An Effective Field Model of the Amorphous Antiferromagnet

Abstract

An effective field model of an amorphous antiferromagnet is developed assuming a distribution of near neighbour distances and hence a distribution of effective field coefficients between interacting atom pairs. It is shown that such a material is characterized by a symmetrical distribution of the total effective field, which, in the absence of any spin correlation, is approximately Gaussian. The model predicts a precise critical or N&l temperature proportional to the square root of the average number of interacting near neighbours, and an unusual downward curvature of the reciprocal susceptibility variation with decreasing temperature (see Fig. 5 and 6). Two classes of amorphous antiferromagnet are examined: those with and those without magnetically isolated paramagnetic atoms. The limited experimental data support the former class.Es wird ein Modell des effektiven Feldes eines amorphen Antiferromagneten entwickelt, wobei eine Verteilung der Abstiinde der niichsten Nachbarn und damit eine Verteilung der effektiven Feldkoeffizienten zwischen wechselwirkenden Atompaaren angenommen wird. Es wird gezeigt, daB solches Material durch eine symmetrische Verteilung des totalen effektiven Feldes, das wegen Fehlen irgendeiner Spinkorrelation niiherungsweise gaussformig ist, charakterisiert wird. Das Modell sagt eine genaue kritische oder NBel-Temperatur, die proportional zur Quadratwurzel der mittleren Zahl der wechselwirkenden niichsten Nachbarn ist, und eine ungewohnliche, abwiirts gerichtete Kriimmung der rcziproken Suszeptibilitiitsiinderung mit fallender Temperatur voraus. Zwei Klassen amorpher Antiferromagneten werden untersucht ; solche mit und solche ohne magnetisch isolierte paramagnetische Atome. Die begrenzten experimentellen Daten unterstiitzen den ersten Fall. X I = s (1 -X I 171) Y E'ig. 5. The reciprocal susceptibilities versus temperature plotted (full curves) for an average of four near neighbours (2 = 4) with a = 1. The graphs are plotted in reduced units of temperature divided by the paramagnetic Nee1 temperature B and units of susceptibility divided by xn (given by equation (18)). The graph also shows calculated reciprocal susceptibility-temperature relationships (dashed curves) for a crystalline material with the same parameters as the amorphous material, assuming nearest neighbour interaction only

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“…The model predicts that below a transition temperature, the Neel temperature TN, the average atomic susceptibility X of a random assembly of magnetic ions coupled by negative exchange interactions is (3) where e, the paramagnetic Neel temperature, is given by (4) and ~ is a known temperature-dependent parameter related to the effective field distribution in the material, and Z and "9 are, respectively, the mean number of neighbors interacting with each ion, and the mean pair effective field coefficient. The susceptibility of the coupled amorphous antiferromagnetic, as given by Eq.…”

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