R. Chatterjee

Zero-field splitting of Mn++ in La2Mg3(NO3)12 . 24H2O

Abstract The zero-field splitting parameter D for Mn ++ in La 2 Mg 3 (NO 3 ) 12 ·24H 2 O has been calculated from seven different mechanisms. The theoretical and experimental values agree for one site, but not for the other.

The derivation of a symmetry‐adapted generalized spin Hamiltonian

The formulation of a generalized spin Hamiltonian using the decomposition of double tensor operators into products of single tensor operators is reexamined critically using their transformation properties under parity, time reversal, charge and Hermitian conjugation, as well as the imposition of symmetry constraints. These properties depend on their polar or axial vector classification. It is concluded that limitations in the parameterization of experimental EPR and ENDOR spectral data are associated with an excessively restrictive interpretation of the constraints imposed in the derivation of phenomenological and generalized spin Hamiltonians. It is shown that the correct imposition of these constraints using the double tensor formulation leads to a symmetry adapted generalized spin Hamiltonian which includes additional zero field splitting terms characteristic of the various crystallographic groups and described by odd rank tensor operators whose matrix elements are nonzero provided account is taken of ...

The theory of spin correlated crystal fields

Effective operators of the spin correlated crystal field have been derived using a second order perturbation mechanism which couples an exchange interaction with the crystal field. We have taken into account the effect of excited configurations involving np and np orbitals. Relativistic wavefunctions have been used to calculate radial integrals. Second order degenerate perturbation theory has been employed, in projector form, to find an equivalent operator which acts only within the ground manifold of total angular momentum.

The generalized Korteweg-de Vries equation for interacting phonons in a coherent state basis

Abstract The higher order Korteweg-de Vries (KdV) equation of interacting phonons is obtained for a one-dimensional anharmonic lattice where fifth order anharmonicity in the potential is taken and justified from the classical continuum approximation method. The possible solitary wave solutions are discussed.

Comments on the use of the effective operator method in the relativistic crystal field model

Abstract An attempt is made to interpret the origin of the symmetry adapted equivalent operators describing relativistic crystal field effects. The physical significance of the coupling mechanisms which generate these operators is discussed. It is shown that the same form of an equivalent operator can be obtained from numerous mechanisms of different origins. The method is numerically illustrated for the Mn 2+ ion in an environment of C 3 symmetry. New information on the role of configuration mixing interactions is obtained.

The theory of spin-correlated crystal fields: Application to Gd3+ in C3h symmetry

Application of the recently formulated theory of spin-correlated crystal fields is made to the Gd3+ ion in ethysulphate lattices. Detailed calculations of the spin-correlated crystal field contribution to the zero field splitting are found to be of the correct sign but its magnitude is too large. It is comjectured that similar types of mechanisms involving excitations to other sites may be responsible for the discrepancy.

Effective operators of the spin correlated crystalline electric field

Abstract The effective operators of the spin correlated crystal field have been formed by coupling the exchange with the crystal field. The exchange field is a scalar in spin space so the effective operators will still have the same rank as that of the crystal field but will give non-zero matrix elements between the states 2S+1LJ of the half filled shells, contrary to the zero value obtained for a pure crystal field tensor.

Comments on the properties of one- and two-body double tensor operators

Recently, the parity, charge, time and Hermitian conjugation properties of one-body tensor operators have been reexamined and the Racah algebra has been formally extended to two-body tensor operators. In this paper we consider several important aspects related to these problems. First, we present a proof of the communication relations for two-body operators which was previously postulated. Then, comparing the reduced matrix elements for one- and two-body operators we find the normalization constant for the latter. We subsequently show that the P- and T-conjugation relations for tensor operators are relativistically invariant. Finally, we analyze the question of Hermitian conjugation of double tensor operators and conclude that previously stated conditions on their ranks were too restrictive and resulted in omissions of some terms from theoretical analyses. We show examples of tensor operators which were customarily neglected but indeed should be retained in the effective Hamiltonian.

Comments on the relativistic crystal field

The contributions of the large and the small components of the radial wavefunctions to the relativistic crystal field are calculated from Wybournes (1965) expression. It is shown that both mechanisms for the ground-state splittings of S-state ions, proposed by Lulek (1969) and Chatterjee et al (1973), are obtained from the small and the large components of the radial wavefunctions respectively.

Estimate of relativistic radial integrals from the optical spectra of Sm2+ in tetragonal compounds

Abstract Relativistic radial integrals have been estimated from the parameters obtained by fitting an effective hamiltonian to the optical spectrum of Sm2+ in two complexes.