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

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Figure 1

The arrangement of the polyhedrons surrounding the 3d metal ions in the (a) spinel, (b) garnet, (c) M-hexaferrite, and

(d) perovskite crystal structures. For garnet the dodecahedrons of the R ions are also shown. For M-hexaferrite and

perovskite structures the cation sites, which are not occupied by the 3d metal ions, are represented by circles.

1260

Transition Metal Oxides: Magnetism

can be divided into four blocks designated as

SRS*R*. The S block has the spinel structure, while

symmetry of R is rhombohedral. Asterisk means a

rotation of the block by p around the hexagonal axis.

There are ﬁve sublattices occupied by Fe

3 þ

ions. The

superexchange interactions, all of an antiferromag-

netic character (Nova

k et al. 1989), lead to a collinear

ferrimagnetic ordering of spins (Table 1). Substitu-

tion of various cations in all the Fe sublattices as well

as in the M sublattice can be made. Technological

applications of these materials are described in Alni-

cos and Hexaferrites.

Hexagonal ferrites with a more complicated struc-

ture contain a hexagonal block T, in addition to

blocks R and S. Examples are W, Y and Z hexafer-

rites with the chemical compositions BaM

, and Ba

, respectively.

2.4 Perovskites

The most important transition metal perovskites are

orthoferrites RFeO

(where R is yttrium or a rare-

earth ion) and mixed valence manganites

1x

MnO

(where M is a bivalent or monovalent

cation such as Ca

2 þ

,Sr

2 þ

,Ba

2 þ

,Pb

2 þ

,Na

, and

). All these compounds have a distorted perovs-

kite structure. The Fe

3 þ

,Mn

3 þ

, and Mn

4 þ

ions are

octahedrally coordinated while the R and M ions

have 12 oxygen ligands. The orthoferrites are basi-

cally antiferromagnetic, but there is a weak ferro-

magnetism due to a canting (about 0.51) of the

antiferromagnetically oriented Fe

3 þ

spins.

In manganites containing bivalent M ions the ion

distribution is (R

3 þ

1x

2 þ

)(Mn

3 þ

1x

4 þ

2

.Ifx is

smaller than E0.1 an antiferrodistortive ordering of

the local Jahn–Teller deformations associated with

the Mn

3 þ

ions exists. The systems are nonmetallic

and antiferromagnetic. For higher M concentrations

the double-exchange interaction prevails over the su-

perexchange, the systems are then metallic-like and

ferromagnetic. The Curie temperature depends on the

difference of R

3 þ

and M

2 þ

ionic radii and it reaches

B370 K in the (LaSr) system. A rich phase diagram

exists for xE0.5. Depending on the R

3 þ

and M

2 þ

cations the system may exhibit a Mn

3 þ

–Mn

4 þ

charge

ordering and it is then nonmetallic and antiferromag-

netically ordered. In other cases ferromagnetic order-

ing and the metallic-like conductivity is observed.

2.5 Chromium Dioxide

CrO

has a rutile structure with two formula units per

unit cell. It is an unusual transition metal oxide as it is

ferromagnetic, rather than ferrimagnetic. The tetra-

valent state of chromium is expected with the electron

conﬁguration [Ar]3d

. The magnetic moment per unit

cell is then 4 m

(assuming that the orbital angular

momentum is quenched by the crystal ﬁeld) in rea-

sonable agreement with the experimental data.

3. Important Properties

3.1 Temperature Dependence of Magnetization

In the molecular ﬁeld approach the temperature de-

pendence of the sublattice magnetizations of a ferri-

magnetic system is calculated from the coupled

system of equations:

; M

ðTÞ¼M

ð0ÞB

ðx

Þ;

¼ðg

=kTÞB

ð6Þ

where

is the magnetization of the sublattice a, l

are the molecular ﬁeld coefﬁcients, connected with

the exchange integrals J

(see Eqn. (4)) by:

ð7Þ

the site i( j) belongs to the sublattice a(b), z

is the

number of neighbors, n

is the number of j-type sites

for whatever is the quantity of material to which the

magnetization is related. g

, g

E2 are the respective g-

factors. B

is the Brillouin function. For a ferrimag-

netic system with two magnetic sublattices, three

possible types of the M(T) dependence are obtained

(Fig. 2).

In systems where the double exchange dominates,

the molecular ﬁeld approach leads to a different set of

equations (see Kubo and Ohata 1972). The M(T) de-

pendence is more convex, compared to a system de-

scribed by the Heisenberg–Hamiltonian.

3.2 Magnetocrystalline Anisotropy

The main mechanism which gives rise to the magne-

tocrystalline anisotropy originates from the interplay

Table 1

Fe sublattices in MFe

. Two alternative notations for sublattices used in the literature are given.

Fe1 Fe2 Fe3 Fe4 Fe5

Sublattice 2a 4e (2b) 4f1 4f2 12k

Coordination Octahedral Bipyramidal Tetrahedral Octahedral Octahedral

Spin Up Up Down Down Up

1261

Transition Metal Oxides: Magnetism

of the crystal ﬁeld, spin-orbit, and exchange interac-

tions. The anisotropic part of the free energy then has

a single ion character, i.e., it may be expressed as the

sum of the contributions of individual magnetic ions,

present in the system, the same holds also for the an-

isotropy constants. A large contribution give ions the

orbital moment of which is not quenched by the crys-

tal ﬁeld. Examples are the Co

2 þ

and Fe

2 þ

ions in the

octahedral co-ordination and all trivalent lanthanide

ions, with the exception of La

3 þ

,Gd

3 þ

, and Lu

3 þ

The temperature dependence of the single ion con-

tribution k to the anisotropy constant follows the

l(l þ1)/2 law:

kðTÞ

kð0Þ

mðTÞ

mð0Þ



lð lþ1Þ=2

ð8Þ

where m(T) is the magnetic moment of the ion at

temperature T, l ¼2and4fortheﬁrstanisotropy

constant in the axial and cubic symmetry, respectively.

In systems with symmetry lower than cubic the di-

polar and anisotropic exchange interactions may also

contribute to the magnetocrystalline anisotropy. In

many ferrites with nominally cubic symmetry an axial

magnetocrystalline anisotropy may be induced by

annealing the system in a magnetic ﬁeld.

3.3 Electrical Conductivity and Magnetoresistance

In many transition metal oxides the same cation may

exist in several different valence states. Such a ‘mixed

valence’ situation is connected with the presence of

oxygen or cation vacancies and/or caused by cation

substitution. An example is the Y

garnet

(YIG), in which all cations are trivalent, providing

the system is ideally stoichiometric. Substitution of

4 þ

for Fe

3 þ

in the tetrahedral sublattice then in-

duces the change of valency of the octahedral Fe ion

3 þ

-Fe

2 þ

The charge carriers are in most cases described as

polarons (electrons or electron holes plus the lattice

distortion) moving by hopping or in a band. The

electrical conductivity may be of n-type (e.g., YIG:Si)

or p-type (e.g., YIG:Ca) and it can be very low in

nearly stoichiometric compounds (10

11

c in YIG at

300 K, see Winkler 1981). A special case is represent-

ed by magnetite (Fe

3 þ

)[Fe

3 þ

2 þ

with the equal

number of ferrous and ferric cations in the octahedral

sublattice. The d.c. conductivity of Fe

is larger

than 10

1

at 300 K.

The importance of the ferromagnetic, metallic-like

mixed valence manganites (see Sect.2.4) is increasing.

Above T

the conductivity in these compounds has a

hopping character, while below T

it is metallic-like.

At temperatures close to T

an external magnetic

ﬁeld markedly inﬂuences the spin conﬁguration and

has a large effect on the electrical conductivity, lead-

ing to ‘‘colossal’’ magnetoresistance.

3.4 Optical and Magneto-optical Properties

At long wavelengths l41.5 mm the optical absorp-

tion in ferrites is mainly caused by the lattice vibra-

tions. Between B1.5–5.0 mm the so-called infrared

window exists, in which the absorption coefﬁcient a

can be very low (ao0.03 cm

1

for the yttrium iron

garnet). At shorter wavelengths the absorption in-

creases due to the electronic transitions between the

states of the transition metal ions as well as the

charge transfer transitions involving the oxygen lig-

ands. If the rare earth ions are present, characteristic

absorption bands appear in the far infrared region.

The absorption is also very sensitive to the presence

of the charge carriers (Fe

2 þ

or Fe

4 þ

ions).

The rotation of the plane of linearly polarized light

(Faraday effect) was most thoroughly studied in gar-

net ferrites (see Winkler 1981). The specific Faraday

rotation y

lies in the range from 1 10

–

1 10

1cm

1

and it depends on the wavelength of

the light beam, temperature, composition of the

Figure 2

Three types of temperature dependence of the

magnetization in a two-sublattice ferrimagnet. Dashed

curves correspond to the magnetizations of the

sublattices. Full curve is the total magnetization. T

comp

denotes the compensation temperature.

1262

Transition Metal Oxides: Magnetism

garnet, external magnetic ﬁeld, etc. y

is strongly

enhanced by the presence of the Bi

3 þ

ion in the do-

decahedral sublattice.

See also: Growth and Magnetic Properties of YIG

Films; Perovskites: Resistivity Behavior

Bibliography

Brabers V A M 1995 Progress in spinel ferrite research. In:

Buschow K H J (ed.) Handbook of Magnetic Materials. Else-

vier, Amsterdam, Vol. 8, pp. 189–234

Kanamori J 1963 Anisotropy and magnetorestriction of ferro-

magnetic and antiferromagnetic materials. In: Rado G T,

Suhl S (eds.) Magnetism. Academic Press, New York, Vol. 1,

pp. 127–203

Kojima H 1982 Fundamental properties of hexagonal ferrites

with magnetoplumbite structure. In: Wohlfarth E P (ed.)

Ferromagnetic Materials. North-Holland, Amsterdam, Vol.

3, pp. 305–92

Krupic

ka S, Nova

k P 1982 Oxide spinels. In: Wohlfarth E P

(ed.) Ferromagnetic Materials. North-Holland, Amsterdam,

Vol. 3, pp. 189–304

Kubo K, Ohata N 1972 A quantum theory of double exchange

I. J. Phys. Soc. Jap. 33, 21–32

McCurrie R A 1994 Ferromagnetic Materials Structure and

Properties. Academic Press, London

Nova

k P, Idland K, Zalesskij A V, Krivenko V G, Kunevitch A

V 1989 Magnons and sublattice magnetizations in hexagonal

Ba ferrite. J. Phys. Condens. Matter 1, 8171–9

Ramirez A P 1997 Colossal Magnetoresistance. J. Phys. Con-

dens. Matter 9, 8171–99

Winkler G 1981 Magnetic garnets. Vieweg Tracts in Pure and

Applied Physics, Vol. 5. Vieweg & Sohn, Braunschweig,

Germany, Vol. 5

P. Nova

Institute of Physics ASCR, Prague, Czech Republic

Transparent Rare Earth Compounds:

Magnetic Circular Dichroism

Magnetic circular dichroism (MCD) is the difference

in molar absorptivities for left and right circularly

polarized light, De ¼ðe

LCP

 e

RCP

Þ, and is measured

as a function of frequency (or wavenumber) on sam-

ples placed in a longitudinal magnetic ﬁeld. In this

chapter, MCD spectroscopy of transparent rare-earth

compounds in the solid and liquid state is described,

with special emphasis on the MCD spectra of triva-

lent europium ions. The majority of the MCD studies

on trivalent rare-earth ions have been devoted to the

3 þ

ion. The trivalent Eu

3 þ

ion (4f

electronic

conﬁguration) has the advantage of a nondegenerate

ground state (

) and the presence of excited states

with a small total angular momentum J (e.g.

and

). This makes the MCD spectrum of Eu

3 þ

relatively easy to interpret, in comparison with the

MCD spectra of the other trivalent rare-earth ions.

The Eu

3 þ

MCD spectrum is dominated by signals

which have the shape of the ﬁrst derivative of a

Gauss-curve. These signals are the so-called A-terms.

An A -term can have a positive or negative sign. A

positive A-term has its positive lob at the high wave-

number side of the spectrum.

In this case, the absorption of left circularly po-

larized light takes place at a higher energy (or wave-

number) than the absorption of right circularly

polarized light. For a negative A-term, the reverse is

true. As will be discussed further, the sign of the A -

terms in the MCD spectrum depends on the symme-

try of the ﬁrst coordination sphere around the Eu

3 þ

ion. The information obtained by MCD is similar to

what can be extracted from a classical Zeeman spec-

troscopy experiment, where the splitting and mixing

of energy levels in a magnetic ﬁeld are studied. How-

ever, MCD can also be measured in the case of broad

absorption bands. Typical MCD applications are the

assignment of electronic transitions, measurement of

the Zeeman splitting, investigation of magnetic and

symmetry properties of electronic states, polarization

studies and testing the reliability of crystal-ﬁeld wave

functions and intensity parameters. An MCD spec-

trum has a higher information content than the cor-

responding absorption spectrum, since in addition to

the intensity, the MCD signal is characterized by a

sign (positive or negative). MCD is an excellent

method for detecting the presence of overlapping

transitions in the absorption spectrum. The method is

very sensitive to changes in the electronic structure,

and therefore to changes in the physical structure.

1. Measurement of MCD Spectra

The measurement of MCD spectra is rather similar to

the measurement of absorption spectra. The primary

differences are that the radiation incident on the

sample must be circularly polarized and that the

sample is placed in a longitudinal magnetic ﬁeld

(magnetic ﬁeld lines parallel to the light beam). Most

magnetic circular dichroism spectrometers are circu-

lar dichroism spectrometers extended with a magnet,

although some instruments are especially designed

for MCD measurements. A permanent magnet, elec-

tromagnet or superconducting magnet can be used.

The permanent magnet has the disadvantage that the

magnetic ﬁeld is rather weak and that the magnetic

ﬁeld cannot be switched off for CD measurements.

An electromagnet is often the best choice, because it

can produce a moderate magnetic ﬁeld (ca. 1 T), it

can be switched off and it is simple in use. A super-

conducting magnet can provide a strong magnetic

ﬁeld (typically 5–7 T), but cooling with liquid helium

is necessary. The light beam from the light source is

ﬁrst linearly polarized and then circularly polarized

1263

Transparent Rare Earth Compounds: Magnetic Circular Dichroism

by a Pockels cell or photoelastic modulator. Typical-

ly, MCD instruments have a single-beam setup.

There are some constraints on the samples which

can be used in MCD measurements. The circular

polarization of the incident light beam may only be

altered by sample absorption, resulting in elliptically

polarized light. This means that MCD can only be

recorded for optical isotropic samples or in an iso-

tropic direction for anisotropic samples. Solutions

will give no problems. Cubic crystals and especially

glasses have to be checked for the absence of internal

stress. Uniaxial crystals can be measured along the

unique optic axis. In this case, adequate orientation

of the sample is crucial. In principle, MCD spectra of

biaxial crystals cannot be measured. Finally, it is dif-

ﬁcult to record the MCD spectrum of powdered

samples, because of the effects of light scattering.

MCD data are obtained with an MCD spectrome-

ter in terms of ellipticities y (in millidegrees). The re-

lation between y and De is given by the expression:

y ¼

33000De

ð1Þ

where l is the optical path length (in cm) and C is the

concentration (in molL

1

2. Basis MCD Theory

An elaborate discussion of the theory of MCD can be

found in the work of Stephens (1970, 1974, 1976) and

of Piepho and Schatz (1983). MCD spectra ﬁnd their

origin in the magnetically induced optical activity,

due to the Zeeman effect. The Zeeman effect predicts

that all the energy level degeneracy is lifted in the

presence of a magnetic ﬁeld. In the case of a rare-

earth ion coordinated by ligands according to a de-

ﬁned geometry, the energy levels in question are the

levels obtained after introduction of the crystal-ﬁeld

perturbation on the free-ion levels. The Hamiltonian

of such a system can be written as:

H ¼ H

þ H

SOC

þ H

Zeeman

ð2Þ

where H

is the Hamiltonian in the central-ﬁeld ap-

proximation, H

is the electron repulsion Hamil-

tonian (the prime indicates that the Hamiltonian

describes a perturbation), H

SOC

is the spin-orbit cou-

pling Hamiltonian, H

is the crystal-ﬁeld Hamil-

tonian and H

Zeeman

is the Zeeman Hamiltonian. The

wavefunctions are those which diagonalize the total

Hamiltonian (including the Zeeman effect). In an

MCD measurement, the magnetic ﬁeld is applied

parallel to the propagation direction of the light. The

propagation direction is called z; therefore the mag-

netic ﬁeld component to be considered is H

.Ina

crystal with the principal site symmetry axis parallel

to z, the Zeeman levels are described and labeled with

respect to this z-axis.

According to a notation used by Judd (1962), the

Zeeman levels of the ground state can be written as:

7 ¼

/4 f

c JM7a

ð3Þ

where A is a crystal ﬁeld level with Zeeman compo-

nent a, a

are coefﬁcients, 4f

indicates the 4f

con-

ﬁguration with N electrons in the valence shell, c is

an additional quantum number, J is the total angular

momentum, and M is the z-component of J. For the

excited state, an analogous expression can be written:

S ¼

74 f

S ð4Þ

For the discussion of the MCD signals it is sufﬁ-

cient to consider only the M quantum numbers:

7 ¼

/M7a

ð5Þ

S ¼

S ð6Þ

If the rare-earth ions are in an uniaxial single crys-

tal with the main symmetry axis parallel to the prop-

agation direction of the light, light absorption only

takes place in the xy plane. For an electric dipole

transition, the operators are:

absorption of RCP :

þ1

1

ﬃﬃﬃ

ðm

þ im

Þ¼7e7D

ð1Þ

þ1

ð7Þ

absorption of LCP :

1

ﬃﬃﬃ

ðm

 im

Þ¼7e7D

ð1Þ

1

ð8Þ

where m

, m

are the electric dipole operators for

light polarized according to the x or y directions, and

7e7 is the absolute charge of the electron. D

ð1Þ

is a

tensor of rank 1, with polarization numbers r ¼þ1

for RCP and r ¼–1 for LCP. In the case of a mag-

netic dipole transition, the operators are:

absorption of RCP :

þ1

1

ﬃﬃﬃ

ðm

þ im

Þ¼

7e7

2mc

ðL þ 2SÞ

ð1Þ

þ1

ð9Þ

absorption of LCP :

1

ﬃﬃﬃ

ðm

 im

Þ¼

7e7

2mc

ðL þ 2SÞ

ð1Þ

1

ð10Þ

where m is the electron mass, c is the speed of light, L

is the orbital angular momentum and S is the spin

angular momentum. Since the Zeeman components

are characterized by the quantum numbers M, one

can understand that circularly polarized light induces

transitions between Zeeman levels. Depending on the

quantum number M of the ground state /A

7 and

1264

Transparent Rare Earth Compounds: Magnetic Circul ar Dichroism

the quantum number M

of the excited state 7A

either left circularly polarized light (LCP, r ¼–1) or

right circularly polarized light (RCP, r ¼þ1) can be

absorbed preferentially. The conditions for absorp-

tion in terms of M, M

and r can be formulated by

selection rules.

The relative order of the splitting of a J-level by a

magnetic ﬁeld in its M components is deﬁned by the

Lande

-factor g:

g ¼ 1 þ

JðJ þ 1ÞLðL þ 1ÞþSðS þ 1Þ

2JðJ þ 1Þ

ð11Þ

If g is positive, the sign of the A-term of Eu

3 þ

determined by the sign of the M

quantum number

used to label the Zeeman level to which left circularly

polarized light is absorbed. If g is negative, the ab-

sorption of right circularly polarized light has to be

evaluated. For the observable

2S þ1

levels of Eu

3 þ

g is always positive.

3. MCD Select ion Rules

3.1 Electric Dipole Transitions

Although no electric dipole transitions can occur for

3 þ

, it is instructive to start with this case. The

classical example to illustrate the MCD signal of an

electric dipole transition is the

P’

S transition. In a

magnetic ﬁeld, the

P state splits into three compo-

nents:

þ1

(7M

S ¼ 7 þ 1S),

(7M

S ¼ 70S) and

1

(7M

S ¼ 7  1S). The selection rule, which can

be obtained by evaluating 3j symbols in the transition

moment integral, is:

DM ¼ M

 M ¼r ð12Þ

When the ground state is characterized by /M7 ¼

/07, as in the case of

, the selection rule is reduced

to:

DM ¼ M

¼r ð13Þ

In other terms, left circularly polarized light (r ¼–1)

is absorbed to the upper Zeeman component charac-

terized by 7M

S ¼ 7 þ 1S (g is positive). For the

same reason, right circularly polarized light is ab-

sorbed to the lower Zeeman component 7M

S ¼

7  1S. The corresponding MCD signal will be a

positive A-term.

3.2 Magnetic Dipole Transitions

The same considerations as for an electric dipole

transition, lead to the selection rule for a magnetic

dipole transition:

DM ¼ M

 M ¼r ð14Þ

which can be rewritten in the case that the ground

state is characterized by /M7 ¼ /07, to:

DM ¼ M

¼r ð15Þ

The MCD selection rules for electric dipole and

magnetic dipole transitions are thus the same. A pos-

itive A-term is observed if the Zeeman component

7 þ 1S is at a higher energy than the 7  1S compo-

nent. An example is the magnetic dipole transition

’

in the MCD spectrum of Eu

3 þ

(at ca.

19000 cm

1

), which always shows a positive A-term.

It has been suggested to use this transition as a sign

reference transition, in order to see if the magnetic

ﬁeld lines are parallel or antiparallel to the magnetic

ﬁeld lines (Go

rller-Walrand 1985). The MCD and

axial absorption spectrum of the

’

transition

in LiYF

:Eu

3 þ

is shown in Fig. 1.

3.3 Induced Electric Dipole Transitions

According to the Judd–Ofelt theory (Judd 1962,

Ofelt 1962), the occurrence of intraconﬁgurational f–f

transitions is explained by nonsymmetric interactions

which mix states of opposite parity into the 4f

Figure 1

MCD and axial absorption spectra of the

’

magnetic dipole transition of LiYF

:Eu

3 þ

at ambient

temperature. The A-term has a positive sign.

1265

Transparent Rare Earth Compounds: Magnetic Circular Dichroism

conﬁguration. A simple mechanism is the coupling of

states of opposite parity by the effect of the odd terms

in the crystal-Hamiltonian H

odd

¼7e7V

odd

k;q

ðkÞ

ð16Þ

where B

is a crystal-ﬁeld parameter and D

ðkÞ

is a

tensor of rank k (k is odd) (Go

rller-Walrand and

Binnemans 1996). The important point is that, de-

pending on the values of k and q which are deter-

mined by the ﬁrst coordination sphere around the

lanthanide ion, mixing occurs between states of op-

posite parity and the Zeeman components, which are

characterized by linear combinations of /M7 func-

tions in the ground state and by linear combinations

of 7M

S functions in the excited state. The selection

rule for an induced electric dipole transition is

DM ¼ M

 M ¼ðr þ qÞð17Þ

In the case where the ground state is characterized by

/M7 ¼ /07, as for the

ground state of Eu

3 þ

, the

selection rule is simpliﬁed to:

DM ¼ M

¼ðr þ qÞð18Þ

The sign of the A-term is identical to the sign of the

value that satisﬁed the selection rule for r ¼1.

Whereas the sign of the A-term of an electric dipole

transition or a magnetic dipole transition is only de-

pendent on the free-ion properties, the sign of the A-

term of an induced electric dipole transition depends

on the site symmetry of the lanthanide ion (Go

rller-

Walrand and Fluyt-Adriaens 1985; Go

rller-Walrand

et al. 1985). The selection rules are valid for the in-

termediate coupling scheme (J is a good quantum

number), but relaxation of the selection rules can oc-

cur when J-mixing is strong.

4. Use of M CD for Site Symmetry Determination

The sign of the MCD-signal of the induced electric

dipole transition

’

(at ca. 21500 cm

1

) can be

used to probe the site symmetry of the Eu

3 þ

ion and

the type of the idealized coordination polyhedron. A

positive A-term is found for the Eu

3 þ

ion in a C

symmetry (q ¼0), whereas a negative A-term is ex-

pected for D

(q ¼7 2) and D

symmetry (q ¼7

3). It is not possible to discriminate between D

and

symmetry on the basis of the sign of the

’

transition alone, but in the case of D

symmetry, the MCD signal of the

’

transi-

tion is twice as intense as the intensity of the MCD

signal of the

’

transition, whereas in the

case of D

symmetry the two MCD signals have an

equal intensity. Ideally, C

is the symmetry of a

monocapped square antiprism (coordination num-

ber, CN ¼9) or of a distorted square antiprism

(CN ¼8). D

is the symmetry of a tricapped tri-

gonal prism (CN ¼9) and D

is the symmetry of a

dodecahedron (CN ¼8). These coordination polyhe-

dra are the most often observed coordination poly-

hedra of lanthanide complexes.

5. Check of the Reliability of Intensity Parameters

The spectral intensities of magnetic dipole transitions

can be calculated exactly, provided that a good set of

wavefunctions is available. The spectral intensities of

induced electric dipole transitions in the absorption

spectrum for lanthanide ions in single crystals are

commonly parametrized in terms of B

lkq

or A

in-

tensity parameters (Go

rller-Walrand and Binnemans

1998). Since these parameters are related to the ex-

perimental dipole strength by nonlinear equations,

solution of the problem is not straightforward. The

sign of the parameters is indeterminate: a change of

all the signs of the parameters will result in exactly

the same calculated dipole strength. The extracted

parameter set depends largely on the chosen starting

values. Different parameter sets may give the same

ﬁgure of merit for the calculated dipole strengths. It is

very difﬁcult to select the most adequate set of in-

tensity parameters. Simulation of the MCD spectrum

can help. Calculation of the MCD signals does not

require more parameters than the crystal ﬁeld and

intensity parameters extracted from the absorption

spectrum. If these parameters are adequate, they

should allow a good simulation of the MCD spec-

trum. In the past, the MCD spectrum was often de-

scribed by the Faraday parameters or MCD

parameters A

, B

and C

(Stephens 1970). In the

Stephens-formalism several approximations are

made, and these are not always valid for lanthanide

systems, especially not for single crystals. An as-

sumption is, for instance, that the Zeeman splitting is

small compared to the crystal ﬁeld splitting within a

multiplet. This is not true for small crystal ﬁeld split-

tings and a strong magnetic ﬁeld. The Zeeman effect

cannot be considered as a small perturbation com-

pared to the crystal ﬁeld effect.

Not only do the free ion and the crystal ﬁeld

Hamiltonian have to be included in the total Ham-

iltonian, but also the Zeeman Hamiltonian (as de-

scribed in Sect. 2). After diagonalization, the Zeeman

levels are directly found, instead of the crystal ﬁeld

levels. The MCD of a transition is calculated as

the difference in intensity between the absorption of

left circularly polarized to the Zeeman levels of a

2S þ1

term and the absorption of right circularly

polarized light (Fluyt et al. 1996). The MCD of a

transition has to be reported as an intensity differ-

ence. A positive sign indicates that left circularly po-

larized light is absorbed more effectively than right

circularly polarized light. A negative sign indicates

the opposite. In the case of overlapping bands, the

band width of the curves used for the simulation will

affect the overall appearance of the MCD signal to a

1266

Transparent Rare Earth Compounds: Magnetic Circul ar Dichroism

large extent. For single crystals, a Lorentzian shape

function often gives the best results for the graphical

simulation.

MCD can sometimes be used to detect transitions

that are not resolved in the absorption spectrum. A

condition is that the MCD signals of transitions to

the closely spaced crystal ﬁeld levels, which give

rise to overlapping absorption bands, have an op-

posite sign. However, if the MCD signals of the

transitions to the nearly degenerate crystal ﬁeld

levels have the same sign, the MCD spectrum is not

advantageous.

6. MCD of Bioinorganic Compounds and

Macrocyclic Complexes

Because lanthanide ions can subsitute for Ca

2 þ

different proteins, it was suggested that MCD spec-

troscopy of lanthanide-substituted proteins could be

used to probe the Ca

2 þ

active sites of these pro-

teins. The fact that Ca

2 þ

active sites were being

probed by luminescence spectroscopy after Eu

3 þ

substitution, and the sensitivity of the MCD

spectrum towards small changes in the environment

of the coordinated lanthanide ions, suggested that

MCD could be a good technique to study the metal-

ion site structure. In the past, several MCD studies

were devoted to lanthanide ions (mainly Nd

3 þ

)

bound to proteins, but these studies were qualitative

in nature, pointing to the differences of the MCD

spectra of lanthanide ions in aqueous solution and

of protein–lanthanide complexes. The use of MCD

spectroscopy of lanthanide ions in bioinorganic

chemistry has been reviewed (Dooley and Dawson

1984), but there has been little activity in this re-

search ﬁeld.

Bibliography

Dooley D M, Dawson J H 1984 Bioinorganic applications of

magnetic circular dichroism spectroscopy: copper, rare-earth

ions, cobalt and non-heme iron systems. Coord. Chem. Rev.

60, 1–66

Fluyt L, Couwenberg I, Lambaerts H, Binnemans K, Go

rller-

Walrand C, Reid M F 1996 Magnetic circular dichroism of

Nd(ODA)

2NaClO

6H

O. J. Chem. Phys. 105, 6117–27

rller-Walrand C 1985 Eu

3 þ

as an MCD probe? Chem. Phys.

Lett. 115, 333–4

rller-Walrand C, Behets M, Porcher P, Laursen I 1985 Se-

lection rules in rare earth MCD spectra. An experimental

conﬁrmation. J. Chem. Phys. 83, 4329–37

rller-Walrand C, Binnemans K 1996 Rationalization of Crys-

tal Field Parametrization. In: Gschneidner K A Jr, Eyring L.

Handbook on the Physics and Chemistry of Rare Earths.North

Holland, Amsterdam, Vol. 23, Chap. 155, pp. 121–283

rller-Walrand C, Binnemans K 1998 Spectral intensities of f–

f transitions. In: Gschneidner K A Jr, Eyring L. Handbook on

the Physics and Chemistry of Rare Earths. North-Holland,

Amsterdam, Vol. 25, Chap. 167, pp. 101–264

rller-Walrand C, Fluyt-Adriaens L 1985 Selection rules for

rare-earth magnetic circular dichroism spectra. J. Less-Com-

mon Met. 112, 175–91

Judd B R 1962 Optical absorption intensities of rare-earth ions.

Phys. Rev. 127, 750–61

Ofelt G S 1962 Intensities of crystal spectra of rare-earth ions.

J. Chem. Phys. 37, 511–20

Piepho S B, Schatz P N 1983 Group Theory in Spectroscopy.

With Applications to Magnetic Circular Dichroism. Wiley,

New York

Stephens P J 1970 Theory of magnetic circular dichroism. J.

Chem. Phys. 52, 3489–516

Stephens P J 1974 Magnetic circular dichroism. Annu. Rev.

Phys. Chem. 25, 201–32

Stephens P J 1976 Magnetic circular dichroism. Adv. Chem.

Phys. 25, 197–264

C. Go

rller-Walrand and K. Binnemans

K.U. Leuven, Heverlee, Belgium

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1268

LIST OF CONTRIBUTORS

Contributors are listed in alphabetical order together with their addresses. Titles of articles that they have

authored follow in alphabetical order. Where articles are coauthored, this has been indicated by an asterisk

preceding the title.

Amato, A.

Paul Scherrer Institute, Villigen, Switzerland

Muon Spin Rotation (mSR): Applications in

Magnetism

Andra

,W.

Institut fu

r Physikalische Hochtechnologie e.V. Jena

Germany

*Magnets: Biomedical Applications

*Stress Coupled Phenomena: Magnetostriction

Andreev, A. V.

Institute of Physics, Prague, Czech Republic

*Magnetoelastic Phenomena

Atkinson, R.

The Queen’s University, Belfast, UK

Faraday and Kerr Rotation: Phenomenological

Theory

Magneto-optical Effects, Enhancement of

Aziz, M. M.

University of Manchester, Manchester, UK

*Magnetic Recording: Rigid Media, Recording

Properties

Bain, J. A.

Carnegie Mellon University, Pittsburgh

Pennsylvania, USA

Magnetic Recording Devices: Inductive Heads,

Properties

Banhart, J.

Fraunhofer-Institut fu

r Angewandte

Materialforschung, Bremen, Germany

*Magnetoresistance, Anisotropic

Bardeen, J.

University of Illinois, Urbana, Illinois, USA

Superconducting Materials: BCS and Phenomenological

Theories

Barthe

my, A.

UMR CNRS-Thomson CSF and Universite

Paris

Sud, Orsay, France

*Giant Magnetoresistance

Battle, P. D.

University of Oxford, UK

Magnetoresistance in Transition Metal Oxides

Bauer, E.

Institut fu

r Experimentalphysik, Wien, Austria

Intermediate Valence Systems

Kondo Systems and Heavy Fermions: Transport

Phenomena

Beckley, P.

Newport, UK

Steels, Silicon Iron-based: Magnetic Properties

Berkov, D.

Innovent, Jena, Germany

*Stress Coupled Phenomena: Magnetostriction

Bertotti, G.

Istituto Elettrotecnico Nazionale Galileo Ferraris

Turin, Italy

Magnetic Losses

Bhushan, B.

Ohio State University, Columbus, Ohio, USA

Magnetic Recording Devices: Head/Medium

Interface

Binnemans, K.

K.U. Leuven, Heverlee, Belgium

*Transparent Rare Earth Compounds: Magnetic

Circular Dichroism

Bissell, P. R.

University of Central Lancashire, Preston, UK

Magnetic Recording: VHS Tapes

Magnetic Recording Materials: Tape Particles,

Magnetic Properties

Bousack, H.

Forschungszentrum Ju

lich, Germany

*SQUIDs: Nondestructive Testing

Bozovic, I.

OXXEL GmbH, Bremen, Germany

*Superconducting Thin Films: Materials, Preparation,

and Properties

Brinkmann, D.

University of Zurich, Switzerland

High-temperature Superconductors, Cuprate: Magnetic

Properties by NMR/NQR

1269