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The demagnetizing ﬁeld is always directed perpen-

dicular to the ﬁlm plane with H

¼M

, where M

is the perpendicular magnetization of the ﬁlm. A

careful examination shows that during the course of a

conventional hysteresis loop measurement in the ﬁlm

plane, the internal ﬁeld rotates when the direction of

the external ﬁeld is held ﬁxed (see Fig. 3). Since a

proper hysteresis measurement implies that the ap-

plied ﬁeld direction is not changed, results from a

conventional hysteresis loop measurement are highly

misleading. Keeping the internal ﬁeld direction ﬁxed

therefore requires that the direction of the external

ﬁeld be continuously adjusted during the measure-

ment. These compensated measurements have been

done (Bernards and Cramer 1992, Richter 1993a) and

they indicate that the intrinsic properties of ME are

excellent: a very square loop with a high squareness

and a narrow SFD has been observed.

4. Recording Properties

The ultimate recording potential of ME and MP tape

was estimated in Sect. 1. The considerations there

imply that the dominant noise source in a recorder is

the particle noise of the magnetic medium. In a re-

corder, however, there are other noise sources present

and the absolute output signal of the medium be-

comes important, especially for inductive readout.

This favors high-magnetization media, such as ME

and MP tape, and consequently none of the older

particulate media are considered for high-density

tape recording. The introduction of magnetoresistive

(MR) heads, which are more sensitive than inductive

heads, de-emphasizes the output requirements.

The most critical parameter in a recording system

is the head-to-medium spacing. At read-back, the

ﬂux decreases exponentially with distance to the tape

surface:

fpexpðkzÞ3  55z=l dB ð5Þ

where z is the distance from the top surface of the

medium, k ¼2p/l, and l is the recorded wavelength

of a sinusoidal magnetization.

Equation (5) is called ‘‘spacing loss’’ and is an in-

evitable consequence of the Laplace equation in two

dimensions (Mallinson 1993, Bertram 1994). The der-

ivation assumes that the track width is much larger

than the other dimensions of the recording system,

which is the case in all practical recorders. In addi-

tion to the reading spacing loss, there is a writing

spacing loss. The writing spacing loss is of the order of

45z/l dB (Bertram and Niedermeyer 1982), such that

the total spacing loss amounts to roughly 100z/l dB.

In order to reduce head-to-medium spacing, it is

therefore required to create a very smooth tape sur-

face. Unfortunately, adhesion occurs between exces-

sively smooth surfaces, so that one has to strike a

delicate balance between electrical and mechanical

performance.

To achieve a high output, the width of a magnet-

ization transition between regions magnetized in op-

posite directions needs to be kept as small as possible.

To ﬁrst order, the effect of transition width on the

recording output is the same as that of a spacing loss

(Bertram 1994). The width of a transition is deter-

mined by the following factors:

(i) Demagnetization. This occurs at the instant of

writing and is proportional to the ratio of remanent

magnetization and coercivity of the medium. The ﬁrst

paper to recognize this was that of Williams and

Comstock (1971).

(ii) Particle length (‘‘length loss’’). The transition

width cannot be smaller than the length of a particle

(Richter and Veitch 1996). Early MP tapes had par-

ticle lengths of 150 nm or even longer which affected

recording of very short wavelength. Modern MP

tapes have particle lengths down to 100 nm and lower

such that the length loss effect is small. In addition,

smaller particles potentially allow smoother tape sur-

faces. Shorter lengths will be necessary if the linear

recording density is to be increased. Particles of about

60 nm have been made (Hisano and Saito 1998) but

they suffer from a poorer SFD.

(iii) Switching ﬁeld distribution. This would deter-

mine the transition width if no demagnetization and

no limitation by the particle length were present. For

ME tape, the SFD can considered to be very small;

for MP tape the narrowest values achieved are about

0.2.

(iv) Coating thickness. This obviously determines

the output of the tape. However, thicker coatings

generally produce wider transitions, either caused by

greater demagnetization or by geometrical effects

(Richter 1997). Examples for some transitions are

given in Fig. 4. For many tapes, however, the total

thickness of the coating is not at all relevant. The

depth of recording is roughly equal to the gap length

of the writing head such that the particles at the bot-

tom of a thick magnetic coating remain untouched

(partial penetration recording). In addition, spacing

loss effects attenuate the contributions from the

deeper layers of the tape, especially for short wave-

lengths. ME tape coatings are 150–200 nm thick, but

even those are not fully recorded throughout their

depth. It has been shown experimentally and theo-

retically that thin-ﬁlm MP tapes do not have a higher

Figure 3

Evolution of internal ﬁeld during a hysteresis loop

measurement of ME tape.

910

Metal Particle versus Metal Evaporated Tape

output at short wavelength than thick tapes (Richter

and Veitch 1995, Richter 1997). On the contrary,

thinner tapes show a lower output for long-wave-

length recording. Thin magnetic coatings are advan-

tageous for overwrite behavior (Richter and Veitch

1995, Veitch et al. 1999). For identical coating thick-

ness, ME tape is found to have a much improved

overwrite over MP tape owing to its superior intrinsic

properties and the tilt of the easy axis.

(v) Direction of the easy axis. It has been discovered

that ME tape exhibits a recording anisotropy: the

recording output in the two directions differs by

about 6 dB. The high output is observed when the

recording head runs over the medium as shown in

Fig. 4. Modeling results indicate that the optimum tilt

of the easy axis is between 201 and 301 out of the ﬁlm

plane and that the output increase over an easy axis

in the tape plane is only moderate (Richter 1993b,

Stupp et al. 1994). The oblique recording inherent to

ME tape also reduces nonlinear intersymbol interfer-

ence (Mallinson 1989, Cumpson and Stupp 1997).

5. The Future: ME or MP Tape?

As discussed in Sect. 2, ME tape has a higher re-

cording potential and some other advantages in re-

cording behavior. Apart from the improved

recording performance, ME tape can also be made

thinner. If the base ﬁlm, for example, has a thickness

of 5 mm, the total thickness of the tape is roughly

5.2 mm. This has to be contrasted with MP tape,

where the total tape thickness is roughly 6 mm. The

MP tape is thicker because any particulate coating

(double layer, single layer) cannot yet be made thin-

ner than roughly 1 mm, and thus more ME tape than

MP tape can be wound into a given cassette.

However, ME tape can be recorded in only one

direction, which effectively limits its use to helical

scan systems, whereas the major new data storage

systems (Digital Linear Tape and Linear Tape Open)

use serpentine linear recording, reversing direction at

the end of the tape. While ME is simply ruled out for

these systems, it may seem surprising that it has not

been adopted for the latest helical scan data system

DD4. We can conclude that the advantages of ME

tape over MP tape are too small to justify moving to

a new technology. It should not be forgotten that a

technology switch is also associated with risks, and—

although tremendous progress in ME tape has been

made—the tribological properties of particulate tape

still have to be regarded as superior to those of ME

tape. It is therefore likely that MP tape will be the

dominant tape recording medium in the future.

See also: Magnetic Recording: Flexible Media,

Tribology; Magnetic Recording Media: Advanced;

Metal Evaporated Tape; Magnetic Recording Tech-

nologies: Overview

Bibliography

Aharoni A 1986 Perfect and imperfect particles. IEEE Trans.

Magn. 22, 478–83

Bernards J P C, Cramer H A J 1991 Vector magnetization of

recording media: a new method to compensate for demag-

netizing ﬁelds. IEEE Trans. Magn. 27, 4873–5

Bertram H N 1994 Theory of Magnetic Recording. Cambridge

University Press, Cambridge

Bertram H N, Niedermeyer R 1982 The effect of spacing on

demagnetization in magnetic recording. IEEE Trans. Magn.

18, 1206–8

Cumpson C R, Stupp S E 1997 Experimental and theoretical

studies of nonlinear transition shift in metal evaporated tape.

IEEE Trans. Magn. 33, 2968–70

Hisano S, Saito K 1998 Research and development of metal

powder for magnetic recording. J. Magn. Magn. Mater. 190,

371–81

Inaba H, Ejiri K, Abe N, Masaki K, Araki H 1993 The ad-

vantages of the thin magnetic layer on a metal particulate

tape. IEEE Trans. Magn. 29, 3607–12

Inaba H, Ejiri K, Masaki K, Kitahara T 1998 Development of

an advanced metal particulate tape. IEEE Trans. Magn. 34,

1666–8

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recorder. IEEE Trans. Magn. 5, 182–6

Mallinson J C 1989 Proposal concerning high-density digital

recording. IEEE Trans. Magn. 25, 3168–9

Mallinson J C 1991 A new theory of recording media noise.

IEEE Trans. Magn. 27, 3519–31

Figure 4

Schematics of recorded transitions for MP and ME tape.

In MP tape, the top layers of the tape are recorded

further downstream, while the opposite is true for ME

tape. The dashed line in the upper ﬁgure indicates how

thick is a ‘‘thin’’ MP tape coating.

911

Metal Particle versus Metal Evaporated Tape

Mallinson J C 1993 The Foundations of Magnetic Recording,

2nd edn. Academic Press, San Diego, CA

Richter H J 1993a An analysis of magnetization processes in

metal evaporated tape. IEEE Trans. Magn. 29, 21–33

Richter H J 1993b An approach to recording on tilted media.

IEEE Trans. Magn. 29, 2258–65

Richter H J 1997 A generalized slope model for magnetization

transitions. IEEE Trans. Magn. 33, 1073–84

Richter H J, Veitch R J 1995 Advances in magnetic tapes for

high density information storage. IEEE Trans. Magn. 31,

2883–8

Richter H J, Veitch R J 1996 A reconsideration of length loss

effects. J. Magn. Magn. Mater. 155, 335–7

Saitoh S, Inaba H, Kashiwagi A 1995 Developments and ad-

vances in thin layer particulate recording media. IEEE Trans.

Magn. 31, 2859–64

Seberino C, Bertram H N 1999 Numerical study of hysteresis

and morphology in elongated tape particles. J. Appl. Phys.

85, 5543–5

Sharrock M P, McKinney J T 1981 Kinetic effects in coercivity

measurements. IEEE Trans. Magn. 17, 3020–2

Shinohara K, Yoshida H, Odagiri M, Tomago A 1984 Colum-

nar structure and some properties of metal evaporated tape.

IEEE Trans. Magn. 20, 824–6

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

hysteresis in heterogeneous alloys. Trans. R. Soc. A240,

599–642

Stupp S E, Cumpson S R, Middleton B K 1994 A quantitative

multi-layer recording model for media with arbitrary easy

axis orientation. J. Magn. Soc. Jpn. 18 (Suppl. S1), 145–8

Veitch R J, Ilmer A, Lenz W, Richter V 1999 MP technology

for a new generation of magnetic tapes. J. Magn. Magn.

Mater. 193, 279–83

Veitch R J, Richter H J, Poganiuch P, Jakusch H, Schwab E

1994 Thermal effects in small metallic particles. IEEE Trans.

Magn. 30, 4074–6

Williams M L, Comstock R L 1971 An analytic model of the

write process in digital magnetic recording. AIP Conf. Proc.

5, 738–42

H. J. Richter

Seagate Recording Media, Fremont, California, USA

R. J. Veitch

BASF AG, Ludwigshafen, Germany

Metamagnetism: Itinerant Electrons

Itinerant electron metamagnetism (IEM) is a ﬁrst-

order ﬁeld-induced transition from the paramagnetic

state to the ferromagnetic one in itinerant electron

systems. This phenomenon is closely related to the

instability of ferromagnetism (see Itinerant Electron

Systems: Magnetism (Ferromagnetism)). Since this

phenomenon was predicted to occur by Wohlfarth

and Rhodes (1962), many experimental studies using

ultrahigh magnetic ﬁelds have been done to observe

it. Now, many metamagnetic compounds such as py-

rites Co(S

1x

)

, Laves phase compounds such as

YCo

, Y(Co

1x

)

, LuCo

, and Lu(Co

1x

)

are

found. This article ﬁrst outlines theoretical concepts

of IEM and then presents experimental results on the

magnetic and electrical properties and magnetovol-

ume effects of these compounds together with alloy-

ing and pressure effects on the metamagnetic

transition.

1. Theoretical Background

Wohlfarth and Rhodes (1962) ﬁrst discussed IEM

using a Landau-type expression for the free energy of

the itinerant electron system based on the Stoner

model. They pointed out that IEM is expected to

occur in a strongly exchange-enhanced paramagnet

with a broad maximum in the temperature depend-

ence of the susceptibility. More detailed conditions

for the appearance of IEM at T ¼0 were given by

Shimizu (1982). Later, a theory of IEM at ﬁnite tem-

perature, based on the spin ﬂuctuation model, was

developed by Moriya (1986) and Yamada (1993).

The magnetic behavior of itinerant electron para-

magnets in magnetic ﬁelds depends on the shape of

the density of states (DOS) near the Fermi level (see

Itinerant Electron Systems: Magnetism (Ferromag-

netism)). The paramagnet does not satisfy the Stoner

condition for the appearance of ferromagnetism,

Ir(e

)41, where I is the exchange energy of elec-

trons and r(e

)(¼r

) þr

)) is DOS at the

Fermi level e

.Ifr(e

) increases with ﬁeld in a

strongly exchange-enhanced paramagnet, however,

the Stoner condition will be satisﬁed in a high mag-

netic ﬁeld and a ferromagnetic state will appear.

When the function of r(e) has a positive curvature

near e

, r(e

) increases with ﬁeld. This is one of the

conditions for IEM, as discussed below.

The equation of state for the itinerant electron

system at T ¼0 is written as

B ¼ aM þ bM

þ cM

ð1Þ

where B is the magnetic ﬁeld, M the magnetic mo-

ment, and a the inverse susceptibility w

1

(Shimizu

1982). The coefﬁcients a, b, and c are functions of

DOS and its derivatives at e

. At a temperature T40,

the coefﬁcients in Eqn. (1) are renormalized by ther-

mal spin ﬂuctuations and the equation is rewritten as

B ¼ AðTÞM þ BðTÞM

þ CðTÞM

ð2Þ

where A(T) is the inverse susceptibility w(T)

1

(Moriya

1986, Yamada 1993). The coefﬁcients A(T), B(T), and

C(T) are functions of a, b, c, and the square of the

amplitude of thermally ﬂuctuating moment x(T)

x(T)

is an increasing function of T and proportional

to T

at low T.

Moriya (1986) determined the magnetic phase

diagram for a40, bo0, and c40. The negative

value of b indicates that the DOS curve has a positive

912

Metamagnetism: Itinerant Electrons

curvature near the Fermi level. The ground state is

paramagnetic for ac/b

43/16. IEM appears under

the condition

ð3Þ

However, IEM does not occur for ac/b

X9/20. For

0oac/b

o3/16, the ground state becomes ferromag-

netic even in zero ﬁeld although the Stoner condition

(ao0) is not satisﬁed. Figure 1 shows the theoretical

phase diagram for a40, bo0, c40 in the narrow

region 0.16pac/b

p0.21 near the appearance of

ferromagnetism. Since the value of cx(T)

/7b7 in-

creases monotonically with increasing T, the ordinate

is considered as the T axis. The ferromagnetic tran-

sition (FT) occurs on the T

curve. FT is second or-

der for 0oac/b

o5/28 and ﬁrst order for 5/28o

ac/b

o3/16, where the value of T

abruptly decreases

with increasing ac/b

. The type of FT changes at

point T

on the T

curve. Note that IEM appears also

just above T

in 5/28oac/b

o3/16. The T

line

merges into the T

line at T

The inverse susceptibility is given by the relation

(Yamada 1993)

1

¼ a þ

bxðTÞ

cxðTÞ

ð4Þ

Under the condition ac/b

45/28, w becomes maxi-

mum at a temperature T

max

. Thus, the paramagnetic

system with IEM has a broad maximum in w(T),

which increases in proportion to T

at low T. The

system with the ﬁrst-order FT also has a broad max-

imum in w(T) above T

The temperature dependence of the average critical

ﬁeld for IEM is given by

ðTÞ¼B

ð0Þþ

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

7b7=3c

7b7xðTÞ

ð5Þ

Therefore, the critical ﬁeld increases with T as T

low T (Yamada 1993).

2. Observations of Itinerant Electron

Metamagnetism

2.1 Laves Phase Compounds MCo

(M: Y and Lu)

The Laves phase compounds YCo

and LuCo

are

typical 3d systems with IEM. ScCo

is believed to

exhibit IEM. These compounds are strongly ex-

change-enhanced paramagnets. The susceptibility

w(T) increases with T at low T followed by a max-

imum at a temperature T

max

. At high T, w(T) obeys

the Curie–Weiss law. w(T) in the low T region in-

creases in proportion to T

. The T

dependence is

caused by the excitation of spin ﬂuctuations and can

be explained with Eqn. (4) (Yamada 1993).

Goto et al. (1989, 1990) observed IEM in YCo

and LuCo

around 70 T. The magnetization curve of

LuCo

is shown in Fig. 2 (see Fig. 3 for that of

YCo

). In ScCo

, however, IEM does not occur in

ultrahigh magnetic ﬁelds up to 120 T. The high-ﬁeld

susceptibility of YCo

and LuCo

is very large above

Figure 1

Theoretical phase diagram for a40, bo 0, c40 in the

narrow region 0.16pac/b

p0.21 near the appearance of

ferromagnetism.

Figure 2

Magnetization curve of LuCo

. The metamagnetic

transition can clearly be seen.

913

Metamagnetism: Itinerant Electrons

, which indicates that the magnetization is not

completely saturated by the metamagnetic transition

(MT). MT is very sharp at low T, but becomes broad

with increasing T. The critical temperature for the

disappearance of the ﬁrst-order MT is determined to

be T

¼100710 K for YCo

(Goto et al. 1994).

According to the band model of IEM, the critical

ﬁeld is expected to change sensitively by shifting the

position of the Fermi level in the DOS curve. This

phenomenon has been examined using samples of Y

(Co

1x

)

(M ¼Fe, Ni, and Fe

0.5

) (Goto et al.

1994). Iron substitution shifts the Fermi level to the

lower energy side, while nickel substitution shifts it to

the higher energy side. With increasing x, B

decreases

in Y(Co

1x

)

, but increases in Y(Co

1x

)

. The

change of B

can easily be understood by considering

the band structure. Since iron substitution increases

the DOS at the Fermi level, the parameter a in Eqn.

(1) decreases. This causes the reduction of B

. How-

ever, an increase in B

is expected by nickel substitu-

tion. In the case of doping with equal amount of iron

and nickel, no change of B

is expected. In fact, the

observed change of B

is very small for the doping.

The substitution of aluminum for cobalt in YCo

expands the lattice and enhances the susceptibility w

(Yoshimura et al. 1985). The position of T

max

shifts

to the low T side and a weak ferromagnetism appears

in Y(Co

1x

)

with 0.12pxp0.19. Figure 3

shows the magnetization curves of paramagnetic

Y(Co

1x

)

with xX 0.11 at low T (Goto et al.

1994). These compounds exhibit IEM. The average

critical ﬁeld B

decreases nearly linearly with increas-

ing x and is found to be proportional to T

max

¼0.29 [T/K] (Goto et al. 1994).

The ﬁeld B

of LuCo

also decreases and a

ferromagnetic state becomes stable by replacing co-

balt with gallium (Murata et al. 1993). The critical

concentration of Lu(Co

1x

)

for the onset of

ferromagnetism is x

E0.095 (Saito et al. 1997). The

ﬁeld-induced moment in the paramagnetic compound

is consistent with the spontaneous moment M

of the

ferromagnetic one. Figure 4 shows the value of M

and T

as a function of x, which increases abruptly at

, where B

becomes zero (Saito et al. 1997). These

results imply that the appearance of IEM is related to

the instability of ferromagnetism.

When the nonmagnetic M atom in MCo

is re-

placed with magnetic rare earth R, the cobalt mo-

ment is induced by the effective ﬁeld from the R site.

The effective ﬁeld can be evaluated using the relation

eff

¼84(g

 1)J [T], where g

is the g-factor of R

and J the total angular momentum (Goto et al. 1989).

The induced cobalt moment is found to increase rap-

idly at about 70 T, indicating that the effective ﬁeld

produces MT. This value corresponds to the critical

ﬁeld of YCo

2.2 Pyrites Co(S

1x

)

The CoS

compound with the pyrite structure is an

itinerant ferromagnet with T

D120 K. The substitu-

tion of selenium for sulfur in CoS

makes the 3d band

wider and changes the second-order FT to the ﬁrst-

order one accompanied by a rapid decrease of T

The Co(S

1x

)

compounds with xX0.12 are par-

amagnetic and exhibit a broad maximum in w(T).

IEM was ﬁrst observed in paramagnetic Co(S

1x-

)

by Adachi et al. (1979). Later, detailed studies

were done by Goto et al. (1997). Figure 5 shows the

magnetization curves of Co(S

1x

)

for 4.2 K (Goto

et al. 1997). The average critical ﬁeld B

increases lin-

early with x. The magnetization in the induced ferro-

magnetic state is consistent with the spontaneous

Figure 3

Magnetization curves of paramagnetic Y(Co

1x

)

with xX 0.11 at low T.

Figure 4

Spontaneous magnetization M

and the Curie

temperature T

of Lu(Co

1x

)

914

Metamagnetism: Itinerant Electrons

moment of the ferromagnet. In Co(S

0.9

0.1

)

with a

ﬁrst-order FT at 27 K, a metamagnetic transition

(MT) is found to appear just above T

. However,

CoS

with a second-order FT does not exhibit MT

above T

. The critical ﬁeld for 0.1px shifts in pro-

portion to T

as B

(x,T) ¼B

(x,0) þT

in the low T

region To70 K. The T

dependence can be explained

by the theory of IEM.

Figure 6 shows the magnetic phase diagram of

Co(S

1x

)

in the x–T plane, where T

is the critical

temperature for the disappearance of IEM (Goto et al.

1997). The type of FT changes from second-order to

ﬁrst-order at T

on the T

curve. The position of T

can

be determined from the critical concentration x

( ¼1%) at which w(T

max

)

1

becomes zero. FT is sec-

ond-order for 0pxo1%, but ﬁrst-order for

1%oxo11%. The value of T

on the ﬁrst-order

phase boundary decreases abruptly with increasing x.

MT appears between the T

and T

curves. The ex-

perimental phase diagram can be compared with the

theoretical one shown in Fig. 1. Since ac/b

for

Co(S

1x

)

increases with x, the abscissa of the the-

oretical phase diagram is considered as the x axis. On

the other hand, the ordinate corresponds to the T axis

of the phase diagram of Co(S

1x

)

. The theoretical

phase diagram reproduces well the experimental one.

3. Pressure Effects

The theoretical phase diagram suggests that the ap-

plication of high pressure rapidly decreases the value

of T

of the ferromagnet with the ﬁrst-order transi-

tion because ac/b

increases with pressure. Figure 7

shows the magnetization curve of ferromagnetic

Co(S

0.9

0.1

)

for 4.2 K at various pressures (Goto

et al. 1997). The compound becomes paramagnetic at

P40.21 GPa and exhibits IEM. Similar phenomena

were also found in ferromagnetic Lu(Co

1x

)

Goto et al. (1994). The critical pressure for the dis-

appearance of ferromagnetism in Co(S

0.9

0.1

)

is es-

timated to be P

¼0.25 GPa from the relation

) ¼0atT ¼0. Since T

is 27 K at 0 GPa, the

pressure effect on T

is evaluated to be dT

dP ¼108 K/GPa, which is extremely large com-

pared with usual itinerant ferromagnets. The increase

of B

comes mainly from the suppression of the

Figure 5

Magnetization curves of Co(S

1x

)

with 0pxp0.2

for 4.2 K.

Figure 6

Magnetic phase diagram of Co(S

1x

)

in the x–T

plane.

Figure 7

Magnetization curve of ferromagnetic Co(S

0.9

0.1

)

for

4.2 K at various pressures.

915

Metamagnetism: Itinerant Electrons

Stoner enhancement factor. However, the second-

order FT is expected to change to the ﬁrst-order one

by the application of pressure. In fact, the FT of

CoS

changes into the ﬁrst-order one at 0.4 GPa and

MT is found just above T

for P40.4 GPa. The ap-

plication of pressure also affects the susceptibility w.

In Lu(Co

0.92

0.08

)

, w is found to decrease and is

accompanied by an increase of T

max

with increasing

P, which is also caused by the suppression of the

enhancement factor (Goto et al. 1994).

4. Magnetovolume Effects

In the itinerant electron system, the appearance of a

magnetic moment M produces a volume magneto-

striction o( ¼DV/V), which is related to M, o ¼nM

where DV is the volume change and n is the magne-

toelastic coupling constant (see also Magnetoelastic

Phenomena). Figure 8 shows the magnetostriction

curve of Lu(Co

0.94

0.06

)

at 4.2K in high magnetic

ﬁelds up to 40 T (Goto and Bartachevich 1998). The

volume expands by MT. The estimated value of n is

10.1 10

3

/Co)

in the paramagnetic state and

5.0 10

3

/Co)

in the induced ferromagnetic

one. The reduction of n is also found in the

Lu(Co

1x

)

and Y(Co

1x

)

systems, originat-

ing from the change in the electronic structure of the

d electron system caused by MT.

5. Electrical Properties

The spin ﬂuctuation contribution to the electrical re-

sistivity r

(T) has been estimated by subtracting the

resistivity of YAl

from those of YCo

, LuCo

, and

ScCo

(Gratz et al. 1995). The r

(T) curves increase

steeply at low T followed by a maximum. At high T,

(T) decreases nearly linearly with increasing T.

(T) in the low T region is proportional to T

(T) ¼AT

. The A/g ratios (where g is the coefﬁ-

cient of the electronic specific heat) for these

compounds satisfy the Kadowaki–Woods relation,

A/g ¼1.0 10

5

mOcm (KmolmJ

1

)

, as well as heavy

fermion compounds. This relation can be explained

in terms of a spin ﬂuctuation theory (Wada et al.

1993). The longitudinal magnetoresistance of

Lu(Co

0.91

0.09

)

has been measured at 4.2 K in high

magnetic ﬁelds (K Murata, unpublished data). Ini-

tially the resistance R decreases gradually with in-

creasing ﬁeld. At MT of 5 T, a large reduction of R by

13% has been observed, which is caused mainly by

the suppression of spin ﬂuctuations (see also Inter-

metallic Compounds: Electrical Resistivity).

6. Conclusion

IEM observed in cobalt-based Laves phase com-

pounds and cobalt pyrites originates from a special

shape of the DOS curve near the Fermi level, which

enhances spin ﬂuctuations at ﬁnite temperature. The

unusual magnetic properties of these compounds can

be explained well with the theory of IEM based on

the spin ﬂuctuation model. The metamagnetic tran-

sition and the susceptibility are sensitively changed by

pressure. Magnetostriction measurements suggest

that the electronic structure of the ﬁeld-induced

ferromagnetic state is quite different from that of

the paramagnetic state. The electrical resistivity is

largely affected by the spin ﬂuctuations.

See also: Itinerant Electron Systems: Magnetism

(Ferromagnetism); Spin Fluctuations

Bibliography

Adachi K, Matsui M, Omata Y, Mollymoto H, Motokawa M,

Date M 1979 Magnetization of Co(S

1x

)

under high

magnetic ﬁeld up to 500 kOe. J. Phys. Soc. Jpn. 47, 675–6

Duc N H, Goto T 1999 Itinerant electron metamagnetism of Co

sublattice in the lanthanide–cobalt intermetallics. In:

Gschneidner Jr. K A, Eyring L (eds.) Handbook on the Phys-

ics and Chemistry of Rare Earths. Elsevier, Amsterdam, Vol.

26, pp. 177–246

Goto T, Aruga Katori H, Sakakibara T, Mitamura H,

Fukamichi K, Murata K 1994 Itinerant electron metamag-

netism and related phenomena in Co-based intermetallic

compounds (invited). J. Appl. Phys. 76, 6682–7

Goto T, Bartashevich M I 1998 Magnetovolume effects in

metamagnetic itinerant-electron systems Y(Co

1x

)

and

Lu(Co

1x

)

. J. Phys. Condens. Matter 10, 3625–34

Goto T, Fukamichi K, Sakakibara T, Komatsu H 1989 Itin-

erant electron metamagnetism in YCo

. Solid State Commun.

72, 945–7

Goto T, Sakakibara T, Murata K, Komatsu H, Fukamichi K

1990 Itinerant electron metamagnetism in YCo

and LuCo

J. Magn. Magn. Mater. 90/91, 700–2

Goto T, Shindo Y, Takahashi H, Ogawa S 1997 Magnetic

properties of itinerant metamagnetic system Co(S

1x

)

Figure 8

Magnetostriction curve of Lu(Co

0.94

0.06

)

for 4.2 K in

high magnetic ﬁelds up to 40 T.

Metamagnetism: Itinerant Electrons

916

under high magnetic ﬁelds and high pressure. Phys. Rev. B

56, 14019–28

Gratz E, Resel R, Burkov A T, Bauer E, Markosyan A S,

Galatanu A 1995 The transport properties of RCo

com-

pounds. J. Phys. Condens. Matter 7, 6687–706

Moriya T 1986 On the possible mechanism for temperature-

induced ferromagnetism. J. Phys. Soc. Jpn. 55, 357–66

Murata K, Fukamichi K, Sakakibara T, Goto T, Suzuki K

1993 Itinerant electron metamagnetism and a large decrease

in the electronic specific heat coefﬁcient of Laves-phase com-

pounds Lu (6

1x

)

. J. Phys. Condens. Matter 5, 1525–34

Saito H, Yokoyama T, Fukamichi K 1997 Itinerant-electron

metamagnetism and the onset of ferromagnetism in Laves

phase Lu(Co

1x

)

compounds. J. Phys. Condens. Matter

9, 9333–46

Shimizu M 1982 Itinerant electron metamagnetism. J. Phys. 43,

155–63

Yamada H 1993 Metamagnetic transition and susceptibility

maximum in an itinerant-electron system. Phys. Rev. B 47,

11211–9

Yoshimura K, Nakamura Y 1985 New weakly itinerant ferro-

magnetic system, Y(Co

1x

)

. Solid State Commun. 56,

767–71

Wada H, Shimamura N, Shiga M 1993 Thermal and transport

properties of Hf

1x

. Phys. Rev. B 10221–6

Wohlfarth E P, Rhodes P 1962 Collective electron metamag-

netism. Philos. Mag. 7, 1817–24

T. Goto

University of Tokyo, Japan

Metrology: Superconducting Cryogenic

Current Comparators

The superconducting current comparator (SCC) is a

development of the magnetic d.c. comparator (DCC),

introduced in 1964 and which operates at room tem-

perature. Initial attempts (Harvey 1972) to develop a

superconducting version included enclosing the high

m magnetic core of the DCC in a superconducting

shield, but it was soon realized (Sullivan and Dziuba

1974, Grohman et al. 1974) that this was unnecessary,

the superconducting shield alone was sufﬁcient; in

fact the magnetic core could contribute excessive

noise to the detector.

The basic operating principle of the SCC relies on

the Meissner effect (see Electrodynamics of Supercon-

ductors: Flux Properties) and can be understood by

imagining a very long superconducting tube, open at

both ends, and having a thickness greater than the

penetration depth of the superconductor. Two sepa-

rate wires (they need not themselves be supercon-

ducting) thread the cylinder. Currents I

and I

ﬂowing in the wires induce a circulating current

¼(I

þI

) in the wall parallel to I

þI

on the

inside surface of the cylinder. I

completes a path

round the cylinder creating a magnetic ﬁeld that is

measured with a suitable detector on the outside of

the cylinder. If I

¼I

then I

¼0 and, assuming that

magnetic ﬁeld contributions to the detector due to

end effects (insufﬁcient length of cylinder) or direct

interference from I

and I

outside the cylinder can be

eliminated, the device is a perfect comparator and can

be used to compare currents with a sensitivity that

depends on the minimum resolution of the detector

relative to the magnitude of I

Two versions of the SCC designed to satisfy the

criteria outlined above have been described: type I

(Sullivan and Dziuba 1974) is the most common so

far in the metrology community, and is often de-

scribed as the ‘‘snake swallowing its own tail’’ com-

parator; and type II (Grohman et al. 1974), a toroidal

version of type I, which is more difﬁcult to fabricate

but is under development for very high current

(p100 A) and a.c. applications.

1. Type I SCC

The SCC (Fig. 1) comprises a torus (made from

Tufnol or machinable glass–ceramic) on which a coil,

with as many separate windings as necessary for the

intended purpose (e.g., in a typical SCC to be used in

an n:1 (np10) resistance ratio bridge, there are n þ2

windings each having 64 turns), is wound. The wind-

ings are NbTi, copper-clad, single-core, insulated

superconducting wire with an overall diameter

ofB65 mm, and impregnated with epoxy glue or

Figure 1

Type I SCC.

917

Metrology: Superconducting Cryogenic Current Comparators

otherwise tightly wrapped to prevent movement. The

coil is covered with a toroidal superconducting lead

shield (0.15 mm thick lead foil carefully soft-soldered

to prevent pinholes), with each overlapped turn in-

sulated by thin tape (0.1 mm Kapton). The ends of

the windings are brought to the exterior inside 10 cm

long, insulated, coaxial lead tubes joined to each turn

of the shield. Typically 2.5 overlapped turns are suf-

ﬁcient to meet the requirements set out in the intro-

duction and to obtain the desired accuracy.

The detector coil, with inductance L

, is wound

with superconducting (niobium or NbTi) wire on a

Tufnol or machinable glass–ceramic former and

inserted coaxially into the middle of the shield. It is

connected as a ﬂux transformer to the input coil,

inductance L

, of a d.c. or radio-frequency (RF)

superconducting quantum interference device

(SQUID). The whole construction, SCC and SQUID,

is enclosed in a superconducting shield surrounded by

cryoperm, a low-temperature, high m magnetic shield

and lowered into a cryostat containing liquid helium.

Optimum ﬂux transfer from the SCC to the SQUID

occurs for L

and a typical sensitivity for a single

winding in the SCC is 4.5 mA/j

, where j

is the ﬂux

quantum. Since an RF SQUID may have a noise

sensitivity of 10

4

1/2

, the sensitivity of a

64-turn single winding is approximately 7 pAHz

1/2

and it is relatively easy to detect current inbalances

top1 part in 10

To check the ratio accuracy of the SCC, equivalent

windings are connected in series-opposition and en-

ergized with a current large enough to resolve any

inbalances. By using a ‘‘binary buildup’’ procedure it

is possible to determine the accuracy of any integer

ratio. The highest accuracy, reported in 1991 for a 2:1

ratio derived from 10

turns per winding, is a few

parts in 10

2. Type II SCC

In the type I SCC the ratio windings are on the inside

of the overlapping superconducting shield and the

detector coil sensing ﬂux inbalance on the outside.

The topology of the type II SCC is exactly reversed

from this, with the detector coil wound toroidally on

a former located on the inside of a toroidally shaped

superconducting shield with an insulated, overlapped

gap region. The ratio windings are also wound tor-

oidally on the outside of the shield and for this

reason it is possible for them to carry more current

than the type I SCC, without the risk of driving part

of the superconducting shield into its normal

state. When the detector coil is connected to a

SQUID similar to that used for the type I described

above, the current sensitivity of a single turn is

somewhat less, but since one reason for choosing this

design is to compare currents up to 100 A, this is not

relevant.

3. SCCs in Resistance Ratio Bridges

The main application of the SCC in metrology is in

the measurement of the ratio of two standard resis-

tors R

and R

, which are maintained at precisely

controlled temperatures in suitable enclosures. For

the most accurate measurements four terminal resis-

tors and an SCC are connected in a bridge arrange-

ment (Delahaye 1978). A fully automated version

(Williams and Hartland 1991) is shown in Fig. 2.

Current I

from a primary electronic constant cur-

rent source S

ﬂows through resistance R

and an

in-series primary winding N

of a type I SCC. A sec-

ondary current I

E(N

, from source S

, de-

rived from a voltage generated by I

, is arranged to

ﬂow in resistance R

and a secondary winding of N

turns of the SCC. The two windings of the SCC are

connected in opposite senses to produce approxi-

mately zero ﬂux, sensed by an RF SQUID closely

coupled by a ﬂux transformer to the SCC. Since the

relative accuracy of the winding ratio N

is typ-

ically smaller than 1 part in 10

any departure in the

current ratio I

from that in the winding ratio is

corrected by feedback of the SQUID out-of-balance

signal to S

. The ratio R

is determined from the

output of the null detector D. This output can also be

used to generate a balance current I

, which ﬂows in

Figure 2

SCC resistance ratio bridge.

918

Metrology: Superconducting Cryogenic Current Comparators

an auxiliary winding of N

turns of the SCC and

brings the detector D to zero balance, so ensuring

that the gain stability and linearity of the detector are

not significant. Combining the expressions for the

detector balance, R

R

¼0, and for the SCC

balance, (N

þI

I

¼0, one obtains

1 þ



if I

is small. The current I

is measured using a re-

sistor and digital voltmeter (DVM), and a large val-

ue, accurately known resistor shunting R

is used to

calibrate I

. Attention must be paid to the elimination

of unwanted leakage currents and that offset currents

from the high-impedance buffer ampliﬁer have no

significance in the potential circuit.

The operation of the bridge is controlled by a

computer, which reverses the direction of I

(and I

)

to eliminate the effect of thermal e.m.f.s in the po-

tential circuit, and takes readings of the DVM. For

low power dissipation (p1 mW) in R

, relative ran-

dom uncertainties (type A) of R

of B1 part in 10

can be achieved for measurement times of about 10

minutes.

The SCC bridge is widely used by national labo-

ratories to determine the value of standard resistors

in terms of the quantum standard of resistance R

(25812.807O); to compare quantized Hall resist-

ances fabricated from different materials; and to

compare the standard resistors of different national

laboratories, with accuracies of a few parts in 10

Since 1996 the SCC resistance-ratio bridge has been

produced commercially by two companies located in

the UK.

See also: Josephson Voltage Standard; SQUIDs: The

Instrument

Bibliography

Delahaye F 1978 A double constant current source for a cryo-

genic current comparator and its applications. IEEE Trans.

Instrum. Meas. IM-27, 426–9

Grohman K, Hahlbolm H D, Lu

bbig H, Ramin H 1974 Iron-

less cryogenic current comparator for a.c. and d.c. opera-

tions. IEEE Trans. Instrum. Meas. IM-23, 261–3

Harvey I K 1972 A precise low temperature d.c. ratio trans-

former. Rev. Sci. Instrum. 43, 1626–9

Sullivan D B, Dziuba R F 1974 Low temperature direct current

comparator. Rev. Sci. Instrum. 45, 517–9

Williams J M, Hartland A 1991 An automated cryogenic cur-

rent comparator resistance ratio bridge. IEEE Trans.

Instrum. Meas. IM-40, 267–70

A. Hartland

National Physical Laboratory, Teddington, UK

Micromagnetics: Basic Principles

A small class of materials exhibit the important

property of long range magnetic order. Fundamen-

tally, this arises because of the so-called ‘‘exchange

energy’’ which can, under certain circumstances, lead

to parallel alignment of neighboring atomic spins.

Given the link between the atomic spin and magnetic

moment, the spin order gives rise to the observed long

range magnetic order. The origin of the long range

magnetic order is a fundamental scientific problem

which has been studied extensively, both theoretically

and experimentally and is now understood in some

depth. However, within magnetism there is a major

problem when relating fundamental atomic proper-

ties to magnetization structures and magnetization

reversal mechanisms in bulk materials.

The problem was described vividly by Aharoni

(1996) in his discussion of magnetostatic effects. The

essential idea is that the material properties are de-

termined by the exchange energy, which in principle

is effective on a length scale of subnanometers, and

the magnetostatic energy, which has contribution

from the boundaries of the material itself and which

introduce a different length scale entirely. The chal-

lenge of micromagnetics is to develop a formalism in

which the macroscopic properties of a material can be

simulated including the best approximations to the

fundamental atomic behavior of the material.

In brief, the classical approach to micromagnetics

replaces the spin by classical vector ﬁeld which initially

allows the determination of magnetostatic ﬁelds within

the system. In addition to this a different approach to

the exchange interaction much be formulated which

can replace the quantum mechanical exchange inter-

action with a formalism appropriate for the limit of

continuous material. This, coupled with an energy

minimization approach, forms the basis of classical mi-

cromagnetics which will be outlined in a later section.

The history of micromagnetics starts with a 1935

paper of Landau and Lifshitz on the structure of a

wall between two antiparallel domains, and several

papers by Brown around 1940. A detailed treatment

of micromagnetism is given by Brown in his 1963

book (Brown 1963).

For many years micromagnetics was limited to the

use of standard energy minimization approaches to

determine domain structures and classical nucleation

theory to determine magnetization reversal mecha-

nisms in systems with ideal geometry. Arguably, the

current interest in micromagnetics arises from the

availability, from about the mid-1980s onward, of

large-scale computing power which enabled the study

of more realistic problems which were more amena-

ble to comparison with experimental data.

One important realization during this period was

the fact that energy minimization approaches in

919

Micromagnetics: Basic Principles