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On the Use of Thiele's Semi‐Invariants in Ferromagnetism
Author(s) -
FerrisPrabhu A. V. M.
Publication year - 1966
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.19660140208
Subject(s) - magnetization , conjecture , eigenvalues and eigenvectors , invariant (physics) , ferromagnetism , expression (computer science) , mathematics , spectrum (functional analysis) , order (exchange) , physics , mathematical physics , condensed matter physics , mathematical analysis , pure mathematics , quantum mechanics , magnetic field , computer science , finance , economics , programming language
The semi‐invariants of Thiele are used to calculate the effect of the kinematical interactions on the temperature dependence of the magnetization on the spinwave model of ferromagnetism. It is first assumed that the only effect is to restrict the spinwave eigenvalue spectrum to 2 S . The semi‐invariants are calculated exactly and an expression is obtained for the magnetization which contains only half odd integer powers of T . The coefficients contain the factor 1–(1 + 2 S ) − n /2 and as S → ∞ reduce to Dyson's coefficients. Next the interaction of the spinwaves is specifically included. The first three semi‐invariants are calculated exactly. A conjecture is made as to the form of the first order term of the n ‐th semi‐invariant from which the magnetization is calculated. The expression bears an interesting resemblance to Watson's generalized integral.