Correlated polaron transport and metal-insulator transition in
La1−xSrxMnO3
N. B. Srivastava, L. N. Singh, and C. M. Srivastava
Citation: J. Appl. Phys. 105, 07D704 (2009); doi: 10.1063/1.3055283
View online: http://dx.doi.org/10.1063/1.3055283
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JOURNAL OF APPLIED PHYSICS 105, 07D704 共2009兲
Correlated polaron transport and metal-insulator transition in La1−xSrxMnO3
N. B. Srivastava,1,a兲 L. N. Singh,2 and C. M. Srivastava3
1
Department of Physics, R. Jhunjhunwala College, Ghatkopar, Mumbai 400 086, India
Department of Physics, Dr. Babasaheb Ambedkar Technological University, Lonere 402103, India
3
Department of Physics, Indian Institute of Technology, Powai, Mumbai 400 076, India
2
共Presented 12 November 2008; received 16 September 2008; accepted 3 October 2008;
published online 3 February 2009兲
The transport behavior of La1−xSrxMnO3 in the antiferromagnetic insulator, ferromagnetic insulator,
and ferromagnetic metallic phases is shown to follow from the correlated polaron mechanism and
a single transport equation accounts for the temperature dependence of resistivity for 0 艋 x
艋 0.40 in the 0 – 400 K range. In the low temperature range zero-point lattice vibration plays a
dominant role in the transport in the metallic phase. © 2009 American Institute of Physics.
关DOI: 10.1063/1.3055283兴
The phenomenon of metal-insulator transition and electronic phase diagram in doped manganese oxides
R1−xAxMnO3 共R = rare earth and A = Ca, Sr, Ba, and Pb兲 with
perovskite structure has not been satisfactorily explained despite extensive efforts.1,2 A recent review of the existing
models of the colossal magnetoresistance in manganites by
Ramakrishnan3 shows that the phenomenon is complicated
due to the interdependence of the electronic, structural, and
magnetic effects. The end member LaMnO3 is a charge
transfer insulator in which the gap transition corresponds to
O 2p → Mn 3d transfer. On hole doping in the eg band with
the divalent Sr atom, an antiferromagnetic insulating 共AFI兲
to ferromagnetic insulating 共FMI兲 transition occurs at xc1
= 0.08.4 On further increasing the hole concentration the
compound becomes a ferromagnetic metal 共FMM兲 at x
= 0.16 and continues to remain metallic until x = 0.6. The
resistivity curve ␳共T兲 in the AFI phase shows a monotonic
increase with a decrease in temperature, while the one in the
FMI region shows a discontinuity at the critical point Tc 共Fig.
1兲. A marked change in the ␳共T兲 curve occurs at the FMIFMM phase boundary, x = 0.16. At x = 0.15 there is a semiconducting type divergence as T → 0 with ␳共0兲 reaching
103 ⍀ cm, while for x = 0.175 there is a metal to insulator
transition near Tc after which ␳ decreases monotonically
reaching 10−3 ⍀ cm at T → 0 K. On further increase in x,
␳共0兲 decreases and is less than 100 ␮⍀ cm for x = 0.30
The crystallographic properties of La1−xSrxMnO3 change
with doping and are discussed in Ref. 5. The parent compound LaMnO3 is the Jahn–Teller distorted perovskite. On
doping the room temperature structure is orthorhombic for x
less than 0.16 and rhombohedral for larger x 共Fig. 2兲.
We show in this paper that the correlated polaron model
proposed by Srivastava6 gives a satisfactory account of the
changes in the resistivity curve with hole concentration. The
model is based on the Holstein Hamiltonian for a molecular
crystal in which a charge carrier is shared between two atoms. The treatment for small polaron transport follows
Reik.7 The Hamiltonian consists of free field Hamiltonians
a兲
Electronic mail: neetabគ[email protected].
0021-8979/2009/105共7兲/07D704/3/$25.00
+
for the polaron 共l+i , li兲 and the displaced phonon 共bq␭
, bq␭兲
and a small interaction term that describes the Frank–
Condon 共FC兲 transitions,
H = 兺 共␧i − ␧ p兲l+i li + 兺 共tijl+i l jXij + HC兲
i
ij
+兺
+
ប␻q␭bq␭
bq␭ ,
共1兲
q␭
where ␧i is the on-site energy of the eg electron, ␧ p is the
small polaron stabilization energy, tij is the transfer integral,
Xij describes the FC factor, and ␻q␭ is the phonon frequency
of wave vector q and polarization ␭. The dc conductivity is
given by
␴=
冑␲
2
n
冉冊 冉 冊 冉 冊
t
h
2
e 2a 2␶
1
␧p
sec h2
e−U/kBT .
k BT
2kBT
共2兲
Here n is the number of polarons, a is the separation between
the sites to which the electron hops, t = 具tij典, ␶ is the relaxation time, and U is the activation energy. In the correlated
polaron model that applies to a mixed valence compound8
3+
like La1−xSrxMn1−x
Mn4+
the valence exchange
x O3
FIG. 1. Variation in the resistivity with temperature in La1−xSrxMnO3, x
= 0.0, 0.05, 0.10, 0.15, 0.20, 0.30, and 0.40 共Ref. 4兲, compared to Eq. 共5兲
with parameters given in Table I. In all cases the Debye temperature ␪D is
425 K. Note that the metal-insulator transition occurs at Tc in the FMI and
FMM phases and is reproduced by theory.
105, 07D704-1
© 2009 American Institute of Physics
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07D704-2
J. Appl. Phys. 105, 07D704 共2009兲
Srivastava, Singh, and Srivastava
␺1 and ␺2 of a mixed valence metal ion M n+ / M p+ 共n ⫽ p兲 on
a linear chain, ␺1 = ¯ M n+M p+M n+M p+¯ and ␺2
= ¯ M p+M n+M p+M n+¯, through a longitudinal optic phonon
mode of frequency ␯ph discussed in Ref. 8 is
␴=
FIG. 2. Variation in the critical temperature Tc with strontium concentration
x in La1−xSrxMnO3 共0 艋 x 艋 0.4兲 from Ref. 4 is compared with Eq. 共6兲 共see
text兲. The room temperature crystallographic phase change from orthorhombic to rhombohedral coincides with the electronic FMI to FMM phase
change. PMI and PMM denote the paramagnetic insulator and paramagnetic
metal phases, respectively. TN denotes the Néel temperature of the antiferromagnetic insulator phase.
冉冊
t
= ␯ph关1 + c共1 − m2兲␴2a兴,
h
U = U0共1 − m
k
␳共T兲 =
共3b兲
m共tc兲 = M共T兲/M共Tc兲,
2
␴2a = 共1 − 0.75tca
兲,
共3c兲
tc = T/Tc ,
共3d兲
tca = T/Tca .
Here m is the reduced magnetization and is given by the
Brillioun function for spin Â1/2 , Tc is the Curie temperature
and ␴a is the atomic 共charge/orbital兲 order parameter. The
temperature Tca denotes the order-disorder crossover tem3+
Mn4+
perature of a binary alloy Mn1−x
x and is higher than the
6
curie temperature Tc. Here c and k are constants; c arises
from the low temperature spin wave excitations and k from
the critical point magnetic excitations near Tc.9
The physical basis of Eq. 共2兲 obtained for the correlated
polaron transport is as follows. The expression for conductivity that arises on coupling between two degenerate states
冋
␪D
A
共1 − f兲 cosh2共2␧ p/kB␪D兲
n
4
册
+ fT cosh2共␧ p/2kBT兲 关1 + c共1
− m2兲␴2a兴exp关U/kBT兴,
共3a兲
兲␴2a ,
共4兲
where n, a, and ␧ p are the same as in Eq. 共2兲. For m → 1 Eq.
共2兲 reduces to 共4兲 except for a small constant factor 冑␲. The
mobility in Eq. 共4兲 is given by the Einstein relation, ␮
= eD / kBT, with the diffusion constant D = a2␯ph. The other
temperature dependent sech ␰ term arises from the occupancy factor, electron polaron at lattice site i and hole at j. At
low temperature the electron-phonon coupling is through
zero-point lattice vibration and the resistivity is given by10
共Mn+4Mn3+ ↔ Mn+3Mn4+兲 takes place and the following relations hold6
␶−1 =
冉 冊 冉 冊
1
␲ 2 2
␧p
ne a ␯ph
sec h2
,
2
k BT
2kBT
共5兲
where A = 1.13kB / ne2a2␯ph, f = 关exp共␧ p / kBT兲 + 1兴−1, and ␪D is
the Debye temperature.
The resistivity curves for La1−xSrxMnO3 single crystal
with x = 0.0, 0.05, 0.10, 0.15, 0.175, 0.20, and 0.40 in Ref. 4
and for thin film with x = 0.16 in Ref. 11 are compared to Eq.
共5兲 with the parameters given in Table I. This is shown in
Fig. 1 for the single crystal data. The following conclusions
can be drawn. 共i兲 For AFI and FMI phases at low temperature
the behaviour of ␳共T兲 is similar to a semiconducting compound with a band gap Eg ⬃ U0 = 0.18 eV in the AFI phase
and 0.08 eV in the FMI phase. 共ii兲 In both the FMI and FMM
phases a metal 共⳵␳ / ⳵T ⬎ 0兲 to insulator 共⳵␳ / ⳵T ⬍ 0兲 transition occurs at Tc. This is well represented by Eq. 共5兲 共Fig. 1兲.
共iii兲 In the metallic phase the low temperature transport is
dominated by the zero-point lattice vibration so the residual
resistivity is small in the 0.10– 1 m⍀ cm range and is almost
independent of hole concentration. 共iv兲 In the metallic phase
the number of charge carrier per Mn atom n is large of the
TABLE I. The physical parameters obtained from the fit to Eq. 共5兲 to the temperature variation in the resistivity of La1−xSrxMnO3 共0 艋 x 艋 0.40兲 single crystal
data in Ref. 4 and to x = 0.16 thin film data in Ref. 11. The Debye temperature ␪D is 425 K in all cases. TN is from Ref. 4 and Tc is from best fit to Eq. 共5兲.
The electronic phases are from Ref. 4. AFI, FMI, and FMM denote the antiferromagnetic insulator, ferromagnetic insulator, and ferromagnetic metal phases,
respectively. n / x is the ratio of the carrier concentration data from Eq. 共5兲 and the nominal hole concentration from composition.
Compound
La共1−x兲SrxMnO3
x
0.0 共sc兲
0.05 共sc兲
0.10 共sc兲
0.15 共sc兲
0.175 共sc兲
0.20 共sc兲
0.30 共sc兲
0.40 共sc兲
0.16 共thin film兲
0.16 共thin film兲 H = 5 T
Phase
Tc / TN
共K兲
A/n
共⍀ cm K−1兲
n / Mn
Tca
共K兲
␧p
共K兲
Uo
共K兲
K
c
n/x
Ref.
AFI
AFI
FMI
FMI
FMM
FMM
FMM
FMM
FMM
FMM
143
139
150
240
284
310
369
371
278
305
4.88⫻ 10−4
2.4⫻ 10−5
5.2⫻ 10−4
5.98⫻ 10−5
4.89⫻ 10−6
8.46⫻ 10−6
2.32⫻ 10−6
1.49⫻ 10−6
3.78⫻ 10−6
2.86⫻ 10−6
0.0088
0.18
0.0082
0.071
0.872
0.504
1.83
2.86
1.13
1.49
¯
¯
425
425
950
865
1375
1400
500
500
¯
¯
300
545
280
150
140
100
100
130
2200
2300
950
545
700
625
550
400
550
550
¯
¯
¯
0.75
0.75
0.75
0.75
0.75
2.0
2.0
¯
¯
¯
1
2
2
2
2
2
2
¯
¯
0.08
0.5
5.0
2.5
6.1
7.15
7.0
7.0
4
4
4
4
4
4
4
4
11
11
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07D704-3
J. Appl. Phys. 105, 07D704 共2009兲
Srivastava, Singh, and Srivastava
order of 2 compared to the nominal hole concentration of
0.30–0.40 共Table I兲. This is similar to the Hall effect density
that is reported to be six to eight times the nominal hole
concentration.12 For good metallic samples, n / x is in the
range of 6–7; x = 0.30 and 0.40 for single crystal and 0.16 for
thin film 共Table I兲. 共v兲 The large n / x ratio occurs in the
rhombohedral crystallographic phase with its value dropping
in the orthorhombic phase 共Fig. 2兲.
A plot of Tc as a function of the hole concentration x is
given in Fig. 2. An expression for the critical temperature is
obtained by de Gennes13 assuming a superexchange contribution from localized states and a kinetic contribution from
itinerant states,
Tc = Tc共ex兲 + Tc共ki兲 = Tc共ex兲 + 52 ztx共1 − x兲.
共6兲
Here t is the transfer integral and is equal to h␯ph with ␯ph as
the frequency of the optic phonon mode to which the electron is coupled. In Eq. 共6兲 z is the number of Mn–O bonds. A
plot of Tc versus x from Eq. 共6兲 with Tc共ex兲 = 84 K, z = 6, and
t = 500 K is given and compared with experiment in Fig. 2.
The agreement is satisfactory. We conclude that the metalinsulator transition and the transport phenomenon in
La1−xSrxMnO3 in the range 共0 艋 x 艋 0.40兲 can be explained
on the correlated polaron model.
M. B. Salamon and M. Jaime, Rev. Mod. Phys. 73, 583 共2001兲.
See, e.g., C. N. R. Rao and B. Raveau, Colossal Magnetoresistance,
Charge Ordering and Related Properties of Manganese Oxides World Scientific, Singapore, 共1998兲, p. 14.
3
T. V. Ramakrishnan, J. Phys.: Condens. Matter 19, 125122 共2007兲.
4
A. Urushibara, Y. Moritomo, T. Arima, A. Asamitsu, G. Kido, and Y.
Tokura, Phys. Rev. B 51, 14103 共1995兲.
5
A. Asamitsu, Y. Moritomo, R. Kumai, Y. Tomioka, and Y. Tokura, Phys.
Rev. B 54, 1716 共1996兲.
6
C. M. Srivastava, J. Phys.: Condens. Matter 11, 4539 共1999兲.
7
H. G. Reik, in Polarons in Ionic Crystals and Polar Semiconductors,
edited by J. T. Dervee 共North-Holland, Amsterdam, 1972兲, pp. 679–714.
8
G. Srinivasan and C. M. Srivastava, Phys. Status Solidi B 103, 665 共1981兲;
The valence exchange and the correlated polaron model in mixed-valent
compound Fe3O4 was first introduced in this paper. It is used by G. Glitzer
and J. B. Goodenough, Struct. Bonding 共Berlin兲 61, 1 共1985兲 and for
manganites and high Tc superconductors by C. M. Srivastava, J. Magn.
Soc. Jpn. 22, 15 共1998兲.
9
K. Ghosh, C. Lobb, R. Greene, S. G. Karabashev, D. A. Shulyatev, A. A.
Arsenov, and Y. Mukovskii, Phys. Rev. Lett. 81, 4740 共1998兲.
10
Saket Asthana et al., Physica B 371, 241 共2006兲.
11
H. Ju and H. Lo, Appl. Phys. Lett. 65, 2108 共1994兲.
12
S. Chun, M. Salamon, and P. Han, J. Appl. Phys. 85, 5573 共1995兲.
13
P. G de Gennes, Phys. Rev. 188, 141 共1960兲.
1
2
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