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stress-induced phase transformation recovers totally

when applied stress is removed. However, as in the

conventional case SE behavior is obtained only in a

rather narrow temperature region, the magnetically

assisted superelasticity of the martensitic MSM alloys

can be realized in a broad temperature range.

The behavior of MSM alloys at a variable mag-

netic ﬁeld and under constant transversal stress is

presented in Fig. 3. This behavior is applied in ac-

tuators (Fig. 1 (3)). The reversible strain (e

rev

) ob-

served under these conditions (see insert at Fig. 3) has

the maximum at a certain optimal value of blocking

stress (O’Handley and Allen 2001, Likhachev et al.

2001). With this optimum blocking stress, the MSM

element is brought back to the initial state when the

magnetic ﬁeld is removed (Fig. 3). In case the stress is

below the optimum, it cannot move the twin bound-

aries back totally and, therefore, the cycling shape

change is only partial. Furthermore, if the optimum

value is considerably exceeded, this disables the

MFIS.

Many other alloy systems (Vasil’ev et al. 2003,

derberg et al. 2004) (e.g., Fe–Pd, Fe–Pt, Ni–Mn–

Al, Co–Ni, Co–Ni–Al, Co–Ni–Ga and Ni–Fe–Ga)

having magnetic and martensitic transformations are

at present under intensive investigation as promising

candidates for MSM applications.

See also: Magnetostrictive Materials; Magnetoelastic

Phenomena; Magnetoelasticity in Nanoscale Hetero-

geneous Materials; Stress Coupled Phenomena:

Magnetostriction

Bibliography

Heczko O, Straka L 2003 Temperature dependence and tem-

perature limits of magnetic shape memory effect. J. Appl.

Phys. 94, 7139–43

Likhachev A A, Sozinov A, Ullakko K 2001 Inﬂuence of ex-

ternal stress on the reversibility of magnetic-ﬁeld-controlled

shape memory effect in Ni–Mn–Ga. Proc. SPIE 4333,

197–206

Murray S J, Marioni M, Allen S M, O’Handley R C, Lograsso

T A 2000 6% magnetic-ﬁeld-induced strain by twin-bound-

ary motion in ferromagnetic Ni–Mn–Ga. Appl. Phys. Lett.

77, 886–8

O’Handley R C, Allen S M 2001 Shape memory alloys, mag-

netically activated ferromagnetic shape memory materials.

In: Schwartz M (ed.) Encyclopedia of Smart Materials. John

Wiley and Sons, New York, pp. 936–51

Sozinov A, Likhachev A A, Lanska N, So

derberg O, Ullakko

K, Lindroos V K 2003 Effect of crystal structure on mag-

netic-ﬁeld-induced strain in Ni–Mn–Ga. Proc. SPIE 5053,

586–94

derberg O, Ge Y, Sozinov A, Hannula S-P, Lindroos V K

2004 Giant magnetostrictive materials. In: Buschow K H J

(ed.) Handbook on Magnetic Materials. Elsevier Science,

Amsterdam (to be published)

Tellinen J, Suorsa I, Ja

skela

inen A, Aaltio I, Ullakko K 2002

Basic properties of magnetic shape memory actuators. In:

Borgmann H (ed.) Proc. 8th Int. Conf. on New Actuators,

Actuator 2002. Messe Bremen GMBH, Bremen, Germany,

pp. 566–9; http://www.adaptamat.com/publications/

Ullakko K 1995 A method for producing motion and force by

controlling the twin structure orientation of a material and its

uses. European patent EP 0 838 095

Ullakko K, Huang J K, Kantner C, O’Handley R C, Kokorin V

V 1996 Large magnetic-ﬁeld-induced strains in Ni

MnGa

single crystals. Appl. Phys. Lett. 69, 1966–8

Vasil’ev A N, Buchel’nikov V D, Takagi T, Khovailo V V,

Estrin E I 2003 Shape memory ferromagnets. Phys. Usp. 46

(6), 559–88; arXiv:cond-mat/0311433 v1, 19 Nov 2003

O. So

derberg, A. Sozinov and V. K. Lindroos

Helsinki University of Technology, Laboratory of

Physical Metallurgy and Materials Science, P.O. Box

6200 (Vuorimiehentie 2A), FIN-02015 HUT

Espoo, Finland

Growth and Magnetic Properties

of YIG Films

Yttrium iron garnet (YIG), Y

, is a typical

ferrimagnetic material. In this article, ‘‘YIG’’ is used

to refer not only to Y

, but also to any other

magnetic garnet crystal, including Fe

3 þ

ions, such

as Y

3y

5x

and Bi

3y

5x

where R denotes a rare-earth element and A denotes

a non-magnetic element. The use of YIG has been

studied for a long time. In the 1970s, YIG crystals

were used in bubble memory devices for computers.

Figure 3

MFIS at constant blocking stress. e

rev

is the reversible

strain. Inset shows inﬂuence of blocking stress on e

rev

at constant magnetic ﬁeld H ¼800 kA m

1

260

Growth and Magnetic Properties of YIG Films

A bubble memory is created when the magnetic

domains in a YIG crystal ﬁlm are placed under an

external static magnetic ﬁeld. Later, YIG was used

in optical isolators, a key device in optical commu-

nication systems. The optical isolator is based on the

Faraday effect, which is a magneto-optic property of

YIG. For these applications, YIG ﬁlm crystals have

been used. On the other hand, spherical YIG

crystals have been used in microwave isolators and

resonators. These devices are based on spin waves

and magnetostatic waves (MSW), which are high-

frequency microwaves that propagate through YIG

when an external static magnetic ﬁeld is applied.

Recently, there has been active research on MSW

propagating through YIG ﬁlm. MSW are a mode of

electromagnetic wave generated in ferrite crystals

(see Ferrite Ceramics at Microwave Frequencies) when

microwaves are coupled with electron spins in the

material. An MSW is characterized by a frequency

that changes as the external static magnetic ﬁeld is

varied. In this article, we shall consider the properties

of YIG crystals, growth techniques with regard to

MSW applications, and an MSW device called an

S/N-enhancer. The S/N-enhancer is a noise-reduction

device that improves the reception of direct-broad-

casting satellite receivers.

1. YIG Crystals

The lattice constant of a YIG crystal is 1.2373 nm. The

growth techniques for YIG crystals have been

developed for applications in bubble memories,

microwave devices, and optical devices. A garnet

crystal (space group: Ia3d)isformedfromeight

sub-units. In a YIG crystal, 24 C-sites

with Y

3 þ

are each at the center of a dodecahedron

whose apexes are occupied by oxygen atoms. Simi-

larly, 16 A-sites with Fe

3 þ

and 24 D-sites with Fe

3 þ

are each at the center of a tetrahedron and an

octahedron, respectively, whose apexes are occupied

by oxygen atoms. A YIG crystal can be designed for

applications in speciﬁc devices, because the composi-

tion of a solid solution of YIG can be easily controlled

by doping cations.

A fraction of the D-site cations can be replaced

with non-magnetic cations, such as Ga

3 þ

or Al

3 þ

,to

decrease the saturated magnetization (Ms). On the

other hand, a fraction of the A-site cations can be

replaced with non-magnetic cations, such as In

3 þ

,to

increase the Ms. In addition, a fraction of the C-site

cations can be replaced with Bi

3 þ

or rare-earth

atoms, such as La

3 þ

, to modify the lattice parameter

of the YIG and adjust it to that of the garnet

substrate for epitaxial growth. For example, the

lattice constant of Gd

(gadolinium gallium

garnet, or GGG), which is usually used as the

substrate crystal for YIG epitaxal ﬁlms, is 1.2383 nm.

Figure 1 shows the phase diagram of the Fe

–

YFeO

system obtained by Van Hook (1962). As

the phase diagram shows, YIG crystals cannot be

obtained from a stoichiometric melt, because YIG

decomposes into YFeO

and Fe

at around

1580 1C. Therefore, YIG ﬁlms are grown by liquid-

phase epitaxy (LPE). LPE uses ﬂux, and growth is

done under a thermo-equilibrium condition, so the

YIGﬁlmsobtainedshouldhavegoodcrystallinity.A

solvent mixture of PbO and B

is usually used as the

ﬂux, and the ﬁlms are grown on a crystalline substrate

with a garnet structure. Although YIG crystals are

grown by LPE for both optical and MSW devices,

there are great differences between the epitaxial ﬁlms

required for each application. In optical applications,

such as optical isolators, the ﬁlm thickness is at least

several hundred micrometers, and the ﬁlm surface

must be polished to prevent optical scattering. In

MSW applications, the ﬁlm thickness is less than a

hundred micrometers, and in order to reduce cost, the

as-grown ﬁlms have no surface treatment.

2. Growth of YIG Films

In LPE, the solute for the crystal and the solvent are

put into a crucible, and the crucible is kept at a

constant temperature under constitutional supercool-

ing condition of the solution. The crystal substrate is

then dipped into the solution in the crucible, and the

crystal ﬁlm grows epitaxally on the substrate. There

are two important things to note concerning the

temperature in the crucible. First, the temperature

proﬁle must be kept uniform; and second, tempera-

ture ﬂuctuations must be minimized. That is the

reason why the crystal grows under quasi-equilibrium

conditions.

Figure 1

Phase diagram for the Fe

-YFeO

system.

261

Growth and Magnetic Properties of YIG Films

Figure 2 shows a typical growth furnace for LPE.

The furnace includes three heater units, which can be

controlled independently. The platinum crucible is

at the center of the furnace. Five donut-shaped

platinum reﬂectors are positioned above the crucible

to reﬂect thermal radiation and control airﬂow. The

temperature distribution in the crucible under opti-

mum furnace conditions is shown in Fig. 3, where the

gas-solution interface is set as the origin, and

temperature ﬂuctuations are shown by error bars.

The temperature gradient in the solution was as small

as 0.03 1Cmm

1

at 40 mm, where the LPE growth

temperature had a ﬂuctuation of less than 0.5 1C. If

there had been much temperature difference between

the regions above and below the gas–solution inter-

face, or much temperature ﬂuctuation in the solution,

YIG crystals could have easily nucleated and clung to

the substrate when it was dipped.

Next, the YIG growth example is described. In this

case, the YIG ﬁlms were designed for application in

an S/N-enhancer, for which the target composition

was La

0.07

2.93

0.45

4.55

(LaGa:YIG) with an

operating frequency range of 1.03 to 1.35 GHz. The

starting materials with a total weight of about 10 kg

were Fe

(4N), Y

(4N), Ga

(4N), and La

(4N) as the crystal constituents; and PbO (4N) and

(4N) as the ﬂux. Figure 4 shows the phase

diagram for the PbO–Fe

–Y

system. Fe

and

are the solutes, and PbO is the main constituent

of the solvent. The garnet structure can be obtained

in a deﬁnite region. The B

controls the viscosity of

the solvent and deters YIG nucleation. The typical

compositions of the starting materials are described

in Table 1 using Blank’s R-parameter.

As shown in Fig. 2, the starting materials were

mixed and placed in the platinum crucible, 150 mm in

diameter and 150 mm in height. Each (111)-oriented

GGG substrate of 76 mm in diameter was held

horizontally by the platinum holder and dipped into

the melt solution during growth. The substrates were

Figure 2

Schematic cross section of an LPE growth furnace.

Figure 3

Temperature proﬁle in the growth furnace. The origin of

the vertical axis is the gas-melt interface.

Figure 4

Phase diagram for the PbO-Fe

-Y

system.

262

Growth and Magnetic Properties of YIG Films

rotated horizontally by rotating the holder, and the

rotation direction of the substrate was changed at

regular intervals. Typical growth temperature was

860 to 920 1C. The rotation rate was 100 rpm, and the

intervals between changing the direction were 15 s.

As-grown (111)-oriented YIG wafers of 25 mm,

50 mm, and 76 mm in diameter are shown in Fig. 5.

All epitaxial YIG wafers were grown on both sides of

the GGG substrate. The thickness distribution, which

was measured using an optical-interference thickness-

measuring system, was 10.070.5 mm for the as-grown

YIG ﬁlms on the 76-mm substrate.

3. Magnetic Properties

For MSW applications, the important magnetic

properties of YIG ﬁlms are the Ms and the half-line

width of the ferromagnetic resonance (FMR), or DH.

To examine these properties, FMR spectra were

measured using the electric spin resonance (ESR)

method with X-band microwaves (9.2 GHz). Square

samples 2.0 2.0 mm

in size were cut from the as-

grown YIG wafers, and the YIG ﬁlm on one side of

each sample was removed. After measurement, the

DH was calculated from peak to peak by Lorenz-type

resonance in the FMR spectra. The Ms-Ha, where

Ha is the anisotropic magnetic ﬁeld, was calculated

by using Kittel’s resonance equation with the results

from applying two resonant external magnetic ﬁelds,

one parallel to the ﬁlm and one perpendicular.

For the S/N-enhancer application, the Ms must be

kept within 120.075.0 mT, and the DH must be less

than 80 A m

1

. For the YIG ﬁlms above mentioned,

both the DH and Ms (the Ha was estimated at 3.0 mT

by using other measurements) met the requirements

for the S/N-enhancer.

To satisfy the requirement for magnetic properties,

there are some important conditions for YIG growth.

First, a suitable growth furnace must be used to

control the temperature proﬁle. Second, the impurity

concentrations of the starting materials must be

carefully controlled. For example, nine elements

(silicon, titanium, chromium, cobalt, hafnium, tin,

germanium, magnesium, and tantalum) degraded the

FMR properties, at concentrations ranging from 10

to 50 ppm by weight in the starting materials.

Finally, a periodic layer structure (PLS) in a YIG

ﬁlm is effective in improving the FMR properties.

Figure 6 shows an x-ray rocking curve measurement

using a monochrometer consisting of four crystals. The

main peak corresponds to the YIG (888) reﬂection,

and the second peak corresponds to the GGG (888)

reﬂection. A pair of reﬂections is found, symmetrical

around the main YIG peak. These satellite reﬂections,

indicated by the two arrows, indicate the existence of a

PLS, like a superlattice of compound semiconductor

Table 1

Blank’s R-parameters. R

shows the molar ratio.

R-parameter Molar ratio



½Fe



½Y

þ½La



20.0–25.0



½Fe



½Ga



20.0–25.0



½PbO

½B



14.0–16.0



½Fe

þ½Y

þ½La

þ½Ga



½PbOþ½B

þ½Fe

þ½Y

þ½La

þ½Ga



0.10–0.11



½Y



½La



5.00–7.00

Figure 5

As-grown YIG wafers of 25 mm, 50 mm, and 76 mm in

diameter.

263

Growth and Magnetic Properties of YIG Films

materials. The PLS was estimated to be around 150 nm

long, based on the angular difference between the main

and satellite peaks. This indicates that the length of the

PLS can be controlled by changing the LPE growth

conditions, such as the growth temperature or the

interval of changing the rotation direction. Figure 7

shows the FMR spectra with and without a PLS. At

a ﬁlm thickness of 20 mm, both FMR spectra were

excellent. However, at 5 mm, only that with a PLS was

excellent. This explains why the magnetic direction is

ordered above the ﬁlm-substrate interface for the YIG

ﬁlm with the PLS.

4. S/N-enhancer

An S/N-enhancer is an MSW device that cancels

noise and emphasizes the signal in direct-broad-

casting satellite receivers. It utilizes the nonlinear

characteristics of MSW propagation through YIG

ﬁlms, so that the MSW output power ﬁnally saturates

with increasing input power, as shown in Fig. 8(a).

The device operates as shown in Fig. 8(b). The input

microwave is divided, and each part passes a separate

YIG ﬁlm. In path (1), the signal amplitude decreases

while the noise level does not change, because the

signal amplitude is above the saturation level and

the noise amplitude is below it. After propagating

through the YIG ﬁlm, the microwave amplitude

decreases further at the attenuator (Att-1).

In path (2), both the signal and noise amplitudes

decrease at the attenuator (Att-2), but they do not

change in the YIG ﬁlm because they have already

decreased below the saturation level. Furthermore, the

phase shifter creates a 1801 phase difference between

paths (1) and (2). The noise amplitude is then reduced

after the two microwaves are added, because the noise

amplitude through path (1) is almost similar to that

through path (2). As a result, the ratio of the signal

and noise amplitudes (S/N) is emphasized. Thus, the

performance of the two YIG ﬁlms in the S/N enhancer

Figure 7

Effect of a PLS on FMR spectra.

Figure 6

Measured x-ray rocking curve using Cu-K a

. The main

peak shows the YIG (888) reﬂection.

Figure 8

Relationship between input power (P

) and output power (P

out

) for propagation through a YIG ﬁlm. P

out

saturated at

a high P

level. (b) Operating principle of a S/N enhancer with two YIG ﬁlms.

264

Growth and Magnetic Properties of YIG Films

must be uniform. As shown in Fig. 9, the S/N

enhancer improves the quality of TV pictures.

See also: Ferrite Ceramics at Microwave Frequencies

Bibliography

Blank L S, Nielsen W J 1972 The growth of magnetic garnet by

liquid phase epitaxy. J. Cryst. Growth 17, 302–11

Geho M, Fujino M, Fujii T 1999 Growth of magnetic garnet

single-crystal ﬁlms for the S/N-enhancer device. Key Eng.

Mater. 157–158, 143–50

Helszajn J 1985 YIG resonators and ﬁlters. Wiley-Interscience,

New York

Small M B, Giess E A, Ghez R 1994 Handbook of Crystal

Growth: 3a—Basic Techniques. Elsevier, Amsterdam

Shinmura S, Okada T 1997 Murata S/N-enhancers stress

signal for dbs receivers. Nikkei Electronics Asia. August,

pp. 70–3

Spark M 1964 Ferromagnetic-Relaxatuon Theory. McGraw-

Hill, New York

Stancil D D 1993 Theory of Magnetostatic Waves. Springer-

Verlag, New York

Tolksdorf W, Welz F 1978 Crystals—Properties and Applica-

tions: 1. Springer-Verlag, New York

Van Hook J H 1962 Phase relations in the ternary system

–FeO–YFeO

. J. Am. Ceram. Soc. 45 (4), 162–5

Zvezdin A K, Kotov V A 1997 Studies in Condensed Matter

Physics: Modern Magnetooptics and Magnetooptical Materi-

als. Institute of Physics Publishing, Bristol, UK

T. Fujii and Y. Sakabe

Murata Manufacturing Company Ltd., Shiga

Japan

Figure 9

Photographs showing the effect of a S/N enhancer on

TV pictures: (a) picture output with S/N enhance; (b)

original picture.

265

Growth and Magnetic Properties of YIG Films

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266

Half-metallic Magnetism

The electronic structure of a magnetic solid can be

described by two independent band structures for

the two spin directions in the absence of spin–orbit

interactions. A half-metal is deﬁned as a solid with

metallic properties for one of the spin directions only.

As a consequence, the electrical conduction takes

place for one spin direction exclusively. Also the

magnetic moment of a half-metal is integral. This

follows from the integer number of electrons for the

nonconducting spin direction as well as the integral

total number of electrons. Historically, the possibility

of unusual physics in magnetic systems with integral

magnetic moments was recognized as early as 1950

(Pickett and Moodera 2001), however, the ﬁrst dis-

cussion on half-metallicity and its origin appeared in

1983 (De Groot et al. 1983).

1. Physical Origin of Half-metallicity

A remarkable feature of a half-metal is the occur-

rence of a bandgap for one spin direction. Bandgaps

occur for distinct physical and chemical reasons,

leading to distinct behavior as function of pressure,

disorder, surface sensitivity, etc. Because of this, the

origin of the bandgap is a useful criterion for the

classiﬁcation of half-metals (Fang et al. 2002). Three

categories exist.

1.1 Systems with Covalent Bandgaps Such As in

III–V Semiconductors

Although the origin of the bandgap in this category is

the least straightforward, the materials, in which half-

metallicity was ﬁrst described (NiMnSb), fall into this

category. NiMnSb crystallizes in the Heusler C1

structure. This structure consists of a face-centered

cubic Bravais lattice with Ni in the origin, Mn at

;

and Sb at

;

. So this structure is quite similar as the

zinc-blende structure. Both the Mn and the Sb have

the fourfold tetrahedral coordination characteristic

for the zinc-blende structure. The band structure and

chemical bonding for the minority spin direction is

very similar as in the III–V semiconductors. The extra

atom, Ni, mediates the interactions, while the role of

the p-electron of the metal in the III–V semiconduc-

tor is played by an Mn t

-electron in NiMnSb. A

bandgap results very similar as for the zinc-blende

semiconductors. The metallic spin direction is char-

acterized by four extra d-electrons 4 eV lower in en-

ergy due to the exchange splitting. Wide bands,

without any bandgap, result for the majority spin

direction like in an alloy (see Fig. 1). The role of the

-electron in the band formation has two important

consequences. First, it implies NiMnSb is a weak

ferromagnet: strong magnetism and half-metallicity

are mutually exclusive in this category. Second, the

d-electron can play the role of a p-electron in the

zinc-blende structure only as long as inversion sym-

metry is absent. Hence, no half-metallicity in this

category exists in the Heuslers L2

structure, since

it possesses inversion symmetry. Several other C1

Heusler alloys have been investigated.

Isoelectronic PtMnSb shows also half-metallicity

(De Groot et al. 1984), but the spin–orbit interaction

will cause the Fermi energy to cross the top of the

valence band. PbMnSb shows a small overlap of the

Fermi energy with the top of the valence band for

the minority spin directions. In IrMnSb, RhMnSb,

PtMnSn, and OsMnSb, the Fermi level overlaps with

the top of the valence band (De Groot and Buschow

1986). CoMnSb (Ku

bler 1984) as well as FeMnSb

(De Groot et al. 1986) are calculated to be half-

metals; however, CoMnSb crystallizes in a super-

structure and FeMnSb is always Fe-deﬁcient when

synthesized. Extrapolation of the measured moment

Figure 1

Band structure of NiMnSb for the majority spin

direction (a) and minority spin direction (b). The zero of

the energy scale coincides with the Fermi level.

267

to the stoichiometric composition leads to the re-

quired integral moment 2m

, however. A more recent

development is the growth of transition-metal pnic-

tides and chalcogenides in the zinc-blende structure

as a meta-stable phase on top of III–V semiconduc-

tors. Successful experiments on CrAs (Akinaga et al.

2000) as well as CrSb (Zhao et al. 2001) have been

reported. The magnetic moment in these cases is 3m

1.2 Strongly Magnetic, Ionic Compounds

Strong magnetic materials are deﬁned as solids,

where a hypothetical increase in exchange splitting

does not lead to an increase in magnetic moment.

This means, in practice, that for a transition metal the

majority spin d-states are completely ﬁlled or the mi-

nority spin d-states are completely empty. The former

is, for example, the case of Ni. However, there are

still itinerant s–p electrons present, which show hard-

ly any spin polarization and are responsible for nor-

mal metallic behavior. In an ionic compound, these

mobile electrons are localized on some anion and

half-metallic properties emerge. Up till now, the

occurrence of half-metals in this category is conﬁned

to systems with an empty minority d-shell. The band-

gap is of the charge transfer type, whereas the

conduction band-minimum has primarily transition-

metal d-character. Examples in this category are

CrO

(Schwartz 1986) and the double-exchange per-

ovskite materials (Pickett and Singh 1996).

1.3 Narrow Band Materials

In systems, where bandwidths are smaller than inter-

actions like crystal ﬁeld and exchange splittings, several

bandgaps will show up in a d-manifold. Usually, these

systems will be Mott insulators. If, however, the band-

widths are not too small and show metallic behavior,

the multitude of bandgaps makes the occurrence of

half-metallicity likely. The most predominant example

in this category is the mineral magnetite, Fe

(Yanase and Siratori 1984), above the Verwey transi-

tion of 120 K. CoS

is nearly half-metallic and can be

transferred into a half-metal by substituting part of the

Co by Fe (Mazin 2000). Several other half-metals have

been reported in this category such as Heusler L2

phases (Fujii et al. 1995, Weht and Pickett 1999) as

well as several nitrides (Fang et al. 2002). The bandgap

of the semiconducting spin direction is of the d–d type:

both the top of the valence band as well as the bottom

of the conduction band are primarily derived from

transition-metal d-states. Hence, half-metals in this

category should be classiﬁed as weak magnets.

2. Physical Pro perties of Half-metals

Most of the early work on half-metallic magnet-

ism was based on electronic structure calculations,

presumable because, in spite of the profound inﬂu-

ences of half-metallicity, there is no real simple

‘‘smoking gun experiment’’ to prove its existence in a

specific compound. The requirement of an integer

moment is a necessary but certainly not a sufﬁcient

condition. The test of the integral moment should be

applied with care on partially substituted systems

such as Fe

1x

since an integral moment per

formula unit can be obtained with integral number

of atoms in the formula unit only. In considering

experiments, surface-sensitive ones should clearly be

distinguished from bulk measurements. The most

stringent one in the last category is without doubt

spin-resolved positron annihilation. Positron annihi-

lation measures the Fermi surface of a solid. Since

positrons obtained from b-decay are spin polarized

and the annihilation process of an electron–positron

pair in a singlet state is easily discriminated from that

of a triplet pair, the measurement of the Fermi sur-

face can be realized spin dependent. In the case of

NiMnSb, it was proven that only for one spin direc-

tion a Fermi surface exists (Hanssen et al. 1990).

Unfortunately, measurements of this type on other

half-metals are lacking.

Surface-sensitive measurements are less clear be-

cause of the occurrence of surface segregations, sur-

face reconstructions (Ristoiu et al. 2000), or simply

by the fact that even a perfect surface of a half-metal

is not necessarily half-metallic itself. Spin-resolved

photoemission showed La

1x

MnO

to be half-

metallic, although the interpretation of these meas-

urements is not uncontroversial (Park et al. 1998).

Andreev reﬂection on NiMnSb showed a spin polar-

ization of the electrons at the Fermi energy of 58%

only, whereas spin-polarized tunneling shows 28%

polarization only (Tanaka et al. 1999). The highest

degree of spin polarization of the conduction elec-

trons measured by Andreev reﬂection is CrO

: 90%

(Soulen et al. 1998). Under some conditions, inverse

photoemission shows close to 100% spin polarization

in NiMnSb (Ristoiu et al. 2000).

There exists some confusion in the literature about

the inﬂuence of disorder, specifically in the ﬁrst cat-

egory of half-metals. Since interchange of nickel and

manganese in NiMnSb will sacriﬁce the tetrahedral

coordination of the latter atom, it is very effective in

destroying the half-metallic properties (Orgassa et al.

1999). This has fuelled some belief that the lack of

spin polarization at its surface is an indication of such

disorder at the surface or even in the bulk. While the

latter is in disagreement of the spin-resolved positron-

annihilation measurements, the introduction of the

former is unnecessary: the presence of the surface it-

self breaks the tetrahedral symmetry already sufﬁ-

ciently to destroy the half-metallic properties locally

(genuine half-metallic interfaces are possible, however

(De Wijs and De Groot 2001)). Moreover, Ni–Mn

interchange is energetically unfavorable. Although it

was possible to prepare highly disordered Ni

MnSb

268

Half-metallic Magnetism

by molecular beam epitaxy, recent NMR work on

thin-ﬁlm NiMnSb shows a very low amount of dis-

order and of a type (Mn–Sb interchange) that does

not inﬂuence the half-metallic properties (Van Roy

et al. 2003).

3. Half-metallic Antiferromagnetism

The average magnetic moment in half-metals in the

Heusler structure is well described by a generalized

Slater–Pauling curve (Ku

bler 2000). This calculated

curve shows materials with an averaged moment of

zero. Besides a nonmagnetic solution this can imply

an unusual form of magnetism: half-metallic antif-

erromagnetism (Van Leuken and De Groot 1994).

Half-metallic antiferromagnets differ from traditional

antiferromagnets, because local moments on cry-

stallographically different sites cancel. Theoretically,

they are predicted to show an unusual form of mag-

netism (Rudd and Pickett 1998). Experimentally, they

have not been realized yet (Pickett 1998).

See also: Spintronics in Semiconductor Nano-

structures

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R. A. de Groot

University of Nijmegen, The Netherlands

Hard Magnetic Materials, Basic

Principles of

The progress in the ﬁeld of permanent magnets has

been dramatic since the 1960s. This would have been

impossible without a fundamental understanding of

the physical phenomena responsible for hard magnet

properties, which led to the discovery of new families

of permanent magnet materials based on rare

earth(R)–transition metal (T) compounds (see Rare

Earth Magnets: Materials). The search for new com-

pounds with superior properties focuses on materials

269

Hard Magnetic Materials, Basic Pr inciples of