A computational method of determination of constants of spin Hamiltonian of fine structure ESR spectra

A fast computational method of determining accurate spin-hamiltonian parameters for ions (S>1/2) in crystals

“…For the present case of one orientation of B, the procedure is found to be selfconvergent, independent of the values of ABi, which is in contradiction to the conclusion drawn by Uhrin [5] for the case of many orientations. Convergence is guaranteed irrespective of the initial values of parameters Bl m and M, except when all the initial Bi m are zero simultaneously and when the initial B2 ~ and B22 are simultaneously greater than their expected values.…”

“…This method, though applicable for any strength of crystal field and convenient to handle, takes a much larger time than the least-squares method. The method suggested by Uhrin [5] is based on the construction of step fields. For every step the same convergence process is used.…”

“…~B~m' Otm; m=0,1,2 .... ; m<<.l, 3. DESCRIPTION OF UHRIN'S METHOD The iterative technique of Uhrin [5] solves the secular matrix equation of the spin-hamiltonian using exact numerical diagonalization. Originally Uhrin designed the method for calculation of N parameters using 2S transition fields (AM s = + 1) per orientation of B, for Q orientations, such that 2SQ >>.…”

“…In 1973, Uhrin [5] developed an iterative method based on exact numerical diagonalization of the spin-hamiltonian matrix. This method can be used to calculate as many parameters as desired for any value of spin S > 89 The method evaluates accurate numerical values of the parameters and is faster than other methods [1][2][3][4].…”

A Fast Computational Method to Obtain Spin‐Hamiltonian Parameters of S and I = 5/2 Ions

“…To obtain the Hamiltonian parameters an iterative method based on the complete diagonalization of the spin-Hamiltonian matrix was developed by Uhrin [ 5 ] . This niet,hod, beside being faster than the other diagonalization methods, can handle as niany parameters as required for S > 112.…”