Sushil K. Misra

SPIN-HAMILTONIAN FORMALISMS IN ELECTRON MAGNETIC RESONANCE (EMR) AND RELATED SPECTROSCOPIES

The historical development leading to, and the current status of, the spin-Hamiltonian (SH) formalisms, characterizing electron magnetic resonance (EMR), also referred to as electron paramagnetic (or spin) resonance (EPR or ESR), is reviewed. The spin-Hamiltonian concept is briefly outlined to set a framework for definitions of relevant terms. Meanings of the terms which are often confused with each other, e.g. physical versus effective Hamiltonian, real versus effective versus fictitious spin, microscopic SH (MSH), zero-field-splitting (ZFS) Hamiltonian, generalized SH (GSH), and phenomenological SH (PSH), are elucidated. Various general approaches to ‘derive’ MSH as well as to ‘construct’ GSH for transition ions are discussed. This enables clarification of relationship between the ZFS Hamiltonian and (a) the crystal-field (CF), (b) electronic spin-spin, and (c) nuclear-quadrupole Hamiltonians. The inadmissibility of the odd-order ZFS terms (l = 3, 5) is also discussed. A brief general classification of the major operator and parameter notations used in the literature to describe ZFS Hamiltonian is provided. Other important areas relevant to EMR, where the SH concept plays a central role, are outlined.

Evaluation of spin-Hamiltonian parameters from EPR data by the method of least-squares fitting

A quick, accurate procedure (LSF method) is developed, using Feynmans theorem, for application of a least-squares-fitting method to the analysis of electron paramagnetic resonance data. As it utilizes numerically computed eigen-values and their derivatives with respect to the spin-Hamiltonian parameters, the LSF method is not limited by the size of the off-diagonal matrix elements of the spin Hamiltonian. To accomplish orthogonal-axis consistency, the resonant magnetic field values corresponding to two, or more, directions of the magnetic field are simultaneously taken into account. The method is illustrated by analyzing the room-temperature X-band data for Gd3+ in SmCl3·6H2O, which is characterized by large off-diagonal matrix elements. The resulting parameters and chi-squared values of the fit (∼10−4 GHz2) compare quite well with those obtained using a recently developed “brute-force” method. Only one set of input data (the initially guessed values of large parameters) is required and computing time is reduced by a factor of ∼70. The method is immediately applicable to the analysis of other resonance data which depend upon the differences in eigenvalues, such as NMR, NQR, and molecular spectroscopy.

IFOM, a formula for universal assessment of goodness-of-fit of gamma ray spectra

Abstract A formula is suggested which can be used for examining the goodness-of-fit of all types of spectral peaks — wide or narrow, strong or weak (relative to the associated background). This formula has been successfully applied to a large number of test cases and has been found to work successfully in all these cases. A few examples, representative of different situations, are provided for illustrative purposes.

The role of reduced graphene oxide capping on defect induced ferromagnetism of ZnO nanorods

In this study, the effect of different numbers of layers of reduced graphene oxide (RGO) on the ferromagnetic behavior of zinc oxide-reduced graphene oxide (ZnO-RGO) hybrid architectures has been investigated. Scanning and transmission electron microscopy along with x-ray diffraction of these hybrids confirm that ZnO nanorods are wrapped with different numbers of layers of RGO in a controlled way and their hexagonal phase is unaffected by these layers. Raman and photoelectron spectroscopy of these hybrids reveals that RGO does not alter the nonpolar optical phonon E(2) (high) mode and chemical state of Zn(2+) in ZnO. Electron paramagnetic resonance (EPR) spectra show that RGO passivates singly charged oxygen vacancies (VOS⁺) in ZnO. It correlates the passivation efficiency of VOS⁺ to the number of RGO layers and this has been achieved up to 90% by ∼31 layers of RGO. Due to passivation of VOS⁺ in ZnO by RGO, the ferromagnetic behavior (saturation magnetization and divergence between zero field cooled and field cooled) in ZnO-RGO hybrids is suppressed as compared to ZnO. Combining the EPR and magnetic behavior, a direct link between the passivation of the singly charged oxygen vacancies present on the surface of ZnO nanorods and the number of RGO layers is established.

Estimation of the Mn2+ zero-field splitting parameter from a polycrystalline EPR spectrum

Abstract Details are provided of how to estimate, without extensive computer simulations, the zero-field splitting parameter ( D ) of the Mn 2+ ion characterized by axial symmetry from forbidden-hyperfine doublet separations in the central sextet of the Mn 2+ EPR spectrum in a polycrystalline sample by the use of an analytic expression derived from the eigenvalues calculated to third order in perturbation.

EPR of VO2+ in Cd(NH4)2(SO4)2 · 6H2O and Mg(NH4)2(SO4)2 · 6H2O single crystals: Ligand superhyperfine interaction and bonding coefficients

Abstract Detailed X-band electron paramagnetic resonance (EPR) studies of the VO2+ ion have been carried out in the single crystals of Tutton salts Cd(NH4)2(SO4)2·6H2O (CASH) and Mg(NH4)2(SO4)2·6H2O (MASH) at 295, 80 and 4.2 K. F or both samples the data are indicative of the presence of two magnetically inequivalent, but physically equivalent, VO2+ sites in the unit cell, each consisting of three magnetically inequivalent VO2+ ions, with one of them being present with a very small probability. Each vanadyl hyperfine line is characterized by an anisotropic quintet superhyperfine (SHF) splitting, with the intensity ratios 1:4:6:4:1. For any of the two samples investigated, the maximum separations of the SHF splitting for the two largely populated magnetically inequivalent VO2+ ions, corresponding to any one site, are observed when the orientations of the external magnetic field (B) are along the M2+-H2O(7), and the M2+-H2O(8) directions (M2+ = divalent metal ion, Cd2+ or Mg2+). The temperature dependence of the SHF splitting was found to be different for the two samples. The principal values and direction cosines of the principal axes of the g2 and A2 tensors are evaluated from a simultaneous fitting of the various EPR line positions, using a least-squares fitting program. The following details apply to both the samples: an impurity model of the vanadyl ion, described by the [VO(H2O)5]2+ complex, is found to explain the data adequately. The orientations of the V4+-O2- bonds have been deduced to lie close to either the M2+-H2O(7) and M2+-H2O(8) directions. The SHF structure is explained to be due to the interaction of the unpaired electron of the VO2+ ion with the four protons of its two nearest-neighbor H2O(9) molecules. The principal values and orientations of the principal axes of the SHF interaction tensor have been estimated. Using the reported optical absorption- and the present EPR data, the bonding coefficients of the [VO(H2O)5]2+ complex have been estimated.

Magnetic resonance studies of Co2+ ions in nanoparticles of SnO2 processed at different temperatures

Cobalt doping (⩽1%) produces ferromagnetism at room temperature in semiconducting SnO2, presumably due to oxygen vacancies and/or changes in carrier concentration. Electron paramagnetic resonance (EPR) is a sensitive technique to investigate the Co ionic states and their local environments and/or interactions. This paper reports EPR studies of Co2+ ions doped in chemically synthesized nanoparticles of SnO2 carried out at 5K. EPR spectra were recorded from 600°C prepared SnO2 with Co concentrations of 0.5%, 1%, 3%, 5%, 8%, and 12% and from 1% Co-doped SnO2 prepared at temperatures of 150, 250, 350, 450, 600, and 830°C. Each EPR spectrum in samples with cobalt doping can be simulated as an overlap of spectra due to two broad ferromagnetic resonance lines and those due to interstitially and substitutionally incorporated Co2+ ions with effective spin S=1∕2 characterized by their particular g and A tensors. It is concluded that the Co2+ ions occupy substitutional as well as interstitial sites of SnO2 and that ...

A calculation of effective g-tensor values for R3+ ions in RBa2Cu3O7 − δ and RBa2Cu4O8 (R = Rare Earth): Lowtemperature ordering of Rare-Earth moments

Abstract Effective values of the g -tensor components for the various rare-earth ions ( R 3+ ) in the compounds RBa 2 Cu 3 O 7 − δ and RBa 2 Cu 4 O 8 ( R = Rare Earth) at low temperatures have been calculated using the crystalline electric field parameters as determined by inelastic neutron scattering. The lowest-energy orderings of rare-earth ions in these compounds have been examined. They were predicted on the basis of the Luttinger-Tisza method, taking into account the dipolar interactions between the rare-earth ions, calculated using these g -values. It is found that the predicted low-temperature orderings are generally consistent with the reported experimental orderings.

Electron spin resonance of Gd3+ in trifluorides of La, Ce, Pr, and Nd

An EPR study of Gd3+‐doped single crystals of CeF3, LaF3, PrF3, and NdF3 has been made in order to study the systematics of spectra in these homologous isostructural hosts. The method of preparation of samples is presented. The measurements are carried out at all three—room, liquid nitrogen, and liquid helium—temperatures. Thus, the absolute signs of all the spin Hamiltonian parameters are determined from intensities of lines at liquid helium temperatures. The parameters are evaluated from a simultaneous fitting of all lines observed in the zx and xy planes in a rigorous least‐squares fitting procedure, which utilizes numerical diagonalization of the spin Hamiltonian matrix. As far as the systematics of the parameters are concerned, it is found that the parameter b02 varies linearly with the atomic radius of the host rare‐earth ion, while the parameter b22 does not show any such behavior. It it hoped that the experimental results presented in this paper would be helpful in further theoretical understandin...

SPIN-LATTICE RELAXATION TIMES IN AMORPHOUS MATERIALS AS EFFECTED BY EXCHANGE INTERACTIONS, TUNNELING LEVEL STATES (TLS) CENTRES, AND FRACTONS

Abstract The processes of spin-lattice relaxation (SLR) in amorphous materials are reviewed. In particular, the mechanisms involving exchange interaction, tunneling level states (TLS) centers and fractons predominant in effecting electron SLR at low temperatures in amorphous materials are reviewed. It has been deducded that the former two lead to quadratic temperature dependences at very low temperatures and linear temperature dependences at intermediate temperatures of the relaxation rate in amorphous materials. As for relaxation due to fractons in fractal state, the theories proposed by Alexander, Entin-Wohlman and Orbach (Phys. Rev. B 32 (1985) 6447; Phys. Rev. B 33 (1986) 3935; J. Phys. Lett. 46 (1985) 1555) are reviewed and the temperature dependences of fracton-assisted relaxation rate in the fractal state for Kramers and non-Kramers ions are examined.