-4-chlorobenzyl]-9H-fluoren-9-yl; an organic antiferromagnet with TN= 3.25 K

The crystal structure of the title radical has been determined by X-ray diffraction at ambient temperature. The crystal system is monoclinic with a space group of Cc: a= 33.204(4), b= 9.391(1), c= 15.290(1)Å, β= 101.223(7)°, Z= 8. The final R factor is 0.035 for 2623 observed reflections. There are two crystallographically independent molecules constituting a pair of atropisomers. Two fluoren-9-yl groups and a chlorophenyl moiety are arranged in a propeller shape. The range of the torsion angles of the fluorenyl blades is 25°∼ 33°, and that of the chlorophenyl blades is 55°∼ 59°. The electron-spin exchange pathways are discussed based on the McConnell's spin-density Hamiltonian. The exchange-coupled neighbours are estimated to be z= 6, to which the highest TN among organic radicals can be attributed.