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Craighead W Tennant - One of the best experts on this subject based on the ideXlab platform.
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higher order zeeman and spin terms in the electron paramagnetic resonance spin hamiltonian their description in irreducible form using cartesian tesseral Spherical Tensor and stevens operator expressions
Journal of Physics: Condensed Matter, 2009Co-Authors: Dennis G Mcgavin, Craighead W TennantAbstract:In setting up a spin Hamiltonian (SH) to study high-spin Zeeman and high-spin nuclear and/or electronic interactions in electron paramagnetic resonance (EPR) experiments, it is argued that a maximally reduced SH (MRSH) framed in tesseral combinations of Spherical Tensor operators is necessary. Then, the SH contains only those terms that are necessary and sufficient to describe the particular spin system. The paper proceeds then to obtain interrelationships between the parameters of the MRSH and those of alternative SHs expressed in Cartesian Tensor and Stevens operator-equivalent forms. The examples taken, initially, are those of Cartesian and Stevens' expressions for high-spin Zeeman terms of dimension BS3 and BS5. Starting from the well-known decomposition of the general Cartesian Tensor of second rank to three irreducible Tensors of ranks 0, 1 and 2, the decomposition of Cartesian Tensors of ranks 4 and 6 are treated similarly. Next, following a generalization of the tesseral Spherical Tensor equations, the interrelationships amongst the parameters of the three kinds of expressions, as derived from equivalent SHs, are determined and detailed tables, including all redundancy equations, set out. In each of these cases the lowest symmetry, Laue class, is assumed and then examples of relationships for specific higher symmetries derived therefrom. The validity of a spin Hamiltonian containing mixtures of terms from the three expressions is considered in some detail for several specific symmetries, including again the lowest symmetry. Finally, we address the application of some of the relationships derived here to seldom-observed low-symmetry effects in EPR spectra, when high-spin electronic and nuclear interactions are present.
D G Mcgavin - One of the best experts on this subject based on the ideXlab platform.
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rotation matrix elements and further decomposition functions of two vector tesseral Spherical Tensor operators their uses in electron paramagnetic resonance spectroscopy
Journal of Physics: Condensed Matter, 2000Co-Authors: W C Tennant, C J Walsby, R F C Claridge, D G McgavinAbstract:Matrix elements, Ag,h(k) (k = 1-6), which describe a general Euler angle transformation of coordinates to which tesseral Spherical Tensor operators, k,q, are referred have been calculated and extended to include matrix elements for odd k. The matrix elements have been incorporated into a general axis-transformation computer program which relates to parameter sets in any one of the more commonly used tesseral forms, namely, conventional Stevens, normalized Stevens (Racah normalization) and normalized Spherical Tensor (Koster and Statz normalization) operators. Tables of decomposition functions of tesseral Spherical Tensor operators, k,q(B,J) (J = S,I), are extended to detail decompositions for terms of dimension BJ7 and, implicitly, for decomposition of any two vector operators k,q(V,W) to experimentally usable single vector forms where VkVWkW (one of kV, kW unity) is the dimension of a general term in the decomposition. Tables detailing the symmetry-allowed terms under the 11 Laue (site) crystal classes are also extended to include tesseral Tensorial sets up to rank 8, thus including the new terms. The use of these functions to describe electron paramagnetic resonance studies of high-spin nuclear Zeeman interactions is discussed.
Dennis G Mcgavin - One of the best experts on this subject based on the ideXlab platform.
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higher order zeeman and spin terms in the electron paramagnetic resonance spin hamiltonian their description in irreducible form using cartesian tesseral Spherical Tensor and stevens operator expressions
Journal of Physics: Condensed Matter, 2009Co-Authors: Dennis G Mcgavin, Craighead W TennantAbstract:In setting up a spin Hamiltonian (SH) to study high-spin Zeeman and high-spin nuclear and/or electronic interactions in electron paramagnetic resonance (EPR) experiments, it is argued that a maximally reduced SH (MRSH) framed in tesseral combinations of Spherical Tensor operators is necessary. Then, the SH contains only those terms that are necessary and sufficient to describe the particular spin system. The paper proceeds then to obtain interrelationships between the parameters of the MRSH and those of alternative SHs expressed in Cartesian Tensor and Stevens operator-equivalent forms. The examples taken, initially, are those of Cartesian and Stevens' expressions for high-spin Zeeman terms of dimension BS3 and BS5. Starting from the well-known decomposition of the general Cartesian Tensor of second rank to three irreducible Tensors of ranks 0, 1 and 2, the decomposition of Cartesian Tensors of ranks 4 and 6 are treated similarly. Next, following a generalization of the tesseral Spherical Tensor equations, the interrelationships amongst the parameters of the three kinds of expressions, as derived from equivalent SHs, are determined and detailed tables, including all redundancy equations, set out. In each of these cases the lowest symmetry, Laue class, is assumed and then examples of relationships for specific higher symmetries derived therefrom. The validity of a spin Hamiltonian containing mixtures of terms from the three expressions is considered in some detail for several specific symmetries, including again the lowest symmetry. Finally, we address the application of some of the relationships derived here to seldom-observed low-symmetry effects in EPR spectra, when high-spin electronic and nuclear interactions are present.
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Higher-order Zeeman and spin terms in the electron paramagnetic resonance spin Hamiltonian; their description in irreducible form using Cartesian, tesseral Spherical Tensor and Stevens' operator expressions
Journal of Physics: Condensed Matter, 2009Co-Authors: Dennis G Mcgavin, W. Craighead TennantAbstract:In setting up a spin Hamiltonian (SH) to study high-spin Zeeman and high-spin nuclear and/or electronic interactions in electron paramagnetic resonance (EPR) experiments, it is argued that a maximally reduced SH (MRSH) framed in tesseral combinations of Spherical Tensor operators is necessary. Then, the SH contains only those terms that are necessary and sufficient to describe the particular spin system. The paper proceeds then to obtain interrelationships between the parameters of the MRSH and those of alternative SHs expressed in Cartesian Tensor and Stevens operator-equivalent forms. The examples taken, initially, are those of Cartesian and Stevens' expressions for high-spin Zeeman terms of dimension BS(3) and BS(5). Starting from the well-known decomposition of the general Cartesian Tensor of second rank to three irreducible Tensors of ranks 0, 1 and 2, the decomposition of Cartesian Tensors of ranks 4 and 6 are treated similarly. Next, following a generalization of the tesseral Spherical Tensor equations, the interrelationships amongst the parameters of the three kinds of expressions, as derived from equivalent SHs, are determined and detailed tables, including all redundancy equations, set out. In each of these cases the lowest symmetry, [Formula: see text] Laue class, is assumed and then examples of relationships for specific higher symmetries derived therefrom. The validity of a spin Hamiltonian containing mixtures of terms from the three expressions is considered in some detail for several specific symmetries, including again the lowest symmetry. Finally, we address the application of some of the relationships derived here to seldom-observed low-symmetry effects in EPR spectra, when high-spin electronic and nuclear interactions are present.
Malcolm H. Levitt - One of the best experts on this subject based on the ideXlab platform.
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Theory of long-lived nuclear spin states in methyl groups and quantum-rotor induced polarisation.
The Journal of Chemical Physics, 2015Co-Authors: Jean-nicolas Dumez, Soumya Singha Roy, Salvatore Mamone, Peter Håkansson, Benno Meier, Joseph T. Hill-cousins, Richard C. D. Brown, Giuseppe Pileio, Gabriele Stevanato, Malcolm H. LevittAbstract:Long-lived nuclear spin states have a relaxation time much longer than the longitudinal relaxation time T1. Long-lived states extend significantly the time scales that may be probed with magnetic resonance, with possible applications to transport and binding studies, and to hyperpolarised imaging. Rapidly rotating methyl groups in solution may support a long-lived state, consisting of a population imbalance between states of different spin exchange symmetries. Here, we expand the formalism for describing the behaviour of long-lived nuclear spin states in methyl groups, with special attention to the hyperpolarisation effects observed in (13)CH3 groups upon rapidly converting a material with low-barrier methyl rotation from the cryogenic solid state to a room-temperature solution [M. Icker and S. Berger, J. Magn. Reson. 219, 1 (2012)]. We analyse the relaxation properties of methyl long-lived states using semi-classical relaxation theory. Numerical simulations are supplemented with a Spherical-Tensor analysis, which captures the essential properties of methyl long-lived states.
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Spherical Tensor analysis of nuclear magnetic resonance signals
The Journal of Chemical Physics, 2005Co-Authors: Jacco D. Van Beek, Marina Carravetta, Gian Carlo Antonioli, Malcolm H. LevittAbstract:In a nuclear magnetic-resonance (NMR) experiment, the spin density operator may be regarded as a superposition of irreducible Spherical Tensor operators. Each of these spin operators evolves during the NMR experiment and may give rise to an NMR signal at a later time. The NMR signal at the end of a pulse sequence may, therefore, be regarded as a superposition of Spherical components, each derived from a different Spherical Tensor operator. We describe an experimental method, called Spherical Tensor analysis (STA), which allows the complete resolution of the NMR signal into its individual Spherical components. The method is demonstrated on a powder of a C13-labeled amino acid, exposed to a pulse sequence generating a double-quantum effective Hamiltonian. The propagation of spin order through the space of Spherical Tensor operators is revealed by the STA procedure, both in static and rotating solids. Possible applications of STA to the NMR of liquids, liquid crystals, and solids are discussed.
B C Sanctuary - One of the best experts on this subject based on the ideXlab platform.
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rotation operator approach to spin dynamics and the euler geometric equations
Journal of Chemical Physics, 1994Co-Authors: Jinyuan Zhou, Chaohui Ye, B C SanctuaryAbstract:The rotation operator approach proposed previously is applied to spin dynamics in a time‐varying magnetic field. The evolution of the wave function is described, and that of the density operator is also treated in terms of a Spherical Tensor operator base. It is shown that this formulation provides a straightforward calculation of accumulated phases and probabilities of spin transitions and coherence evolutions. The technique focuses, not on the rotation matrix, but on the three Euler angles and its characteristic equations are equivalent to the Euler geometric equations long known to describe the motion of a rigid body. The method usually depends on numerical calculations, but analytical solutions exist in some situations. In this paper, as examples, a hyperbolic secant pulse is solved analytically, and a Gaussian‐shaped pulse is calculated numerically.