Finite-Temperature Properties. Spin Fluctuations

In order to calculate the partition function of the d-electron Hamiltonian, we rewrite the many-body interaction H, the third term in Eq. (I), as 

Comparison with Eq. (3) shows that the self-consistent local magnetic moment /x/ at r = 0 is now replaced by the fluctuating field /. The magnetic properties at T 0 are obtained as an average over all possible exchange-field configurations = ( i. 

For example, the local magnetization /x/(r) at the atom i is given by the average of the local magnetic moment 2(5/ = i icxi)) which fluctuates at T 0 and 

( ) = —/ BTln[/is the free energy associated with an exchange field acting at atom i and Z = J is the partition function. P/( ) = 

A first insight regarding the magnetic behavior of Fe v and Niyv clusters at T 0 can be obtained by considering the low-temperature limit of F/( ). The local free-energy difference 

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For the sake of clarity we shall first discuss in Section 6.2.1 ground-state properties in the framework of the unrestricted Hartree-Fock approximation. In Section 6.2.2 the theory is extended to finite temperatures by using a functional integral formalism including spin fluctuations. Finally, in Section 6.2.3 we analyze the problem of electron correlations by exact diagonalization of the simpler single-band Hubbard model. 

Magnetic Properties at Finite Temperatures Spin-Fluctuation Effects... 

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