Third order dielectric susceptibility in a model quantum paraelectric
Abstract
In the context of perovskite quantum paraelectrics, we study the effects of a quadrupolar interaction
J
q
, in addition to the standard dipolar one
J
d
. We concentrate here on the nonlinear dielectric response
χ
(3)
P
, as the main response function sensitive to quadrupolar (in our case antiquadrupolar) interactions. We employ a 3D quantum four-state lattice model and mean-field theory. The results show that inclusion of quadrupolar coupling of moderate strength (
J
q
∼
1
4
J
d
) is clearly accompanied by a double change of sign of
χ
(3)
P
from negative to positive, near the quantum temperature
T
Q
where the quantum paraelectric behaviour sets in. We fit our
χ
(3)
P
to recent experimental data for SrTiO
3
, where the sign change is identified close to
T
Q
∼37K
.