Spin exchange parameter

The above mapping analysis reveals that the spin exchange parameter 7 consists of two terms of opposite signs, so it is convenient to write 7 as... 

In general, the magnetic energy levels of a magnetic system are described by employing a Heisenberg spin Hamiltonian Hspi defined in terms of several different spin exchange parameters. 

Using this model in analogy with previous studies we can calculate a magnetic moment (fi) of the system with fixed Stoner exchange parameter Id and occupation of the d states. The total energy could then be calculated as the balance between the kinetic energy and the spin-polarization energy ... 

Fig.4. Potential hypersurfaces of T, (3P0) and r4 (3P,) levels in the e (Q2, Q3) subspace calculated from the Fukuda coupling matrix with the vibronic coupling parameter Are t = 4x 10 9 J/m from Eq. (5) (denoted by b in [84]), the electron (exchange) repulsion parameter G and spin-orbit parameter are both set equal to 0.3 eV...

Just as for the simple, spin compensated situation where pa(r) = pp(r) = j p(r), there are related expressions for the exchange and correlation energies per particle of the uniform electron gas characterized by p (r) pp(r), the so-called spin polarized case. The degree of spin polarization is often measured through the spin-polarization parameter... 

Because analytical calculations using equation (7) are impossible, a special routine for numerical calculations of the spin Hamiltonian exchange parameters was designed (see Ref. [16] for details). In these calculations, the one-centers Hamiltonians of the 5f1, 5f2, and 5f3 configurations of uranium ions were explicitly diagonalized using the actual free-ion parameters (F2 = 43 100, F4 = 41 000, F6 = 23 800, and 5f = 1780 cm 1) and cubic crystal-field parameters [6],... 

The magnitude of the exchange parameters is consistent with a rather high transition point temperature, TN = 30.8 K. The term //3 corresponds to four-spin exchange interactions... 

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