Magnetic exchange integral

Figure 2. The structural energy difference (a) and the magnetic moment (b) as a function of the occupation of the canonical d-band n corresponding to the Fe-Co alloy. The same lines as in Fig. 1 are used for the different structures. In (b) the concentration dependence of the Stoner exchange integral Id used for the spin-polarized canonical d-band model calculations is shown as a thin dashed line with the solid circles. The value of Id for pure Fe and Co, calculated from LSDA and scaled to canonical units, are also shown in (b) as solid squares.

Fig. 3.8 Left-hand panel The on-site atomic energy levels for up and down spin electrons due to the exchange splitting Im where / and m are the Stoner exchange integral and local moment respectively. Right-hand panel The local magnetic moment m, as a function of //2 / where / and h are the exchange and bond integrals respectively. Compare with the self-consistent LSDA solution in the upper panel of Fig. 3.6.

Here k is the Fermi wave vector determined from the value of the hole concentration p assuming a spherical Fermi surface, m is the hole effective mass taken as 0.5/no (mo is the free electron mass), is the exchange integral between the holes and the Mn spins, and h is Planck s constant. The transverse and longitudinal magnetic susceptibilities are determined from the magnetotransport data according to x = 3M/dB and xh = M/B. 

It should be mentioned that several copper oxide compounds are described by this model. These compounds contain CuO chains and Cu — O — Cu angle 6 is near 90° [7]. In this case the usual antiferromagnetic super-exchange of two nearest-neighbor magnetic Cu ions is suppressed and the exchange integral J12 is... 

Extensions to more sophisticated 1-D magnetisms have been performed by Takeuchi22 for 1-D helicoidal systems, and by Duffy and Barr23) for alternating Heisenberg chains (two different exchange integrals). 

This is the expression for the exchange interaction between localized magnetic moments. In Eq. 7.10, J is the exchange integral, given by ... 

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