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new term should be included in the general expression

of the coercivity (3) that becomes

¼ a



1 

25K



1=2

 bM

ð4Þ

The thermal term tends to decrease coercivity by

decreasing the relaxation time. Superparamagnetism

or disappearance of the hysteresis was a surprising

and amazing experimental observation found by

Bean and Livingston (1959) just while they tried to

decrease the particle size in order to prevent domain

wall contribution for ‘‘improving’’ hard properties

(Jacobs and Bean 1963). In 1949, Ne

el had predicted

superparamagnetism (Ne

el 1949). Nowadays, the

nanostructures formed by different amorphous and

nanocrystalline phases with different Curie tempera-

tures have lifted superparamagnetism and, in general,

relaxation processes (Garcı

a del Muro et al. 1997) to

an outstanding position of interest.

6. Effect of the Nanostructure

Finally, three examples, based on fairly recent exper-

iments and illustrative of the inﬂuence of the nano-

structure on the magnetization curve are summarized.

Nanocrystalline materials, composed of ferromag-

netic Fe(Si) nanograins embedded in an amorphous

matrix with lower Curie temperature, T

, exhibit a

noticeable thermal dependence of magnetization as

shown in Fig. 8 (Hernando and Kulik 1994). For

ToT

the coercivity is very low due to the exchange

coupling between the crystallites transmitted by the

matrix. As the temperature rises the magnetization of

the matrix drops and the grains are less coupled giv-

ing rise to a progressive increase of the coercivity that

reaches an abrupt maximum at T

, since at this

temperature the grains behave as single domains.

Further increase of the temperature leads to a super-

paramagnetic transition and the coercivity falls to

zero.

An example of the inﬂuence of the domain wall

width, d, on the coercivity and magnetization curve is

illustrated by Fig. 9 (Arcas et al. 2000). In a sample

composed of iron nanocrystallites embedded in

a FeZr amorphous matrix, d depends on the number

of crystallites. The inﬂuence on d of the exchange

Figure 8

Temperature dependence of the coercive ﬁeld for a

nanocrystalline material. Notice the drastic increase of

the coercive ﬁeld as we approach the Curie temperature

of the amorphous matrix (T

E370 1C).

Figure 9

Coercive ﬁeld and domain patterns of a FeZrBCu

amorphous alloy as a function of the annealing

temperature.

Figure 10

Shifted hysteresis loop, obtained by Kerr effect,

corresponding to an exchange coupled NiO/NiFe thin

ﬁlm system. The sample was cooled under an applied

ﬁeld of H ¼1000 Oe from 370 K down to room

temperature.

450

Magnetic Hysteresis

coupling between the grains analyzed by Herzer (see

Amorphous and Nanocrystalline Materials) is reﬂected

in the coercivity.

Finally an example of minor hysteresis loops ob-

tained around a ﬁxed point of the hysteresis loop,

shifted loops, is outlined. Spin–valve systems allow

the shift of the hysteresis loop through the coupling

between an antiferromagnetic (hard) layer and a

ferromagnetic (soft) layer. Figure 10 shows a typical

shifted hysteresis loop (Dimitrov et al. 1998). The

minor loop corresponding to the reversal of the mag-

netization at the soft layer takes place under the

effective exchange ﬁeld exerted by the hard layer.

Bibliography

Arcas J, Hernando A, Go

mez-Polo C, Castan

o F J, Va

zquez

M, Neuweiler A, Kronmu

ller H 2000 Exchange interaction

through amorphous intergranular layers in a two-phase sys-

tem. J. Phys.: Condens. Matter 12, 3255–65

Barkhausen H 1919 Two phenomena uncovered with help of

new ampliﬁers. Phys. Z 20, 401–3

Bean C P, Livingston J D 1959 Superparamagnetism. J. Appl.

Phys. 30, 120-9S

Becker J J 1970 Rare-earth compound magnets. J. Appl. Phys.

41, 1055–64

Bertotti G 1998 Hysteresis in Magnetism. Academic Press, New

York

Cullity B D 1972 Introduction to Magnetic Materials. Addison-

Wesley, Reading, MA

Dimitrov D V, Prados C, Ni C Y, Hadjipanayis G C, Xiao J Q

1998 Magnetoresistance in NiCoO/Py/Cu/Py. J. Magn.

Magn. Mater. 189, 25–31

Garcı

a del Muro M, Batle X, Labarta A, Gonza

lez J M, Mon-

tero M I 1997 The effect of magnetic interaction in barium

hexaferrite particles. J. Appl. Phys. 81, 3812–4

Givord D, Lu Q, Rossignol M F 1991 Coercivity in hard mag-

netic materials. In: Hadjipanayis G C, Prinz G A (eds.) Sci-

ence and Technology of Nanostructured Magnetic Materials.

Plenum, New York, pp. 635–56

Gonza

lez J M, Salcedo A, Cebollada F, Freijo J J, Mun

oz J L,

Hernando A 1999 Thermally activated demagnetization in

Co/Ni multilayers involving discrete identiﬁable stages. Appl.

Phys. Lett. 75, 847–9

Hernando A, Kulik T 1994 Exchange interactions through

amorphous paramagnetic layers in ferromagnetic nanocrys-

tals. Phys. Rev. B 49, 7064–7

Herzer G 1989 Grain structure and magnetism of nanocrystal-

line ferromagnets. IEEE Trans. Magn. 25, 3327–9

Jacobs I S, Bean C P 1963 Fine particles, thin ﬁlms and ex-

change anisotropy. In: Rado G T, Suhl H (eds.) Magnetism.

Academic Press, New York, Vol. III, pp. 271–350

Kronmu

ller H, Durst K-D, Sagawa M 1988 Analysis of the

magnetic hardening mechanism in RE-FeB permanent mag-

nets. J . Magn. Magn. Mater. 74, 291–302

el L 1949 Inﬂuence des ﬂuctuations thermiques sur l

aiman-

tation des grains ferromagne

tiques tre

s ﬁns. Comp. Rend.

228, 664–6

el L 1978 Oeuvres Scientiﬁques de Louis Ne

el. Editions du

CNRS, Paris

Reininger T, Kronmu

ller H, Go

mez-Polo C, Va

zquez M 1993

Magnetic domain observation in amorphous wires. J. Appl.

Phys. 73, 5357–9

Sixtus K J, Tonks L 1931 Propagation of large Barkhausen

discontinuities. Phys. Rev. 37, 930–58

Stoner E C, Wohlfarth E P 1948 A mechanism of magnetic

hysteresis in heterogeneous alloys. Philos. Trans. R. Soc. A

240, 599–642

A. Hernando, P. Crespo, P. Marı

n, and A. Gonza

lez

Instituto de Magnetismo Aplicado, Universidad

Complutense de Madrid-RENFE

Spain

Magnetic Layers: Anisotropy

A dictionary definition of anisotropy is ‘‘a difference

of property or of effect in different directions.’’ Mag-

netic anisotropy in materials is concerned with the

observation that the magnetization prefers to point

parallel or antiparallel to a particular direction or

axis. A detailed treatment of the fundamentals of

magnetic anisotropy is given by Chikazumi (1997).

Anisotropy can be related to the crystal structure

of the material and, in the case of thin-ﬁlm materials,

to the form of the material, to the importance of

the break of symmetry at the surfaces of the thin

layer, to any strain in the thin ﬁlm, to the morphol-

ogy of the microstructural units making up the ﬁlm,

to any directional atomic ordering in the ﬁlm, and

to any other interface effects at the junction of over-

laid ﬁlms. It is clear that perpendicular anisotropy,

i.e., anisotropy favoring an orientation of the mag-

netization normal to the plane of the ﬁlm, is one of

the most important materials requirements in MO

recording technology.

To a sufﬁcient approximation the effective aniso-

tropy, K

EFF

, can be written phenomenologically in

terms of a volume term, K

, and a surface term, K

EFF

¼ K

þ 2K

ð1Þ

where t

is the thickness of the magnetic element. K

necessarily contains a magnetocrystalline anisotropy

term, any stress term, any shape anisotropy term, any

growth-induced anisotropy term, and any other vol-

ume sources of anisotropy. The demagnetizing energy

for a ﬁlm magnetized normal to its surface is also

included as the last term:

¼ðK

þ K

?  m

=2Þð2Þ

In the case of a thin ﬁlm the surface term, which

accounts for the two surfaces, is only of significance if

is of nanometer dimensions. This can occur prac-

tically in multilayer systems. K

EFF

is positive for per-

pendicular magnetization.

451

Magnetic Layers: Anisotropy

1. Magnetocrystalline Anisotropy

The microscopic origin of this anisotropy is related to

the spin state of the magnetic moments and by the

symmetry of their arrangement in the crystal lattice

that involves spin–lattice coupling. It occurs in all

crystalline ferro- and ferrimagnetic materials.

The anisotropy can be describe phenomenological-

ly in terms of the direction cosines of the magneti-

zation with respect to rectangular coordinate axes or

in terms of spherical harmonics. Any perpendicular

magnetization will realistically occur in an effectively

uniaxial system. The latter representation gives, for a

simple hexagonal symmetry:

¼ K

sin

y þ K

sin

y þ ? þ K

sin

y cos 6j

ð3Þ

in terms of the anisotropy constant K

and the polar

and azimuthal angles y and j between the magnet-

ization and the c- and a-axes. In an oriented ﬁlm with

an easy axis normal or close to normal to the surface

of the ﬁlm, perpendicular magnetization can be

achieved, in the absence of any other sources of an-

isotropy, if the magnetocrystalline anisotropy energy

is greater than the demagnetizing energy. This re-

quires, following Eqn. (2), to a sufﬁcient approxima-

tion neglecting higher terms K

/2.

2. Stress Anisotropy

This anisotropy comes from stresses produced in the

ﬁlm by the deposition process or by thermal expan-

sion differences between the substrate and the mag-

netic ﬁlm. The magnetoelastic energy produced by

a stress s is essentially the product of this stress and

the resulting value of magnetic strain or magneto-

striction, l. Again, assuming a uniaxial system the

volume magnetoelastic energy is given by

¼ 23sl

cos

y=2 ð4Þ

where l

is an isotropic magnetostriction coefﬁcient

and y is the angle between the magnetization M

and

s. Stress can therefore create uniaxial anisotropy with

a relevant stress-induced anisotropy constant given by

¼ 3sl

=2 ð5Þ

The stress axis is an easy direction of magnetization

if sl

40, i.e., positive magnetostriction will promote

perpendicular magnetization for a compressive stress

in the ﬁlm while a negative constant requires a tensile

stress.

3. Shape Anisotropy

In general magnetostatic energy in a thin ﬁlm acts to

orient the magnetization in the plane of the ﬁlm as

suggested above. However, many deposited ﬁlms can

contain microstructural units that by their shape and

orientation favor magnetization normal to the ﬁlm.

This is very possible in ﬁlms that contain columnar

grains or directional voids. In a prolate spheroid the

magnetostatic energy can be written as

¼ m

ðN

 N

ÞM

sin

y=2 ð6Þ

where N

and N

are constant factors known as de-

magnetizing factors related to the semiminor and

semimajor axes, respectively, and y is the angle be-

tween M

and the c-axis. In analogy to the case of

stress, a shape anisotropy constant can be written as

¼ m

ðN

 N

ÞM

=2 ð7Þ

If N

then the shape anisotropy is a minimum

with M

along the c-axis.

4. Growth-induced Anisotropy

Thin ﬁlms essentially condense and grow in a unidi-

rectional manner from the substrate surface. This can

lead to particular growth morphologies and also

directional ordering of atoms and a so-called growth-

induced anisotropy. This source of anisotropy is im-

portant in ferrite and garnet ﬁlms and in amorphous

alloy ﬁlms.

In amorphous ﬁlms single magnetic ions may have

a particular atomic coordination, say in the plane of

the ﬁlm, which gives rise to a directional magnetic

coupling and perpendicular anisotropy. Also, atom

pairs may order preferentially parallel or normal to

the surface, and in mixed oxide crystalline ﬁlms at-

oms may occupy lattice sites in a preferential manner,

so reducing the magnetic symmetry of the system.

The anisotropy may be represented phenomenolog-

ically in terms of the direction cosines of the mag-

netization with respect to any lattice and the normal

to the growth surface. Again, for a uniaxial system

¼ K

sin

y ð8Þ

where y is the angle between the growth direction and

the magnetization.

5. Surface or Interface Anisotropy

Interface or surface anisotropy is related to the re-

duced symmetry, lower coordination numbers, the

presence of localized near-surface and interface

states, and other effects at a surface (Bayreuther

1989). The reduced symmetry at the surface modiﬁes

the magnetocrystalline anisotropy and this contribu-

tion can, in fact, be positive or negative encouraging

out-of-plane and in-plane magnetization. There can

also be a contribution to the interface anisotropy that

is magnetoelastic in origin. This is related to stress

452

Magnetic Layers: Anisotropy

relief by defect formation at interfaces. It is inversely

related to the layer thickness and may therefore be

significant at small thicknesses.

Phenomenologically the effect of surface aniso-

tropy can be represented by a term K

added to the

volume anisotropy in an equation for the total

anisotropy, as shown in Eqn. (1). Conventionally, a

positive K

EFF

signiﬁes a perpendicular anisotropy

and a plot of K

EFF

against t

gives a slope of K

and an intercept of 2K

There is one further anisotropy that will be men-

tioned only briefly as it is not important here: ex-

change anisotropy. This effect is unidirectional and

involves the pinning of moments in a ferromagnet

layer by an adjacent antiferromagnet layer on cooling

through the Ne

el temperature of the antiferromagnet

in an applied ﬁeld. Exchange anisotropy is of growing

importance in several magnetic thin-ﬁlm devices such

as giant magnetoresistance sensors.

6. Materials

6.1 Rare Earth–Transition Metal Alloy Films

The generic materials that form the various layers in

the storage medium in MO recording are amorphous

rare earth–transition metal alloy (RE–TM) ﬁlms.

RE–TM ﬁlms are treated in a review by Grundy

(1994). In brief, the deposition and alloying of the

heavy rare earths gadolinium, terbium, and dyspro-

sium with cobalt and/or iron produces thin ferrimag-

netic ﬁlms with the necessary magnetic coercivity, in

relation to the compensation phenomenon, and

perpendicular anisotropy to store stable magneto-

optically written bits in the memory layer. The per-

pendicular anisotropy is composition dependent and,

more than any other magnetic parameter, it can be

strongly dependent on fabrication conditions and

microstructure. For example, early measurements

showed that K

EFF

40 for bias sputtered GdCo and

evaporated GdFe ﬁlms, whereas K

EFF

o0 for evap-

orated and zero-bias sputtered GdCo and GdFe

sputtered at relatively high biases. In most situations

several sources of anisotropy may be active. Meas-

ured values of the principal perpendicular anisotropy

constant for compositions of interest are of the order

of 5 10

3

Magnetocrystalline anisotropy is not relevant in

amorphous ﬁlms and the potential sources of anisot-

ropy therefore come from any growth-induced struc-

tural anisotropy, atomic ordering, stress, or shape

effects. The ﬁrst growth-induced anisotropy to be

considered is single-ion anisotropy (Suzuki et al.

1987) that may be present with non-S state ions such

as terbium and with dysprosium but not with gado-

linium. An anisotropic distribution of atoms is as-

sumed with more nearest neighbors in the plane of

the ﬁlm. Interactions such as that between the RE 4f

electrons and the surrounding ions give perpendicular

anisotropy in such a ‘‘bond-order’’ anisotropy

(Prados et al. 1997).

The second ordering effect, that of pair ordering

(Mizoguchi and Cargill 1979), has also found favor in

explaining the perpendicular anisotropy in RE–TM

alloy ﬁlms. The atomic arrangement in amorphous

ﬁlms is only pseudorandom and may include slight

chemical order in which some TM–TM or RE–TM

pairs are oriented parallel or normal to the plane of

the ﬁlm. There appears to be experimental evidence

for such an arrangement in TbFe ﬁlms (Hufnagel

et al. 1995) and good correlation between modiﬁca-

tions of such an anisotropic local atomic arrangement

on annealing with loss of magnetic anisotropy

(Harris et al. 1993). Calculations of anisotropy from

such arrangements suggest that only a few percent of

atoms need be coupled in this way to promote per-

pendicular magnetization. The large anisotropies ob-

served in some substituted TbREFe alloys may only

be explained by a pair ordering mechanism, but the

complete picture is not always clear.

Stress in thin ﬁlms is related to the deposition

process and deposition conditions, e.g., the argon

pressure during sputtering and the substrate temper-

ature. A change from compressive to tensile stress

with increasing argon pressure has been observed in

sputter-deposited RE–Fe. In general, RE–TM ﬁlms

deposited at ambient temperatures should not suffer

much thermal stress due to mismatch of the expan-

sion coefﬁcients for the ﬁlm and the substrate. Any

residual stress will couple with magnetostriction and

produce stress-induced anisotropy. Magnetostriction

in Gd–TM alloys is relatively small at B10

6

–10

5

whereas measurements for TbFe and TbFeCo and

TbDyFe ﬁlms ﬁnd values of B2 10

4

–7.5 10

4

(Williams and Grundy 1994). Clearly, in terbium-

based alloys magnetostriction can play a significant

role in providing stress-induced perpendicular aniso-

tropy (Prados et al. 1997) and residual values of the

order of 3 10

3

have been measured (Cheng

et al. 1989).

PVD techniques, particularly sputter deposition,

can create anisotropic microstructures in thin ﬁlms,

e.g., the well-known columnar structure, which are

dependent on factors such as surface mobility in the

growing ﬁlm and the inclusion of sputtering gas.

These factors appear to be mainly dependent on the

argon pressure and substrate temperature during

deposition and on any target bias. Thermalization of

the sputtering process at higher pressures, the use of

heavier sputtering gases, and reduced bombardment

of the growing ﬁlm lead to coarser microstructures.

The maximum possible value for shape-induced

anisotropy would be 0.5m

or typically 10

–10

3

, and in general this is not sufﬁcient to support

perpendicular magnetization. This model of aniso-

tropy also does not ﬁt with observations that the

anisotropy can vary smoothly through the compen-

sation point, where M

is zero or at least very small,

453

Magnetic Layers: Anisotropy

and that it reaches its largest values in dense, micro-

structurally featureless ﬁlms.

6.2 Magnetic Oxides

Other candidates for MO recording that have been

investigated are garnet and uniaxial ferrite ﬁlms. In

most cases ﬁlms prepared on ambient temperature

substrates are amorphous and must be crystallized to

produce the magnetic mixed oxide. The deposition

conditions and the subsequent nucleation and growth

process on annealing affect the microstructure and

magnetic properties of the ﬁlm. Magnetic properties

can also be tailored in cubic RE

garnet

ﬁlms by substitution with particular ions; dysprosium

typically enhances perpendicular anisotropy and bis-

muth and cerium substitutions improve the magneto-

optic interaction.

Any perpendicular anisotropy in polycrystalline

cubic ﬁlms must originate in stress, growth-induced

ordering, or microstructural inhomogeneities. Meas-

ured K

EFF

values for substituted garnet ﬁlms can

reach B5 10

3

at the compensation tempera-

ture. Calculations of any stress-induced anisotropy

from the thermal mismatch between ﬁlm and subst-

rate give values of this order. Such anisotropy values

are relatively low but, coupled with reduced magnet-

ization values near compensation, are sufﬁcient to

support perpendicular magnetization and reasonable

coercivities.

Cubic and hexagonal ferrite ﬁlms also have useful

magneto-optic properties and can be prepared with

perpendicular anisotropy. The intrinsic uniaxial

magnetocrystalline anisotropy in hexagonal Ba,Sr–

ferrites of the order 5 10

3

is sufﬁcient

to ensure K

EFF

40 in (0001) textured polycrystalline

ﬁlms. The high anisotropy ensures high coercivities in

ﬁlms in which the value of M

can be controlled by

substitution, typically cobalt, titanium, lanthanum,

or zinc (e.g., Atkinson et al. 1994, Ogata et al. 1999).

Cubic ferrites, e.g., CoOFe

also have large intrin-

sic anisotropies that are a disadvantage in attempts to

create a stress-induced preferred direction normal to

the ﬁlm plane.

6.3 Multilayer Films

In nanoscaled multilayered thin ﬁlms the contribution

of any surface anisotropy to the total anisotropy can

become significant. Typical systems in which this is the

case are Co,CoNi/X, where X can be Ni, Cu, Ru, Pd,

V, Pt, and Au, and RE/TM multilayers such as Tb/Fe.

In the ﬁrst group attention has focused on

Co,CoNi/Pt,Pd multilayers for MO recording inves-

tigations. These systems have increased Kerr rota-

tions at short wavelengths. A rough calculation for a

Co/Pt multilayer using the values of K

for f.c.c.

cobalt (the cobalt layers in these systems are in the

cubic phase), a value of 1400 kA m

1

for M

and a

typical value of K

of 0.5 mJ m

2

in Eqn. (1) shows

that the cobalt layers should be less than about 1 nm

thick. A plot of any experimentally determined

EFF

against t

gives an intercept at t

¼0of

the surface anisotropy and the slope gives the volume

contribution. Several sources of anisotropy may be

present and it has been shown that magnetostrictive

stress-induced anisotropy makes a significant contri-

bution to the volume anisotropy in Co/Pd multilayers

but not in Co/Pt multilayers (Umeda et al. 1996). In

practice the cobalt layer is maintained below

B0.4 nm in the multilayers whereas the thickness of

the platinum layer is not critical in affecting the ef-

fective anisotropy but values below 2 nm are usual.

The effective anisotropy of the multilayer can be

affected by the growth conditions. The use of differ-

ent substrates, the inclusion of underlayers, the use of

different sputtering gases at different pressures, and

different substrate temperatures have all been shown

to affect the microstructure of multilayer ﬁlms. A

volume contribution can be obtained by a preferred

texture, which is usually /111S in polycrystalline

cubic ﬁlms, and the surface contribution is dependent

on the form and sharpness of the interfaces in the

system. This ﬁts well with the observation of im-

proved /111S texture with underlayer thickness. In-

vestigations of the effects of the sputtering gas show

that thermalization of the deposition process and the

reduction in bombardment of the growing ﬁlm can

increase interface roughness but lead to increased in-

terface anisotropy (Carcia et al. 1993).

Other multilayer ﬁlms explored for their anisotropic

properties and their potential for MO recording

investigations are RE/TM systems with the basic

compositions Gd,Tb/Fe,Co (e.g., Jamet et al.1996).

For example, perpendicular anisotropy is observed in

sputter-deposited Tb/Fe and Tb/Co multilayers, as in

Co/Pt systems, when the thickness of the layers is be-

low 1 nm or 2 nm. Again, the value of K

EFF

depends

on the thickness of the TM layers and indicates the

presence of a significant surface anisotropy. Typical

values of K

EFF

can vary between 5 10

3

for

Tb/Co multilayers and 10

3

for Tb/FeCo.

However, these values can be dependent on the

details of the coupling between the RE and TM layers

and an additional property of these systems is that

they can show antiferromagnetic coupling and ferri-

magnetic ordering and a compensation temperature.

This behavior can be tuned by varying the relative

thicknesses of the two layers and also in proportion

to the composition of the equivalent alloy. Magnetic

spin reorientation effects also occur as a function of

temperature, in which the system is dominated by the

RE and TM magnetization in different temperature

ranges as in homogeneous alloys. The crystal struc-

ture of the layers is also unusual in that for the thin-

ner layers the RE and TM are amorphous but for

thicker layers the TM is crystalline.

454

Magnetic Layers: Anisotropy

Exchange coupled layers are the basis of media for

super-resolution MO storage techniques. Although

not multilayers in the usual sense, temperature-

dependent spin reorientations occur also in these bi-

or trilayer structures that are used in the read-out

process (e.g., Nishimura et al. 1996). The perpendic-

ular anisotropy in the memory layer, e.g., TbFeCo,

the mediating effect on exchange coupling of any in-

termediate layer, and the in-plane anisotropy in the

read-out layer, e.g., GdFeCo, can clearly be control-

led by adjustment of compositions for the required

temperatures (Stavrou et al. 2000) (see also Magneto-

optic Recording: Overwrite and Associated Problems).

6.4 Other Materials

The ﬁrst requirement of a thin-ﬁlm material for MO

recording is significant magneto-optic activity at

wavelengths of interest. As already made clear, the

second requirement is perpendicular anisotropy that

is sufﬁciently strong to maintain magnetization nor-

mal to the plane of the ﬁlm. This ﬁrst property has

been the trigger for successful investigations of many

metallic alloys, oxides, and composite materials but

the second property has often not been realized. Sev-

eral materials of the many that have been investigated

can be addressed.

The relatively high Kerr rotations observed for

CoPt alloys, rather than multilayers, has suggested

their possible use as MO recording media. Growth on

oriented platinum underlayers at temperatures B200–

500 1C can result in ﬁlms with a perpendicular K

EFF

greater than 10

3

(Lin and Gorman 1992).

Equiatomic CoPt ﬁlms grown at B500 1C show or-

dered face-centered tetragonal (f.c.t.) and disordered

cubic phases with /111S and /200S preferred

orientations and CoPt

ﬁlms grown at B200 1C are

also f.c.t. The large effective anisotropies have been

associated with the large K

along the tetragonal

c-axis that is oriented normal to the ﬁlm plane (Iwata

et al. 1999).

Alloys related to the Heusler alloys have very in-

teresting MO properties. PtMnSb, with the C1

struc-

ture has a very large Kerr rotation of B21 at 633 nm.

This is related to its semimetallic nature and unusual

band structure. Unfortunately the compounds have

cubic symmetry and deposited ﬁlms show in-plane

anisotropy and low coercivities (Attaran and Grundy

1989, Carey et al. 1993). MnBi, MnSb, and related

compounds, such as MnGaGe, have also been inves-

tigated for MO applications over many years but

have not been adopted because, although their mag-

neto-optic properties are very attractive, difﬁculties in

thin-ﬁlm fabrication and magnetic and structural in-

stabilities make them unsuitable.

See also: Magnetic Films: Anisotropy; Mono-

layer Films: Magnetism; Magneto-optic Recording

Materials: Chemical Stability and Life Time; Mag-

neto-optic Recording: Total Film Stack, Layer Con-

ﬁguration; Magneto-optic Multilayers

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P. J. Grundy

University of Salford, Manchester, UK

Magnetic Levitation: Materials and

Processes

Magnetic levitation is one of the most outstanding

properties of superconductors, which in addition has

launched the development of several electromechan-

ical systems. The simplest experiment consists of a

single permanent magnet levitating in a stable posi-

tion over a superconducting pellet refrigerated with

liquid nitrogen.

It is indeed the characteristic of stable levitation

that gives rise to great interest in devices such as

magnetic bearings, rotating machinery, linear trans-

port systems, etc.

The axial vertical force of a permanent magnet over

a superconductor stems from the ﬂux exclusion asso-

ciated with materials with high critical currents (Moon

1994). In this case, the following can be written:

ðM

r

ÞB

ext

where M is the magnetization of the superconductor,

ext

is the magnetic ﬁeld generated by the permanent

magnet, and the integral is extended over the whole

volume of the superconductor.

Therefore a body may magnetically levitate if the

vertical gradient of the magnetic induction displays a

positive F

component, which eventually overcomes

the weight of the permanent magnet. From the su-

perconducting material point of view, the generation

of a large magnetization requires current loops

shielding the magnetic ﬁeld generated by the perma-

nent magnet. According to the critical state model, a

partial ﬂux penetration occurs in which the ﬂux gra-

dient obeys the Ampere law rotB ¼m

, where J

the critical current of the superconductor. Hence, the

magnetization of the superconductor increases only if

7 or the area of the corresponding current loop

increases.

Consequently, applications based on the magnetic

levitation phenomenon require large quasisingle-crys-

talline superconducting materials with high critical

currents.

An additional advantage of the high critical cur-

rent density is the enhanced lateral and vertical sta-

bility, since magnetic stiffness is proportional to the

pinning capability of the vortices penetrated within

the superconductor. It must also be noted that be-

cause of the hysteretic nature of the magnetization of

hard superconductors the magnetic levitation force

will also be history dependent (Fig. 1). For instance,

if the cooling of the superconductor is performed

with the permanent magnet in close contact with the

superconductor (ﬁeld cooling procedure), an attrac-

tive force will be generated when retrieving it and,

hence, the phenomenon of a stable magnetic suspen-

sion may also be obtained.

1. Superconducting Materials

The development of practical applications based on

magnetically levitating systems working at liquid

nitrogen temperature requires the use of supercon-

ducting materials with high critical currents at the

magnetic ﬁelds generated by high-power NdFeB or

SmCo magnets (B

E1 T; see Magnets: Sintered).

Among the different high-temperature supercon-

ducting phases, that presenting the highest J

at 77 K

is YBa

(Y-123), which displays an irreversi-

bility line (the magnetic ﬁeld where J

E0) at 77 K

around 5–7 T. Also the isomorphous systems Re-123

(Re ¼Nd, Sm), which may have irreversibility lines as

high as 10 T at 77 K, should be considered.

Also to be taken into account is the fact that the

critical currents of cuprate superconductors are

strongly anisotropic, the highest being those ﬂowing

within the ab-planes. For this reason, an optimized

Figure 1

Hysteretic levitation force measured when a permanent

magnet approaches a superconductor in a zero-ﬁeld

cooling process (1) for the ﬁrst time and (2) after a whole

cycle when some ﬂux has been trapped in the

superconductor.

456

Magnetic Lev itation: Materials and Processes

material for magnetic levitation should have the ab-

planes perpendicular to the vertical component of the

magnetic ﬁeld of the permanent magnet. In conclu-

sion, the most appropriate materials for magnetic

levitation are bulk quasisingle-crystalline ReBa

(Re ¼Y, Nd, Sm) pellets with ab-planes ori-

ented parallel to the basal surface.

2. Processing of Bulk ReBa

(Re ¼Y, Nd, Sm)

The preparation of large-grain Y-123 ceramics is

based on melt texturing processes. Essentially these

techniques rely on a controlled crystallization from

a semisolid state following the peritectic reaction

BaCuO

(s)þ3BaCuO

(l)þ2CuO(l)-2YBa

The peritectic decomposition temperature of Y-123

occurs at T

E1010 1C, thus melt processing requires

heating the samples at temperatures above T

,typi-

cally 1040–1110 1C, and cooling them at a typical rate

of 1 mmh

1

in such a way that a single large grain

may be grown.

The generation of single-grain Y-123 materials re-

quires carrying out a directional solidiﬁcation process

where a selection of the nucleation centers is done

and the conditions of a plane growth front are still

maintained. Two techniques have been used success-

fully for this purpose: the Bridgman growth method

where a temperature gradient is imposed (typically

10 1Ccm

1

) and the top seeding growth (TSG)

technique where the nucleation is generated at a

crystalline seed while the homogeneous nucleation is

avoided through a limitation of the degree of under-

cooling of the liquid.

The Bridgman technique appears to be more

adapted to long ceramic shapes while the TSG tech-

nique enables one to grow large-diameter samples

having the ab-planes oriented parallel to the basal

surface. Thus, the TSG technique is the most suit-

able for preparing samples for magnetic levitation

applications. The seeds that have been found to be

chemically and structurally compatible with the high-

temperature semisolid state are MgO and ReBa

(Re ¼Nd, Sm) single crystals. Re-123 crystals

are preferred because they have a crystalline structure

closer to that of the Y-123 phase. However, they have

peritectic decomposition temperatures only 30–50 1C

above that of Y-123 and thus they may display some

solubility that has to be controlled.

Single-grain cylindrical materials with diameters

up to 10 cm and the ab-planes oriented parallel to the

basal plane have been grown based on this method-

ology. Levitation forces greater than 1676 N can be

reached with a single SmCo permanent magnet with

¼0.4 T, which corresponds to a magnetic pressure

greater than 2.2 10

3

(Sawamura 1999).

In order to grow large domains it is essential to select

a narrow temperature window where crystallization

is initiated only at the seed and still providing enough

driving force to the growth front. In situ optical ob-

servation of the growth process shows that a progres-

sive decrease of the growth rate may occur, probably

because of a change of the liquid composition

(Gautier-Picard et al. 1997).

Analysis and control of the microstructure of the

single-domain material is essential, both to understand

the growth process and to optimize the superconduct-

ing performance. Several additives are included in the

green pellets to minimize the liquid loss and reﬁne the

ﬁnal size of the Y-211 precipitates, which remain em-

bedded in the matrix as a consequence of the sluggish

character of the peritectic reaction. Platinum and

CeO

particles are found to fulﬁll perfectly this second

requirement by keeping the Y-211 particles in the

submicrometer range, thus avoiding the coarsening of

Y-211 particles in the semisolid state (Fig. 2).

The beneﬁcial effects of the Y-211 precipitates are

twofold: they increase the mechanical toughness and

they enhance the critical currents that rise typically to

5 10

Acm

2

at 77 K and null ﬁeld. A typical op-

timal composition of Y-123/211 ceramic tiles used for

magnetic levitation would be 64% YBa

35% Y

BaCuO

þ1% CeO

Large batch processes of up to 30 samples having

diameters of 40 mm have been demonstrated using

quasi-isothermal furnaces with a good reproducibility

of their performance. Thus there is no major limitation

to scale-up of the TSG process to industrial produc-

tion (Cardwell et al. 1998, p. 75, Ullrich et al.1999).

Additionally, it is well known that the supercon-

ducting properties of the Y-123/211 composites may

be strongly modiﬁed through changes of the micro-

structure (Sandiumenge et al. 1997). Postprocessing

methodologies, such as oxygenation, isostatic press-

ing, or irradiation, show strong modiﬁcation of the

critical currents of Y-123/211 melt textured ceramics.

For instance, an enhanced pinning capability with

Figure 2

Scanning electron microscopy image of a YBa

BaCuO

composite where the Y-211 precipitates

imbedded in the superconducting matrix can be

observed.

457

Magnetic Lev itation: Materials and Processes

E10

Acm

2

at 77 K has been demonstrated

through a cold isostatic pressing postprocessing treat-

ment at 300 1C under 2 kbar of argon (Martinez et al.

1999). This process generates nanometric stacking

fault loops that are very effective vortex pinning cen-

ters. Its potential relies in the enhanced levitation

force that can be obtained in large-scale ceramic

fabrication.

New effective ﬂux pinning centers have also been

generated in Re-123 (Re ¼Nd, Sm) materials dis-

playing a large ﬁshtail effect at 77 K. Actually,

these materials form a solid solution, Re

1 þx

2–x

7 þd

, and the degree of Re substitution at the

barium sites can be controlled through processing.

When a small excess, in the region xE0.05, is in-

cluded there is a tendency to the formation of nano-

metric clusters where the local oxygen content is

higher. These nanometric clusters have a decreased

superconducting order parameter and consequently

they become normal when a magnetic ﬁeld is applied,

thus becoming ﬂux pinning centers at intermediate

ﬁelds. The ﬁnal concentration of neodymium excess

and its pinning effectiveness is found to depend on

the oxygenation pressure during the growth and

postprocessing treatment (Puig et al. 1998).

The potential of Re-123 ceramic tiles for use in

magnetic levitation or as trapped-ﬁeld magnets ap-

pears to be very high; however, owing to the com-

plexity of their phase diagrams the preparation

process must be tightly controlled (Murakami 1998).

The most successful nondestructive testing meth-

odologies of the ﬁnal superconducting tiles are the

measurement of the levitation force, which may be

considered as an integral process, or the determina-

tion of the magnetic remanence ﬂux proﬁles by means

of Hall effect microprobes. In the latter case, it ap-

pears very easy to detect any remaining grain bound-

ary or even subgrain boundaries and macroscopic

compositional inhomogeneities (Fig. 3).

Demonstrations that bulk melt textured tiles may

be integrated in real systems such as magnetic bear-

ings, motors, ﬂywheels, etc., continue. In this respect,

the feasibility appears very promising of cutting, as-

sembling, or even welding these materials for large-

diameter rotors or the buildup of more complex

shapes (Cardwell et al. 1998).

See also: Magnetic Levitation: Superconducting

Bearings; Superconducting Permanent Magnets:

Potential Applications; Superconducting Permanent

Magnets: Principles and Results

Bibliography

Cardwell D A, Murakami M, Salama K 1998 Processing and

applications of superconducting (Re)BCO large grain mate-

rials. Mater. Sci. Eng. B53, 1–237

Gautier-Picard P, Beaugnon E, Tournier R 1997 In-situ

YBa

growth analysis. Physica C 276, 35–41

Martı

nez B, Richard L, Sandiumenge F, Puig T, Rabier J,

Obradors X 1999 Enhanced critical currents in melt textured

YBa

by cold isostatic pressing. Appl. Phys. Lett. 74,

73–5

Moon F C 1994 Superconducting Levitation. Wiley, New York

Murakami M 1998 Key issues for the characterization of

Re–Ba–Cu–O systems (Re: Nd, Sm, Eu, Gd). Appl. Super-

cond. 6, 51–9

Sandiumenge F, Martı

nez B, Obradors X 1997 Tailoring of

microstructure and critical currents in directionally solidiﬁed

YBa

. Supercond. Sci. Technol. 10, A93–119

Puig T, Obradors X, Martı

nez B, Alonso J A 1998 Enhanced

interface and aging by high pressure oxygenation of melt

textured Nd

1 þx

2–x

7-d

. Physica C 308, 115–22

Sawamura M 1999 Recent activity of bulk material development

and application. Workshop on Bulk High Temperature Super-

conductors and their Applications. Argonne National Labo-

ratory, Argonne, IL

Ullrich M, Walter H, Leenders A, Freyhardt H C 1999 Batch

production of high-quality customized-shaped monolithic

HTSC. Physica C 311, 86–92

X. Obradors and T. Puig

Institut de Cie

ncia de Materials de Barcelona

Spain

Figure 3

Micrograph of a YBa

pellet prepared by TSG

and ﬂux remanence proﬁle of the superconducting

cylinder after a partial penetration of magnetic ﬂux in a

zero-ﬁeld cooling process. The observed asymmetries

correspond to subgrain boundaries within a single

domain.

458

Magnetic Lev itation: Materials and Processes

Magnetic Levitation: Superconductin g

Bearings

Passive superconducting bearings are based on the

stable levitation of a permanent magnet over a bulk

superconductor. This stable levitation is due to the

pinning of magnetic ﬂux surrounding the permanent

magnet on defects within the superconductor. The

interest in superconducting bearings strongly in-

creased since bulk, melt-textured YBa

7x

(YBCO) is available, because this high-temperature

superconductor exhibits large critical current densi-

ties at liquid nitrogen temperatures. Superconducting

bearings can be used for rotating machines and for

linear transportation systems. The main parameters

of superconducting bearings as the levitation force

and the magnetic stiffness will be discussed.

1. Levitation and Superconducting Magnetic

Bearings

One of the most promising applications of bulk

high-T

superconductors is the superconducting

levitation which can be used in rotating supercon-

ducting magnetic bearings and in noncontact linear

transportation. The advantage of superconducting

magnetic bearings is that the levitation of a ferro-

magnetic permanent magnet over a bulk YBCO

sample is completely passive. Contrary to this, no

stable levitation is possible for two permanent

magnets which interact via a 1/r

force law the

Earnshaw’s theorem (Earnshaw 1842). Such an in-

verse square law is governed by the Laplace equa-

tion and allows only saddle-type equilibria resulting

in unstable levitation. Therefore, conventional mag-

netic bearings composed of ferromagnetic perma-

nent magnets require an active feedback control in

order to stabilize the levitation. Inherently stable

levitation can be achieved by introducing diamag-

netic materials such as superconductors (Braunbeck

1939). The ﬁrst superconducting bearing was devel-

oped for a small motor (Buchhold 1960) using low-

temperature superconductors cooled with liquid

helium. The interest in superconducting bearings

strongly increased after the discovery of high-T

su-

perconductors (HTSs), when levitation experiments

could be done in open styrofoam containers ﬁlled

with liquid nitrogen. Rotating HTS bearings are

particularly interesting for cryogenic turbopumps,

superconducting motors, high-speed centrifuges, and

for ﬂywheel energy storage systems, whereas linear

HTS bearings can advantageously used for noncon-

tact transport systems in clean rooms of microelec-

tronic factories.

2. Materials Aspects: Bulk YBCO

Superconductors

The material of choice for superconducting bearings

is bulk YBCO. YBCO has a superconducting tran-

sition temperature of 92 K and a relatively high ir-

reversibility ﬁeld of H

irr

B7 T at 77 K for magnetic

ﬁelds oriented parallel to the crystallographic c-axis.

Applications are restricted to magnetic ﬁelds below

irr

, because the critical current density disappears

at the irreversibility ﬁeld H

irr

with H

as the

upper critical ﬁeld.

The levitation force of a superconducting bearing

is proportional to the magnetization M of the bulk

superconductor which is given by M ¼ Aj

d, where A

is a constant, j

is the critical current density, and d is

the grain diameter. The trapped ﬁeld properties and

the critical current density of bulk, polycrystalline

YBCO material with randomly oriented grains are

strongly limited by its pronounced weak link be-

havior. Only very small currents are able to ﬂow

across the grain boundaries, especially if a magnetic

ﬁeld is applied. Weak links can be avoided by grow-

ing large grains using melt processing techniques.

Several techniques have been found to be suitable for

the growth of large single-domain YBCO material

without high-angle grain boundaries (Murakami

1993, Krabbes et al. 1997).

In most cases, seed crystals (Sm-123 or MgO) are

used in order to orientate the c-axis of the YBCO

sample perpendicular to the plane surface of the

sample. Large superconducting domains with a c-axis

texture can be produced in this way. In the present

state of the art, bulk, single-domain YBCO samples

with diameters up to 10 cm can be produced.

3. Levitation Force

The most important feature of superconducting bear-

ings is the levitation force between the superconduc-

tor and the permanent magnet. Other relevant

properties of superconducting bearings are their stiff-

ness and dynamic performance. Several reviews are

available describing levitation forces and the appli-

cation of superconducting bearings (Moon 1994, Hull

2000).

Stable levitation of a YBCO disk above a perma-

nent magnet (see Fig. 1) can be achieved both from

diamagnetic and ﬂux pinning properties of the su-

perconductor. The diamagnetic repulsive levitation is

based on the ﬂux exclusion and can be realized by

cooling the superconductor below the superconduct-

ing transition temperature in a large distance from

the permanent magnet. This is called zero-ﬁeld cool-

ing. In the case of YBCO, it is convenient to use

liquid nitrogen as coolant. By reducing the distance

between superconductor and permanent magnet, a

459

Magnetic Levitation: Superconducting Bearings