Experimental identification of fourth-order exchange interactions in magnets with pure spin moments

It is shown experimentally, that fourth-order exchange interactions, i.e. biquadratic, three-spin and four-spin interactions, are able to create a particular order parameter which we have called O-4. Consistently, the ordering type of O-4 always conforms to the sign of the fourth-order interaction sum evaluated from measurements of the cubic susceptibility chi (3). Earlier investigations suggest that O-4 can be identified with the expectation value of the transverse spin component, <S-x>, while the conventional (Heisenberg) order parameter, O-2, is given by <S-z>. Therefore, the observed ordering temperature of O-4 is never larger than the ordering temperature of O-2. The experimental signatures of O-4 are illustrated using the cubic pure spin magnets Eu0.75Sr0.25Te, GdAg, GdMg, EuS and EuO as examples. These materials provide all ferromagnetic and antiferromagnetic combinations for O-2 and O-4. For the ferromagnets EuS and EuO, second-order and fourth-order interactions are known to be ferromagnetic. This is the most complicated situation for the identification Of O-4. Ac susceptibility measurements performed at different angles to an applied static magnetic field reveal the conventional rotational symmetric state around the field axis. However, measurements in the critical temperature range indicate a discontinuous rise of O-2 which is in contrast to all hitherto reported results but in agreement with mean field predictions. In most antiferromagnets in which susceptibility measurements reveal ferromagnetic O-4 the associated ordered moment is usually too small to be detected with neutron scattering without polarization analysis.