On-site Coulomb repulsion in the small polaron system La
1 x
Ca
x
MnO
3
D. C. Worledge
Department of Applied Physics, Stanford University, Stanford, California 94305-4085
L. Mie
´
ville
Department of Applied Physics, Stanford University, Stanford, California 94305-4085
and Conductus, 969 West Maude Avenue, Sunnyvale, California 94086
T. H. Geballe
Department of Applied Physics, Stanford University, Stanford, California 94305-4085
Received 16 December 1997; revised manuscript received 17 February 1998
Conductivity measurements from 300 to 1200 K of La
1-x
Ca
x
MnO
3
thin films, with doping from x =0 to
x =1, show that the entire doping range fits the adiabatic small polaron model =( A / T )exp(-E
a
/kT). Fur-
thermore the x dependence of A explicitly shows the effects of on-site Coulomb repulsion, i.e., a polaron
cannot hop into an occupied site. Instead of increasing monotonically as more carriers are introduced, A starts
to decrease at x =0.2 and, as expected for Hubbard band splitting, is reduced to almost zero when the lattice is
full. S0163-18299801424-6
I. INTRODUCTION
Since the first reports of colossal magnetoresistance in
La
1 -x
A
x
MnO
3
, where A is a divalent cation, there has been
an ongoing effort to understand the origin of such a large
magnetoresistance. La
1 -x
Ca
x
MnO
3
is a useful system for
such studies since there is no solubility gap. Understanding
the transport of these materials at low temperatures is com-
plicated by the coupling of charge, lattice, and spin degrees
of freedom. By moving to higher temperatures we can study
these materials without some of the complications of the spin
degrees of freedom. This simplifies the physics and may be
viewed as a first step towards understanding the manganites
as a whole, leaving an essential ingredient for colossal mag-
netoresistance for subsequent study. With this point of view
the present investigation is concerned with the high-
temperature resistance of thin films of La
1 -x
Ca
x
MnO
3
, with
0 x 1. We establish two main points: the high-
temperature conduction mechanism, and the existence of on-
site Coulomb repulsion.
Early investigations
1
of the resistivity of La
1 -x
Ca
x
MnO
3
,
noted that the resistivity increases roughly exponentially
with inverse temperature. More recently the exact nature of
the conduction mechanism has been ascribed to variable
range hopping,
2–4
semiconduction,
5
or small polarons.
6
Ohtaki et al. first showed that the resistivity of the composi-
tion La
0.1
Ca
0.9
MnO
3
fits the adiabatic small polaron model.
6
Evidence for small polarons in La
1 -x
Ca
x
MnO
3
has been re-
ported for only a few specific doping levels mostly x =
1
3
,
7
and only over a small temperature range around T
c
so nar-
row that it is not possible to discriminate between different
models in any convincing way.
8
However, by using a large
enough temperature range it is easily possible to discriminate
between different prefactors in the conductivity, as has been
done to show that variable range hopping and semiconduc-
tion do not agree with the experimental data for the compo-
sition La
0.67
Ca
0.33
MnO
3
.
7
In the present study, by extending
the temperature range from 300 to 1100 K, and the doping
range from x =0 to x =1, we show that the conductivity of
La
1 -x
Ca
x
MnO
3
has the temperature dependence predicted
by the Emin-Holstein theory of adiabatic small polarons
across the entire doping range. Recent work on the manga-
nites has shown qualitative evidence for small polarons.
Namely, there are lattice distortions present above T
c
that are
relaxed below T
c
, as expected for a polaronic state above
T
c
.
9–11
Also oxygen isotope exchange experiments have
demonstrated the existence of strong electron lattice
coupling.
12,13
While these qualitative measurements show
that the lattice distortions exist, they do not quantitatively fit
to a theory of small polarons. Furthermore, Seebeck
measurements
14
have suggested small polarons but are diffi-
cult to interpret since the available theory
15,16
for the behav-
ior of small polarons is only valid at inaccessibly high
temperatures.
16
For Chaikin and Beni’s generalization of the
Heikes formula to be valid the thermal energy must be much
larger than the energies associated with the kinetic energy of
the carriers.
16
Our resistivity measurements show that the
binding energy of the polarons is larger than 2000 K for
x =0.33. On the other hand, since the conductivity of adia-
batic small polarons is well understood theoretically,
17
con-
ductivity measurements are a straightforward and quantita-
tive way to discriminate between models.
If adiabatic small polaron hopping is responsible for con-
duction in La
1 -x
Ca
x
MnO
3
, then it should be possible to ob-
serve something new: the effect of on-site Coulomb repul-
sion in the conductivity. This is because each small polaron
is localized to within one unit cell of the lattice, and, in order
to minimize its Coulomb energy, will only hop into a vacant
site. Despite intensive investigation of the manganites, there
has been no indication of the expected behavior due to on-
site Coulomb repulsion, for arbitrary doping.
18–21
Further-
more, in other polaron systems the observation of on-site
Coulomb repulsion in the conductivity has not been possible
because of the complication of finding a system that can be
doped from zero to one polaron per site, and the difficulty of
making high-quality samples.
In this paper we show that the conductivity of
La
1 -x
Ca
x
MnO
3
has the temperature dependence predicted
PHYSICAL REVIEW B 15 JUNE 1998-II VOLUME 57, NUMBER 24
57 0163-1829/98/5724/152675/$15.00 15 267 © 1998 The American Physical Society