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

Подождите немного. Документ загружается.

Magnetism: Applications of Synchrotron

Radiation

Magnetism in solids covers a large variety of prop-

erties ranging from bulk characteristics of permanent

magnets or recording and storage devices to funda-

mental microscopic phenomena in quantum systems.

The measurement of bulk magnetic properties (such

as susceptibility, magnetization, and anisotropy) rep-

resents the ﬁrst and necessary step to determine the

magnetic state of a material. However, a proper un-

derstanding of the magnetic properties requires a

knowledge of the electronic ground state. Magnetic

moments originate from unpaired electrons; the elec-

tron spins interact through various exchange cou-

plings to form ordered spin structures, while the

electron orbital moments contribute to the total mag-

netization via spin–orbit couplings.

Therefore, magnetism depends on electronic prop-

erties at the atomic level and/or at the electron

band level. The observation of transport properties

provides information on the electronic properties.

Nevertheless, the understanding of magnetism neces-

sitates the determination of the electronic states that

carry the magnetization, and the knowledge of the

magnetic order and magnetic interactions at a mi-

croscopic level. Local probes (NMR, Mo

ssbauer

spectroscopy, mSR) can be exploited to obtain some

insight as to the nature of the magnetization. Scat-

tering techniques provide microscopic details about

the magnetic sites, the arrangement, and the dynam-

ics of the ordered magnetic moments. (For NMR and

ssbauer spectroscopy see Cahn and Lifshin

(1993); for mSR see Muon Spin Rotation (mSR):

Applications in Magnetism.)

Scattering experiments convey information on spa-

tial Fourier transforms of correlation functions. Dif-

fraction experiments reveal static correlations,

including short- and long-range ordered structures,

while inelastic scattering experiments are used to ob-

serve time-dependent correlations, i.e., ﬂuctuations,

normal modes, and collective or localized excitations.

The energy range spanned by the excitations is related

to the size of the interactions, which are roughly de-

ﬁned by the ordering temperature in the range 1–300 K

(0.1–30 meV energy range). However, the energy scales

associated with electronic bands are in the electron

volt range. An ideally suited scattering probe should

cover all these energies. Traditionally neutron scatter-

ing is the probe of choice. However, in the past optical

effects in the visible range (Faraday and magneto-Kerr

effects) have conﬁrmed the existence of interactions

between photon polarization and magnetization: the

polarization of light is rotated upon transmission

through, or reﬂection from, a magnetized medium.

Similar phenomena (dichroic signals) are ob-

served in soft and hard x-ray absorption experiments,

when the photon energy is adjusted near an x-ray

absorption edge of a magnetic atom. Reciprocally,

x-ray scattering experiments show large resonant

enhancements of the scattered intensities yielding

count rates in the range 10

–10

photons s

1

. These

resonant effects in x-ray scattering are superimposed

on nonresonant effects, which are much weaker. The

developments in the use of x rays rely on tunable

photon sources and the scientific interest in the ap-

plications of x-ray methods to probe magnetism has

increased since the development of modern synchro-

tron radiation sources.

1. Scattering Probes: Synchrotron X Rays vs.

Neutrons

X-ray and neutron scattering techniques are analo-

gous in many ways but their strengths are comple-

mentary. Neutrons are considered as the probe of

choice for the study of magnetism by means of scat-

tering methods for two reasons (Squires 1978): (a)

neutrons possess a spin and the associated neutron

magnetic moments couple significantly to the magnet-

ization in materials; and (b) the rather low kinetic

energy of neutrons (3–100 meV at reactor sources)

allows easy inelastic experiments adapted to magnetic

properties. A large fraction of the understanding of

microscopic magnetism (magnetic structures, magnetic

excitations) comes from neutron scattering results.

However, neutron beams have low ﬂux and neutron

scattering experiments require large scattering vol-

umes. Furthermore, neutrons as a magnetic probe are

sensitive to the total magnetization and do not distin-

guish readily contributions from different elements,

different electronic shells, or spin vs. orbital momen-

tum. Neutrons cannot probe electronic properties.

X rays, when applied to magnetism, suffer from a

serious drawback: the nonresonant coupling between

the electromagnetic ﬁeld associated with the photons

and the spin and orbital momentum distributions is

weak. This interaction was evidenced experimentally

in the early 1970s (de Bergevin and Brunel 1972) but

was considered as a curiosity until more powerful

x-ray sources became available. The reason behind

the use of x-ray methods for the study of magnetism

arises from the unique properties of x-ray synchro-

tron radiation: (i) a high brilliance, which gives a

large particle ﬂux over an extremely small beam size;

(ii) a wide range of photon energy tunability; and

(iii) a well-deﬁned polarization state of the emitted

radiation. Modern synchrotron sources available

worldwide can accommodate different undulators as

radiation sources which produce x rays with energy

ranging from a few hundred electron volts to

30–40 keV. On the high-energy side, multipole wig-

glers produce photons up to 300 keV. High brilliances

up to 10

photons s

1

2

mrad

2

per 0.1% band-

width have been reached at the European Synchro-

tron Radiation Facility (ESRF) in Grenoble, France.

740

Magnetism: Applications of Synchrotron Radiation

The x-ray polarization is readily tunable, with an al-

most perfect degree of linear polarization. Special in-

sertion devices are designed to produce elliptically or

circularly polarized radiation.

The high photon ﬂux available at synchrotrons

compensates for the weakness of the nonresonant

magnetic x-ray scattering amplitude, and the easily

tuned photon energy has boosted resonant studies.

Magnetic resonant x-ray scattering combined with

the high brilliance of synchrotron x-ray beams makes

it possible to investigate small scattering volumes

(microcrystals, thin ﬁlms, surfaces) or weak magnetic

moments (down to 0.01m

). The resonant process is

element selective and electronic shell sensitive, allow-

ing detailed studies of the origin of magnetic mo-

ments. The time structure of the synchrotron

radiation (x-ray bunches at 357kHz at the ESRF)

can be exploited to study the dynamics of magnetic

processes in real time down to the nanosecond scale

(Bonﬁm et al. 1998).

When used together, x-ray and neutron methods

offer a broad range of capabilities and the choice of

the technique depends on the details of the problem

to be solved. Neutrons are essential in determining

magnetic structures (magnetic powder diffraction)

and in characterizing magnetic excitations (the ob-

servation of magnetic excitations will not be dis-

cussed). However, synchrotron x rays provide more

information about the electronic character of mag-

netism (separation of orbital momentum and spin,

sensitivity to the electronic shell and to the chemical

species). Owing to the properties of synchrotron

x-ray beams (brilliance, collimation, time structure),

x rays are preferred over neutrons for the investigation

of minute samples (surfaces, thin ﬁlms), time-resolved

studies, and high Q-resolution experiments. However,

in the case of scattering experiments, the high colli-

mation of synchrotron beams must be matched by the

crystalline quality of the materials. As a consequence,

only good-quality crystals can be studied; for powder

samples, ab initio magnetic structure determinations

are performed using neutron diffraction.

In the following, the basic character of the inter-

actions of x rays with magnetism is outlined, includ-

ing a description of the scattering amplitudes (elastic

Bragg scattering or diffraction and Compton scatter-

ing) and the spin-dependent x-ray absorption meth-

ods (magnetic dichroism). Potential applications are

indicated and comparison with neutron methods is

made when appropriate.

2. Scattering Cross-sections

The x-ray or neutron intensity diffracted by an as-

sembly of atoms is written in terms of an elastic scat-

tering cross-section:



iQR

ðk

; k

; _oÞ



ð1Þ

where _o is the x-ray energy, k

and k

are the inci-

dent and scattered wave vectors of the photons, Q is

the probe momentum transfer (Q ¼k

k

), and f

represents the scattering amplitude from the nth at-

om. Two limiting regimes are distinguished for x rays:

the resonant scattering (when the incident photon is

close to an absorption edge of a magnetic species in

the material) and the nonresonant scattering (when

the photon energy is far from any absorption edge). It

is convenient to separate the different contributions:

ðk

; k

; _oÞ¼f

charge

ðQÞþf

nonres

ðk

; k

þ f

res

ðk

; k

; _oÞð2Þ

where f

charge

denotes the familiar Thomson scattering

from charge distribution, f

nonres

is the nonresonant

magnetic scattering, and all contributions to the res-

onant scattering are included in f

res

The processes discussed here correspond to coher-

ent elastic scattering; there are also inelastic processes,

known as Compton scattering, during which photons

exchange energy with the scattering system. In such a

case, the scattering is incoherent and photons are

scattered by individual electrons.

The absorption cross-section, which is measured in

spin-dependent absorption experiments, is related to

the scattering amplitude in Eqn. (2) through the op-

tical theorem:

¼ 2lIm½f

ðk

; k

; _oÞ ð3Þ

These different cases for x rays are discussed in the

following sections. Neutrons are used in the scatter-

ing mode only. Furthermore, only the elastic case is

considered here.

3. Nonresonant Regime

The nonresonant x-ray regime encompasses coherent

Bragg scattering (diffraction) and the Compton in-

elastic process.

3.1 Nonresonant X-ray Magnetic Bragg Scattering

The nonresonant x-ray magnetic scattering amplitude

is written as (Blume and Gibbs 1988):

nonres

ðk

; k

Þ¼ir





ðQÞAðe

; e

ÞþS

ðQÞBðe

; e



ð4Þ

where L

(Q) and S

(Q) are the Fourier transforms of

the orbital momentum and spin magnetization den-

sities (form factors) at the nth site, r

is the classical

radius of the electron (2.8 10

15

m), a standard unit

741

Magnetism: Applications of Synchrotron Radiation

in atomic scattering processes, and mc

is the rest

energy of the electron (511 keV). The vector quanti-

ties A(e

, e

) and B(e

, e

) depend on the polarization

vectors e

and e

of the incident and scattered wave

vectors, respectively; they are not identical and have

distinct Q dependencies.

A compact expression has been obtained:

nonres

ðk

; k

Þ¼ir



QÞ

cos yS

sin y½cos yðS

þ L

sin yS



sin y½cos yðS

þ L

Þ cosy½S

þ 2sin

M

þsin yS



ð5Þ

where y istheBraggangleand



is the Compton

wavelength ( ¼3.81 10

3

). L(Q)andS(Q) are given

by their components (a ¼1,2,3) in the coordinate

system u

, u

, where u

is directed along k

þk

, u

is perpendicular to the scattering plane and parallel to

k

, and u

is along Q. The matrix form for

nonres

ðk

; k

Þ is used to describe the polarization de-

pendence. The basis vectors for the polarization e

and e

correspond to a linear polarization either per-

pendicular (s) or parallel (p) to the scattering plane.

From Eqn. (5) it can be seen that the contributions

from L and S to the total magnetization M ¼L þS

can be obtained separately from magnetic x-ray scat-

tering data. Such a separation is not readily possible

in neutron diffraction experiments because neutrons

are sensitive to the total moment. It should be noted

that f

nonres

ðk

; k

Þ is not a spherical tensor formed

with (e

, e

) in contrast to the usual Thomson scat-

tering:

charge

ðQÞ¼r

rðQÞe

 e

ð6Þ

This difference helps in separating the Thomson

charge from purely magnetic x-ray scattering. Com-

parison of Eqns. (5) and (6) provides a rough estimate

for the relative amplitude of magnetic scattering and

charge scattering. If all form factors and geometrical

factors in A(e

, e

) and B(e

, e

) are set to unity, then:

nonres

charge



Eð



 QÞ



ð7Þ

where m is the electron average magnetic moment

(expressed in m

)andN

is the number of magnetic

electrons compared to the total number of electrons,

N,atsiten. For conventional diffraction cases,

7Q7¼1–6 A

1

, N

/N ¼0.1, and the ratio of intensi-

ties is around 10

6

. In practice, this ratio is even

smaller because of the geometrical factors in Eqn. (5).

This explains why the advent of bright third-genera-

tion synchrotron sources has boosted the development

of x-ray techniques by alleviating the consequences of

the inherent weakness of nonresonant x-ray magnetic

scattering amplitudes.

The neutron counterpart of Eqn. (4) is written as:

neutron

ðQÞ¼f

nuc

ðQÞþr

p ðQ ½Q  MðQÞÞ ð8Þ

where p is the neutron beam polarization, g is the

neutron gyromagnetic factor ( ¼1.91), M(Q) is the

Fourier transform of the total magnetization, and

nuc

(Q) is the scattering amplitude from the nuclei in

the solid. Note that neutrons couple to the Fourier

transform M(Q) ¼L(Q) þ2S(Q) of the total magnet-

ization. The L/S separation can only be achieved by

modeling the Q dependence of the two contributions,

L(Q) and S(Q).

In the case of ferro- or ferrimagnetic materials, the

magnetic Bragg peaks occur at the same positions in

reciprocal space as the more intense crystal structure

peaks. Interferences between the magnetic scattering

amplitude and the scattering amplitude from the

crystal structure allow the observation of the mag-

netic signal. A practical way to extract the magnetic

information is to reverse the magnetization direction

by applying an alternating magnetic ﬁeld (reversing

the interference term) and to collect the intensity as a

function of ﬁeld orientation; this gives the so-called

ﬂipping ratio, R, deﬁned as:

R ¼

IðmÞI ðkÞ

IðmÞþI ðkÞ

In the x-ray case, because f

nonres

ðk

; k

Þ and f

charge

ðQÞ

are out of phase by p/2 (Eqns. (4) and (6)), interfer-

ence only occurs in the case of circular polarization

(the e

and e

vectors are complex) or if the crystal

structure factor is imaginary (large absorption and/or

noncentrosymmetric structure). In the neutron case, a

ﬁnite neutron polarization is required to have inter-

ference effects. In this case, R is obtained by ﬂipping

the polarization of the neutron beam:

R ¼

1 þ 2pAðQÞþAðQÞ

1  2pAðQÞþAðQÞ

where p is the neutron polarization and

AðQÞ¼

MðQÞ

nuc

ðQÞ

Owing to the larger neutron magnetic scattering

amplitude, weak magnetic moments M(Q) can be ex-

tracted (i.e., ﬁeld-induced magnetization in paramag-

nets) provided f

nuc

(Q) and p are known accurately.

Usually, neutrons can detect magnetic moments down

to 0.05m

. However, x rays have an advantage over

neutrons when the sample under investigation is very

small, because of the high brilliance of synchrotron

sources. Ferromagnetic thin ﬁlms or multilayers and

742

Magnetism: Applications of Synchrotron Radiation

interfacial magnetism are routinely studied by means

of magnetic x-ray scattering.

In the case of antiferromagnetic systems, the mag-

netic diffraction peaks occur at positions in reciprocal

space that are forbidden for crystal structure reﬂec-

tions, and the limiting factor for detection is the

scattered intensity. Figure 1 shows examples of data

obtained from third-generation synchrotron sources.

Figure 1(a) gives an indication of the scattered in-

tensities available at modern synchrotron sources.

Also shown in Fig. 1 are the magnetic form factors

L(Q) and S(Q) that have been determined independ-

ently by exploiting the polarization dependence of the

scattering amplitude in Eqn. (5) (Fernandez et al.

1998). It is worth noting that at the high-energy limit

for Bragg scattering (low Bragg angle y), the x-ray

magnetic scattering is dominated by the spin contri-

bution, whereas the orbital momentum part becomes

negligible (Eqn. (5)).

An important aspect of diffraction experiments is

the Q-resolution. Owing to the highly collimated

beams, synchrotron x-ray experiments allow high

Q-resolution conditions which cannot be reached

with neutron scattering experiments. This is particu-

larly useful in detecting minute changes in the lattice

parameters occurring at magnetic phase transitions

due to magnetostriction effects.

3.2 Magnetic Compton Scattering

Inelastic Compton scattering is an incoherent process

where the scattering cross-section can be written as

(Lovesey and Collins 1996):

dOdo

¼ N







charge

Jðp

Þþ



mag

spin

ðp

ð9aÞ

where J(p

) is the usual Compton proﬁle (a two-

dimensional average perpendicular to the scattering

vector of the momentum density). The magnetic

Compton proﬁle given by J

spin

) ¼

1/2

)

)] is the difference between the proﬁles of

spin-up electrons and spin-down electrons. The dif-

ferential cross-sections contain geometrical and po-

larization factors:



Charge

ð1 þ cos

yÞ



spin

¼r

ð1  cos yÞð

cos y þ

Þz ð9bÞ

where z is the unit vector parallel the magnetic axis,

and

are unit vectors along k

and k

; and p

is the

degree of circular polarization of the incident x-ray

beam. Similarly to the previous discussions on ferro-

magnets, the magnetic Compton proﬁle is isolated

from the total spectrum by reversing either the mag-

netization direction, z, or the x-ray helicity, p

.By

measuring proﬁles along several directions, it is pos-

sible to reconstruct the three-dimensional spin polar-

ized momentum density and compare it with

theoretical electronic band calculations. Only mag-

netic Compton experiments can supply these exper-

imental conﬁrmations.

Figure 1

Nonresonant magnetic x-ray scattering from NiO.

(a) Angular proﬁle of an antiferromagnetic peak. (b)

Q-dependence of the spin and orbital moment form

factor as extracted from the polarization analysis of

experimental data.

743

Magnetism: Applications of Synchrotron Radiation

4. Resonant Regime

The nonresonant x-ray magnetic scattering amplitude

in Eqn. (5) vanishes in the forward direction at Q ¼0,

leading to the absence of magnetic effects in x-ray

transmission or x-ray reﬂection measurements. How-

ever, the optical index in the visible region varies with

the magnetization direction relative to the light po-

larization, which is the origin of magneto-optics. In

the hard x-ray region, the optical index is very close

to unity, and similar effects are not observed. Only

near an absorption edge does the x-ray index differ

from unity due to the anomalous part of the scatter-

ing amplitude, and magnetic effects are detected. The

scattering experiments and the absorption methods

can be treated in parallel near resonance. Indeed,

resonant scattering originates from second-order per-

turbation processes which can be pictured as the ab-

sorption of an incident photon, the creation of a

short-lived intermediate state, followed by decay

back to the ground state. In the case of elastic scat-

tering, a photon is elastically scattered during the

decay. These intermediate states correspond to the

promotion of an inner shell electron to a bound or

nearly bound level in an outer shell with a high den-

sity of states, leaving behind a core hole. The same

intermediate levels contribute to the white line in

normal x-ray spectroscopy. The outer electronic

shells are sensitive to the local symmetry of atomic

sites and the scattering amplitude reﬂects the sym-

metry of the associated wave functions with respect

to the relative orientation of the incident x-ray po-

larization. When the incident photon energy is tuned

to a resonance, the scattering amplitude contains

terms which reﬂect the local symmetry, possibly lead-

ing to new Bragg peaks which are forbidden away

from resonance (Templeton 1994).

The onset of local magnetic moments is a partic-

ular case of symmetry breaking which induces reso-

nant terms in the x-ray scattering amplitude, f

res

contributing to the total scattering amplitude in Eqn.

(2) (Blume 1994). The resonance occurs through elec-

tric multipole transitions from a core level into empty

electronic shells. The sensitivity to the magnetization

arises from the difference in transition probabilities

due to the spin polarization of the intermediate states,

the spin–orbit couplings, and the exchange interac-

tions. The strength of the resonance is given by the

multipole electric transition matrix elements and

the spin polarization of the intermediate states. The

strongest transition is the electric dipole (E1 with

Dl ¼1) contribution; the next strongest is given by the

electric quadrupole (E2 with Dl ¼2) contribution, but

the relative weakness of the E2 contribution must be

balanced with the size of the spin polarization of the

associated intermediate states. This is illustrated with

the example of 4f and 5f systems. The f electronic

states which carry the main magnetic moments are

probed directly by E1 transitions at the M

and M

edges (3d-f). They are also examined by E2 tran-

sitions at the L

and L

edges (2p-f); but at the same

and L

edges, the d moments, which are polarized

by the f electrons, are probed by E1 transitions (2p-

d). This example demonstrates the versatility and the

electronic selectivity for the study of the origin of

magnetic moments. The resonant process is also

chemical selective, because the resonant energy

changes with the chemical species and valence state.

The resonant scattering amplitude can be expressed

as a series expansion:

res

ðk

; k

; _oÞ¼f

res

nE1

ðk

; k

; _oÞ

þf

res

nE2

ðk

; k

; _oÞþ? ð10aÞ

where f

res

nEL

ðk

; k

; _oÞ are contributions from E1 and

E2 transitions (Hannon et al. 1988).

The E1 contribution to the scattering has the form:

res

nEI

ðk

; k

; _oÞ¼F

ð0Þ



cos 2y



 iF

ð1Þ



z

cos y þ z

sin y

cos y þ z

sin y

z

cos y



þ F

ð2Þ



ðz

sin y þ z

cos yÞ

z

ðz

sin y  z

cos yÞ

cos

yðz

tan

y þ z



ð10bÞ

where z

are components of the moment direction z

in the coordinate system deﬁned above. F

(n)

are res-

onant amplitudes which contain a resonant denom-

inator

 E

þ _o  i

dipole radial matrix elements /c7r7aS, and spin po-

larization of the intermediate states (only in the case

of F

(1)

and F

(2)

) (Hannon et al. 1988). E

, 7aS and E

7cS are the energies and wave functions of the

ground and intermediate states, respectively, and G is

the inverse lifetime of the intermediate state.

The ﬁrst term in Eqn. (10b) is independent of z and

does not contribute to the magnetic scattering; it is the

usual anomalous x-ray scattering term which contrib-

utes to white lines in the ﬂuorescence signal. The sec-

ond term is linear in z and contributes to the amplitude

of magnetic Bragg peaks. The third term is quadratic

in z and leads to second-order resonant harmonics.

More complex terms appear in the E2 contribution,

which contains terms up to fourth-order in z produc-

ing third- and fourth-order resonant harmonics.

In order to exploit the resonant enhancement for a

given magnetic species, the photon energy is tuned

to an absorption edge where the core electron is

promoted into the electronic shell that carries the

magnetization via the strong E1 transitions. Examples

744

Magnetism: Applications of Synchrotron Radiation

are given in Table 1. Theoretical estimates for the

resonant enhancements predict that the resonant scat-

tering amplitude would reach 10r

at the M edges of

actinides and even 100r

at the M edges of rare earths,

but would be more modest at the L edges of rare

earths, around 0.1r

. A severe limitation arises from

the long wavelengths associated with the strongest

resonances. At wavelengths larger than 5A

, diffraction

experiments are difﬁcult owing to absorption prob-

lems and to the lack of accessible Bragg peaks. In

practice, actinide materials are studied at the L

2,3

and

4,5

edges, which allows the study of both the f and d

magnetism.

For rare earth materials, resonant scattering ex-

periments are performed at the L

2,3

edges, where d

electrons are probed. In the soft x-ray range the M

4,5

edges that give access to the f magnetism, allow

measurements of magnetic x-ray reﬂectivity and spin-

dependent absorption. The 3d transition metals can

be investigated at the L edges, where only reﬂectivity

measurements or studies of artiﬁcial multilayers can

be performed. The resonant process at the K edge

involving p electrons is weak and complex.

Figure 2 shows an example of the resonant en-

hancement as observed in the antiferromagnetic com-

pound UAs. At the M

edge of uranium, the resonant

enhancement of the x-ray magnetic scattering ampli-

tude has been measured to be 9r

yielding scattered

intensities in the 10

counts s

1

range. Such a large

scattering amplitude leads to potential applications,

which complement neutron diffraction results, taking

advantage of the resonant selectivity and of the large

resonant enhancement coupled with the large available

x-ray ﬂux. In short, resonant x-ray scattering makes it

possible to search for weak signals and to disentangle

magnetic properties of different chemical elements or

electronic shells. It should be pointed out that the gain

in scattered intensity at resonance does not make mag-

netic powder diffraction experiments readily feasible

with x rays, because of absorption and ﬂuorescence

effects. Powder neutron diffraction remains the probe

of choice for structure determination.

Weak scattering signals arise either from small

magnetic moments or from small scattering volumes.

There exist systems which possess extremely small

magnetic moments that neutrons cannot ‘‘see’’ unless

a large amount of material is available. Resonant

x rays are perfectly suited to studies of such systems

with constrained dimensions (microcrystals, surfaces,

and interfaces). Magnetic thin ﬁlms and magnetic

surfaces are investigated by using soft x-ray reﬂec-

tivity (Kao et al. 1994, Tonnerre et al. 1995) or

by scattering methods in the harder x-ray region

Figure 2

Resonant scattering at the M

and M

edges of uranium:

resonant enhancement of the antiferromagnetic

diffracted intensity in UAs as a function of the incident

photon energy. The two resonances are clearly seen. The

energy line shape of the intensity corresponds to the sum

of two interfering amplitudes with resonant

denominators.

Table 1

Significant resonances for selected magnetic species.

Resonant energy

Magnetic species Resonance process Energy (keV) Wavelength (A

)

3d transition metal Fe E1 p2d L

0.71 17.5

E1, E2 s2p, d K 7.1 1.75

5d transition metal Pt E1 p2d L

11.5–13 1.08–0.95

E1, E2 s2p, d K 78.4 0.16

4f rare earth Gd E1 d2f M

1.22–1.19 10.2–10.4

E1, E2 p2d, f L

7.9–7.2 1.57–1.72

5f actinide U E1 d2f M

3.7–3.5 3.35–3.54

E1, E2 p2d, f L

20.9–17.2 0.59–0.72

745

Magnetism: Applications of Synchrotron Radiation

(Watson et al. 1996, MacKay et al. 1996). The rela-

tionship of the magnetic spatial proﬁle and magnetic

roughness to the chemical or charge proﬁle can then

be determined owing to these enhanced intensities.

The chemical selectivity of resonant x-ray scatter-

ing is demonstrated in Fig. 3 which shows the

incident photon energy dependence of an antiferro-

magnetic Bragg peak from a mixed compound,

0.5

, containing two magnetic species,

uranium and neptunium. Tuning the photon energy

to a given edge (e.g., uranium M

edge), turns on the

signal from the uranium magnetization, while the

neptunium response is extinct (or at least several or-

ders of magnitude weaker). Conversely, data taken at

the neptunium M

edge probe the behavior of the

neptunium moments only. This selectivity of the

scattering species constitutes an advantage of x-ray

resonant techniques over nonresonant x-ray methods

and neutron techniques.

5. Spin Polarized Photon Absorption

The x-ray absorption cross-section is given by the

imaginary part of the scattering amplitude at Q ¼0

and resonant magnetic effects are also seen in ab-

sorption measurements. The observed effects are

related to the x-ray polarization. The absorption

coefﬁcients vary when the easy direction of the mag-

netization is changed with respect to the incident

x-ray polarization or vice versa: this effect is called

magnetic linear dichroism. The absorption of circu-

larly polarized x rays depends also on the helicity of

the incident photons relative to the direction of the

magnetization: this is magnetic circular dichroism

(MCD). In all measurements, the magnetic contrast

in the absorption process is obtained by changing the

relative orientation of the polarization and the mag-

netization. The observed dichroic signal is taken as

the ratio

R ¼

mðLÞmðRÞ

mðLÞþmðRÞ

where L and R denote the two photon helicities,

and m is the ﬂuorescent signal or the absorption

coefﬁcient.

Similarly to the resonant scattering amplitude, the

MCD signal is simply proportional to the spin polar-

ized density of states of the intermediate states that are

excited during the transition (Schu

tz et al.1987).

However, the orbital moment of the intermediate

states is also likely to play a significant role in deter-

mining transition probabilities, especially in the cases

of localized f-electron states. Indeed, a sum rule for the

integral of the dichroic signal (the imaginary part

of the magnetic scattering amplitude with y ¼0in

Eqn. (10b) over a given edge has been derived (Thole

et al. 1992) which allows a determination of the

ground state value of the orbital moment in the elec-

tronic available states. This sum rule, which is rigor-

ously valid only in the atomic case, has been extended

to single electron band models. Furthermore, other

sum rules have also been obtained involving expecta-

tion values of the spin operators (Carra et al. 1993).

Sum rules are derived for the absorption coefﬁ-

cient, related to f

¼Im{f

¼k

, _o)}; equivalent

sum rules for the scattering case, where the total

scattering amplitude 7 f

is measured, would be

more difﬁcult to extract. The dichroism methods can

bring new information on the ground state electronic

properties of magnetic systems. Compared to scat-

tering techniques, absorption methods have two con-

siderable advantages: (a) they can be performed

extremely rapidly (only the incident photon energy is

varied and nothing else changes); and (b) they do not

require single-crystal samples (any type of sample can

be studied). However, no information in Q-space is

obtained and MCD experiments can only probe

magnetized samples, such as ferromagnets and ferri-

magnets.

Dichroic effects are studied at low-energy absorp-

tion edges (L edges for 3d transition metals and M

edges of rare earths) by using ﬂuorescence or electron

Figure 3

Demonstration of chemical selectivity. The intensity of

the antiferromagnetic intensity from Np

0.5

measured as a function of photon energy around the

4,5

edges of uranium and neptunium. At the

neptunium M

edge the signal arising from the

magnetization on the neptunium sites is greater than the

uranium contributions by four or ﬁve orders of

magnitude.

746

Magnetism: Applications of Synchrotron Radiation

yield methods. At these energies, experiments are

sensitive to the surface state and to the magnetism at

surfaces. Local magnetic environments of magnetic

species are revealed by magnetic ﬂuorescence spectra.

Because of the chemical selectivity, the various com-

ponents of magnetic alloys and compounds can be

studied independently. Even images of ferromagnetic

domains have been obtained, leading to technological

applications (Schu

tz et al. 1997, Schneider et al.

1997). The combined use of MCD methods and x-ray

zone played microscopy can provide high-resolution

images of ferromagnetic domains with spatial reso-

lution of 50 nm and real time evolution. Figure 4

shows a magnetic domain pattern in a microstruc-

tured CoPt multiplayer. The pattern is obtained by

subtracting two images recorded at the cobalt L

edges with opposite radiation helicity. The resulting

contrast arises from the relative orientation of the

cobalt magnetization and light incidence. The white

(black) areas correspond to regions with magnetiza-

tion parallel (antiparallel) to the incident light as in-

dicated by the arrow. The magnetization is

perpendicular to the incident light in the gray areas.

A very promising application of MCD experiments

is the possibility of performing time-resolved studies.

The combination of the pulsed time structure of the

synchrotron x-ray beam and the fast acquisition rate

of MCD allows studies of magnetic dynamics of

ferromagnets. The use of energy-dispersive x-ray ab-

sorption enables fast dynamics to be studied (down to

nanoseconds) over a typical size of 20 mm. An exam-

ple is given in Fig. 5. The MCD signal has been

measured from a complex magnetic system consisting

of hard magnetic grains (Nd

B) embedded in a

soft matrix (spring magnet) at the L

edge of neo-

dymium. Owing to the selectivity of the MCD meth-

od, the neodymium hysteresis cycle can be observed

together with the relaxation response of neodymium

under the application of a pulse ﬁeld (Fig. 5). The

determination of the relaxation time makes it possible

to analyze the different mechanisms driving the

coercivity. Other applications include the studies of

dynamics of recording or switching devices (Bonﬁm

et al. 1998). The uniqueness of the chemical selectivity

makes time-resolved MCD an ideal diagnostic probe

for the magnetic properties of multicomponent mag-

netic devices such a spin valves and spring magnets.

6. Future Directions

Synchrotron methods for the study of magnetism

have been in use since the early 1980s, and the most

remarkable achievements using resonant scattering

have been obtained since the early 1990s. New ap-

plications have appeared, some of which have arisen

owing to the progress in instrumentation and some

from a better understanding of the physics. Synchro-

tron sources and x-ray instruments are likely to im-

prove, yielding new prospects for more applications

(studies of microcrystals, coherent effects and mag-

netic speckles, magnetic inelastic x-ray scattering,

time-resolved studies). Theoretical approaches, which

have been stimulated by experimental results, will in

turn lead to more fundamental applications and

studies of the microscopic magnetic properties of

solids. Synchrotron x rays will offer new tools for

detailed studies of magnetism, which complement

neutron scattering techniques.

See also : Magnetic Excitations in Solids; Muon Spin

Rotation: Applications in Magnetism; Transparent

Rare Earth Compounds: Magnetic Circular Dichro-

ism; Thin Film Magnetism: PEEM Studies

Figure 4

Difference images of magnetic domains in a patterned

CoPt multilayer taken at the cobalt L

edge. Squares

have side length of 20 mm. The arrow indicates the

incidence direction of the circularly polarized x rays.

Figure 5

Time response of neodymium magnetization under the

application of a pulsed magnetic ﬁeld of 300 mT.

747

Magnetism: Applications of Synchrotron Radiation

Bibliography

de Bergevin F, Brunel M 1972 Observation of magnetic super-

lattice peaks by x-ray diffraction of an antiferromagnetic

NiO crystal. Phys. Lett. 39A, 141–2

Blume M 1994 Magnetic effects in anomalous dispersion. In:

Materlik G, Sparks C J, Fischer K (eds.) Resonant Anoma-

lous X-ray Scattering. Elsevier, Amsterdam

Blume M, Gibbs D 1988 Polarization dependence of magnetic

x-ray scattering. Phys. Rev. B 37, 1779–89

Bonﬁm M, MacKay K, Pizzini S, San Miguel A, Tolentino H,

Giles C, Hagelstein M, Baudelet F, Malgrange C, Fontaine A

1998 Nanosecond-resolved XMCD on ID24 at the ESRF to

investigate the element-selective dynamics of magnetization

switching of Gd–Co amorphous thin ﬁlm. J. Synchrotron

Rad. 5, 750–2

Cahn R W, Lifshin E 1993 Concise Encyclopedia of Materials

Characterization. Pergamon, Oxford

Carra P, Ko

nig H, Thole B T, Altarelli M 1993 Magnetic x-ray

dichroism: general features of dipolar and quadrupolar spec-

tra. Physica B 192, 182

Fernandez V, Vettier C, de Bergevin F, Giles C, Neubeck W

1998 Observation of orbital momentum in NiO. Phys. Rev. B

57, 7870–6

Hannon J P, Tramell G T, Blume M, Gibbs D 1988 X-ray

resonance exchange scattering. Phys. Rev. Lett. 61, 1245–8

Kao C-C, Chen C T, Johnson E D, Hastings J B, Lin H I, Ho G

H, Meigs G, Brot J M, Hulbert S L, Idzerda Y U, Vettier C

1994 Dichroic interference effects in circularly polarized soft

x-ray resonant magnetic scattering. Phys. Rev. B 50, 9599–602

Lovesey S W, Collins S P 1996 X-Ray Scattering and Absorption

by Magnetic Materials. Oxford Science, New York

MacKay J F, Terchert C, Savage D E, Lagally M G 1996 El-

ement specific magnetization of buried interfaces by diffuse

x-ray resonant magnetic scattering. Phys. Rev. Lett. 77, 3925–8

Schneider C M, Fro

mter R, Ziethen C, Swiech W, Brookes N

B, Scho

nhense G, Kirschner J 1997 Magnetic domain imag-

ing with a photoemission microscope. Mater. Res. Soc.

Symp. Proc. 475, 381–92

Schu

tz G, Fischer P, Attenkofer K, Ahlers D 1997 New ap-

plications of x-ray magnetic circular dichroism. In: Johnson

R L, Schmidt-Bo

cking H, Sonntag B F (eds.) Proc. X-ray and

Inner-Shell Processes. AIP, Hamburg, Germany, pp. 512–33

Schu

tz G, Wagner W, Wilhelm W, Kiemle P, Zeller R, Frahm

R, Materlik G 1987 Absorption of circularly polarized x rays

in iron. Phys. Rev. Lett. 58, 737–40

Squires G L 1978 Introduction to the Theory of Thermal Neutron

Scattering. Cambridge University Press, Cambridge

Templeton D H 1994 X-ray resonance, then and now. In:

Materlik G, Sparks C J, Fischer K (eds.) Resonant Anoma-

lous X-ray Scattering. Elsevier, Amsterdam

Thole B T, Carra P, Sette F, van der Laan G 1992 X-ray cir-

cular dichroism as a probe of orbital magnetization. Phys.

Rev. Lett. 68, 1943–6

Tonnerre J M, Seve L, Raoux D, Rodmacq B, Souille G, Wolfers

P 1995 Soft x-ray resonant magnetic scattering from a mag-

netically coupled Ag/Ni multilayer. Phys. Rev. Lett. 75,740–3

Watson G M, Gibbs D, Lander G H, Gaulin B D, Berman L E,

Matzke H J, Ellis W 1996 X-ray scattering study of the

magnetic structure near the (001) surface of UO

. Phys. Rev.

Lett. 77, 751–4

C. Vettier

European Synchrotron Radiation Facility

Grenoble, France

Magnetism: High-ﬁeld

The effect of an applied magnetic ﬁeld on matter de-

pends on whether the ﬁeld is large enough to compete

with the magnetic interactions that are present within

the material. Only then can a modiﬁcation of the

magnetic state can be induced. The related change in

magnetization should be large enough to be observed

with sufﬁcient accuracy. High magnetic ﬁelds are

generated worldwide, in many laboratories and in

special user facilities. After a brief review of the tech-

niques that are applied to produce high magnetic

ﬁelds, this article focuses on a representative selection

of the large variety of phenomena that may be ob-

served in the magnetization of magnetic materials

when they are exposed to high magnetic ﬁelds. Also,

the information that can be deduced from the ob-

served high-ﬁeld behavior will be briefly discussed.

In magnetic materials, the exchange interaction

between the magnetic moments generally is the most

prominent interaction. Depending on the solid, the

exchange interaction may be of different type, and, at

temperatures where the thermal energy is lower than

the strength of the exchange interaction, will give rise

to an ordered structure of the magnetic moments.

The strength of the exchange interaction may be ex-

pressed in terms of an internal ‘‘exchange ﬁeld’’ that

acts on the magnetic moments and that may be as

high as 1000 T. Also, the magnetocrystalline aniso-

tropy in solids may be appreciable and, in specific

materials, may be equivalent to a few hundred teslas.

The examples discussed in this article have been

taken from the vast body of high-ﬁeld research that

has been carried out on transition metals, rare-earth

metals, alloys, and intermetallic compounds. For

other specific subjects and other categories of mate-

rials in which the response to high magnetic ﬁelds

may play a significant role, for instance low-dimen-

sional spin systems, critical phenomena, low-dimen-

sional semiconductor structures, heavy-fermion

systems, and superconductors, the reader is referred

to the articles devoted to these subjects and materials.

1. Production of High Magnetic Fields

Static magnetic ﬁelds can be generated by transmit-

ting electrical current through resistive coils that have

to be water-cooled in order to remove the dissipated

heat or by transmitting current through supercon-

ducting coils. In resistive coils, the largest ﬁelds made

in this way are in the range 30–35 T, whereas in su-

perconducting coils made of conventional supercon-

ductors, the maximum ﬁeld is around 23 T. Larger

static magnetic ﬁelds (up to 40–45 T) can be gener-

ated in hybrid magnets, in which superconducting

coils are placed around a water-cooled resistive-coil

system, in this way providing a supporting back-

ground ﬁeld of the order of 10 T.

748

Magnetism: High-ﬁeld

In resistive-coil systems, the value of the highest

possible ﬁeld is mainly determined by the available

electrical power and by the limited cooling capacity.

In the case of superconducting coils, the main lim-

iting factor is the ﬁeld at which the coil material

looses its superconducting properties and becomes

normal. Coils made of high T

superconductors may

lead to significant progress. However, for this to be

possible, a number of important technological prob-

lems, for instance the production of wire of adequate

mechanical strength, have to be solved.

The range of possible ﬁelds is appreciably larger if

pulsed ﬁelds are considered. In pulsed magnets, the

coils are energized only for a short time during which

the dissipated heat cannot be removed by the cooling

water and is mainly absorbed by the coil, which

therefore increases in temperature during the pulse.

For pulsed ﬁelds, the coils are usually energized by

capacitor banks or ﬂywheel generators. In practice,

two time regimes are distinguished for the duration of

the ﬁeld pulse:

 long pulses with a duration of the order of 10 ms

to 1 s that produce ﬁelds in the range 60–80 T; and

 short pulses with a duration in the microsecond

region that produce ﬁelds in the range 100–500 T.

In general, short-pulse experiments are more dif-

ﬁcult than long-pulse experiments and, as a conse-

quence, less accurate. Also, in a metallic material, a

pulsed magnetic ﬁeld induces a current that is pro-

portional to the change of the ﬁeld with time. There-

fore, experiments on this important category of solids

should be performed in static ﬁelds, in ﬁelds that are

kept constant for a sufﬁciently long time, or in long-

pulse ﬁelds that vary only slowly with time. The

magnetization measurements presented in this article

have been performed in long-pulse ﬁelds. Some ex-

amples of facilities where long-pulse ﬁelds are gener-

ated are given in Table 1.

2. 3d Magnetism

In 3d metal-based metallic substances with itinerant

electrons, the magnetism arises from electrons that

occupy allowed states in incompletely ﬁlled electron

bands that are ﬁlled up to the Fermi energy and that

can be subdivided into two subbands with opposite

spin directions that are equally occupied in the par-

amagnetic state. In a ferromagnet, and if a magnetic

ﬁeld is applied also in a paramagnetic metal, the two

subbands are unequally occupied, thus giving rise to

a magnetic moment (see Itinerant Electron Systems:

Magnetism (Ferromagnetism)). Besides the exchange,

the density of electron states at the Fermi level and its

energy dependence determine the magnetic response

of a metal to an applied magnetic ﬁeld. In exchange-

enhanced (Pauli) paramagnetic substances with a

peculiar band structure near the Fermi energy, an

applied magnetic ﬁeld may induce a ﬁrst-order phase

transition from the paramagnetic to the ferromag-

netic state. Transitions of this type, from a state with

a relatively small magnetic moment to one with a

larger moment, are generally denoted as metamag-

netic transitions and occur, as discussed below, in

many different types of magnetic materials. YCo

(Fig. 1) is an example of a nearly ferromagnetic com-

pound that undergoes such a transition at low tem-

peratures at a critical ﬁeld as high as 69 T,

(see Metamagnetism: Itinerant Electrons).

3. 4f Magnetism

The rare-earth (R) metals with their partially ﬁlled 4f

shell and R-based compounds exhibit a large diver-

sity of magnetic structures which result from the

competition of the exchange interaction, the crystal-

line electric ﬁeld (CEF) interaction, and the quadru-

polar interaction, the latter in general being much

smaller than the former two (see Localized 4f and 5f

Table 1

Examples of long-pulse facilities.

Location

Maximum ﬁeld

in length

(T in mm)

Pulse length

(ms)

KU Leuven 60 in 20; 73 in 10 20; 10

NHMFL Los

Alamos

68 in 15; 60 in 32 20; 100

LNCMP

Toulouse

61 in 14 200

NRIM Tsukuba 65 in 16 100

Figure 1

Magnetization of YCo

at 10 K (after Duc and

Brommer 1999).

749

Magnetism: High-ﬁeld