Fourth-order exchange interactions in Gd xEu 1− xS

Abstract

We report on investigations of fourth-order exchange interactions, i.e. biquadratic, three-spin and four-spin interactions in Gd x Eu 1− x S using measurements of the cubic susceptibility χ 3 and the magnetic specific heat c p . In the paramagnetic phase of GdS these interactions are ferromagnetic since χ 3 is negative (the magnetization increases stronger than linearly with magnetic field). At the Néel temperature of GdS of 59 K the onset of a strong field dependence of the linear susceptibility χ 1 has early been observed. This feature is attributed here to a quasi-ferromagnetic ordering process induced by the fourth-order exchange interactions. Evidence for this is provided by a divergence of the cubic susceptibility χ 3 at 59 K. Two further magnetic phase transformations were observed in GdS: (a) at 47 K the magnetic susceptibility and specific heat exhibit small but definite anomalies and, (b) below 27 K a second critical field curve reaching only 2.6 T for T→0 is observed. Also these phase transitions are attributed to the fourth-order interactions which apparently are not constant but change from ferromagnetic at high temperature to antiferromagnetic at low temperature. The critical magnetic behavior of the magnetic specific heat, c mag, at T N=59 K is as complicated in GdS as in EuTe because two ordering phenomena superpone. A description by power laws with Heisenberg critical exponents is inadequate. On substituting Gd by Eu fourth-order interactions change, as usual, rapidly as function of composition. One sample with composition Gd 0.8Eu 0.2 was investigated in detail. In this sample the total fourth-order interaction is antiferromagnetic at the Néel temperature of T N=55 K. As a consequence, the ferromagnetic component observed in GdS is absent and a second critical field curve reaching only 5.5 T occurs below 55 K.