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Dynamic Spin Hamiltonian Formalism and Mössbauer Study of Spin—Lattice Relaxation of Paramagnetic Fe 3+ ( 6 S) Ions
Author(s) -
Srivastava K. K. P.,
Mishra S. N.
Publication year - 1980
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221000105
Subject(s) - hyperfine structure , paramagnetism , condensed matter physics , phonon , ion , spin–lattice relaxation , hamiltonian (control theory) , debye , debye model , relaxation (psychology) , chemistry , physics , atomic physics , quantum mechanics , psychology , mathematical optimization , social psychology , mathematics
In a crystal field potential the 6 S state of a paramagnetic 57 Fe 3+ (3d 5 , 6 S) ion splits into three Kramers spin doublets S z = ± 5/2, ± 3/2, and ± ½ and each doublet produces its own Mössbauer magnetic hyperfine spectrum at low temperatures as a result of the slow spin relaxation rate. These Mössbauer hyperfine spectra are used to study the temperature dependence of Fe 3+ spin lattice relaxation rate falling in the region 10 6 to 10 9 s −1 . The dynamic spin Hamiltonian formalism is utilised to explicitly calculate the spin—lattice relaxation rate of the three Kramers doublets for one‐phonon and two‐phonon processes in different temperature regions. It is further assumed that the various modes of acoustic phonon propagation are direction independent, the phonon spectrum is of Debye type, and the dynamic crystal field parameters are very similar to the static ones. It is found that for Fe 3+ ions the one‐phonon relaxation process is most dominant and the theoretical results are in a very good agreement with the experimental observations. These calculations may be equally applicable to other S‐state paramagnetic ions.