Influence of lattice polarizability on interacting Li-induced dipoles
distributed in incipient ferroelectric KTaO
3
Yuki Ichikawa and Koichiro Tanaka*
Department of Physics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
Received 15 March 2007; revised manuscript received 27 February 2008; published 2 April 2008
Susceptibility purely originated from the Li-induced quasistatic dipoles in relaxor K
1-x
Li
x
TaO
3
has been
extracted from low-frequency permittivity using terahertz time-domain spectroscopy. The temperature depen-
dence of the extracted susceptibility has an anomaly at the critical temperature T
a
near 100 K with the critical
slowing down of the low-frequency relaxation process. From a detailed analysis of the extracted susceptibility,
we attributed the main part of the susceptibility for x 0.036 to the high-frequency relaxation process and
concluded that there are two relevant interactions that govern the ferroelectric coupling between Li-induced
dipoles and that the interplay of the two interactions gives rise to a complex temperature dependence of the
susceptibility originated from Li-induced dipoles. Below the critical concentration x 0.022, short-range in-
teraction between individual Li ions should be dominant. Above the critical concentration, x 0.022, Coulomb
interaction should be dominant. The crossover from the low-temperature glasslike phase to the low-
temperature ferroelectric domain-state across x
c
in K
1-x
Li
x
TaO
3
is attributed to the interplay of the two kinds
of interaction.
DOI: 10.1103/PhysRevB.77.144102 PACS numbers: 77.22.-d, 07.57.-c, 78.20.Ci, 78.30.-j
I. INTRODUCTION
A system in which impurity-induced dipoles are mediated
in a highly polarizable lattice is one of the most attractive
subjects in solid state physics because the combination of the
dipoles and highly polarizable bulk phonon brings about
novel critical phenomena.
1–4
KTaO
3
doped with lithium in a
small concentration, K
1-x
Li
x
TaO
3
KLT, is such a material,
and it provides an ideal system for the subject. The pure
KTaO
3
maintains an ABO
3
cubic Perovskite structure as low
as the liquid-helium temperature without undergoing a ferro-
electric phase transition quantum paraelectricity.
5
The soft-
ening of the lowest transverse optical mode TO
1
mode is
suppressed by the quantum effect. The impurity lithium ion
replaces the potassium ion in the A-site of the host lattice.
Because of the ion-radius misfit, small lithium ions take
sextet-degenerate off-center positions along three equivalent
100 directions with a displacement as large as a quarter of
the lattice constant.
6,7
The off-center displacements of
lithium ions produce electric dipole moments, and the di-
poles change their directions with the thermal hopping mo-
tions of lithium ions. The total relative complex dielectric
constant in this system at frequency 10 THz can be
expressed as
˜
r
= ˜
Li
+ ˜
TO
1
+ ˜
, 1
where ˜
Li
and ˜
TO
1
are the susceptibilities of Li-
induced dipoles and the lattice polarization due to the TO
1
mode, respectively. ˜
represents the contributions of other
polarizations with higher energy than that of the TO
1
mode.
In frequencies lower than the THz region, we can regard ˜
as a real constant.
KLT has been intensively investigated since Yacoby et al.
discovered the off-center displacement of the impurity Li by
their Raman-scattering experiment.
8,9
The orientational re-
laxation of quasistatic dipoles due to the off-center hopping
motion of Li ions undergoes critical slowing down toward
the dipole freezing temperature.
10–12
Figure 1 shows a broad-
band spectrum of the complex dielectric constant from 1 Hz
to 10 THz in KLT crystal x = 0.020, just above the dipole
freezing temperature.
10–12
The upper and lower panels are the
real and imaginary parts of the complex dielectric constant,
respectively. A relaxation Debye step below 1 MHz is evi-
dent, as is the oscillation resonance at 1 THz. The former,
which corresponds to ˜
Li
, is the orientational relaxation
originated from Li-induced dipoles.
10–12
The latter, which
corresponds to ˜
TO
1
, is the dispersion of the TO
1
soft
mode in the KTaO
3
host lattice, whose frequency decreases
with decreasing temperature by the anharmonicity of
lattice.
13,14
Below the dipole freezing temperature, Kleemann
et al. proposed, using birefringence measurements, that the
phase boundary between the low-temperature glasslike phase
x x
c
and ferroelectric domain-state-like phase x x
c
ex-
ists at around x
c
0.022.
15
The macroscopic dielectric properties of KLT, such as the
dielectric susceptibility and residual polarization, have been
FIG. 1. Broadband dispersion of the complex dielectric constant
in K
1-x
Li
x
TaO
3
x = 0.020 at 59 K, just above the dipole-freezing
temperature. The dispersion from 100 Hz to 1 MHz is measured by
measuring the ac impedance using an LCR meter. The dispersion in
the THz region is determined by THz-TDS in this work. The solid
curves are guides for the eye.
PHYSICAL REVIEW B 77, 144102 2008
1098-0121/2008/7714/1441029 ©2008 The American Physical Society 144102-1