Open AccessUtilization of the Spin Symmetry in Fitting the Magnetic Data lor Large Exchange Clusters
Author(s) -
Roman Boča
Publication year - 2013
Publication title -
nova biotechnologica et chimica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.212
H-Index - 9
eISSN - 1339-004X
pISSN - 1338-6905
DOI - 10.2478/nbec-2013-0006
Subject(s) - hamiltonian (control theory) , chemistry , exchange interaction , magnetization , magnetic susceptibility , eigenvalues and eigenvectors , spin (aerodynamics) , quantum number , quantum mechanics , condensed matter physics , physics , mathematics , ferromagnetism , magnetic field , thermodynamics , mathematical optimization
The Heisenberg Hamiltonian appropriate to exchange clusters commutes with the square of the total spin ant its third component. Therefore in studying the exchange coupled clusters of medium/high nuclearity the spin quantum number S can be utilized in factoring of large interaction matrices (dimension of which is 10 4 - 10 5 ). Then the blocks of much lower size can be diagonalized using the desktop computers. To this end, the eigenvalues form the partition function Z(T,B) from which all thermodynamic properties, including the magnetization M(B,T 0 ) and the magnetic susceptibility χ (T,B 0 ), can be reconstructed. The matrix elements of the interaction operators in the coupled basis set of spin kets have been generated with the help of the irreducible tensor operators for a loop for S = S min until S = S max . In addition to the modelling of energy levels for different topologies, a fitting of magnetic data is exemplified by a number of examples like [Fe 6 ] and [Mn 3 Cr 4 ] systems