A study on fe induced structural, magnetic and transport properties in colossal magnetoresistive nd0 67sr0 33mno3 polycrystalline bulk and films 1

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites



1

Introduction to Magnetoresistance Phenomenology and Theory of
Colossal Magnetoresistive Manganites




1.1 Introduction
In recent years, the discovery of colossal magnetoresistance (CMR) properties in
mixed valence manganites [1 - 3] has demonstrated for the second time after the break
through about high T
c
superconducting cuprates that oxides offer a very promising field
for the investigation of new materials with specific properties susceptible to be involved
in device applications. Magnetic systems of great potential are those with limited ability
to transport electricity in zero field, resulting from competing dissimilar ground states.
Giant magnetoresistance (GMR) multilayer metallic films show a relatively large
sensitivity to magnetic fields. The mechanism in these films is largely due to spin valve
effect between polarized metals. If an electron in a regular metal is forced to move across
spin-polarized metallic layers, it will suffer spin-dependent scattering. The observed
magnetoresistance (MR) is a few percent and has the very important advantage of not
being limited to low temperatures. Its giant magnetoresistive head proved to be an
improvement from the inductive read head and showed a clear advantage in read signal
amplitude. With the rapid development in the magnetic data storage industry spin valve
head with higher sensitivity was evolved. It has been used in the magnetic storage
industry for several years now. While the physical mechanism that produces the

magnetoresistance is well understood, the technological challenges involved in the
1

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites

production of small devices of high sensitivity are the bottleneck of an industry ever
hungry for smaller-faster-better sensors.
On the equally speculative note, it would seem that colossal magnetoresistive
material has a bright potential future in the world of magnetic recording industry.
Manganites are ideal compounds for magnetic sensor devices since the ground states are
metallic and semiconducting, respectively. It has been known and studied as long as 50
years ago (van Santen and Jonker, 1950) [4, 5], however a more recent development
involves the study of the unusually large effect an external field has on their ability to
transport electricity and heat. The energy scale of the phenomenon produces the most
interesting effects, such as the metal-insulator transition and the maximum sensitivity to
external field, at temperatures close to room temperature [6]. Manganites are prototypical
of correlated electron systems where spin, charge, and orbital degrees of freedom are at
play simultaneously. The rich solid state physics make these compounds unique in terms
of colossal magnetoresistance and also the potential applications as not only sensor
devices but also as solid electrolytes, catalysts, and novel electronic materials. Several
excellent review articles such as by Ramirez [7], Coey et al. [8], Tokura and Tomioka
[9], Rao et al. [10], Salamon and Jaime [11] and edited books by Rao and Raveau [12],
Tokura [13] are available in the literature now which discuss the properties of manganites
in detail.
We have organized this chapter into three main modules. The choice of material is
intended to provide the basic concepts of the various field of physics involved in the
manganites system. The first part examines the basic principle of various types of
magnetoresistance, MR with emphasize on the colossal magnetoresistive manganites. A
2

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites

simple introduction to the general description of various magnetoresistance phenomena,
following the chronological sequence of discovery will be reviewed. In the second part,
the basic concepts and underlying physical properties of manganites and the various
magnetoresistance phenomena, observed by state of art of experiments and interpreted
with modern theories are presented. We also introduce the subject with a brief historical
summary of the experimental results and theoretical developments since the discovery of
manganites in the early 1950s. This includes the correlation between crystal structure,
magnetic and transport properties in the systems. Special attention will be paid to the
“colossal magnetoresistive” material. The fundamental physical properties of the
perovskite-structure, ABO
3
(A = trivalent/divalent cations, B = cations) and the
underlying physics involved, observed by the state of art of experiments, will be
discussed. The concept of double exchange and the importance of Jahn-Teller coupling in
particular are presented. More recent research is then described, treating the variety of
ground states including ferromagnetic metals, orbital- and charge-ordered
antiferromagnets etc. that emerge as divalent atoms are substituted for trivalent rare earth
ions. Due to the scientific importance and potential applications in magnetic sensors for
storage devices and nonvolatile magnetic random access memory, the last section is
devoted to review the atypical magnetic, electrical transport and magnetoresistive
properties of the half-metallic ferromagnetic colossal magnetoresistive compounds. We
end the chapter with a summary and an outlook of the overall dissertation.



3

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites

1.2 Overview of the magnetoresistance (MR) phenomenology
Magnetoresistance (MR) refers to the relative change in electrical resistivity ρ of a
metal or semiconductor when placed in a magnetic field. It is generally defined by

() ()( )
[]
()
TTHTT ,0/,,0],0[ ρρρρρ−=∆=MR (1 – 1)
where and are the resistances or resistivities at a given temperature in
the presence and absence of a magnetic field, H, respectively. It can be positive or
negative depending on its definition. Generally, the MR effect depends on both the
strength of the magnetic field and the relative direction of the magnetization with respect
to the current. In this section, we will briefly review the mechanism involved in the four
distinct types of MR. They are the normal magnetoresistance (NMR), anisotropic
magnetoresistance (AMR), giant magnetoresistance (GMR) and colossal
magnetoresistance (CMR), the latter being the main focus of this dissertation.
(
TH,ρ
) )(
T,0ρ

1.2.1 Normal magnetoresistance (NMR)
Normal magnetoresistance (also known as ordinary magnetoresistance) refers to
the change in electrical resistance/resistivity of a metal or semiconductor when placed in
an applied magnetic field. The existence of this phenomenon was intuited by E. H. Hall
in 1879. However, Hall’s effort to determine the extra resistance was unsuccessful. It was
demonstrated that the NMR effect originated from the Lorentz force on the electron
trajectories in an applied magnetic field. Let us assume a simple classical one carrier
model (free electron theory). We consider the effect of field B acting on a conduction

electron having an average velocity v perpendicular to the applied magnetic field in a
sample. It experiences a force acting normal to both directions (v and B) and moves in
4

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites

response to this force and the force effected by the transverse electric field. We assume
that a constant current I flows along the x-axis from left to right in the presence of a z-
directed magnetic field. Electrons subject to the Lorentz force initially drift away from
the current line toward the negative y-axis, resulting in an excess surface electrical charge
on the side of the sample. This charge results in the Hall voltage cause by the transverse
electric field, a potential drop across the two sides of the sample. The accumulation of the
charge continues until the resulting transverse electric field becomes large enough to
cause a force that is equal and opposite to the magnetic field. Under equilibrium
conditions, the motion of the charge carriers is identical in the presence or absence of a
magnetic field. Therefore, no resultant magnetoresistance was observed because of this
transverse electric field.
However, in the two-band model and complex Fermi surface where both electrons
and holes are present, then all charge carriers do not have the same properties. When the
current flow is disturbed by the presence of a magnetic field, some of the charge carriers
are forced to travel a different path between the electrodes, which lead to more scattering
than in the absence of a field. Then a larger observed resistivity is expected. The
difference between the zero field resistivity and the measured resistivity under the applied
magnetic field is known as normal magnetoresistance. This magnetoresistance is always
positive and varies as B
2
. The magnitude of this type of magnetoresistance is usually
negligible (eg. 0.8% for Fe and ∼ 0% for Fe
80
B

20
) [14].



5

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites

1.2.2 Anisotropic magnetoresistance (AMR)
In contrast to the normal magnetoresistance, anisotropic magnetoresistance
(AMR) is only observed in ferromagnetic (FM) metal and alloys. AMR originates from
the spin-orbit interaction between the electron trajectory (orbit) and the magnetization
(spin) [15]. It depends on the relative orientations of the magnetization and the electric
current. When an external field is applied to the sample, the electron cloud about each
nucleus deforms slightly as the direction of the magnetization rotates. This deformation
changes the amount of scattering undergone by the conduction electrons when traversing
the lattice as shown in figure 1 – 1.




Ma
g
netic field
I
M
e
Ma
g

netic field
I
M
e

Figure 1 – 1 Schematic diagram demonstrating the physical origins of AMR. Shaded
yellow ovals represent the scattering cross-sections of bound electronic orbits. The
arrows (black) indicate the deflected conduction electrons when traversing the electronic
orbits.


The sample resistance is the greatest when the current, I flows parallel to the
magnetization, M. If the magnetization and current are oriented parallel to the external
field, then the electronic orbits are perpendicular to the current. The cross-section for
scattering is increased giving a high resistance. Conversely, if the magnetization and
current are oriented perpendicular to the external field, then the electronic orbits are in
6

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites

the plane of the current. The cross-section for scattering is decreased giving a low
resistance state.

1.2.3 Giant magnetoresistance (GMR)

Giant magnetoresistance (GMR) was originally discovered by Baibich et al. in
1988 in Fe/Cr multilayers [16]. Like other magnetoresistive effects, GMR is the change
in electrical resistance in response to an applied magnetic field. Contrary to NMR and
AMR, GMR arises from the dependence of the resistivity in layered and granular
magnetic structures on the local magnetic configuration. It was called “giant

magnetoresistance” or GMR because the observed magnetoresistive effect was found to
be much larger than either NMR or AMR. The underlying physics can be qualitatively
understood using Mott’s model, which was introduced as early as 1936 [17] to explain
the sudden increase in resistivity of FM metals as they are heated above room
temperature.
The GMR that is present in magnetic/nonmagnetic metal multilayers can easily be
explained by Mott’s argument as follows: First we consider the magnetizations in the
multilayer to be aligned collinearly as shown in figure 1 – 2.





Figure 1 - 2 Schematic illustration of electron transport in magnetic/nonmagnetic metal
multilayers for antiparallel (left) and parallel (right) magnetization of successive
ferromagnetic (dark green) and nonmagnetic (light green) metal layers.
Up
Down spin
Up Down spin
7

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites


The magnetic layers are antiferromagnetically coupled (or antiparallel) in the
absence of external field. The electrons with spin projections parallel and antiparallel to
the magnetization of the ferromagnetic layers will experience different scattering rates
when they enter the multilayer [18]. This is called spin-dependent scattering. Let us
assume that electrons with spin antiparallel to the magnetization are scattered strongly.
We shall see that in the antiparallel-aligned multilayer, the up-spin and down-spin

electrons are scattered strongly both in the first and second ferromagnetic layers. Hence
the total resistance of the multilayer in its antiferromagnetic configuration is high. When
a strong enough field is applied to align the magnetizations of the adjacent magnetic
layers as in the parallel-aligned magnetic layers case, the up-spin electrons will pass
through the structure with minimum scattering due to parallel arrangement of the spins
with the magnetization of the layers. On the contrary, the down-spin electrons are
scattered strongly within both ferromagnetic layers because their spins are antiparallel to
the magnetization of both layers. This is represented in figure 1 – 3 which shows the
resistance change as a function of applied magnetic field.
The same argument can also be used to explain the GMR observed in granular
materials. The magnetic moments of the ferromagnetic granules are randomly oriented in
the absence of a magnetic field. Both the up- and down-spin electrons are scattered
strongly by the granules. Thus the resistance will be large. When a saturating magnetic
field is applied, the magnetic moments are aligned and the resistance will be low.


8

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites


H
H
S

R
AP

R
P

R







Figure 1 – 3 Schematic representation of the GMR effect. The graph shows the change
in the resistance of the magnetic multilayer as a function of applied magnetic field. The
figure shows the magnetization configuration (indicated by the arrows in white) of the
trilayer at various magnetic fields. The magnetizations are aligned antiparallel at zero
field and parallel at an external field H larger than the saturation field H
s
.



Thus we can adopt the definition of ‘optimistic’ GMR ratio as the ratio of the
maximum difference in resistance over the minimum resistance:
GMR ratio
p
pap
R
RR −
≡ (1 – 2)
where is the resistance when the magnetizations are parallel and is the resistance
when the magnetizations are antiparallel. The optimistic GMR ratio is unbounded but the
‘pessimistic’ GMR ratio is

p
R
ap
R
ap
pap
R
RR −
, which is also in use, is never greater than 1. GMR
is always the property of a device consisting of alternating layers of different materials.
The discovery of GMR has created great excitement since this magnetoresistive effect
has important applications, particularly in magnetic information storage technology.
Magnetoresistive reading heads are commercially available and have since become the
leading technology beyond the year 1990 [19]. The highest published values of GMR to
9

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites

date are 220% in Fe/Cr multilayer [20] and 120% in Co/Cu multilayer [21]. From the
results published, it is crucial that a good matching of the multilayer is done since the
magnitude of GMR varies considerably depending on the chemical constituents of the
multilayer.


1.2.3.1 Spin Valve

Spin valve structure consists of uncoupled magnetic thin films which can be
switched from the antiparallel to parallel configuration. It was developed by Dieny et al.
[22] in order to overcome the large saturating fields required to rotate the magnetization
to the ferromagnetic configuration in GMR structure. For example, the saturation fields in

the Fe/Cr multilayer [16] are of the order 10 – 20 kG which is three orders of magnitude
higher than the field required for applications. The spin valve shown in figure 1 – 4 has
four layer structures consisting of a magnetically soft ferromagnetic (FM) layer (free
layer) and a second FM layer (pinned layer), which is exchange-coupled to an
antiferromagnetic (AFM) layer. The two thin magnetic films are separated by a non-
magnetic spacer.


Lead
Lead
Spacer
Free FM Layer
Hard Magnet Hard Magnet
Pinned FM Layer
+
NM Layer
NM Layer
AFM Pinning Layer
Figure 1 - 4 Schematic cross section of a spin valve GMR read head with exchange-
pinned layer and longitudinal hard bias. The nonmagnetic (NM) layer under the hard
magnet is for controlling the coercivity and thickness of the hard magnet.

10

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites


The lower film has its magnetization pinned in one orientation (by exchange
coupling to the pinning layer), while the upper magnetic layer (sense layer) is free to
switch back and forth (indicated by two headed black arrow) in the presence of a

magnetic field. The thickness of the non-magnetic spacer layer should be made large
enough to avoid negligible coupling between the two magnetic layers. Thus the field
dependence of the effect is low. The principle for lowering the resistance is the same as
in the GMR multilayer as mentioned in section 1.2.3. The spin dependent scattering gives
a low resistance state when the magnetic layers are ferromangetically aligned while a
high resistance state is obtained in the AFM configuration.




1.2.4 Colossal Magnetoresistance (CMR)
Colossal magnetoresistance has recently been discovered in L
1-
x
M
x
MnO
3
(L =
trivalent cations such as La
3+
; M = divalent cations such as Ca
2+
, Sr
2+
, etc.) perovskite
structures. Besides the raised expectations for the development of new generation
magnetic devices and sensors, perovskite manganese oxides (manganites) also provide an
ideal natural laboratory for studying the physics of strongly correlated electronic systems,
since they allow many basic interactions, such as the coupling between electrons and the

crystal lattice, to be varied at will. The term colossal arises from the huge MR effects
observed in the studies of thin films of La
0.67
Ca
0.33
MnO
x
with several orders of magnitude
larger than the typical GMR multilayer films. For example, an MR ratio as large as
127000% was discovered near 77 K in the La-Ca-Mn-O epitaxial films [3]. Here MR
11

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites

ratio is defined as ∆R/R(H) = (R(0)-R(H))/R(H), where R(0) and R(H) are the resistances
without and with a magnetic field H, respectively. Later similar CMR effect was found in
other perovskite manganites (L = La
3+
, Y
3+
, Nd
3+
) at different compositions, x. For
example, Xiong et al. [23] have reported a colossal factor of ∆R/R(H) ∼ 7000% in as-
grown Nd
0.7
Sr
0.33
MnO
δ

thin films. Its MR was so large that it could not be compared with
any other forms of magnetoresistance.
The following section reviews the basic crystalline structure, transport and
magnetic properties with reference to the ABO
3
(A
2+
and/or A
3+
cations and B cations)
perovskite manganites. After describing the electronic configuration and double exchange
interaction of Mn ions placed in the perovskite manganites, the magnetic and electronic
phase diagram when some of the A sites ions are substituted by second alkaline earth ions
is presented. We also highlight the intrinsic CMR regimes as dominated by the competing
phases in the manganites from the extrinsic MR by the grain boundary effects, with
published experiment results. We conclude this chapter with a summary and an
organization of this dissertation.

1.2.4.1 Crystalline Structure
Nearly half a century ago, Jonker and van Santen [5] discovered a striking
correlation between magnetic order and conductivity in a number of mixed oxides
containing manganese or cobalt. They have also successfully reported the existence of
ferromagnetism in mixed crystals of LaMnO
3
-CaMnO
3
, LaMnO
3
-SrMnO
3

, and LaMnO
3
-
BaMnO
3
. The end members of La
3+
Mn
3+
O
3
2-
, Ca
2+
Mn
4+
O
3
2-
, Sr
2+
Mn
4+
O
3
2-
, and
Ba
2+
Mn

4+
O
3
2-
are in the AFM and insulating state. CaMnO
3
forms a cubic perovskite
12

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites

ABO
3
structure with a lattice constant of 3.73 Å. Mn ions are six fold coordinated with
oxygen ions along the Cartesian axes: <100>, <010> and <001> directions, while Ca ions
are twelve fold coordinated with oxygen ions lying along its <110> directions. In other
words, the six oxygen ions form an octahedral cage for the Mn ions, with the cages linked
by the oxygen ions. However, LaMnO
3
was found to be in a strongly distorted
orthorhombic structure as reported by Elemans et al. [24]. In this structure, the O
octahedron rotates and distorts strongly. The Mn-O bond lengths, which are 1.97 Å in the
isovolume cubic perovskite structure, become 1.91, 1.96, and 2.18 Å. The distortion from
the cubic structure has been ascribed to the Jahn-Teller instability as the d
4
ion is
perturbed by the crystalline electrostatic field due to the oxygen anions during the
formation of MnO
6
octahedra in the perovskite structure, forming rhombohedral or

orthorhombic lattice as shown in figure 1 – 5.
Such a lattice distortion of the ABO
3
perovskite is governed by the so-called
tolerance factor f [25], which is defined as
()(
oAoB
rrrrf ++= 2/
)
(1 – 4)
Here,
(i = A, B or O) represents the (averaged) ionic size of each element.
i
r


13

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites


Figure 1 – 5 Schematic structures of distorted perovskites of manganites; orthorhombic
(left) and rhombohedral (right). Reproduced from Tokura et al. (1999) [9].


f measures, by definition, the lattice-matching of the sequential AO and BO
2
planes.
When f is close to 1, the cubic perovskite structure is realized. As or equivalent
decreases, the lattice structure transforms to the rhombohedral (0.96 < f < 1) and then to

the orthorhombic structure (f < 0.96), in which the B-O-B bond angle is bent and deviated
from 180°. When f varies, the bond angle θ changes accordingly as in the case of the
orthorhombic lattice as shown in figure 1 – 5. To facilitate the calculation of f, the
relevant ionic radii for ions in perovskite-structure oxides are listed in Apendix A at the
end of this dissertation.
A
r



1.2.4.2 Magnetic Structure
As mentioned earlier, the field of manganites started with the seminal paper of
Jonker and van Santen where the existence of ferromagnetism in mixed crystals of
LaMnO
3
-CaMnO
3
, LaMnO
3
-SrMnO
3
, and LaMnO
3
-BaMnO
3
was reported. More
detailed information about the magnetic structures of the La
1-
x
Ca

x
MnO
3
compounds were
14

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites

later determined by Wollan and Koehler [26] in 1955 using neutron scattering technique
as a function of Mn
4+
content. In their study, the neutron data revealed rich magnetic
phase diagram such as antiferromagnetic (AFM), ferromagnetic metal (FMM),
ferromagnetic insulator (FMI) and charge-ordered (CO) phases. The different types of
phases were found to contain nontrivial arrangements of charge at hole densities with the
different chemical doping level from 0 < x < 1. The La
3+
Mn
3+
O
3
end member contains
only Mn
3+
magnetic ions which arrange themselves in the A-type planar
antiferromagnetic structure at the Neel temperature T
N
= 140 K. The arrangement in the
a-b plane is ferromagnetic but the successive planes are coupled antiferromagnetically.
The end member of Ca

2+
Mn
4+
O
3
is a G-type antiferromagnet, where the nearest Mn
4+

spins always point to the opposite direction. For lightly doped region the spin state is the
mixture of the ferromagnetic and antiferromagnetic domains. As hole-doping level
increases, the ordered spins cant towards the c-axis direction, resulting in rich electronic
and magnetic phase diagrams. For example, the structure with x = 0.5 has mixture of the
C- and E-type magnetic unit cells and was labeled as the “CE-type” insulating state.
Figure 1 – 6 shows the seven possible spin arrangements A, B, C, D, E, F and G in the
unit cell with the spins of the relevance being those located in the manganese ions.
Thus, the change of magnetic structure with hole doping, x, reflects the great
dependence of the magnetic structure on the Mn
4+
concentration. Figure 1 – 7 shows the
ferromagnetic and antiferromagnetic moments as a function of sample ion composition.
The quantities obtained from the measured intensities refer to the individual ionic
moments pointing in different ways depending upon the structure and the particular
reflection (hkl) considered. It was evident from the figure that the growth of the effective
hkl
µ
15

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites

ferromagnetic moment with increasing Mn

4+
content in the low Mn
4+
percentage region
was less rapid than the line from 0 to x = 0.25. From the magnetization measurements,
the compounds with x ≈ 0.33 also give the moments with close approximation to the
expected spin-only value. The magnetic phase diagrams in the temperature (T) versus
hole concentration (x) for the prototypical compounds: (a) La
1-
x
Ca
x
MnO
3
, (b) La
1-
x
Sr
x
MnO
3
, (c) Nd
1-
x
Sr
x
MnO
3
, and (d) Pr
1-

x
Ca
x
MnO
3
are shown in figure 1- 8, taken from
Schiffer et al. (1995) and Tokura et al. (1999) [27, 9]. The hatched lines in the La
1-
x
Ca
x
MnO
3
phase diagram indicate the approximate boundaries between the different
ground states. In the case of Nd
1-
x
Sr
x
MnO
3
, the FM metallic phase shows up for 0.2 < x <
0.5, yet in the immediate vicinity of x = ½ the FM state transits into the charge-ordered
insulating (COI) state with COI transition temperature, T
CO
= 160 K. This COI state
accompanied by the AFM ordering of orbitals and spins is denoted as the CE-type state.

16

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites

A-type B-type C-type D-type
E-type F-type G-type

Figure 1 – 6 Possible magnetic structures and their labels. The circles represent the
position of Mn ions, and the sign that of their spin projections along the z-axis. The G-
type is the familiar antiferromagnetic arrangement in the three directions, while B is the
familiar ferromagnetic arrangement.



Figure 1 – 7 Ferromagnetic and antiferromagnetic moments as a function of sample ion
composition. Taken from [26].

17

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites



Figure 1 – 8 The magnetic as well as electronic phase diagrams of upper panel (a) La
1-
x
Ca

x
MnO
3
, lower panel (b) La
1-
x
Sr
x
MnO
3
(left), (c) Nd
1-
x
Sr
x
MnO
3
(middle), and (d) Pr
1-
x
Ca
x
MnO
3
(right). The PI, PM and CI denote the paramagnetic insulating, paramagnetic
metallic and spin-canted insulating states, respectively. The FI, FM and AFM denote the
ferromagnetic insulating, ferromagnetic metallic and antiferromagnetic metallic states,
respectively. The COI and CAFI denote the charge-ordered insulating and canted
antiferromagnetic insulating states, respectively. Taken from Schiffer et al. (1995) and
Tokura et al. (1999) [27, 9].

18

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites

1.2.4.3 Electronic structure
The perovskite-structure oxides ABO
3
with A = La
3+
and a closed-shell ion with
B = Mn
3+
, Sc
3+
, or Sr
3+
are transparent insulators. When they are doped, the general
chemical formula becomes RE
1-x
AE
x
BO
3
(A = RE
1-x
AE
x

). Here RE refers to the trivalent
rare earth and AE refers to the divalent alkali earth cations. Oxygen is in O
2-
state and the
relative fraction of Mn
4+
and Mn
3+
is regulated by “x”. The electronic structure of
manganese ions in B sites of the perovskite structure are coordinated by an octahedron of
oxygen neighbors. The system may be regarded as a cubic close-packed array with AE
2+

and/or RE
3+
cations occupying the body centre and Mn
4+
(3d
3
) and Mn
3+
(3d
4
) occupying
all the corners of the cube. The O
2-
is positioned at the midpoint of each edge as shown in
figure 1 – 9.

Figure 1 – 9 The ideal, cubic perovskite structure, (RE/AE)MnO
3
with an octahedrally
packed MnO
6
structure sitting in the center of it. represents the RE and/or AE cations
and it should be relatively comparable to the size of O
2-
ions. are the oxygen anions
surrounding the smaller Mn
3+
and/or Mn
4+
cations represented by .



19

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites

Isolated transition ion with partially filled 3d-shells has 5-fold degenerate orbitals.
When the transition metal (TM) ions are put into a crystal, in the case of RE
1-x
AE
x
MnO
3
,
the interelectronic correlations which give rise to Hund’s rules for the free ion are

perturbed by the crystalline electrostatic field due to the oxygen anions. The spherical
symmetry of an isolated ion is reduced and consequently some of the orbital degeneracy
is lifted. The 5-fold orbitally degenerate levels are split into three degenerate levels with
lower energy, t
2g
-levels (d
xy
, d
yz
, and d
zx
) and double degenerate levels forming the e
g
-
levels ( and ) with higher energy as shown in figure 1 – 10. This is called the
splitting of levels due to a crystal field (CF).
22
yx
d
−
22
yz
d
−




22
yz

d
−
22
yx
d
−
e
g


3d orbitals

d
xy

t
2g

d
yz
, d
zx


crystal-field
splitting
Jahn-Teller
distortion

Figure 1 – 10 The crystal-field splitting of five-fold degenerate atomic 3d levels into
lower t
2g
(triply degenerate) and higher e
g
(double degenerate) levels. Jahn-Teller
distortion of MnO
6
octahedron further lifts each degeneracy.



Therefore the five d-orbitals, each of which can accommodate one electron of
each spin, are split by the octahedral crystal field into a group of three t
2g

- orbitals (d
xy
,
20

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites

d
yz
and d
zx
) which have lobes oriented between the oxygen neighbors and a group of two
e
g

- orbitals ( and ) which are directed towards the oxygen neighbors. Figure 1 –
11 illustrates the orbital overlap in 2-dimensional plane of the perovskite structure as
mentioned above.
22
yx
d
−
2
z
d



O
Mn
Mn d
xy

O p
y

O
Mn d
y
2

Mn d
x
2

O p
x

Figure 1 – 11 Illustration of the orbital overlap in a plane of the perovskite structure. The
d
xy
orbital (a t
2g

– orbital) has little overlap with the 2p orbitals of the oxygen neighbors,
whereas
and orbitals (e
2
x
d
2
y
d
g
– orbitals) overlap strongly with the oxygen p
x
or p
y

orbitals.


The t
2g

– orbitals are lower in energy than the e
g
– orbitals because of the
electrostatic repulsion of electrons on neighboring sites and the crystal field splitting ∆
(≡ 10 Dq) between t
cf
2g

and e
g
orbitals is of order 1.5 eV. Manganese ions (which follows
Hund’s rule) are generally in the high-spin state. For example, the divalent ion Mn
2+
has
a very stable 3d
5
configuration with a half-filled shell t and S = 5/2. Trivalent
↑↑
23
2 gg
e
21

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites

manganese Mn
3+
ion has 3d
4
configuration with and S = 2, whereas

quadrivalent manganese Mn
↑↑
13
2 gg
et
↑
3
2g
t
4+
ion has 3d
3
configuration with and S = 3/2. The spin-
only moments of these ions are
5 and, respectively [8]. When the oxygen
octahedron distorts, the symmetry of the cubic crystal field is lowered in such a way that
the t
BB
µµ 4,
B
µ3
2g

levels and the e
g
levels are unchanged. However, Mn
2+
and Mn
4+
will not benefit

from such a distortion while Mn
3+
can lower its energy in proportion to the distortion.
Thus the marked tendency of d
4
ions is to distort their octahedral environment in order to
lower their energy. This is called the Jahn-Teller effect.
When some of the A sites ions are substituted by a small proportion, x, of divalent
cations as in case of RE
1-
x
AE
x
MnO
3
(RE = La
3+
and AE = Ca
2+
, Sr
2+
or Ba
2+
), we are
actually removing x electrons, i.e. creating x holes in the e
g
-band (or create x Mn
4+
(t )
ions). The proportion of Mn

3
2g
4+
increases and the material becomes ferromagnetic with a
well-defined Curie temperature at a finite x and metallic below T
c
. Jonker and van Santen
[5] have concluded that the compounds were neither ferromagnetism nor good electrical
conductors at the extreme end of x = 0 or 1. Only compounds with intermediate values of
x were ferromagnetic, with the strongest ferromagnetism occurring in the optimum range
of 0.2 < x < 0.4, which implies that the e
g
electrons play a role of conduction electrons
here. Such electrons in general can indeed move through the crystal. The basic concept
used to explain the appearance of ferromagnetism in these systems and its interplay with
the metallic conductivity is through the double exchange model, first developed by Zener
[28, 29], later put on firmer theoretical ground by Anderson and Hasegawa [30] and De
Gennes [31]. According to Zener’s double exchange mechanism, the basic process
involves the hopping of a d-electron, which we refer to as the Zener electrons, from one
22

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites

Mn site to another with spin memory. As shown in figure 1 – 12(a), the double-exchange
(DE) can be considered as the transfer of an electron from the Mn
3+
(d
4
,t , S = 2) site
to the central oxide ion and simultaneously the transfer of an electron from the oxide ion

to the Mn
13
2 gg
e
↓
3
3,
2
Mn
4+
site (d
3
, , S = 3/2) such as → where 1,
2, and 3 label electrons that belong either to the oxygen between manganese, or to the e
3
2g
t
+
↓↑
+
↑
4
3,2
3
1
MnOMn
+
↑
+
↑

1
4
OMn
g
-
level of the Mn ions. In this process there are two simultaneous motions (thus the name
double-exchange) involving electron 2 moving from the oxygen ion to the right Mn ion,
and electron 1 from left Mn ion to the oxygen ion. The system will be in the lowest
energy at low temperature provided the spins of the two adjacent cations are in the
parallel alignment.


e
g

Mn
3+
Mn
4+
O
2-

t
2g
Mn
4+
Mn
3+
O
2-

(a) (b)
Figure 1 – 12 (a) Sketch of the double exchange mechanism which involves two Mn ions
and one O ion. (b) The mobility of e
g
-electrons improves if the localized spins are
polarized.



If the manganese spins are not parallel or if the Mn-O-Mn bond is bent, the
electron transfer becomes difficult and their mobility decreases. Zener estimates the
23

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites

splitting of the degenerate levels to be given by the ferromagnetic transition temperature
and using classical argument, predicts the electrical conductivity to be as follows:
cB
Tk















=
T
T
ah
xe
c
2
σ
(1 – 3)
where x is the doping concentration and a is the Mn-Mn distance. Equation (1 – 3) agrees
with the Jonker and van Santen’s available experimental results in the limited region of
0.2 < x < 0.4.
An alternative way to visualize DE process was presented in detail by Anderson
and Hasegawa (1955) and it involves a second-order process in which the two states
described above go from one to the other using an intermediate state
. The
effective hopping for the electron to move from one Mn site to the next is proportional to
the square of the hopping involving the p-oxygen and d-manganese orbitals (t
+
↑↓
+
↑
3
23
3
1

MnOMn
pd
). In
addition, if the localized spins are considered classical and with an angle θ
ij
between
nearest-neighbor, then the effective hopping becomes proportional to cos(θ/2). The
effective hopping expression can be given as
2
cos
ij
effpd
ttt
θ
=→ (1 – 4)
where θ
ij
is the angle between spins of the sites i and j while t is the hopping matrix
element of the extra electron. For purely antiferromagnetic ordering θ
ij
= π and t 0,
then the hopping cancels. On the other hand, if the system is made ferromagnetic, θ
=
eff
ij
= 0
t, then hopping is the largest and the electrons can move freely. The quantum
version of this process has been described by Kubo and Ohata (1972) [32].
=
eff

t

24

Chapter One: An Overview and Theory of Colossal Magnetoresistive Manganites


1.2.4.4 Electrical transport properties
van Santen and Jonker [4, 5] have first reported the resistivity measurements on
ceramic samples of (La
1-
x
A
x
)MnO
3
(A = Ba, Ca or Sr) as a function of temperature, T and
compositions. They found striking correlation between the magnitude of the resistivity
and the magnetic state of the compounds. Most of these manganese perovskites are
paramagnetic insulators at ordinary temperatures and exhibit an increase in electrical
resistivity with a decrease in temperature. Compositions that are ferromagnetic show an
insulator-like behaviour above T
c
and a decrease in electrical resistivity as they are cooled
below T
c
. The insulator-to-metal (I-M) transition is identified as a maximum in the
resistivity and different compositions induces different insulator-to-metal transition
temperature, T
im

. The sharpness of the transition in polycrystalline samples and films is
often dependent on the purity of the samples.

A) Paramagnetic state with T > T
c

The temperature dependence of the resistivity, ρ, of the manganites in the
paramagnetic state generally show two types of behavior as seen in figure 1 – 8. The
manganites that are doped with large A-site cations radii <r
A
> such as Sr, Ba and Pb have
larger bandwidth. As a result the paramagnetic state can be metallic (PMM) or insulating
(PMI) with a small gap. However, for manganites with relatively smaller cations like Ca,
the bandwidth would be small and the paramagnetic phase is generally insulating (PMI).
Thus, whether the T > T
c
phase is PMM or PMI depend entirely on the bandwidth. In
order to investigate what gives rise to the different physical behavior above T
c
, three
25