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.     

EPR spectroscopy of weak exchange interactions between Co2+ ions in ZnO

Electron paramagnetic resonance (EPR) is used to identify the next nearest neighbour Co²⁺ pairs coupled by spin–spin interaction in Co‐doped ZnO single crystals grown by the hydrothermal technique. These dimer centers are described by a spin Hamiltonian with exchange coupling terms written as interaction between identical effective spins S^eff = 1/2 of the lowest ground state Kramers doublets of the two Co²⁺ ions. The exchange parameters of weakly ferromagnetically coupled next nearest neighbor Co²⁺ pairs are estimated. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magnetic anisotropy of antiferromagnet (CH3)4NMnCl3

The parameters of the electron paramagnetic resonance (EPR) spectra of S ion pairs in diamagnetic crystals are analyzed. A relation between the spin Hamiltonian constants is established for solitary ions and pairs for (CH₃)₄NCdCl₃: Mn²⁺ crystals. In contrast to solitary ions, an additional contribution (which is a linear function of the exchange field) to the “single-ion” spin Hamiltonian constants appears in the case of pairs. It is shown that anisotropic exchange mechanisms do not play a significant part in the formation of the axial constant of the spin Hamiltonian for this crystal. Some aspects of the method of studying “single-ion” anisotropy predicted by the two-ion model are developed with the help of an isostructural diamagnetic analog with impurity concentration of the paramagnetic ions of a magnetically concentrated substance sufficiently high for observing the EPR spectrum of the pairs. It is found that the microscopic quantities determined partially from the EPR spectra for pairs and solitary Mn²⁺ ions in (CH₃)₄NCdCl₃ are in accord with the experimental value of the effective field for the (CH₃)₄NMnCl₃ crystal anisotropy which can be described primarily by the dipole and “single-ion” mechanisms of the exchange origin.     

Exchange-coupled pairs of Fe3+ ions in beryl

The EPR spectrum of first nearest neighbour pairs of Fe³⁺ ions substituting for Al³⁺ ions in beryl is reported. The form of the pair spin Hamiltonian is discussed, and operator equivalent factors for fourth-order terms are tabulated. The Fe³⁺ pair interionic coupling corresponds to isotropic antiferromagnetic exchange with J = + 1.7 cm^-1 plus anisotropic dipolar coupling. The pair value of the zero-field splitting parameter D is + 0.0206 cm^-1 and shows a substantial shift from the single-ion value. It is proposed that resonance lines previously attributed to Fe³⁺ ions in Be²⁺ or Si⁴⁺ sites are due to Fe³⁺ pairs.     

EPR of Er3+, Nd3+, and Ce3+ ions in YAlO3 single crystals

EPR spectra of the Er³⁺, Nd³⁺, and Ce³⁺ ions substituting for the Y³⁺ ion in the YAlO₃ yttrium orthoaluminate lattice are studied. The EPR spectra of these rare-earth ions are described by a spin Hamiltonian of rhombic symmetry with an effective spin S=1/2. The principal values of the g tensors were determined from an analysis of the angular dependences of the EPR spectra. The orientation of the local magnetic axes of paramagnetic centers relative to the YAlO₃ crystallographic directions are shown to depend on the actual rare-earth species. The EPR spectra exhibit a hyperfine structure due to the ¹⁶⁷Er, ¹⁴³Nd, and ¹⁴⁵Nd odd isotopes, which permitted unambiguous identification of these spectra. The hyperfine coupling constants for the odd erbium and neodymium isotopes are determined.     

Electron paramagnetic resonance of Ce3+ ions in lead thiogallate single crystals

The results of electron paramagnetic resonance (EPR) studies of Ce³⁺ impurity ions in single crystals of lead thiogallate PbGa₂S₄ have been reported. The Ce³⁺ ions substitute for Pb²⁺ ions in the crystal lattice of PbGa₂S₄. A number of paramagnetic cerium centers in lead thiogallate have been observed. The spectra are described by the spin Hamiltonian of rhombic symmetry with the effective spin S = 1/2. The g factors of the main cerium centers have been determined. A large number of paramagnetic centers are due to both nonequivalent positions of lead and local charge compensation under the substitution Ce³⁺ ?? Pb²⁺.     

Ground state energy of dilute magnetic alloys

The ground state energy of dilute magnetic alloys as described by thes-d-exchange Hamiltonian is calculated within the Nagaoka-Suhl theory. For integral impurity spinS it is shown that for positive coupling constantγ the energy is a holomorphic function ofγ. For negative coupling one obtains an additional singular contribution of the form (?1) ^s?1 e ^1/γ (γ<0). As this changes sign for different integral s-values, the interpretation of the singular part as a binding energy suggested previously does no longer hold. For half integral spin the energy is a singular function for bothγ>0. The singularities are not as elementary as in the case of integral spinS, but are rather related to those of the exponential integral function. In particular, forγ>0 the origin (γ=0) is a branch point. Earlier variational calculations are compared with our new results.     

Algebraic solution of the Hubbard model on the infinite interval

We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the infinite line at zero density. This enables us to diagonalize the Hamiltonian algebraically. The eigenstates can be classified as scattering states of particles, bound pairs of particles and bound states of pairs. We obtain the corresponding creation and annihilation operators and calculate the S-matrix. The Hamiltonian on the infinite line is invariant under the Yangian quantum group Y(su(2)). We show that the n-particle scattering states transform like n-fold tensor products of fundamental representations of Y(su(2) ) and that the bound states are Yangian singlet.     

The ground state of the neutral Hubbard model

The ground state energy of the neutral Hubbard model is calculated by BCS methods for all values of total spinS _z . Numerical results are given for the simple cubic and for the body centred cubic lattice. Antiferromagnetic ordering and a finite paramagnetic susceptibility is found for all values of the coupling constantV ₀.     

Wide-band EPR spectroscopy of YAlO3: Tm3+ single crystals

The YAlO₃: Tm³⁺ single crystal has been studied on a wide-band EPR spectrometer. The EPR spectra of Tm³⁺ ions in the frequency range of 90–160 GHz have been detected for the first time. It has been confirmed that thulium ions substitute the position of Y³⁺ in the crystal lattice. The detected spectra have been described with the use of a spin Hamiltonian with the effective spin S = 1/2. A comparative analysis of the orientation of the magnetic axes of the Tm³⁺ paramagnetic center with earlier data on other rare-earth ions has been performed.     

Multifrequency EPR spectra of molecular oxygen in solid Air

Multifrequency EPR spectra in the 94 to 550 GHz range were performed on solid air samples condensed at 5 K in the waveguide of a single pass probe. The spectra of molecular oxygen were observed and interpreted in the frame of the spin Hamiltonian model as axial S = 1 spectra with a zero field splitting parameter D = 3.572(3) cm⁻¹. The result of this study is relevant in the field of high field–high frequency EPR application in which solid air O₂ is a common paramagnetic impurity.     

Comments on57Fe Mössbauer spectra for Kramers doublets: A phenomenological interpretation

A static effective spinS=1/2 Hamiltonian is usually specified by a phenomenonological parameter, set, but the typical choice of parameters could be inappropriate. Two main issues are addressed: (i) Which spin Hamiltonian parameters are observable at a given applied field strength, and (ii) how should one deal with skewsymmetric components of the electronic Zeeman and magnetic hyperfine tensors that can be present for spin-coupled multinuclear complexes. Certain Mössbauer experiments were selected, somewhat arbitrarily, as examples; this analysis can be applied to other spectroscopic techniques as well.     

On the production of paramagnetic defects in silicon by electron irradiation

Monocrystalline silicon samples of different impurity contents have been irradiated with 1.5 MeV electrons in order to produce divacancies in their negative charge state. In these samples different combinations of defects have been observed with electron paramagnetic resonance. The conditions for production and observation of these defects are compared. For two new EPR spectra, labelled (Si-) NL11 and (Si-) NL12, the spin Hamiltonian parameters are reported. For NL11, which arises from an S = 1 spin state, the obvious identification with the neutral charge state of the divacancy can not be confirmed.     

Studies on the local structures and the spin Hamiltonian parameters for Fe3+ in CdX (X = S,Se, Te)

The improved perturbation formulas of the spin Hamiltonian parameters (zero-field splitting D and g factors) for a 3d⁵ ion in trigonally distorted tetrahedra are constructed from the cluster approach by including both the crystal-field and charge-transfer contributions. These formulas are applied to the studies of the local structures and the electron paramagnetic resonance (EPR) spectra for Fe³⁺ in CdX (X = S, Se, Te). The impurity Fe³⁺ is found not to occupy exactly the host Cd²⁺ sites but to experience the small outward shifts 0.014 and 0.006 Å away from the ligand triangles along the C₃ axis in CdS and CdSe, respectively. The charge-transfer contributions to the spin Hamiltonian parameters are important and increase significantly with increasing atomic number of the ligand (i.e., S^2? < Se^2? < Te^2?) arising from the decreases of charge-transfer energy levels and the increases of ligand spin–orbit coupling coefficients. The results are discussed.     

Coupling of ferromagnetic nanoparticles through dipolar interactions

We consider two ferromagnetic nanoparticles coupled via long-range dipolar interactions. We model each particle by a three-dimensional array of classical spin vectors, with a central spin surrounded by a variable number of shells. Within each particle only ferromagnetic coupling between nearest neighbor spins is considered. The interaction between particles is of the dipolar type and the magnetic properties of the system is studied as a function of temperature and distance between the centers of the particles. We perform Monte Carlo simulations for particles with different number of shells, and the magnetic properties are calculated via two routes concerning the dipolar contribution: one assuming a mean-field like coupling between effective magnetic moments at the center of the particles, and other one, where we take into account interactions among all the pairs of spins, one in each particle. We show that the dipolar coupling between the particles enhances the critical temperature of the system relative to the case in which the particles are very far apart. The dipolar energy between the particles is smaller when the assumption of effective magnetic moment of the particles is used in the calculations.     

A naturally induced hole center in the mineral hypersthene

In natural hypersthene a paramagnetic center in triclinic site symmetry was detected by electron paramagnetic resonance with the following spin. Hamiltonian parameters:g _xx=2.0104,g _yy=2.0256,g _zz=2.0090. This center is most likely formed as a hole on an oxygen of the SiO₄ unit. No hyperfine splitting was detected at room temperature. The EPR signal disappears after heating the crystal at 773 K for 1 h although the colour does not bleach.     

EPR studies of weakly coupled oxomolybdenum (V) and low-spin iron (III) porphyrin centers

Novel compounds containing twoS=1/2 coupled spin centers (Mo(V) and low spin Fe(III) have been investigated in detail by X- and Q-band EPR spectroscopy, spectral simulation and molecular modelling calculations. For one system with a Mo?Fe distance of ≈9.4 Å the dominant dipolar coupling allows distinction among structures that are consistent with molecular modelling calculations. For the second system with a Mo?Fe of ≈ 7.9 Å the exchange interaction is dominant (0.5 <J < 3.0 GHz). These coupled systems are preliminary benchmarks for using EPR to investigate the Mo?Fe interaction in sulfite oxidase.     

Nuclear magnetic relaxation of spin<Emphasis Type="Italic">I</Emphasis>=1/2 scalar coupled to a quadrupolar nucleus in the presence of cross-correlation effects

The rigorous treatment of relaxation for the dipolar-multipolarAX spin system (I=1/2,S>1/2) in the presence of the dipolarI-S coupling, anisotropy chemical shift and quadrupolar interaction ofS spin is proposed. The calculations of the spin evolution under the relaxation Hamiltonian are based on the second-order time-dependent perturbation theory and are carried out in the operator representation. For this task the double commutator identities of the type [[I _±S _z ⁿ ,A _q ^μp ]A _?q ^μp ] and [[I _zS _z ⁿ ,A _q ^μp ]A _?q ^μp. ] are derived. The fist-order differential equations for the evolution of longitudinal two-spin orderI _zS _z ⁿ , z=magnetization ofS spinS _z ⁿ and coherences <I _±S _z ⁿ > in the spin systemIS with scalar coupling between spin 1/2 and quadrupolar spinS>1/2 were obtained. These equations are used to get equations for the evolutions of each component of the multiplet structure of spinI. The imaginary part of the cross-correlation spectral density function and indirect spin-spin coupling Hamiltonian are taken into account. Equations for the longitudinal components of theI spin spectrum in the presence of cross-correlation effects were obtained also. Longitudinal and transverse relaxation times and cross-relaxation times in the presence of cross-correlation D-CSA, Q-CSA, Q-D were analyzed.     

Perturbed angular distributions in the presence of isotropic paramagnetic relaxation

The effect of paramagnetic relaxation on perturbed angular distributions is treated for nuclei interacting with their electronic shells via isotropic hyperfine interaction. The conditions are given under which Blume's analytical stochastic-model result for the nuclear perturbation factorsG _k (t) can be derived quantum mechanically. Systems with arbitrary nuclear spin, but electronic spinS=1/2 may be calculated without resorting to the assumption necessary forS>1/2. Explicit closed expressions forG _k (t) can be found for this particular case.     

Spin relaxation and magnetic properties of benzo-1,2,3-trithiolium radical cations

Magnetic and dynamics properties of paramagnetic centers in various trithiolium cations were characterized by static magnetic susceptibility measurements and EPR spectroscopy. Magnetically correlated units consisting of at least pairs of spins with ferromagnetic exchange coupling were found in some trithioles. The rates of intramolecular spin diffusion and intermolecular spin hopping were estimated separately. The rates and the anisotropy (v/v=20–300) of spin dynamics were shown to depend on the molecular structure.