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

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Fig. 3 as typical compounds of region II. Both com-

pounds exhibit T

values of only a few kelvin without

any magnetic order but they are characterized by a

very large enhancement of the electronic specific heat,

g, at low temperatures. The two curves in Fig. 3 re-

semble each other, showing a large and broad max-

imum at 50–70 K with shoulders at around 5 K. For

temperatures T4T

, the cerium 4f electrons are in a

local and dilute ionic state and experience a CEF with

the Kondo effect acting as a small perturbation. The

RKKY interaction can be neglected. The Seebeck

coefﬁcient in this parameter region has been theoret-

ically investigated by Bhattacharjee and Coqblin

(1976) and Kashiba et al. (1986). According to these

calculations a positive peak of the S(T) curve is ex-

pected at a temperature around about 1/3 to 1/6 of

the overall CEF splitting. The main S peaks of the

two compounds in Fig. 3 are ascribed to interplay of

the Kondo effect and CEF effect splitting. The main

peaks for the two compounds in Fig. 3 are reminis-

cent of the peak of CeNi in Fig. 2; however, they are

of different origins.

The following discussion concerns the initial slope

of S vs. T for T - 0. It is well known that S - 0 for

T - 0 and the initial slope of S(T - 0) reﬂects

details of the DOS at E ¼E

(Ziman 1960). For

CeCu

and CePtIn a very large value of 10 mVK

2

observed. In comparison, the value for CeNi in Fig. 2

is around 0.5 mVK

2

and the value for LaNi, the ref-

erence sample for CeNi, is around 0.01 mVK

2

. Thus,

the initial slope of S(T) is apparently closely related

to the electronic specific heat, g.

The initial slope of S is plotted in Fig. 4 as a

function of g for several cerium compounds belong-

ing to regions I and II. They are CeSn

, CeNi,

CePd

, CeNiIn, and CeNiAl

in region I, and

CeCu

,Ce

0.1

0.9

, CeInCu

, CePtIn, CeCu

CeCu

, CeCu

Al, and CeCu

Ga in region II

(Sakurai 1993).

The estimation of the initial slope of S is noted to

depend on the temperature range of measurements

especially for the compounds belonging to region II.

When the value for CeCu

in Fig. 3 is estimated from

the temperature range above the shoulder around

5 K, the value becomes smaller. S(T) measurements

performed for CeCu

down to 10 mK show another

structure below 1 K and the establishment of the re-

lationships S ¼aT and r ¼cT

(c ¼const.) is possible

only in a very low temperature range, below 30 mK

(Sato et al. 1987). The initial slope of S estimated

below 30 mK approaches a value of 30 mVK

2

. Thus,

in Fig. 4 the values obtained for cerium compounds

belonging to region II for the different temperature

ranges are plotted separately (Sakurai 1993).

The proportionality between the initial slope dS/

dT for T - 0 and the electronic specific heat co-

efﬁcient, g, is conﬁrmed by the experiment, as shown

in Fig. 4. In view of the difﬁculties of obtaining an

accurate estimation of the initial slope of S, the scat-

ter of points near the origin of Fig. 4 is not signif-

icantly important. The very large initial slope of S(T)

for the cerium compounds in region II is a direct

consequence of the DOS at the Fermi level for ToT

originating from the hybridization of the cerium 4f

electrons and the conduction electrons mediated by

the Kondo interaction.

According to the theory of Kawakami et al. (1987)

for the Kondo interaction of dilute cerium impurity

systems, the initial slope of S and g exhibit the same

enhancement factor at low temperatures. It has been

demonstrated that the initial slope of S originates

from the asymmetry of the conduction electron state

density at the Fermi energy but may also depend on

additional interactions of the conduction electron

system.

In region III the cerium compounds are so-called

Kondo antiferromagnets showing both the Kondo

effect and a long-range antiferromagnetic order. Only

a few systems are known with a ferromagnetic

ground state.

The S(T) curves of CePdSn and CePtSn are given

as examples of Kondo antiferromagnets (Sakurai

et al. 1996). Both compounds show antiferromagnetic

order below 7 K, and are characterized by a Kondo

resistivity behavior. The S(T) curves of the two com-

pounds shown in Fig. 5 have maximums around

100 K and minimums at around 20 K. The positive

peaks are ascribed to the Kondo effect in the presence

of the CEF splitting of the ground state multiplet

level of the cerium 4f electron, similarly to the pos-

itive peaks for CeCu

and CePtIn.

The narrow minimums at low temperatures are

characteristic of cerium compounds in region III.

The position of the minimums is typically two or

three times larger than the ordering temperature,

, and hence can be taken as an experimental

Figure 3

S of two polycrystalline heavy fermion compounds

CeCu

and CePtNi plotted as a function of lnT.

1080

Rare Earth Intermetallics: Thermopower of Cerium, Samarium, and Europium Compounds

indication of the onset of short-range antiferromag-

netic correlations.

According to Fischer (1989), a resonance term in S

appears for cerium compounds having strong mag-

netic correlations between the cerium moments. This

term gives rise to a negative S(T) contribution cen-

tered around T* ¼G/k

, where G is the half width of

the quasi-elastic peak deduced by inelastic neutron

scattering, which is a measure of the correlation be-

tween the cerium moments. Thus, it is concluded that

the resonance term of S proposed by Fischer (1989)

gives a theoretical explanation of the minimums in S

vs. T, which seems to originate from the onset of

short-range antiferromagnetic correlations. S vs. T

curves similar to those shown in Fig. 5 have been

observed in many Kondo antiferromagnets, e.g., in

CeAl

, CePb

, CeCu

, CePtGa, CePtGe, CeCu

CePd

, and many others (Sakurai et al. 1996).

Various cerium compounds belonging to region II

show S(T) behavior typical for systems of region III.

Examples are CeAl

(Jaccard and Flouquet 1987),

CeCu

(Jaccard et al. 1985), and CeRu

(Amato

et al. 1988). These compounds are characterized by

a very large enhancement of g with no long-range

antiferromagnetic order. In spite of the absence of

long-range magnetic order in CeRu

, the existence

of short-range magnetic correlation has been veriﬁed

by neutron scattering experiments (Regnault et al.

1988). The minimum in the S vs. T curve for this

compound is observed along the c-axis but not along

the a-axis.

The transition of the S(T) behavior from one

region to another is sometimes clear and well deﬁned.

A striking evolution of S(T) emerges from high-pres-

sure studies of S vs. T. The deep minimum in S(T)

for CeCu

centered around 20 K at zero pressure

vanishes rapidly with pressure and the S(T) curve

shows positive values with a steep initial slope at

higher pressures (Jaccard et al. 1985). The application

of pressure (and hence a decrease of the interatomic

distance) increases the hybridization between the

cerium 4f band states and the conduction band states,

and thus a change takes place from region III into

region II.

Similar changes of the S(T) behavior follow also

from chemical pressure, realized by alloying a com-

pound with an isomorphous one having a slightly

smaller or larger unit cell volume. The S(T) behavior

Figure 4

Initial slope of the thermoelectric power S/T at T ¼0 plotted as a function of the electronic specific heat coefﬁcient, g,

for several heavy fermion and intermediate valence compounds (see text for details).

1081

Rare Earth Intermetallics: Thermopower of Cerium, Samarium, and Europium Compounds

of CePb

belonging to region III changes in the pseu-

dobinary system Ce(Pb

1x

)

towards region II

(Sakurai et al. 1996), and with further addition of tin,

into region I. A similar change of the S behavior from

region III to region II has also been reported for

Ce(Cu

1x

)

and Ce(Cu

1x

)

(Bauer 1991).

In contrast, a reverse change of the S behavior

from region II to region III has been reported for

Ce(Cu

1x

)

(Bauer 1991), owing to the negative

chemical pressure produced by the gold substitution.

Typical features of regions II and III frequently

coexist. The measurement of S( T) for CePdSn has

been carried out down to 0.3 K (Huo et al. 1999).

According to this experiment, a second positive peak

of S(T) at around 1 K is found, in addition to the

positive and negative peaks shown in Fig. 4. The ap-

pearance of this peak may be associated with a weak

enhancement of g of the compound occurring along

with antiferromagnetic order.

Finally, Fig. 6 shows the S(T) curve of CePd

(Sakurai et al. 1996) as an example of cerium com-

pounds in region IV. The compound has a T

value

of 0.5 K, and no Kondo behavior is observed in its

resistivity. The S (T) curve is smooth and corresponds

to small absolute value. It resembles that of the non-

magnetic counterpart LaPd

. Thus, the cerium 4f

electrons in the compound are in well-localized states

without significant hybridization with the conduction

band states. Similar S(T) curves have been reported

for CeMg

(Sakurai et al. 1996).

The thermoelectric power, S, is surely a property

that reﬂects very sensitively the various natures of the

hybridization between cerium 4f electron states and

conduction electron states, and it has been demon-

strated that each of the four regions of the diagram of

Doniach (1977) for the cerium compounds has a very

different and characteristic behavior of the S(T)

curve. However, as discussed above, the boundaries

between different regions are not always strictly de-

ﬁned and may well be changed by applying pressure

or by alloying.

Moreover, four temperature parameters, T

, T

T*, and G, have been used to discuss the S behavior,

while the parameters of Doniach’s diagram are only

the ﬁrst two. Thus, the descriptions given above are

for the purpose of a general qualitative overview, and

it is known that many exceptional cases exist.

See also: Magnetic Fields: Thermoelectric Power

Bibliography

Amato A, Jaccard D, Sierro J, Lapierre F, Haen P, Lejay P,

Flouquet J 1988 Thermopower and magneto-thermopower

of CeRu

single crystals. J. Magn. Magn. Mater. 76/77,

263–4

Bhattacharjee A K, Coqblin B 1976 Thermoelectric power of

compounds with cerium: inﬂuence of the crystalline ﬁeld on

the Kondo effect. Phys. Rev. B 13, 3441–51

Bauer E 1991 Anomalous properties of Ce–Cu- and Yb–

Cu-based compounds. Adv. Phys. 40, 417–537

Doniach S 1977 The Kondo lattice and weak antiferromagnet-

ism. Physica B 91, 231–4

Fischer K H 1989 Thermoelectric power of heavy-fermion

compounds. Z. Phys. B 76, 314–26

Figure 5

S of two antiferromagnetic Kondo compounds CePdSn

and CePtSn plotted as a function of temperature.

Figure 6

S of an antiferromagnetic compound CePd

having

no Kondo character and its nonmagnetic counterpart

LaPd

plotted as a function of temperature, T.

1082

Rare Earth Intermetallics: Thermopower of Cerium, Samarium, and Europium Compounds

Fujii H, Uwatoko Y, Akayama M, Satoh K, Maeno Y, Fujita

T, Sakurai J, Kamimura H, Okamoto T 1987 Magnetic

and transport properties of new Kondo compounds CeTIn

(T, Ni, Pd and Pt). Jpn. J. Appl. Phys. Suppl. 26-3, 549–50

Huo D X, Mori K, Kuwai T, Kondo H, Isikawa Y, Sakurai J

1999 RKKY interaction and Kondo effect in (Ce,La)PdSn.

J. Phys. Soc. Jpn. 68, 3377–82

Jaccard D, Flouquet J 1987 Transport properties of heavy

fermion systems. Helv. Phys. Acta 60, 108–21

Jaccard D, Mignot J M, Bellarbi B, Benoit A, Braun H F,

Sierro J 1985 High pressure transport coefﬁcients of the

heavy-fermion superconductor CeCu

. J. Magn. Magn.

Mater. 47/48, 23–9

Kashiba S I, Maekawa S, Tachiki M, Takahashi S 1986 Effect

of crystal ﬁeld on Kondo resistivity in Ce compounds.

J. Phys. Soc. Jpn. 55, 1341–9

Kawakami N, Usuki T, Okiji A 1987 Thermoelectric power of

the Anderson model at low temperature. J. Phys. Soc. Jpn.

56, 1539–45

Onuki Y, Komatsubara T 1987 Heavy fermion state in CeCu

J. Magn. Magn. Mater. 63/64, 281–8

Regnault L P, Erkelens W A C, Rossat-Mignot J, Lejay P,

Flouquet J 1988 Neutron scattering study of the heavy-fer-

mion compound CeRu

. Phys. Rev. B 38, 4481–7

Sakurai J 1993 Several aspects on thermopower of Ce com-

pounds. In: Oomi G, Fujii H, Fujita T (eds.) Transport and

Thermal Properties of f-Electron Systems. Plenum, New

York, pp. 165–73

Sakurai J, Takagi H, Taniguchi S, Kuwai T, Isikawa Y, Tho-

lence J L 1996 Transport properties of CeNi

and

CePd

: thermoelectric behaviour of Kondo antiferromag-

netic compounds. J. Phys. Soc. Jpn. 65 (Suppl. B), 49–56

Sato H, Zhao J, Pratt W P Jr, Onuki Y, Komatsubara T 1987

The transport properties of heavy-fermion compound CeCu

down to 14 mK. Phys. Rev. B 36, 8841–4

Ziman J M 1960 Electrons and Phonons. Oxford University

Press, Oxford

J. Sakurai

Toyama University, Japan

Rare Earth Magnets: Materials

Rare-earth permanent magnets (RPMS) are based on

intermetallic compounds of rare-earth metals (R) and

the transition metals iron or cobalt. The auspicious

combination of properties of the rare-earth sublattice

and the 3d sublattice lead to the spectacular devel-

opment in hard magnetic materials: the former pro-

viding the high magnetic anisotropy, the latter the

high Curie temperature and magnetization. The two

most relevant classes of RPMs in application are

based on (i) samarium and cobalt which exhibit very

high coercivities and low temperature coefﬁcients,

and (ii) neodymium, iron, and boron which are un-

rivalled in terms of its maximum energy product.

In the present article a brief review will be given of

these two compounds, but also of the other recently

discovered hard magnetic iron-rich compounds such

as ThMn

-type compounds and the interstitial solid

solutions of nitrogen and carbon in R

-type

compounds. The most relevant intrinsic magnetic

properties and micromagnetic parameters (for deﬁ-

nition see Hard Magnetic Materials, Basic Principles

of) of these compounds are listed in Table 1. Sum-

maries of novel developments in manufacturing

routes, with special emphasis on nanostructured

magnets, will be given in the following sections.

The development of NdFeB-type alloys as starting

materials for permanent magnets was triggered by

both Sumitomo Special Metals (using the powder

metallurgical route, Sagawa et al. 1984) and General

Motors (employing the rapid quenching method,

Croat et al. 1984). The usefulness of the tetragonal

B-type compounds (see Fig. 1) led to numer-

ous detailed investigations of the Nd–Fe–B system.

Three stable ternary phases can be found: Nd

(F), Nd

1 þe

(Z), and Nd

(r). An instruc-

tive presentation of the ternary Nd–Fe–B system with

low boron concentrations is given in the liquidus

projection shown in Fig. 2, which marks the binary

phases, ternary phases, and the important reactions

(elucidated in the caption). The F phase is located in

a region where g-Fe is the primary solidiﬁcation

product.

The peritectic formation of the F phase at 1180 1C

will be incomplete in a standard casting process as

residues of primary Fe dendrites are left in the F

grains, the latter in turn being surrounded by neo-

dymium-rich liquid which will solidify at its eutectic

temperature of 630 1C. The presence of the iron crys-

tals is detrimental to the magnet’s performance. This

has important consequences for the manufacturing of

this class of magnets. The analogous PrFeB-based

compounds are of particular relevance for hot-de-

formed magnets and low-temperature applications as

they show no spin reorientation down to 4.2 K (which

occurs at 135 K for Nd

B), but have also been

used more recently for melt-spun and HDDR (see

Magnets: HDDR Processed) materials.

The intrinsic magnetic properties of the related

C are very similar to those of the corre-

sponding borides: the magnetocrystalline anisotropy

is slightly higher and the Curie temperature and

magnetization slightly lower (see Table 1). The for-

mation of the R

C compound proceeds via a

peritectoid reaction from the R

and RFeC

phases. This solid-state transformation temperature

can be increased very effectively with small boron

substitutions for carbon (Eisses et al. 1991) and a

better control of the microstructure (‘‘ingot mag-

nets’’) compared to the NdFeB system is possible.

Unlike the Nd

B phase, the hexagonal SmCo

compound (Strnat et al. 1967) with the CaCu

struc-

ture shows a relatively large homogeneity region in

the Sm–Co phase diagram (Cataldo et al. 1996) as

shown in Fig. 3. This region, however, becomes

asymmetric when approaching the peritectic melting

1083

Rare Earth Magnets: Materials

temperature of 1292 1C. SmCo

magnets obtained by

liquid-phase sintering are characterized by their high

Curie temperatures and coercivities.

Commercially produced Sm–Co-type sintered

magnets based on the 2:17 phase have usually a com-

position close to Sm(Co, Fe, Cu, Zr)

7.5

. The most

outstanding properties of this class of magnets are

their very high Curie temperature and the low tem-

perature coefﬁcients of remanence and coercivity at

elevated temperatures (recently up to 500 1C) in ad-

dition to their excellent corrosion characteristics. A

major drawback is the use of costly Co metal. The

homogeneity region of the 2:17 phase narrows with

decreasing temperature and a ﬁne cellular network of

SmCo

phase precipitates from a single phase meta-

stable precursor on appropriate low-temperature

annealing (B800 1C). The cell interior with a rhombo-

hedral 2:17 (Th

-type) structure shows twin

boundaries in the basal plane and a so-called plate-

let or z phase rich in zirconium is also observed

parallel to the basal plane.

The rhombohedral structure can be derived from

the SmCo

structure by an ordered substitution of

a dumb-bell of cobalt atoms for one-third of the

samarium atoms. Unlike the SmCo

and Nd

magnets, which show a nucleation controlled

Table 1

Structure type, intrinsic magnetic properties (Curie temperature T

, anisotropy ﬁeld H

¼(2K

þ 4K

)/m

anisotropy constant K

, saturation magnetization M

, upper limit of energy density (BH)

max

¼m

/4), domain wall

width d

, and critical single-domain particle size d

of important permanent magnet compounds and for comparison

a-Fe and F

(note: cubic structure) as well as Fe

B (in-plane anisotropy).

Compound Structure type

(K)

(T)

(MJ m

3

)

(T)

(kJ m

3

)

(nm)

(mm)

B Tetragonal 585 6.7 5 1.60 516 4.2 0.3

BNd

B 565 8.7 5 1.56 484 B4 B0.3

CNd

B 532 9.5 1.41 396 B4 B0.3

SmCo

Hexagonal 993 40 17 1.05 219 3.7 1.7

CaCu

Rhombohedral 1100 6.5 3.3 1.30 336 8.6 0.5

1Th

749 21 8.8 1.54 472 3.6 0.4

668 16 7.4 1.45 418 B0.3

26.7

2.3

Monoclinic 683 12 1.33 352 B0.3

(Fe,V)

(Sm

0.75

0.25

) Hexagonal 877 7.7 1.7 575 B0.3

(Fe

0.7

0.3

)

TbCu

NdFe

Tetragonal 743 10 1.11 245 B0.3

ThMn

Sm(Fe

Ti) ThMn

584 10.5 4.8 1.14 259 4.0 0.4

a-Fe b.c.c. 1043 0.046 2.16 928 30 0.007

Cubic 698 0.01 1.7

B Tetragonal 786 B0.4 –0.32 1.62 20

Figure 1

The tetragonal Nd

B structure (after Coey 1996).

1084

Rare Earth Magnets: Materials

coercivity mechanism, a pinning controlled mecha-

nism (see Coercivity Mechanisms) is dominant for the

2:17-type and the copper and zirconium additions

are needed for an effective magnetic precipitation

hardening achieved by an elaborated heat treatment.

Finally, Fe addition is used in order to increase the

remanence. Numerous detailed investigations on, for

example, the location of the zirconium atoms in the

structure and the sequence of solid-state

transformations on aging have been carried out (see

Ray and Liu 1992, Kumar 1988).

Interstitial nitrogen or carbon in rhombohedral

(Th

structure) compounds changes the

magnetic properties dramatically because not only

the Curie temperature is increased due to the lattice

expansion (in the case of nitrogen in Sm

a6%

volume expansion and an increase in T

from 116 1C

to 476 1C are observed) but also the crystalline elec-

tric ﬁeld created by the nitrogen or carbon atoms,

which occupy the large interstitial 9e sites, changes

the magnetocrystalline anisotropy from easy-plane

to easy-axis (Coey and Sun 1990). The correspond-

ing R

(0px p3) nitrides and carbides are,

in contrast to the binary R

compounds, pro-

mising candidates for permanent magnetic materials.

Ternary carbides R

(xp1.5) can be prepared

by standard casting techniques, higher carbon con-

centrations can be achieved by either substitut-

ing gallium for part of the iron in cast materials

or by exposing ﬁne particles of the binary compound

to hydrocarbon gases at elevated temperatures

(Skomski et al. 1995, Fuji and Sun 1995).

Similarly, a simple gas-phase nitrogenation can be

carried out at 1 bar nitrogen gas and temperatures of

about 400–500 1C. The absorption of nitrogen atoms

takes place once the temperature is high enough to

overcome the activation energy for the absorption

process. This gas–solid reaction consists of adsorp-

tion of the gas molecules, their dissociation and sub-

sequent chemisorption of, for example, nitrogen

atoms, and long-range diffusion into the metal ma-

trix. A detailed understanding of this irreversible ni-

trogenation process is necessary in order to optimize

the ﬁnal magnetic properties. It is still a matter of

discussion whether in a thermodynamic equilibrium a

solid solution or ternary nitrides with fully nitrided

and nonnitrided layers are obtained. The relatively

slow diffusion of the nitrogen atoms into the matrix

makes it necessary to use ﬁne ground particles.

Microcracks and grain boundaries provide fast

diffusion paths so that shorter annealing times and

lower temperatures can be used. However, the latter

remain critical processing parameters as a decompo-

sition in RN and Fe is the preferred reaction from a

thermodynamical point of view. Long-range diffu-

sion of metal atoms is required for this reaction and

insufﬁcient kinetics make the preparation of ternary

nitrides possible despite the metastability of the latter

compared to the binary nitride and iron metal. The

limited thermal stability of the ternary nitrides re-

stricts the applicability of this class of compounds to

metal or polymer bonded magnets. The decomposi-

tion temperature can be increased by additions such

as silicon or gallium and generally it can be stated

that the carbides are superior to the nitrides in terms

of their thermal stability. Very small grain sizes are

needed for highly coercive powders and the appro-

priate processing routes have been reviewed by

ller et al. (1996).

The tetragonal Fe-rich RFe

12–x

compounds

(ThMn

structure) with M ¼Ti, V, Cr, and Mo,

etc., are another family of materials with potential for

permanent magnet applications. Their magnetocrys-

talline anisotropy is once again determined by the

superposition of the Fe and R sublattice anisotropies.

Figure 3

Sm–Co phase diagram (after Cataldo et al. 1996).

Figure 2

Liquidus projection of the Nd–Fe–B system. Important

reactions are p

(1180 1C: L þ g-Fe -F), U

(1130 1C:

L þ g-Fe -F þ c(Nd

)), e

(1115 1C: L -Z þF),

(1105 1C: L - F þþg-Fe þ Fe

B), and E

(1095 1C: L -Z þ F þ Fe

B) (after Knoch et al. 1994).

1085

Rare Earth Magnets: Materials

The contribution of the Fe sublattice has the same

magnitude as in the Nd

B compounds and favors

the tetragonal c-axis as the magnetically easy direc-

tion. But the crystal ﬁeld-induced R sublattice an-

isotropy differs in sign and magnitude leaving only

samarium as a suitable R element because for the

other R elements either the c-axis is not favored or an

antiparallel coupling to the Fe sublattice is observed.

SmFe

12–x

, magnetically hardened by melt-spin-

ning or mechanical alloying (see Magnets: Mechani-

cally Alloyed) shows high coercivity and Curie

temperature but the remanence is somewhat low com-

pared to Nd

B. Interstitial nitrogen, introduced

using analogous procedures as described above, leads

to a sign reversal of the R sublattice anisotropy and

thus, of the second-order crystal ﬁeld parameter. The

consequence is that now the samarium-based com-

pounds show easy-plane and the neodymium-based

compounds easy-axis magnetocrystalline anisotropy.

Nitrogen charging is limited to one nitrogen atom per

formula unit and good results have been obtained for

(Wang et al. 1992). For more details

the reader is referred to reviews by Buschow (1991,

1997) and Fuji and Sun (1995).

The monoclinic structure of the R

(Fe,M)

-type

compounds can be described as alternating stack of

1:12 and 2:17 units which also present modiﬁcations

of the CaCu

structure (e.g., Yang et al. 1994). Again,

an enhancement of the Curie temperature, saturation

magnetization, and a change to easy-axis magneto-

crystalline anisotropy is observed upon nitrogen-

ation. In terms of practical use the Sm

(Fe,V)

material appears to be most promising, having an

anisotropy ﬁeld and Curie temperature higher than

B and a slightly lower saturation at room

temperature (Hu et al. 1996).

Finally, the interesting group of materials with the

hexagonal TbCu

-type structure (derived from the

structure but without long-range ordering) is

worth mentioning. These metastable compounds can

be prepared by nonequilibrium processing and it has

been reported that, for example, zirconium substitu-

tion for the rare-earth atom facilitates the formation

of this structure and the hard magnetic properties are

dramatically improved upon nitrogenation (e.g.,

(Sm

0.75

0.25

) (Fe

0.7

0.3

)

, Sakurada et al. 1996).

In the twentieth century, the (BH)

max

doubled ap-

proximately every 12 years (see Hard Magnetic Ma-

terials, Basic Principles of). Nowadays about 90% of

the limit for the energy density (BH)

max

(based on the

B phase) can be achieved in commercially

produced sintered Nd–Fe–B grades (see Magnets:

Sintered). At the end of 2000, however, it appeared

that the search for novel hard magnetic compounds,

helped by a basic understanding of the crystal ﬁeld

parameters, had somewhat stagnated and no further

breakthrough is in sight. On the other hand, only a

small number of ternary and quaternary systems has

been investigated so far.

See also: Ferrite Magnets: Improved Performance;

Magnetic Films: Hard

Bibliography

Buschow K H J 1991 Permanent magnet materials based on

tetragonal rare earth compounds of the type RFe

12–x

J. Magn. Magn. Mater. 100, 79–89

Buschow K H J 1997 Handbook of Magnetic Materials. Else-

vier, Amsterdam, Vol. 10, Chap. 4

Cataldo L, Lefevre A, Ducret F, Cohen-Adat M Th, Allibert C

H, Valignat N 1996 Binary system Sm–Co: revision of

the phase diagram in the Co rich ﬁeld. J. Alloys Comp. 241,

216–23

Coey J M D 1996 Rare Earth Iron Permanent Magnets. Claren-

don, Oxford, UK

Coey J M D, Sun H 1990 Improved magnetic properties by

treatment of iron-based rare earth intermetallic compounds

in ammonia. J. Magn. Magn. Mater. 87, L251–4

Croat J J, Herbst J F, Lee R W, Pinkerton F E 1984 Pr–Fe and

Nd–Fe-based materials: A new class of high-performance

permanent magnets. J. Appl. Phys. 55, 2078–82

Eisses J, de Mooij D B, Buschow K H J, Martinek G 1991

Towards an easy production route for isotropic rare earth

based permanent magnets. J. Less-Common Met. 171, 17–25

Fuji H, Sun H 1995 Handbook of Magnetic Materials. Elsevier,

Amsterdam, Vol. 9, Chap. 3

Hu Z, Yelon W B, Kaogirou O, Psycharis V 1996 Site occu-

pancy and lattice changes on nitrogenation in Nd

29–x

. J. Appl. Phys. 80, 2955–9

Knoch K G, Reinsch R, Petzow G 1994 The Nd–Fe–B phase

diagram and the primary solidiﬁcation of Nd

B. In:

Harris I R, et al. (eds.) Proc. 13th Int. Workshop on RE Mag-

nets and their Applications. Birmingham, UK, pp. 503–10

Kumar K 1988 RETM

and RE

permanent magnets

development. J. Appl. Phys. 63, R13–57

ller K H, Cao L, Dempsey N M, Wendhausen P A P 1996

interstitial magnets. J. Appl. Phys. 79, 5045–50

Ray A E, Liu S 1992 Recent progress in 2:17 type permanent

magnets. In: Proc. 12th Int. Workshop on RE Magnets

and their Applications. University of Western Australia,

Canberra, Australia, pp. 552–73

Sagawa M, Fujimori S, Togawa M, Matsuura Y 1984 New

material for permanent magnets on a base of Nd and Fe.

J. Appl. Phys. 55, 2083–7

Sakurada S, Tsutai A, Hirai T, Yanagida Y, Sahashi M, Abe S,

Kaneko T 1996 Structural and magnetic properties of rapidly

quenched (R, Zr)(Fe, Co)

(R ¼Nd, Sm). J. Appl. Phys.

79, 4611–3

Skomski R, Brennan S, Wirth S 1995 Interstitial Metallic

Alloys. NATO-ASI Series E, Vol. 281, Chap. 16

Strnat K, Hoffer G, Olson J, Ostertag W, Becker J J 1967

A family of new cobalt-base permanent magnetic materials.

J. Appl. Phys. 38, 1001–2

Wang Y Z, Hadjipanayis G C, Kim A, Sellmyer D J, Yelon W

B 1992 Structure and magnetic properties of RFe

compounds. J. Magn. Magn. Mater. 104–107, 1132–4

Yang F-M, Nasunjilegal B, Wang J-L, Pan H-Y, Qing W-D,

Hu B-P, Wang Y-Z, Liu G-C, Li H-S, Cadogan J M 1994

Magnetic properties of a novel Sm

(Fe,Ti)

nitride.

J. Appl. Phys. 76, 1971–3

O. Gutﬂeisch

IFW Dresden, Germany

1086

Rare Earth Magnets: Materials

Single-molecule Magnets

Molecular objects containing a large, but ﬁnite,

number of magnetic centers whose magnetization re-

laxes slowly at low temperature are commonly called

single-molecule magnets (SMMs) (Aromi et al. 1998).

In a sense this is a misnomer, because the term mag-

net must rigorously apply only to systems in which

the spin correlation length diverges, i.e., goes to in-

ﬁnity, and this is clearly not possible in a cluster with

a ﬁnite size. However, the term is evocative, and it

can be used, provided its true meaning is understood.

The ﬁrst compound to show SMM behavior (Ses-

soli et al. 1993) was [Mn

(CH

COO)

O (Mn12Ac), which has a ground S ¼10 state

and a large Ising-type anisotropy. The barrier for the

reorientation of the magnetization is B65K, as

shown in Fig. 1. The discrete levels in the potential

wells are a clear indication of the quantum nature of

the system. Classically the reorientation of the mag-

netization can occur by overcoming the barrier, and

indeed below 15K the relaxation time of the magnet-

ization becomes very long: at 1.5K it is 40 years.

Therefore, Mn12Ac behaves like a bulk magnet and

shows magnetic hysteresis as shown in Fig. 2. At zero

ﬁeld the magnetization may be either positive or neg-

ative, depending on the history of the sample.

Therefore, the SMM is bistable, and in principle it

becomes possible to store information in one single

molecule. Further, the hysteresis shows quantum ef-

fects (Friedman et al. 1996, Thomas et al. 1996) as-

sociated with the small size of the molecule. In fact

the magnetization of a quantum object can reorient

itself also by tunneling below the barrier. Evidence

for this behavior is provided by the hysteresis loop of

Fig. 2. In fact the ﬂat regions in the hysteresis curve

correspond to slow relaxation of the magnetiza-

tion while the steps correspond to comparatively

faster relaxation. The steps occur at H

¼0.4 T, where

i ¼0,1,y. At zero ﬁeld, pairs of 7M levels, as de-

picted in Fig. 1, have the same energy: under these

conditions tunneling is possible, and the relaxation

time of the magnetization becomes comparatively

fast. When a ﬁeld is applied the levels change their

energies and the degeneracy is lost, quenching the

tunneling and lengthening the relaxation time. Since

some of the levels increase their energies, and others

decrease, at some given ﬁeld pairs of levels will again

become degenerate, allowing tunneling and shorten-

ing the relaxation time. The ﬁelds at which the cross-

ings occur can be calculated once the energies of the

levels are known in zero ﬁeld, and they compare very

well with the H

ﬁelds deﬁned above.

The tunneling mechanism described above is a

thermally activated one, in the sense that it does not

occur within the lowest M ¼710 levels, but between

higher M levels which are thermally populated.

In order to observe tunneling a transverse ﬁeld is

needed, which effectively couples the pairs of reso-

nating levels. Mn12Ac has crystal-imposed tetragonal

symmetry; therefore only hexadecupolar transverse

anisotropy is allowed. Therefore, it is very small and

the tunneling process is rather inefﬁcient. In fact at

low temperature, where only the lowest M ¼710

levels are thermally populated, no unambiguous evi-

dence of direct tunneling is found and the relaxation

time is very long. Matters have been found to be

different in another cluster characterized by an S ¼10

Figure 1

Energy levels and anisotropy barrier of the ground

S ¼10 state of Mn12Ac. The levels are labeled by the M

component of the total spin S (MpSpM).

Figure 2

Magnetic hysteresis of a single crystal of Mn12Ac at

2.1K. The magnetic ﬁeld is parallel to the tetragonal axis

of the cluster.

1087

ground state, [Fe

(tacn)

(OH)

]Br

(Fe8). Like

Mn12Ac, the cluster also has Ising-type anisotropy,

but with a non-negligible transverse quadrupolar an-

isotropy (Barra et al. 1996). The barrier is smaller

than in Mn12Ac, B25K, and the relaxation times are

shorter. Below 300mK the relaxation time of the

magnetization becomes independent of temperature

showing that the pure tunneling regime is achieved

for this system (Sangregorio et al. 1997).

The detailed mechanism of tunneling is still a mat-

ter of debate, but magnetic nuclei, through the so-

called hyperﬁne interaction, are expected to play an

important role. Experiments in which the nonmag-

netic nuclei of iron are substituted by the magnetic

Fe, I ¼1/2, show that the relaxation rate of the

magnetization increases in the quantum regime, con-

ﬁrming that the magnetic nuclei are needed to assist

the tunneling. A further conﬁrmation came from a

partially deuterated sample in which the relaxation

time became longer, in agreement with the lower

magnetism of deuterons compared to protons.

The main advantages of SMMs compared with

other types of magnetic nanoparticles is that they are

absolutely monodisperse, all identical to each other,

perfectly known from crystal structure data, and their

properties can be ﬁne-tuned through the techniques

of molecular chemistry. They have allowed for the

ﬁrst time the observation of quantum phenomena in

mesoscopic matter that had been long looked for but

had not been unambiguously proved experimentally.

Beyond the quantum tunneling effects described

above these systems have provided for the ﬁrst

time a conﬁrmation of the Berry phase in magnets

(Wernsdorfer and Sessoli 1999). This effect, which is

similar to the Aharonov–Bohm effect in conductors,

had been suggested to be operative in magnets (Garg

1998) but could not be conﬁrmed until Fe8 became

available. Therefore, SMMs can indeed provide a

rich new physics, at the border between quantum and

classical approaches.

In perspective, SMMs might be considered for ap-

plications in memory storage. Further, if the condi-

tions for observing quantum coherence are met, they

might be used for hardware for quantum computers.

The other developments to be expected are the syn-

thesis of larger clusters, which will be investigated for

a large number of different properties, which can

make them appealing for biocompatibility (for mag-

netic resonance imaging contrast agents, for instance,

or for magnetic drug delivery).

The conditions for obtaining more efﬁcient SMMs,

i.e., systems operating at higher temperatures, are

reasonably well understood. It is necessary to have

molecules with S values as high as possible in the

ground state, with a high Ising-type magnetic aniso-

tropy. In order to reach this goal it would be pre-

ferable to assemble individual magnetic centers with a

large spin, like iron(III) or manganese(II) (S ¼5/2),

and manganese(III) or iron(II) (S ¼2). In order to

have high magnetic anisotropy it is useful to start

from anisotropic centers. This can be achieved, for

instance, by using Jahn–Teller distorted ions like

manganese(III). Many attempts are being made to

synthesize larger clusters that match these require-

ments. Some success has been achieved, not only by

making obvious chemical variations on the Mn12Ac

and Fe8 molecules, but also looking for new systems.

This has been achieved using other metal ions, like

nickel(II), chromium(III), and vanadium(III). It must

be stressed that, although it may be easier to reach

high-spin states starting from individual large spins,

organic approaches can also be used. Several high-

spin molecules have been obtained in this way,

though with small anisotropy. However, if efﬁcient

strategies are developed for synthesizing large poly-

mers, then the organic approach might turn out to be

rewarding.

Bibliography

Aromi G, Aubin S M J, Bolcar M A, Christou G, Eppley H J,

Folting K, Hendrickson D N, Huffman J C, Squire R C, Tsai

H L 1998 Manganese carboxylate clusters: from structural

aesthetics to single-molecule magnets. Polyhedron 17, 3005–20

Barra A L, Debrunner P, Gatteschi D, Schulz Ch E, Sessoli R

1996 Superparamagnetic-like behavior in an octanuclear iron

cluster. Europhys. Lett. 35, 133–8

Friedman J R, Sarachik M P, Tejada J, Ziolo R 1996 Macro-

scopic measurement of resonant magnetization tunneling in

high-spin molecules. Phys. Rev. Lett. 76, 3830–3

Garg A 1998 Lattice distortion mediated paramagnetic relax-

ation in high-spin high-symmetry molecular magnets. Phys.

Rev. Lett. 81, 1513–6

Sangregorio C, Ohm T, Paulsen C, Sessoli R, Gatteschi D 1997

Quantum tunneling of the magnetization in an iron cluster

nanomagnet. Phys. Rev. Lett. 78, 4645–8

Sessoli R, Gatteschi D, Caneschi A, Novak M A 1993 Magnetic

bistability in a metal-ion cluster. Nature (London) 365, 141–3

Thomas L, Lionti F, Ballou R, Gatteschi D, Sessoli R, Barbara

B 1996 Macroscopic quantum tunneling of magnetization in

a single crystal of nanomagnets. Nature (London) 383, 145–7

Wernsdorfer W, Sessoli R 1999 Quantum phase interference

and parity effects in magnetic molecular clusters. Science 284,

133–5

D. Gatteschi

University of Florence, Italy

Solids, Nuclear Magnetic Resonance of

The nuclear magnetic resonance (NMR) pheno-

menon was discovered in the mid-twentieth century.

At about the same time, two different research

groups showed that when samples were placed in a

strong, homogeneous magnetic (applied) ﬁeld, the

sample could absorb and emit radiofrequency (RF)

energy (Purcell et al. 1946, Bloch et al. 1947). A solid

1088

Solids, Nuclear Magnetic Resonance of

material (parafﬁn) was one of the ﬁrst samples used

in the measurement of nuclear magnetic resonance;

however, a wide resonance linewidth prevented any

detailed interpretation of the spectra. Researchers

quickly realized liquid samples provided substantially

improved spectral resolution. With liquid samples

and improvements in instrumentation that quickly

followed, the chemical shift was discovered, along

with the discovery of scalar (spin–spin or ‘‘through-

bond’’) coupling. Chemical shifts are small perturbat-

ions of the exact resonance frequency of a given nu-

cleus caused by differences in the electronic

environment of the individual nuclei. Usually very

small, chemical shifts are typically measured in parts

per million (ppm) relative to the resonance position

of some standard. Magnetic nuclei that share com-

mon electrons can couple with each other, giving rise

to scalar coupling. This spin–spin coupling gives rise

to ﬁne structure (splittings) of the resonances of the

nuclei involved. Of course, the discovery of these two

NMR perturbations provided chemists with a pow-

erful technique for obtaining structural information

on liquid samples. In a short time commercial in-

strumentation was made available to chemists for the

study of liquid or solution samples. Many experi-

ments were developed which exploited chemical shifts

and scalar coupling to obtain detailed structural in-

formation. NMR of solids was left to a relative few

NMR research laboratories.

Work in this area was difﬁcult and slow going,

owing to enormous sensitivity and resolution prob-

lems caused mainly by two factors. First, magnetic

nuclei in solid samples interact with each other

through their magnetic dipole moments. This dipo-

lar, through-space interaction can be much stronger

than the through-bond, scalar interactions. The

strength of the dipolar interaction is proportional to

3cos

ð1Þ

where y is the angle between a vector connecting

the two interacting nuclei and the applied ﬁeld, and

r is their interatomic distance. Thus, the exact reso-

nance position of any nucleus depends on the posi-

tion of the neighboring magnetic nuclei relative to

the applied ﬁeld direction. The exact magnetic ﬁeld

experienced by any particular nucleus will vary from

molecule to molecule in any sample which is less than

a perfect single crystal. These dipole–dipole interac-

tions make it impossible to observe abundant spins

(like protons) at high resolution in a solid by con-

ventional NMR techniques. Usually, proton line-

widths are broadened so all ﬁne structure is hidden.

In liquids however, rapid tumbling quickly averages

Eqn. (1) over all possible values of y, effectively

zeroing the dipolar effect.

A second possible source of broadening in solids is

another orientation effect and is caused by the elec-

tronic environment of nuclei. Electrons near a nucle-

us shield it from the applied ﬁeld causing slight

perturbations in the resonance positions. This effect

gives rise to the chemical shift, the most important

perturbation of the magnetic resonance interaction.

Electron density, however, may not be homogene-

ously distributed about a nucleus. In those cases

where the electron density is not homogeneous about

a nucleus, there will be an orientation dependence of

the shielding. This results in another broadening ef-

fect in randomly oriented solids called chemical shift

anisotropy (CSA). So, in a solid where the molecules

are randomly oriented, chemical shifts (both the iso-

tropic and anisotropic parts) and dipolar interactions

with other nuclei cause resonance lines to broaden

and overlap. (This broadened spectrum is actually

made up of many narrower lines at slightly different

chemical shifts due to these orientation effects.) For a

more formal discussion of these effects see Yannoni

(1982). Pines et al. (1973) published their discovery

that nuclear magnetization could be transferred from

an abundant higher spin, I, to a rare lower spin, S,in

solid samples through a technique they called cross-

polarization (CP).

An initial 901 pulse on the abundant spins is fol-

lowed immediately by a strong RF ﬁeld parallel (or

antiparallel) to the abundant spin magnetization.

This parallel RF ﬁeld prevents the sample abundant

spin magnetization from returning to its equilibrium

position and this is called a ‘‘spin lock.’’ Magnetiza-

tion then transfers to the rare spins by simultaneously

applying a RF ﬁeld to these rare spins, which meets

the Hartmann–Hahn condition (Hartmann and

Hahn 1962):

¼ H

ð2Þ

where g is the magnetogyric ratio and H is the

applied ﬁeld strength of the spins. In the absence of

any relaxation, the magnetization of the rare spins is

enhanced by a factor of g

beyond the magnetiza-

tion expected for a conventional NMR experiment

(a simple 901 pulse). During this CP contact time,

the rare spin magnetization grows at an exponential

rate characterized by the time constant T

(curve (a)

of Fig. 1). Relaxation effects will diminish this en-

hancement factor. As CP progresses, magnetization

is exponentially decaying in a time characterized by

(curve (b) of Fig. 1). As long as T

, the

observed enhancement as a function of CP time, t,

is just

exp 



 exp 



1 

ð3Þ

(curve (c) of Fig. 1).

1089

Solids, Nuclear Magnetic Resonance of