Exchange constant stiffness

The micromagnetic exchange constant (exchange stiffness) A [J/m] is proportional to the exchange integral J. For a cubic lattice having one nonequivalent atom, A is given by [36]... 

The measurements on Euq yoSrp 30S (in powder form) which orders ferromag-netically below = 8.5 K show well-defined spin-wave excitations at 4.5 K (fig. 40a), and a quadratic form of the spin-wave dispersion at low q (eq. 61) similar to pure EuS. The stiffness constant D, related to the exchange constants in the non-diluted ferromagnet by the relation... 

Here Ms(r) is the spontaneous magnetization, A)(r) is the first uniaxial anisotropy constant, A(r) denotes the exchange stiffness, and n(r) is the unit vector of the local anisotropy direction. H is the external magnetic field, and Hd is the magnetostatic self-interaction field. The latter can be written as... 

First, second, and third terms in the equation (3) refer to Coulomb potential, exchange repulsion interaction potential, and Morse potential, respectively. Zj is an atomic charge, e is an elementary electric charge, r is an interatomic distance, and fo is a constant. The parameters a and b in Eq. (3) represent the size and stiffness of the atoms, respectively, in... 

A = exchange stiffness constant. A schematic representation of this model is given in Fig. 4.3-27. The basic effect of decreasing the grain size consists of local averaging of the magnetocrystalline anisotropy energy Ki for D = 10-15 nm at Lq = 30-50 nm (about equal to... 

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