Eur. Phys. J. B 8, 207-216 (1999)
https://doi.org/10.1007/s100510050683

On the T₂ Bloch law in magnets with fourth-order exchange interaction

Institut für Festkörperforschung, Forschungszentrum Jülich, 52425 Jülich, Germany

Received: 23 July 1998
Revised: 12 October 1998
Published online: 15 March 1999

Abstract

For the ferromagnets EuS and GdMg, in which fourth-order exchange interactions (i.e. biquadratic, three-spin and four-spin interactions) have been identified, the deviation of the spontaneous magnetization with respect to the T=0 value is shown to follow a T² law instead of the famous law expected for a Heisenberg ferromagnet. Moreover, the observed T² law holds for temperatures as large as and the extrapolated magnetization value for does not conform to ferromagnetic saturation. This is because the fourth-order exchange interactions generate a second order-parameter which is assumed to govern the order of the transverse moment components. These moment components have a finite expectation value for at the expense of the Heisenberg order parameter. Like the spontaneous magnetization, the critical field curves of the metamagnet EuSe and the antiferromagnet EuTe also start decreasing with a T² term for . It is argued that the T² law is a consequence of the fourth-order exchange interactions. This is shown experimentally by a study of the critical field curves pertinent to the longitudinal (Heisenberg) order-parameter in the diamagnetically diluted antiferromagnets Eu_xSrTe. In this solid solution series a particular composition of x_c=0.85 exists at which the different fourth-order interaction processes compensate each other in the high temperature average. As a consequence, an Eu_xSrTe sample with x=0.85 meets the requirements of a Heisenberg antiferromagnet at least if a quantity is considered for which the high-temperature average over all fourth-order interactions is decisive. This seems to be the case for the critical field curve which gives the phase boundary to the paramagnetic phase. In fact, a crossover from a T² to a law is observed for on approaching x_c. This, we believe, shows the frequently observed T² law is caused by the fourth-order interactions.