Short-range magnetic order

For cases in which the magnetic lattice dimensionality is one (chains) or two (planes), magnetic Short Range Order (SRO) can develop and persist over a wide temperature range, often many tens of kelvins. Effectively, this is an expansion of the critical regime discussed above, which is normally only a few degrees at best for three-dimensional systems. As well as lattice dimensionality, the spin dimensionality must be considered to provide a complete picture. Spin dimensionality is a somewhat more subtle concept that can be best introduced by considering an expansion of the HDW Hamiltonian into its components as in equation (4)... 

Fig. 15. Schematics of (a) magnetic short-range order accounting for high-frequency ha> ss 8 meV), and (b) intermediate-range ( 200A) static order in nominally pure UPtj, as wen as conventional long-range order in (U, jThJ(Pt,Pd)3. (Adapted from Goldman et al. 1986.)...

The Inden model [20] is frequently used to describe second-order magnetic order-disorder transitions. Inden assumed that the heat capacity varied as a logarithmic function of temperature and used separate expressions above and below the magnetic order-disorder transition temperature (TtIS) in order to treat the effects of both long- and short-range order. Thus for z = (T/TtIS) < 1 ... 

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