On the T-2 Bloch law in magnets with fourth-order exchange interaction

For the ferromagnets EuS and GdMg, in which fourth-order exchange interacti ons (i.e. biquadratic, three-spin and four-spin interactions) have been ide ntified, the deviation of the spontaneous magnetization with respect to the T = 0 value is shown to follow a T-2 law instead of the famous T-3/2 law e xpected for a Heisenberg ferromagnet. Moreover, the observed T2 law holds f or temperatures as large as 0.8T(c) and the extrapolated magnetization valu e for T --> 0 does not conform to ferromagnetic saturation. This is because the fourth-order exchange interactions generate a second order-parameter w hich is assumed to govern the order of the transverse moment components. Th ese moment components have a finite expectation value for T --> 0 at the ex pense of the Heisenberg order parameter. Like the spontaneous magnetization , the critical field curves B-c(T) of the metamagnet EuSe and the antiferro magnet EuTe also start decreasing with a T-2 term for T --> 0. It is argued that the T-2 law is a consequence of the fourth-order exchange interaction s. This is shown experimentally by a study of the critical field curves B-c (parallel to)(T --> 0) pertinent to the longitudinal (Heisenberg) order-par ameter in the diamagnetically diluted antiferromagnets EuxSr1-xTe. In this solid solution series a particular composition of x(c) = 0.85 exists at whi ch the different fourth-order interaction processes compensate each other i n the high temperature average. As a consequence, an EuxSr1-xTe sample with x = 0.85 meets the requirements of a Heisenberg antiferromagnet at least i f 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 cr itical field curve B-c(parallel to)(T --> 0) which gives the phase boundary to the paramagnetic phase. In fact, a crossover from a T-2 to a T-3/2 law is observed for B-c(parallel to)(T --> 0) on approaching x(c). This, we bel ieve, shows the frequently observed T2 law is caused by the fourth-order in teractions.