Buschow K.H.J. (Ed.) Concise Encyclopedia of Magnetic and Superconducting Materials

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2.2 Multipole Magnets and Irregularly Magnetized

Permanent Magnets for Sensors

Traditionally an isotropic permanent magnet mate-

rial can be magnetized in a multipole pattern. In most

cases isotropic ferrite rings are magnetized in an n

pole pattern on the circumference with a multipole

coil supplied with a high current pulse of some mi-

croseconds. A large number of these magnets have

been substituted by polymer-bonded anisotropic

magnets. By injection molding of permanent magnet

powder in a polymer matrix it is possible to orientate

the powder particles during the injection process and

thus to form a magnet with multipole anisotropy.

These magnets are often magnetized due to the ori-

entating ﬁeld during the injection process. However,

a ﬁnal pulsed magnetic ﬁeld can improve the mag-

netization by about 5–10%.

As an example Fig. 6 shows a permanent magnet

magnetized on two radii in an irregular pattern for

switching two sensors. By numerical simulation it is

shown that the distance from the magnet to the sen-

sitive Hall element has to be o1.5 mm. This is not

due to the too low ﬁeld at a distance 41.5 mm but

due to the diffuse reﬂection of the magnetization

pattern at a larger distance.

See also: Permanent Magnet Assemblies

Bibliography

Adenot S, Yonnet J-P, Foggia A 1996 Angular position sensors

with permanent magnets. In: Proc 14th Int. Workshop on

Rare Earth Magnets and their Applications, Sao Paulo. World

Scientific, Singapore, pp. 624–31

Akoun G, Yonnet J P 1984 3D analytical calculation of the

forces exerted between two cuboidal magnets. IEEE Trans.

Magn. 20 1962–4

Gro

nefeld M 1990 Grundlagen und anwendungen von perma-

nentmagneten, kunststoffgebundene magnete. In: Fo

rster H,

Hanitsch R (eds.) Magnetische Werkstoffe. Verlag, Cologne,

Germany

Rauscher G, Radeloff C 1991 Large Barkhausen jump in com-

posite wires. IEEE Trans. Magn. 27, 5238–40

Roters H C 1941 Electromagnetic Devices. Wiley, New York,

p. 166

M. Gro

nefeld

Magnetfabrik Bonn GmbH, Bonn, Germany

Perovskites: Resistivity Behavior

Many compounds with perovskite structure are

dielectrics and the temperature dependence of the

resistivity r(T) is of no interest. However, there is

a large class of perovskite compounds in which a

metal–insulator transition (MIT) takes place. Such

perovskite compounds have the chemical formula

1x

, where Ln is a rare-earth atom and A is

a bivalent atom and B may be manganese, nickel,

cobalt, titanium, or vanadium. The MIT can occur as

a consequence of a change in the concentration of A

(especially for manganites Ln

1x

MnO

). In addi-

tion changes in temperature or an external magnetic

ﬁeld may also induce a metal–insulator transition. In

spite of the apparent similarity of the r(T) depend-

encies at the MIT, the underlying physical mecha-

nisms that cause these transitions for different

compounds are different. Following Imada et al.

(1998), we will divide these compounds into three

classes which exhibit a MIT controlled by:

(i) double exchange

(ii) bandwidth, and

(iii) band ﬁlling.

The crystal structure for all these compounds is a

distorted cubic one. However, the distortions can be

of various types and, therefore, they have a different

effect on the band structure. The usual distortions

have orthorhombic Pbnm or rhombohedral R3

C lat-

tice symmetry for the compounds in question, and the

unit cell of the perovskite lattice is shown at Fig. 1.

The substitution of a bivalent element A for Ln in

the compounds LnBO

leads to an increase in current

carriers (holes) and this has a direct effect on the

resistivity. Similarly, a deﬁciency (x)ofLninLn

1x

affects the resistivity; these compounds being

Figure 1

The ideal cubic perovskite structure, showing the AF

type A order for LaMnO

. In the actual structure the

oxygen octahedron is distorted by a combination of the

breathing mode (Q

), the basal-plane distortion mode

), and the octahedral stretching mode (Q

)in

addition to a small rotation of the octahedron.

1040

Perovskites: Resistivity Behavior

related to ionic conductors and their ionic mobility is

high at high temperatures. These deﬁciency com-

pounds can exist in a rather broad range of chemical

composition. In both cases a lattice distortion takes

place due to difference in size between Ln and A (or

vacancy) atoms.

The application of a magnetic ﬁeld can induce a

MIT or shift the temperature at which it occurs; such

changes can cause the resistivity of some manganite

compounds to decrease by several orders of magni-

tude. This effect was discovered in 1993 (von Helmot

et al. 1993, Jin et al. 1994) and was named the co-

lossal magnetoresistive effect (CMR). Figure 2 shows

the temperature dependence of the resistivity, r(T),

and magnetoresistance DR/R for a thin ﬁlm sample of

0.67

0.33

MnO

. The decrease in the resistance can

be as high as a ﬁeld of 1000 in a ﬁeld of 6 T at 200 K.

The physical properties of all compounds with per-

ovskite structure are very sensitive to the method of

preparation and the occurrence of defects.

The interest in these materials arises from the

prospect of their use in various electronic devices

controlled by magnetic ﬁeld, examples of which are

magnetic ﬁeld sensors and more specifically spin

transistors. These CMR materials have also been

found to have a large magneto-optical Faraday ef-

fect, and some new effects have been observed for

these materials in experiments with spin polarized

tunneling in superconductors.

1. Double Exchange System

1.1 Doped Rare-earth Manganites

The compounds Ln

1x

MnO

have rather complex

phase diagrams, and consequently different proper-

ties for different compositions. In compounds such as

1x

MnO

(A ¼Ca, Sr, Ba, Pb; 0.2oxo0.4) at

some temperature, T

, the MIT takes place even

without an external magnetic ﬁeld (Fig. 2 and 3). In

other compounds, such as Pr

0.7

0.3

MnO

the MIT

is induced by a magnetic ﬁeld (Fig. 4). In this instance

the change of r(T) is closely connected with a change

in the magnetic structure.

The maximum in r(T) is situated near the Curie

temperature, T

. In addition, r(T) and DR/R are also

sensitive to changes in the lattice parameter. Values

of DR/R for thin ﬁlms and ceramic polycrystalline

samples are found to be much larger than those ob-

served for the corresponding single crystal samples

with high sample quality. This is especially so in low

magnetic ﬁelds. It has been shown that in polycrystals

and thin ﬁlms, the main contribution to the magne-

toresistance in low magnetic ﬁelds derives from the

grain boundaries. A change in magnetic order often

results in a change of crystal structure in a com-

pound. A deformation of the crystal lattice in the

manganites can also be due to the Jahn-Teller (JT)

effect of Mn

3 þ

Due to the complexity of these compounds there

can be no exhaustive explanation of the CMR effects

in the manganites. These compounds belong to the

class of strongly correlated systems in which electro-

nic, magnetic, and lattice subsystems are intimately

Figure 3

Temperature dependence of resistivity for

1x

MnO

crystals. Arrows indicate the critical

temperature for the ferromagnetic phase transition.

Anomalies indicated by open triangles are due to the

structural transition (after Urushibara et al. 1995).

Figure 2

Temperature dependence of resistivity r,

magnetoresistance DR/R and magnetization M of the

thin ﬁlm La

0.67

0.33

MnO

sample (after Jin et al. 1994).

1041

Perovskites: Resistivity Behavior

linked. The presence of a strong isotopic effect can be

taken as evidence for the important role played by the

electron–phonon interaction. The main theories

adopted to explain the MIT and CMR effects in

manganites are based on the concept of double ex-

change and take account of the Jahn-Teller effect.

1.2 Double Exchange Model

The properties of the doped rare-earth manganites

were ﬁrst discussed by Zener (1951) using a model

based on double exchange. A more detailed consid-

eration of the model was made by Anderson and

Hasegawa (1955). The double exchange represents a

kind of indirect exchange between cations with their

charge states differing by one and linked through an

anion. In the case of the manganites the manganese

ions, Mn

3 þ

and Mn

4 þ

, interact through an O

2

(Fig. 5). The extra electron has an equal probability

of being at the ﬁrst or second Mn site.

That is, the conﬁgurations, Mn

3 þ

–O

2

–Mn

4 þ

and

4 þ

–O

2

–Mn

3 þ

, are equivalent and the ground

state of the system is degenerate. So between Mn

3 þ

and Mn

4 þ

ions a resonance bond exists resulting

from electron transfer. This in turn leads to an energy

lowering that depends on the mutual orientation of

the cation spins S1 and S2. As a consequence of this

degeneracy the spin of the transferred electron in the

lowest energy state must have the same orientation as

S1 and S2, and thus this indirect exchange is ferro-

magnetic. As was shown by Anderson and Hasegawa

(1955), the energy gain is 2b cos(Y/2), where Y is the

angle between S1 and S2 spins (Fig. 5), and b is ex-

pressed through the transfer integral from the ﬁrst to

the second manganese ion.

From the discussion above, it follows that if there

is a distribution of Mn

3 þ

and Mn

4 þ

ions within the

crystal, there can be electron transfer between these

ions and a tendency to orient their spins in a ferro-

magnetic (FM) manner; there will be a feedback be-

tween these processes. The FM ordering of the

compound leads to an increase in the conductivity,

and the application of an external magnetic ﬁeld

leads to an enhancement of FM ordering resulting in

an increase of the conductivity. In the case of

0.7

0.3

MnO

(Fig. 4), an antiferromagnetic com-

pound, an external magnetic ﬁeld results in a FM

state and produces a metal–insulator transition.

A detailed consideration (Millis et al. 1995) of the

role of double exchange in the manganites exhibiting

CMR has revealed that this model does not ade-

quately explain the behavior of the resistivity. Other

models have been proposed that take into account a

strong electron–phonon interaction that results in

polaron formation. In the report of Millis et al.

(1995) it was suggested that the cause for such po-

laron formation is splitting of outer level e

of Mn

3 þ

ion when static or dynamic Jahn-Teller lattice dis-

tortion takes place.

1.3 The Jahn-Teller Effect

The Jahn-Teller (JT) effect involves the partial re-

moval of the d-electron degeneracy for atoms in a

crystal ﬁeld, and results in reduction of symmetry of

the lattice. Since the ground state of the system has an

unstable orbital degeneracy, this degeneracy can be

removed by lowering of the self-symmetry when a

deformation of the surrounding of the ions occurs,

which in turn leads to a reduction in the crystal ﬁeld

energy and removal of the degeneracy.

In the case of the rare-earth manganites with per-

ovskite structure, manganese ions are surrounded by

an octahedron consisting of six oxygen ions (Fig. 1).

The Mn

3 þ

ion with electronic conﬁguration d

a ﬁeld with octahedral symmetry has a half-ﬁlled

low-lying threefold level t

) and a higher-lying

Figure 4

Temperature dependence of resistivity r for

0.7x

0.3

MnO

compound without and in

magnetic ﬁeld of 5 T (after Hwang et al. 1995).

Figure 5

Diagram of the double exchange model.

1042

Perovskites: Resistivity Behavior

twofold level e

containing one electron. Such a con-

ﬁguration is the effect of strong exchange coupling

where, according to the Hund’s rule, all spins are

oriented parallel. As a result of this, there is an ef-

fective hole in one of the orbitals of the cation which

results in stronger screening from both anions along

this orbital axis. Consequently, if the state d

y

2 is

unﬁlled, there is an elongation of the octahedron

along its axis (c4a). If, however, the state d

is un-

ﬁlled there is a distortion in the perpendicular direc-

tion (Fig. 1) and in this case coa. These distortions

involve the removal of the d-level degeneracy and a

reduction in the energy.

If a crystal contains a sufﬁcient number of JT ions,

then a co-operative ordering of the distorted polyhe-

drons may arise such that the crystal symmetry and

the energy is lowered. Such crystal distortions can

only take place at sufﬁciently low temperatures. As

the temperature increases the crystal undergoes a

phase transition at which the lattice symmetry makes

increase. For low concentration of JT ions and at

elevated temperatures a dynamical JT effect may oc-

cur. This consists of an interaction between the local

electron conﬁguration distortions and the lattice vi-

brations (phonons). As a result of this interaction the

local distortion can be removed, and the symmetry

surrounding the cation becomes cubic when averaged

over time. In the doped rare-earth manganites the

dynamical JT effect can occur due to the charge

transfer between Mn

3 þ

and Mn

4 þ

ions.

1.4 Bond Directions

The change of conductivity and MIT in the man-

ganites is also connected with orbital overlap. In the

interaction between two cations through the anion

(C-A-C), there is a weak overlap of cation orbitals,

and the anion fulﬁls a connecting function. This in-

teraction depends on the nature of the interacting

atoms, and is displayed in an anisotropy of the 3d

cation orbitals, the interaction depending on the dis-

tance between atoms and on the bond angle of C-A-

C. A correlation between the C-A-C bond angle and

the nature of the magnetic ordering has been ob-

served, and found to determine the metal–insulator

transition. For ferromagnetic compounds the C-A-C

angle is approximately 1801. Doping of a basic com-

pound by atoms with different size results in a change

of the C-A-C bond angle. They may have conse-

quences for the MIT.

1.5 The Role of Inhomogeneity

Also, it has also been demonstrated that structural

and chemical inhomogeneities play an important

role, and this becomes very important when the con-

centration, x, of a doped element A is small.

It was suggested by Gor’kov (1998) that Cou-

lombic forces result in holes becoming localized near

dopants, which makes the formation of conducting

clusters along these charged centers a major factor in

resistivity behavior of manganites. A charge transfer

in the cluster is possible due to the double exchange

and the localization is due to the JT effect. This is

demonstrated in the data for La

1x

MnO

(Fig. 3),

where the transition between two kinds of r(T) de-

pendence occurs at xB0.16. This corresponds to a

percolation threshold for a three-dimensional system

of random conducting links. Thus the FM phase

and metallic-like conductivity arise in percolating

clusters which develop when the dopant concentra-

tion increases.

1.6 Resistivity Behavior in the Metallic Region

For manganites compounds that undergo the MIT in

a particular concentration range, for example for

0.2oxo0.4 in the La

1x

MnO

system (Urushibara

et al. 1995) or for La

0.67

(Pb,Ca)

0.33

MnO

compound

(Jaime et al. 1998), the resistivity can be described by

r(T) ¼r

þAT

in a fairly wide temperature range

(from 10 K to 200 K, Fig. 6). The nature of such re-

sistivity behavior remains unclear, due mainly to the

lack of detailed experiments performed on good qua-

lity, single crystal samples. Several mechanisms may

be held responsible for the T

-dependence.

Amongst these are electron–electron scattering,

electron–magnon scattering, and a peculiar electron–

Figure 6

Temperature dependence of resistivity in the low-

temperature region (To200 K) for La

1x

CoO

crystals. The T

dependence of resistivity was observed.

Inset: shows the coefﬁcient A against the nominal hole

concentration x. (after Urushibara et al. 1995).

1043

Perovskites: Resistivity Behavior

phonon interaction due to specific features of the

Fermi surface. It has been shown (Jaime et al. 1998)

that the Kadowaki–Woods relation, A ¼Cg

, where g

is the coefﬁcient of the electronic specific heat and C

a universal constant, C ¼10

5

mO cm (molKmJ

1

)

,is

not fulﬁlled in these compounds. This relation pro-

vides an anomalously large value that rules out the

electron–electron scattering mechanism. In addition

the AT

value for 200 K is more than ten times great-

er than the r

value, being as high as B5 mO cm for

the best samples. Therefore any reliable method de-

termining the scattering mechanisms remains absent

at the present time.

2. Bandwidth-controlled MIT Systems

2.1 Ln

1x

NiO

The compounds, LnNiO

, exist for all lanthanide el-

ements and have pseudocubic perovskite structure,

which is rhombohedral R3

C for LaNiO

and ortho-

rhombic Pbnm for the other rare earths (Medarde

1997). The temperature dependence of r(T) for La-

NiO

may be described as metallic (dr/dT40) in the

temperature range T ¼0.4–300 K (Gayathri et al.

1999), but other compounds experience a MIT at a

certain T

M-I

and r(T) exhibits semiconductor behav-

iour (dr/dTo0) (Fig. 7). The evolution of T

M-I

along

the compound series can be correlated with the de-

gree of deviation of each compound from the ideal

perovskite structure, which increases as lanthanum is

replaced by the smaller-size rare earth ions.

The metal–insulator transition occurs close to an

antiferromagnetic transition, and the formation of

ordered spin structures is attributed to the formation

of an orbital superlattice. However, in spite of there

being nominally one electron in the e

orbital, as in

LaMnO

, no evidence for Jahn-Teller distortion has

been found. The 3-D magnetic ordering consists of

alternating converted bilayers AA(AA)AA(AA) y

along the [001] direction, with AA and (AA) repre-

senting the magnetic arrangement of nickel moments

in adjacent (001) planes. The coexistence of F and AF

interactions, which is revealed in the ordered spin

structure, suggests the existence of an orbital super-

lattice such as the regular occupation of either d

y

or d

r

2 type orbitals.

The relevant parameter controlling the transition

at T

M-I

and the Ne

el temperature, T

, as well as the

stability of different crystallographic structures found

along the compound series is the Ni-O-Ni super-

exchange bond angle Y. The insulating state of

LnNiO

should be classiﬁed as a charge-transfer in-

sulator, i.e., the MIT takes place due to the opening

of a charge-transfer type gap below T

M-I

. The high

valency of the Ni

3 þ

ions in LnNiO

makes its charge

transfer energy D as small as B1 eV and stabilizes its

low-spin conﬁguration t

2gm

2gk

. In this system the

ground state has a strong mixture of d

, d

L, and

conﬁgurations, resulting in a net d-electron

number as large as n

¼7.8. The nickel magnetic mo-

ment is found to be B0.91 m

, close to the ionic value

of 1 m

, and this is a result of the charge transfer

which occurs from O 2p orbitals to e

and e

or-

bitals in Ni

3 þ

. One electron is involved in the

hybridization between the t

and e

orbitals on the

mean ﬁeld level, so there is no pair-transfer contri-

bution in the high-spin Ni

3 þ

ion because the spin is

fully polarized (Imada et al. 1998).

For LaNiO

3x

compounds the r(T) behavior

changes with x increasing, and as the number of

vacancies increases r(T) may be approximated by

exp(T

1/4

). This is in accord with the Mott

dependence for disordered systems with random

thermally activated hopping, and B exp(Q/T) for

the ordered vacancies state ( x ¼0.5) (Sanchesz et al.

1996).

For a small oxygen deﬁciency, x, the resistivity

r(T) shows a power-law dependence r(T) ¼r

þaT

1.5

þbf(T), where f(T) is a function leading to a linear

temperature dependence at high temperature

(T4200 K) and to a T

-dependence (n42) at low

temperatures. r

is the residual resistivity and a and b

are constants (Gayathri et al. 1999). The T

1.5

term

implies that the power-law exponent is greater than

unity even at the highest temperatures. Such a strong

dependence can arise from scattering involving opti-

cal phonons in the system. The most metallic sample

has a clear positive magnetoresistance (MR) which

progressively becomes negative as the oxygen deﬁ-

ciency increases. The positive MR may arise from a

band-like contribution, whilst the negative MR, ob-

served for the oxygen-deﬁcient samples, arises from

the weak-localization contribution and is not due to

any magnetic interactions.

Figure 7

Temperature dependence of electrical resistance for

LaNiO

, PrNiO

, NdNiO

, SmNiO

compounds

showing their metal–insulator transitions (after

Medarde 1997).

1044

Perovskites: Resistivity Behavior

3. Filling-controlled MIT Systems

3.1 Ln

1x

TiO

The compound LnTiO

is a typical Mott–Hubbard

insulator with Ti

3 þ

in a d

conﬁguration, and the A

content, x, represents the nominal ‘‘hole’’ concentra-

tion per titanium site or equivalently the 3d band

ﬁlling (n) is given by n ¼1x. The crystalline struc-

ture is an orthorhombically distorted perovskite. The

Ti-O-Ti bond angle distortion, which affects the

transfer energy (t) of the 3d electron or the one elec-

tron bandwidth (W), depends critically on the ionic

radii (Ln, A) or on the tolerance factor. With de-

creasing size of the Ln ion, LnTiO

changes from an

antiferromagnetic (AFM) insulator (LaTiO

)toa

ferromagnetic (FM) insulator (YTiO

). The t

conﬁguration in the nearly cubic LaTiO

is in the

quadruply degenerate spin-orbit ground state.

This develops into two states with have anti-

parallel orbital and spin moments (both directed

in the [111] direction) and alternating between near-

est neighbors, which results in this G-type AFM

state. An increase in the distortion induces greater

hybridization between neighboring xy, yz, and zx

orbitals, leading to an enhancement of the AFM

orbital exchange as well as the FM exchange. This

enhancement derives from Hund’s rule coupling

(Imada et al. 1998). The magnetic ordering favors

the Jahn-Teller distortion, and the t

level is split

into two low-lying levels and one higher level. At each

site one of the two lower orbitals is occupied so that

the neighboring orbitals are approximately or-

thogonal to each other with their spins FM aligned.

Filling control in the 3d band can be achieved by

partially replacing the trivalent ions with divalent

calcium or strontium ions. In Fig. 8 the temperature

dependencies of the resistivity r(T) for CeTiO

3 þy/2

and Ce

1x

TiO

are shown. For CeTiO

3 þy/2

, which

has a relatively weak electron correlation, only a

small amount of hole doping is sufﬁcient to destroy

the AFM state and cause the MIT. The compound

1x

TiO

(0.04oxo0.4) is similar to La

1x

TiO

, and r(T) manifests metallic behavior which can

be modeled over a wide temperature interval by

r(T) ¼r

þAT

is a residual resistivity and A is a

constant) (Fig. 9). This T

dependence of the resis-

tivity is reminiscent of the dominant electron–elec-

tron scattering process, and the Kadowaki–Woods

relation A ¼Cg

is fulﬁlled for these compounds. It

must be noted that the model holds for rather

high temperatures (up to 300 K). The coefﬁcient A

becomes enhanced as the Mott–Hubbard insulator

state is approached from the metallic side.

Figure 8

Temperature dependence of electrical resistivity, r, of (a) Ce

1x

TiO

and (b) CeTiO

3 þy/2

(after Onoda and

Yasumoto 1997).

1045

Perovskites: Resistivity Behavior

3.2 Ln

1x

The parent compound LnVO

has a tetragonal struc-

ture for Ln ¼La, Ce and perovskite structure, with

an orthorhombic distortion for the other lanthanides.

LnVO

is a typical Mott–Hubbard insulator and un-

dergoes an AFM transition at temperatures between

120 K and 150 K. The AFM phase is accompanied by

a spin canting, giving rise to a weak ferromagnetic

component.

With hole doping by partial substitution of diva-

lent ions for rare earth ions, the insulating AFM

phase is suppressed. In Fig. 10 one can see that r(T)

changes from activation type to metallic-like be-

havior for x40.2. With hole doping, the charge-

transfer gap shifts to a lower energy mainly due to the

shift in the 2p band, and the Mott–Hubbard gap is

closed. In the metallic region r(T) (Fig. 11) can be

well expressed by the relation r(T) ¼r

þAT

1.5

. The

1.5

dependence of the resistivity can be interpreted in

terms of the strong Curie-like enhancement of the

spin susceptibility due to strong antiferromagnetic

spin ﬂuctuations (Inaba et al. 1995).

3.3 Ln

1x

CoO

The ground state of LaCoO

is a nonmagnetic insu-

lator and the predominant conﬁguration of the d-

electrons is 3 d

for Co

3 þ

which fully occupy the t

level resulting from crystal ﬁeld splitting (10 Dq); this

slightly exceeds the Hund’s rule coupling energy.

With an increase of the temperature the compounds

undergo a spin-state transition from a nonmagnetic

, S ¼0) to a paramagnetic state ( t

, S ¼1or

, S ¼2). A small amount of hole doping gives

rise not only to a decrease in resistivity but also to a

large change of magnetic susceptibility (Imada et al.

1998). A hole, with O 2p-state character, causes a

Figure 10

Temperature dependence of resistivity, r in

1x

(after Inaba et al. 1995).

Figure 9

Temperature dependence of resistivity, r,in

1x

TiO

; r, is plotted vs. T

. The inset shows r vs.

T plots in the nonmetallic x ¼1 (La

TiO

) and metallic

x ¼0.95 samples (after Tokura et al. 1993).

Figure 11

Temperature dependence of resistivity, r, of samples of

1x

near the metal–insulator phase boundary;

r is plotted vs. T

1.5

. (after Inaba et al. 1995).

1046

Perovskites: Resistivity Behavior

local spin-state transition (low spin to intermediate

spin) over 10–16 cobalt sites around deriving from

strong 2ps3de

hybridization. Such a large spin po-

laron is a precursor state for the FM metallic state in

1x

CoO

(x40.2).

The resistivity r(T) decreases with increasing x and

the behavior of r(T) changes abruptly around the

composition x ¼0.2 (Fig. 12). The resistivity for

xo0.2 follows the dependence r(T) ¼r

exp[(T

/T)

where n ¼S. This is the signature of variable range

hopping in the presence of a Coulomb gap within the

density of states, and it seems to be a consequence of

the cluster nature of the magnetic spins. In com-

pounds with x40.2, the FM as well as the metallic

behavior is related to the formation of Co

4 þ

ions

following from Sr

2 þ

substitution. The macroscopic

metallic state is formed through percolation. As the

temperature is reduced to below approximately

100 K, the spin-state transition will drive most of

the Co

3 þ

ions into the low-spin state, thus gradually

localizing the carriers in the FM clusters (Fig. 13).

Metallic cobaltite compounds show negative mag-

netoresistance (MR), the highest value of MR is ob-

served close to T

. The value of the MR is much

Figure 12

Temperature dependence of resistivity, r,in

1x

CoO

with various doping levels. Triangles

represent the FM transition temperature (after Imada

et al. 1998).

Figure 13

Temperature dependence of resistivity, r, in zero ﬁeld (0 T) and in the ﬁeld of 6 teslas (6 T) for La

1x

CoO

compounds (after Mahendiran and Raychaudhuri 1996).

1047

Perovskites: Resistivity Behavior

smaller than that observed for the manganites. The

negative MR derives from suppression of spin-disor-

der scattering due to the application of an external

magnetic ﬁeld. The spin-ﬂuctuation scattering is

strongest near T

and the negative MR also is at a

maximum. In conclusion La

1x

CoO

is described

as a ﬁlling-controlled system since the doped holes

not only act as metallic carriers but also induce a

ferromagnetic moment.

4. Summary

The resistivity behavior of the compounds with per-

ovskite structure show similar features in spite of

different mechanisms. The presence of Jahn-Teller

ions involves a structural distortion that leads to

band splitting. Magnetic interactions also play a very

important role, and these compounds are strongly-

correlated systems in which electron, lattice, and

magnetic degrees of freedom act together to deter-

mine their physical properties including resistivity.

The peculiarities of the resistivity behavior depend

not only on a specific physical mechanism but also on

the sample quality. A detailed study of these com-

pounds demands fabrication of samples with perfect

structure in order to separate properties intrinsic to

the compound from properties associated with the

preparation conditions and various defects.

See also: Colossal Magnetoresistance Effects: The

case of Charge-ordered Pr

0.5

MnO

Manganite

Thin Films; Giant Magnetoresistance; Magnetore-

sistance: Magnetic and Nonmagnetic Intermetallics;

Magnetoresistance in Transition Metal Oxides; Tran-

sition Metal Oxides: Magnetism

Bibliography

Anderson P W, Hasegawa H 1955 Consideration of double

exchange. Phys. Rev. 100, 675–81

Gayathri N, Raychaudhuri A K, Xu X Q, Peng J L, Greene R

L 1999 Magnetoresistance of the metallic perovskite oxide

LaNiO

3d

. J. Phys. Condens. Matter 11, 2901–7

Gor’kov L P 1998 Lattice and magnetic effects in doped man-

ganites. Uspehi Fizicheskih Nauk (Russia) 168, 665–71

Hwang H Y, Cheong S W, Radaelli P G, Marezio M, Batlogg B

1995 Lattice effects on the magnetoresistance in doped

LaMnO

. Phys. Rev. Lett. 75, 914–7

Imada M, Fujimori A, Tokura Y 1998 Metal-insulator tran-

sitions. Rev. Mod. Phys. 70, 1039–263

Inaba F, Arima T, Ishikawa T, Katsufuji T, Tokura Y 1995

Change of electronic properties on the doping-induced

insulator-metal transition in La

1x

. Phys. Rev. B 52,

R2221–4

Jaime M, Lin M, Salamon N B, Han P D 1998 Low-temper-

ature electrical transport and double exchange in La

0.67

(Pb,Ca)

0.33

MnO

. Phys. Rev. B 58, R5801–4

Jin S, Tiefel T H, McCormack M, Fastnacht R A, Ramesh R,

Chen L H 1994 Thousand-fold change in resistivity in mag-

netoresistance La-Ca-Mn-O ﬁlms. Science 264, 413–5

Mahendiran R, Raychaudhuri A K 1996 Magnetoresistance of

the spin-state-transition compound La

1x

CoO

. Phys.

Rev. B 54, 16044–52

Medarde M 1997 Structural, magnetic and electronic properties

of RNiO

perovskites (R ¼rare earth). J. Phys. Condens.

Matter 9, 1679–707

Millis A J, Littlewood P B, Shraiman B I 1995 Double ex-

change alone does not explain the resistivity of La

1x

CoO

. Phys. Rev. Lett. 74, 5144–7

Onoda M, Yasumoto M 1997 Electronic states of perovskite-

type Ce

1x

TiO

and CeTiO

3 þ y /2

systems with a metal-

insulator transition. J. Phys. Condens. Matter 9, 5623–34

Sanchesz R D, Causa M T, Caneiro A, Butera A, Vallet-Regi

M, Sayagues M J, Gonzalez-Calbert J, Garcia-Sanz F,

Rivas J 1996 Metal–insulator transition in oxygen-deﬁcient

LaNiO

3–x

perovskites. Phys. Rev. B 54, 16574–8

Tokura Y, Taguchi Y, Okada Y, Arima T, Kumagai T, Iye Y

1993 Filling dependence of electronic properties on the verge

of metal—Mott-insulator transitions in of Sr

1x

TiO

Phys. Rev. Lett. 70, 2126–9

Urushibara U, Moritomo U, Arima T, Asamitsu A, Kido G,

Tokura Y 1995 Insulator–metal transition and giant magne-

toresistance in La

1x

CoO

. Phys. Rev. B 51, 14103–9

Von Helmot R, Wecker J, Holzapfel B, Schulz L, Samwer K

1993 Giant negative magnetoresistance in perovskitelike

2/3

1/3

MnO

ferromagnetic ﬁlms. Phys. Rev. Lett. 71,

2331–3

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perovskite structure. Phys. Rev. 82, 403–5

Y. M. Mukovskii

Moscow State Steel and Alloys Institute

Moscow, Russia

Perturbed Angul ar Correlations (PAC)

Among the numerous experimental techniques avail-

able for studying solids, techniques focused on hyper-

ﬁne interactions form a subclass that probes a material

at the smallest possible length scale. After an out-

line of the basic principles of hyperﬁne interactions,

the perturbed angular correlation (PAC) method is

described and compared with the widely used

ssbauer technique (Cahn and Lifshin 1993). Par-

ticular attention is paid to information that can be

obtained from PAC experiments. The extended appli-

cability of the method enabled by employing advanced

ab initio theories is also discussed. Finally, a PAC

study of Fe/Cr multilayers is given as an example.

1. Hyperﬁne Interactions

The simplest nonrelativistic quantum mechanical in-

terpretation of an atom is based on an inﬁnitely

massive and point-like nucleus, and ignoring inter-

actions between electrons. This leads to the well-

known hydrogen-like electron energy levels, with a

1048

Perturbed Angular Correlation s (PAC)

characteristic separation of a few electron volts. In-

cluding electron–electron interactions and relativistic

effects produce both a shift and degeneracy lifting of

these levels on a millielectron volt scale. The resulting

energy level scheme is called the ﬁne structure. An

even more subtle correction to these levels—the

hyperﬁne structure—stems from the nucleus not be-

ing point-like. Deviation from a point can occur both

in real space and in spin space.

In the former case, the simplest nontrivial example

is a description of the charge density within the nu-

cleus as a deformed sphere (prolate or oblate), which

can be characterized by the nuclear quadrupole mo-

ment, Q. In spin space, the smallest deviation from a

point is described by the nuclear magnetic dipole

moment, m. The interaction of both nuclear moments

Q and m with the surrounding electrons leads to a

hyperﬁne structure in the electron energy levels, on a

scale of 10

12

eV. As we are dealing here with an in-

teraction, exactly the same hyperﬁne structure will

occur both in the electronic and in the nuclear energy

levels. The PAC technique is based on the hyperﬁne

structure of nuclear energy levels.

The hyperﬁne interaction operates over a very

short range. It is determined by the nuclear wave

functions—which are only nonzero inside and close

to the nucleus—and the tails of the (valence) electron

wave functions that reach the nucleus. As a conse-

quence, bonding effects on the valence electrons

caused by the atom being contained in a molecule,

liquid, or solid are transferred to the nuclear hyper-

ﬁne structure. Hence, measurements of a hyperﬁne

structure provide information on the chemical envi-

ronment of a particular atom. For research in mag-

netism, the interaction of the nuclear magnetic

moment with the magnetic ﬁeld due to surrounding

electron spins is important.

This interaction is mainly given by the Fermi con-

tact term, which describes a nucleus embedded in a

homogeneous magnetic medium due to the net s

electron spin density, m(0), at the nucleus (in a rel-

ativistic approach p electrons can also penetrate the

nucleus). The magnetic ﬁeld generated this way at a

nucleus is called the magnetic hyperﬁne ﬁeld, B

, and

is given by:

mð0Þð1Þ

where m

is the permeability of vacuum and m

the

Bohr magneton. The splitting of nuclear energy levels

is related to B

by:

ð2Þ

where m is the magnetic dipole moment of the nu-

cleus and I its spin quantum number. Apart from

the Fermi contact term, other (and usually smaller)

contributions to the hyperﬁne ﬁeld originate in or-

bital and spin motion of electrons.

2. Measuring Hyperﬁne Interactions by PAC

Several experimental techniques based on different

principles are available to measure the magnetic

hyperﬁne interaction. In Mo

ssbauer spectroscopy

(MS) recoilless emission and absorption of a Dop-

pler-shifted g-ray by a radioactive nucleus is exploit-

ed. Time differential perturbed angular correlation

(TDPAC or PAC) spectroscopy uses the reorienta-

tion of an oriented ensemble of nuclei under the in-

ﬂuence of a hyperﬁne ﬁeld (Schatz and Weidinger

1996, Catchen 1995). It needs a radioactive nucleus

with a subsequent emission of two g-rays in its decay

scheme. Nuclei emit g-rays preferentially along their

spin direction. Hence, detecting the ﬁrst of the two

g-rays by a ﬁxed detector selects an ensemble of nuclei

with their spin oriented preferentially along this

detector axis.

If a hyperﬁne ﬁeld is present, the hyperﬁne-split

nuclear Zeeman levels are repopulated by the hyper-

ﬁne interaction. This repopulation is equivalent to a

reorientation of the nuclear spin, an effect which in a

semiclassical picture is called the Larmor precession

of the nuclear spin around the direction of the hyper-

ﬁne ﬁeld. Hence, the frequency of this rotation can

be monitored by detection of the second g-ray by a

second detector, making a ﬁxed angle with the ﬁrst

one. After data reduction, the resulting function,

called R(t), is proportional to the time evolution of

the emission probability of the second g-ray in a given

direction and clearly shows the spin precession

(Fig. 1). The relation between the observed preces-

sion frequency, n, and the hyperﬁne ﬁeld is:

n ¼

ð3Þ

where h is Planck’s constant. Information which can

be obtained by analyzing R(t) is discussed in Sect. 4.

3. A Comparison Between PAC and MS

Owing to the fast electronics needed to perform a

PAC measurement (note that the time scale in Fig. 1

is in the nanosecond range) this method is less used

than its ‘‘sister’’ technique MS. Nevertheless, PAC

has some advantages over MS. It is insensitive to

temperature, in contrast to MS where the recoilless

fraction is strongly temperature dependent and pre-

vents the use of MS at too high a temperature.

Therefore, PAC is better suited to follow phenomena

as a function of temperature. The number of radio-

active nuclei which are needed is orders of magnitude

lower than for MS. An absolute amount of 10

–10

PAC probes is sufﬁcient. Hence, if the studied nucle-

us represents an impurity in a material, it has a

1049

Perturbed Angular Correlations (PAC)