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1 Introduction to Magnetoresistance Phenomenology and Theory of Colossal Magnetoresistive Manganites 1.1 Introduction In recent years, the discovery of colossal magnetoresistance CMR p

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

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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

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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, ABO3 (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

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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

MR=[∆ρ ρ( )0,T ]=[ρ( ) (0,T −ρ H,T) ]/ρ( )0,T (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

(H , T

ρ ) ρ(0,T)

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

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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 Fe80B20) [14]

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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

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

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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

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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

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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

p ap

R

R

R −

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

R

R

, 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

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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

Spacer

Free FM Layer Hard Magnet Pinned FM Layer + Hard Magnet

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

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 L1-xMxMnO3 (L =

trivalent cations such as La3+; M = divalent cations such as Ca2+, Sr2+, 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 La0.67Ca0.33MnOx 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

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 = La3+, Y3+, Nd3+) at different compositions, x For

example, Xiong et al [23] have reported a colossal factor of ∆R/R(H) ∼ 7000% in

as-grown Nd0.7Sr0.33MnOδ 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 ABO3 (A2+ and/or A3+ 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 LaMnO3-CaMnO3, LaMnO3-SrMnO3, and LaMnO3

-BaMnO3 The end members of La3+Mn3+O32-, Ca2+Mn4+O32-, Sr2+Mn4+O32-, and

Ba2+Mn4+O32- are in the AFM and insulating state CaMnO3 forms a cubic perovskite

ABO3 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, LaMnO3 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 MnO6 octahedra in the perovskite structure, forming rhombohedral or

orthorhombic lattice as shown in figure 1 – 5

Such a lattice distortion of the ABO3 perovskite is governed by the so-called

tolerance factor f [25], which is defined as

(r B r o) (r A r o

Here, (i = A, B or O) represents the (averaged) ionic size of each element r i

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 BO2 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

LaMnO3-CaMnO3, LaMnO3-SrMnO3, and LaMnO3-BaMnO3 was reported More

detailed information about the magnetic structures of the La1-xCaxMnO3 compounds were

later determined by Wollan and Koehler [26] in 1955 using neutron scattering technique

as a function of Mn4+ 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 La3+Mn3+O3 end member contains

only Mn3+ 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 Ca2+Mn4+O3 is a G-type antiferromagnet, where the nearest Mn4+

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 Mn4+ 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

ferromagnetic moment with increasing Mn4+ content in the low Mn4+ 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-xCaxMnO3, (b) La

1-xSrxMnO3, (c) Nd1-xSrxMnO3, and (d) Pr1-xCaxMnO3 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-xCaxMnO3 phase diagram indicate the approximate boundaries between the different

ground states In the case of Nd1-xSrxMnO3, 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

A-type B-type C-type D-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]

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

1-xCaxMnO3, lower panel (b) La1-xSrxMnO3 (left), (c) Nd1-xSrxMnO3 (middle), and (d) Pr

1-xCaxMnO3 (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]

1.2.4.3 Electronic structure

The perovskite-structure oxides ABO3 with A = La3+ and a closed-shell ion with

B = Mn3+, Sc3+, or Sr3+ are transparent insulators When they are doped, the general

chemical formula becomes RE1-xAExBO3 (A = RE1-xAEx) Here RE refers to the trivalent

rare earth and AE refers to the divalent alkali earth cations Oxygen is in O2- state and the

relative fraction of Mn4+ and Mn3+ 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 AE2+

and/or RE3+ cations occupying the body centre and Mn4+ (3d3) and Mn3+ (3d4) occupying

all the corners of the cube The O2- is positioned at the midpoint of each edge as shown in

figure 1 – 9

Figure 1 – 9 The ideal, cubic perovskite structure, (RE/AE)MnO3 with an octahedrally

packed MnO6 structure sitting in the center of it represents the RE and/or AE cations

and it should be relatively comparable to the size of O2- ions are the oxygen anions

surrounding the smaller Mn3+ and/or Mn4+ cations represented by