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

It is shown experimentally, that fourth-order exchange interactions, i.e. b iquadratic, three-spin and four-spin interactions, are able to create a par ticular order parameter which we have called O-4. Consistently, the orderin g type of O-4 always conforms to the sign of the fourth-order interaction s um evaluated from measurements of the cubic susceptibility chi (3). Earlier investigations suggest that O-4 can be identified with the expectation val ue of the transverse spin component, <S-x>, while the conventional (Heisenb erg) order parameter, O-2, is given by <S-z>. Therefore, the observed order ing 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 s pin magnets Eu0.75Sr0.25Te, GdAg, GdMg, EuS and EuO as examples. These mate rials provide all ferromagnetic and antiferromagnetic combinations for O-2 and O-4. For the ferromagnets EuS and EuO, second-order and fourth-order in teractions are known to be ferromagnetic. This is the most complicated situ ation for the identification Of O-4. Ac susceptibility measurements perform ed at different angles to an applied static magnetic field reveal the conve ntional rotational symmetric state around the field axis. However, measurem ents in the critical temperature range indicate a discontinuous rise of O-2 which is in contrast to all hitherto reported results but in agreement wit h mean field predictions. In most antiferromagnets in which susceptibility measurements reveal ferromagnetic O-4 the associated ordered moment is usua lly too small to be detected with neutron scattering without polarization a nalysis.