U. Kobler et al., Experimental identification of fourth-order exchange interactions in magnets with pure spin moments, J PHYS-COND, 13(31), 2001, pp. 6835-6852
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.