Magnetic systems spin wave model

From the spin wave (or magnon) model of magnetic systems, the heat capacity versus temperature behavior below the ordering temperature is given192 by the following equation ... 

Rajca and co-workers have studied star-branched and dendritic high-spin polyradicals which are potential organic magnets. Representative data were obtained for the model tetra-anionic compound 55. Three redox waves were observed by cyclic voltammetry and differential pulse voltammetry for a four-electron process between the potentials of -2.00 and -1.20 V (vs. SCE). Electrochemical experiments with these materials have usually been performed at 200 K. The polyradicals, which are less stable for systems with more unpaired electrons, have been characterized by spectroscopic studies, ESR data, and SQUID magnetometiy. 

We have performed a model calculation of the electron structure of AF Cr for two types of the unit cell extended along the axes Y and Z, which corresponded, respectively, to the longitudinal and transversal spin density waves (5PW and SDWj ). Recall that the magnetic moment of the system was Z-directed. Additionally, we have varied the number of atoms per unit cell N = 2,4,8,20, and40, which corresponded to = 0,0.5,0.25,0.1,0.05. In all instances the same values of F(r) iuid Ao(r) were used. The spin-polarizing exchange part of the potential AF(r) for different atoms of the unit ceil was defined according to (18). The number of terms in expansion (10) amounted to 12N. 

In order to obtain a bond order formula for open-shell systems that can be applied for both the indep)endent-partide model and correlated wave functions and which simultaneously yields unique bond orders for all spin multiplet components (in the absence of a magnetic field), Alcoba et al. [151, 152] derived a general expression (in the Hilbert space partitioning scheme) from a second-order reduced density matrix. Furthermore, as the first- and second-order reduced density matrices are invariant with respect to the spin projection, they are only a function of the total spin or similarly of the maximum projection S = and the bond order can be evaluated for the highest spin-projected state = S. They arrived at the following expression for the bond order... 

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