The temperature and frequency dependence of the inelastic neutron scattering from an Ising magnet

1968 ◽  
Vol 46 (7) ◽  
pp. 799-802 ◽  
Author(s):  
G. A. T. Allan ◽  
D. D. Betts
Keyword(s):  
Inelastic Scattering ◽  
Inelastic Neutron Scattering ◽  
Three Dimensional ◽  
Ising Models ◽  
Inelastic Neutron ◽  
Square Lattice ◽  
Two Dimensional ◽  
Scattering Function ◽  
Ising Magnet ◽  
Exact Energy

The magnetic inelastic scattering of neutrons from a spin-[Formula: see text] Ising system is considered. For the two-dimensional plane square lattice, the exact energy distribution of the scattering is obtained at all temperatures. It consists of a number of discrete levels, the envelope of which varies most markedly in the critical region. Some qualitative projections are also made concerning three-dimensional systems. For both two- and three-dimensional Ising models there can be no wave-vector dependence of the inelastic scattering function because there is correlation only between z components of the spins on different sites.

Zur Frage der Bestimmung des Frequenzspektrums in festen Körpern durch die unelastische Streuung von kalten Neutronen

1966 ◽  
Vol 21 (10) ◽  
pp. 1770-1786
Author(s):  
W. Kley
Keyword(s):  
Inelastic Scattering ◽  
Frequency Distribution ◽  
Cross Section ◽  
Inelastic Neutron Scattering ◽  
Target Material ◽  
Inelastic Neutron ◽  
Host Lattice ◽  
Scattering Cross Section ◽  
Experimental Conditions ◽  
Scattering Cross

The various possibilities are examined how to measure the frequency distribution of solids by the inelastic scattering of thermal and subthermal neutrons. Particular attention is drawn on measuring-techniques that allow the determination of the frequency distribution even if the scattering cross section of the target material is not totally incoherent but a mixture of a coherent and an incoherent component. It is shown how the frequency distribution of solids can be measured even if the cross section is totally coherent by the use of a doping technique. Atoms as H and V, that have an almost entirely incoherent scattering cross section, are used as impurities in the solid of interest, serving as a probe of the host lattice vibrations. By studiing the difference of the two independent inelastic scattering experiments, one with the pure, the other with the impure solid, it is possible to derive the frequency distribution function of the host lattice itself. Examples are given for Vanadium and Niobium. In addition, evidence is given how the best experimental conditions are selected for this type of inelastic neutron scattering experiments.

Exact Solutions for Correlations in the Kagomé Ising Antiferromagnet

1997 ◽  
Vol 11 (01n02) ◽  
pp. 93-101 ◽  
Author(s):  
J. H. Barry ◽  
M. Khatun
Keyword(s):  
Exact Solutions ◽  
Inelastic Neutron Scattering ◽  
Pair Correlation ◽  
Inelastic Neutron ◽  
Response Functions ◽  
Scattering Function ◽  
Linear Combinations ◽  
Joint Configuration ◽  
Ising Antiferromagnet ◽  
Site Cluster

The kagomé Ising antiferromagnet is highly frustrated with its pair correlation decaying exponentially at large distance for all temperatures including absolute zero. Hence, the spin system does not support long-range orderings and is devoid of any phase transition. One proves, via local star-triangle and decoration-decimation transformations, that correlations in the kagomé Ising antiferromagnet at arbitrary temperatures can be represented as linear combinations of correlations in the honeycomb Ising ferromagnet at high temperatures (disordered region). Existent knowledge of all honeycomb Ising correlations upon a select (spatially compact) 10-site cluster is thus sufficient to determine all present kagomé Ising correlations upon an associated 9-site cluster. Examples of resulting exact solutions for pair and multisite correlations in the kagomé Ising antiferromagnet are presented at all temperatures. Applications include joint configuration probabilities, thermodynamic response functions such as the specific heat and the initial perpendicular susceptibility, and the inelastic neutron scattering function.

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