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

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quite complex, owing to the possibilities of canting,

antiferromagnetic domains, compensated and uncom-

pensated planes, and surface roughness in the anti-

ferromagnet; the result is that the underlying source is

not well understood. It is clear that it is not necessary

for a single sublattice deﬁned over the macroscopic

dimensions of the antiferromagnet to be aligned, but

instead there can be alignment within domains of the

locally deﬁned sublattice physically most near the

ferromagnet. It is also possible to use ferrimagnets

instead of antiferromagnets, or even ferromagnets if

their anisotropy is high enough to prevent switching

in the low ﬁelds used to switch the primary ferro-

magnetic material (e.g., Hellman et al. 1987).

2. Measurements of Anisotropy

The ﬁrst and often most important step is simply to

determine the anisotropy symmetry, i.e., cubic or

uniaxial, perpendicular easy or hard axis. This may

be done in a variety of ways, including M(H) curves,

torque magnetometry, Kerr or Faraday rotation ob-

servations, magnetic force microscopy, even magne-

toresistance with H applied along different directions.

The simplest way to measure anisotropy energy is by

torque magnetometry. The ﬁrst step is to technically

saturate the magnetization of the ﬁlm by applying a

ﬁeld H along an easy axis which is strong enough to

eliminate magnetic domains (H4H

, where H

is the

coercive ﬁeld). Figure 4 shows the geometry for a ﬁlm

with uniaxial anisotropy. Then the direction a of the

magnetic ﬁeld is rotated; for high anisotropy mate-

rials, Miyajima’s a ¼451 method is often used

(if H

oHoH

, we are not in the high ﬁeld limit

often assumed, e.g., by Cullity 1972, p. 215).

The minimum energy would be if the moment M

could follow the direction of the ﬁeld, by physically

rotating the sample so that its easy axis direction re-

mained along the direction of the rotating ﬁeld. If the

sample is physically constrained from doing this, then

it will exert a torque T on the constraint. The energy

of this arrangement can be written as

E ¼MdH þ E

¼MHcosða  yÞþK

sin

y ð5Þ

for a simple uniaxial anisotropy, where y and a are the

angles M and H make with respect to the easy axis, a

is ﬁxed, but y will adjust to minimize the energy, so

dE/dy ¼0. The torque exerted by the sample on the

constraint T ¼M H ¼MHsin(ay) is measured us-

ing one of several techniques. This then effectively

gives y, and hence E

(see, e.g., Hellman et al. 1989

for more details).

It is sometimes possible to make a direct measure-

ment of y by measuring the component of M per-

pendicular to the applied ﬁeld, using for example

quadrature pick-up coils. This is more difﬁcult than

measuring torque, because the perpendicular compo-

nent and y become quite small for large H, while the

torque M H remains large. There are also special-

ized techniques used, e.g., in situ in a vacuum dep-

osition system where a Kerr measurement can be

used to infer the perpendicular component of M and

hence the anisotropy.

Magnetic resonance is another powerful technique

for determining anisotropy. The constant applied

ﬁeld is applied usually along an easy axis. For a uni-

axial sample, the resonance condition is then given by

the sum of the applied ﬁeld and the anisotropy ﬁeld

¼2K

. For cubic systems, K

and K

can

be determined by measuring with H applied along

various axes.

In limited cases, magnetic hysteresis curves can

also be used. Here, the applied ﬁeld is usually applied

along a hard axis, causing magnetization to rotate.

In the limit that there is no domain motion, only

rotation, for example in a uniaxial material, the

magnetization saturates at M

for a well deﬁned ﬁeld

¼2K

(see, e.g., Fig. 1). Alternatively, the

difference in areas between the hard and easy axis

curves is proportional to the anisotropy energy.

3. Summary and Future Directions

Anisotropy in ﬁlms is a sum of contributions from

the intrinsic magnetocrystalline anisotropy expected

from the bulk equivalent material and a number of

effects linked to the fact that the structure of a ﬁlm is

for many reasons not equivalent to the bulk. There

are many sources of these differences, connected both

to the fact that a ﬁlm is grown on a substrate and has

a top and bottom surface whose properties, both

structural and magnetic, are not simply related to the

properties of the bulk material, and to intrinsic effects

of the growth processes used to prepare ﬁlms which

cause a memory of the growth direction to be trapped

into the structure. At present, there is almost no way

to predict the anisotropy of a ﬁlm of a new material;

there are many contributions and it is difﬁcult to

know in advance which effects will dominate.

Experimental efforts to ﬁnd improved materials

often center on taking advantage of the bulk magne-

tocrystalline anisotropy, or on deliberately prepared

multilayers, but in fact growth-induced effects and

other less predictable contributions often dominate,

certainly for materials presently used for practical

applications.

Figure 4

Geometry of torque measurement for uniaxial

anisotropy ﬁlm.

430

Magnetic Fi lms: Anisotropy

See also: Magnetic Films: Hard; Metal Evaporated

Tape; Monolayer Films: Magnetism; Multilayers: In-

terlayer Coupling; Thin Films: Domain Formation;

Thin Films: Stresses

Bibliography

Coffey K R, Parker M A, Howard J K 1995 High anisotropy

thin ﬁlms for longitudinal recording. IEEE Trans. Magn.

31, 2737–9

Cullity B D 1972 Introduction to Magnetic Materials. Addison-

Wesley, Reading, MA

Farrow R F C, Weller D, Marks R F, Toney M F, Cebollada

A, Harp G R 1996 Control of the axis of chemical ordering

and magnetic anisotropy in epitaxial FePt ﬁlms. J. Appl.

Phys. 79, 5967–9

Harris V G, Aylesworth K D, Das B N, Elam W T, Koon N C

1992 Structural origins of magnetic anisotropy in sputtered

amorphous Tb-Fe ﬁlms. Phys. Rev. Lett. 69, 1939–42

Hellman F, Gyorgy E M 1992 Growth-induced magnetic an-

isotropy in amorphous Tb-Fe. Phys. Rev. Lett. 68, 1391–4

Hellman F, Shapiro A L, Abarra E N, Rooney P W, Tran M Q

1999 Magnetic anisotropy and coercivity in magneto-optical

recording materials. In: (eds.) MORIS ’99 Conf. Proc. J.

Magn. Soc. Jpn. 23(Suppl. S1), 79–84

Hellman F, van Dover R B, Gyorgy E M 1987 Unexpected

unidirectional anisotropy in amorphous Tb-Fe/Ni-Fe-Mo

bilayer ﬁlms. Appl. Phys. Lett. 50, 296–8

Hellman F, van Dover R B, Nakahara S, Gyorgy E M 1989

Magnetic and structural investigation of the composition de-

pendence of the local order in amorphous Tb-Fe. Phys. Rev.

B 39, 10591–605

Nogues J, Schuller I K 1999 Exchange bias. J. Magn. Magn.

Mater. 192, 203–32

Shapiro A L, Rooney P W, Tran M Q, Hellman F, Ring K M,

Kavanagh K L, Rellinghaus B, Weller D 1999 Growth-in-

duced magnetic anisotropy and clustering in vapor-deposited

Co-Pt alloy ﬁlms. Phys. Rev. B 60, 12826–36

Tyson T A, Conradson S D, Farrow R F C, Jones B A 1996

Observation of internal interfaces in Pt

1x

(xE0.7) alloy

ﬁlms: a likely cause of perpendicular magnetic anisotropy.

Phys. Rev. B 54, R3702–5

Victora R H, MacLaren J M 1993 Theory of magnetic interface

anisotropy. Phys. Rev. B 47, 11583–6

Wang C T, Clemens B M, White R L 1996 Effects of substrate

on the magnetic properties of epitaxial TbFe

(111) ﬁlms.

IEEE Trans. Magn. 32, 4752–4

Weller D, Brandle H, Gorman G, Lin C-J, Notarys H 1992

Magnetic and magneto-optical properties of cobalt–platinum

alloys with perpendicular magnetic anisotropy. Appl. Phys.

Lett. 61, 2726–8

Weller D, Farrow R F C, Marks R F, Harp G R, Notarys H,

Gorman G 1993 Interface and volume anisotropy of MBE-

grown Co/Pt(111), (110) and (001) and sputtered Co/Pt mul-

tilayers. Mater. Res. Soc. Symp. Proc. 313, 791–7

Yafet Y, Gyorgy E M, Walker L R 1986 Directional depend-

ence of the demagnetizing energy in imperfect thin magnetic

ﬁlms. J. Appl. Phys. 60, 4236–9

F. Hellman

University of California, San Diego

California, USA

Magnetic Films: Hard

The scope of this article is to provide a general

introduction to hard magnetic ﬁlms. It discusses

application-relevant extrinsic magnetic properties

and focuses on a specific hard magnetic material

(Nd

B) to demonstrate the interplay between the

ﬁlm-related microstructure and the magnetic per-

formance. The article by (Kruusing 1999) is a good

addendum, as he reviews Nd

B thin ﬁlms and

describes preparation-specific topics.

1. Applications

One area for application of hard magnetic ﬁlms are

microsystem techniques, especially microelectrome-

chanical systems (MEMS). These devices are pre-

pared from relatively thick ﬁlms (1–5 mm) and the

high-energy product of the rare earth magnets prom-

ises smaller lateral device sizes. Until now, however,

only a few systems have been realized, for example a

sub-millimeter electric motor (Yamashita et al. 1991),

and a stepper motor (Belmans and Hameyer 1998).

The challenge facing rare earth magnets in this ﬁeld is

their high corrosion rate when exposing a large sur-

face after structuring. Another potential application

is in monolithic microwave integrated circuits

(MMICs) (Levy et al. 1996) using thin hard magnet-

ic layers to create bias ﬁelds for ferrite devices. Al-

though an optical isolator could be realized this way,

this technology has to compete with the conventional

technology, which is not based on ferrites.

The largest market for hard magnetic ﬁlms is in

magnetic data storage on computer hard disks. While

the bit density increases by about 60% each year, the

conventional materials (e.g., CoPtCr, CoCrTa) are

expected to reach the superparamagnetic limit by

around 2005, where the small magnetic dots used to

store the information tend to become thermally un-

stable. In order to exceed densities of 100Gbit in

2

materials with a higher uniaxial magnetic anisotropy

are of interest (see Magnetic Anisotropy). The high

perpendicular magnetic anisotropy of Nd

B thin

ﬁlms presents the additional possibility of packing

bits closer together using perpendicular recording,

where the spins representing the bits are oriented

perpendicular to the substrate. Compared to other

applications, the required ﬁlm thickness is small

(20–50 nm).

2. Structure Formation

The Nd

B phase providing the desired intrin-

sic magnetic properties has a tetragonal unit cell

(a ¼8.805 A

, c ¼12,203 A

) comprising 68 atoms (see

Rare Earth Magnets: Materials). At room temperature

431

Magnetic Films: Hard

the magnetic easy axis is along the c-axis. When de-

positing ﬁlms on heated substrates below temperatures

of 500–675 1C, x-ray diffraction patterns reveal only

amorphous spectra and the ﬁlms are soft magnetic.

However, using transmission electron microscopy,

Mapps et al. (1997) observed small inclusions of the

B phase with grain sizes below 10 nm (which

are invisible to x-ray diffraction) already on ﬁlms de-

posited at room temperature. At higher temperatures

a significant amount of the hard magnetic Nd

phase forms, but even at temperatures above 650 1C

part of the material can remain in the amorphous state

(Shima et al.1998).

3. Coercivity Mechanism

Magnetization reversal can be inhibited by two dif-

ferent mechanisms (see Coercivity Mechanisms). In

the nucleation type magnets, domain wall motion in-

side almost perfect grains is easy, but the nucleation

ﬁeld necessary to create new Bloch walls is high, as no

extended defects lower the Bloch wall energy. When

magnetizing this type of material in a ﬁeld below the

saturation ﬁeld, the remaining domain walls cause a

lower remanence than when magnetizing by a ﬁeld

strong enough to remove all domain walls. This co-

ercivity mechanism is usually valid when relatively

large and perfect grains exist and can be used to de-

scribe annealed Nd

B ﬁlms on Ta/Si(111) (Tsai

et al. 1998) (a system showing no intermixing) and

ﬁlms grown on heated W/Si(111) (Tsai et al. 1999a)

where only few neodymium-rich precipitates are

observed.

In pinning type magnets, the nucleation of reversed

domains is not inhibited, but a lot of defects exist—

preferably with a size comparable to the Bloch wall

thickness—where the domain walls are pinned. Mag-

netization reversal occurs when the force exerted on

the domain wall (pinned at the inhomogeneities) be-

comes sufﬁciently strong. In Nd

B ﬁlms depos-

ited on heated Pt/Si(111) (Tsai et al. 1999a) and in

annealed samples on silicon (Tsai et al. 1998) pinning

seems to control the coercivity.

4. Grain and Domain Size

A very effective way to increase coercivity is to reduce

the grain size below the single domain particle size.

This is often found in NdFeB ﬁlms where the domain

size is even larger than the lateral grain size (Gouteff

et al. 1998, Lemke et al. 1997). Here exchange cou-

pling between neighboring grains leads to the occur-

rence of interaction domains. Generally the domain

walls follow the grain boundaries, demonstrating

their pinning effect. Therefore the coercivity typically

increases with decreasing grain size and with decou-

pling of neighboring grains.

The key parameters for controlling grain growth

are the annealing temperature and the annealing

time. When the ﬁlms are deposited at room temper-

ature and annealed afterwards, both parameters can

be controlled but the annealed samples are isotropic,

eliminating the possibility of preparing textured ﬁlms

(having perpendicular anisotropy with respect to the

surface). The crystallization develops via intermedi-

ate stages depending on the composition (Linetsky

et al. 1992). With rapid thermal annealing of 60 s at

500 1C it is possible to obtain grain sizes of 50 nm and

a coercive ﬁeld H

up to 20 kOe—a two-fold im-

provement compared to annealing times in the ten

minute range (Yu et al. 1998).

To achieve a c-axis texture (see below), however,

structure formation is necessary already during dep-

osition, which requires a substrate temperature above

500 1C. Parhofer (1997) observed an increase in the

perpendicular grain size with increasing substrate

temperature but as a variation in temperature also

inﬂuences the phase formation, texture, etc., no sys-

tematic examination of the perpendicular and lateral

grain size and their inﬂuence on the magnetic prop-

erties yet exists.

The deposition method also seems to inﬂuence the

grain size. While sputtered ﬁlms usually have grain

sizes of about 100 nm (Gouteff et al. 1998, Tsai et al.

1998, 1999c), ﬁlms prepared by pulsed laser deposi-

tion (PLD) have smaller grain sizes (down to

12–20 nm) (e.g., Lemke et al. 1997). This is a known

effect originating from the significantly higher kinetic

energy of the deposited particles during PLD com-

pared to other deposition methods (Fa

hler and Krebs

1996). The ions are implanted into the topmost

monolayers (‘‘subsurface growth’’) (Fa

hler et al.

2000) reducing their mobility and the grain size of

laser deposited metallic ﬁlms is usually smaller. On

the other hand, this implantation can cause defects

which reduce the magnetic order and this may be the

reason why the magnetic properties of the PLD ﬁlms

are not improved as expected.

A sharp grain size distribution leads to a simulta-

neous switching of the grains and a more square

magnetization curve. For magnetic recording, a

broad grain size distribution can result in the unde-

sirable failure of some bits. A smooth, round grain

surface is also favored as at asperities the enhanced

stray ﬁeld favors the nucleation of reversed domains.

5. Inﬂuence of Composition

The Nd

B phase shows only a small existence

region so that variations in the concentration result in

an inhomogeneous microstructure with additional

phases which can be used to improve the magnetic

properties. Similar results can be achieved with ad-

ditives in most magnetic systems, but when additives

are solved partly in the main magnetic phase it is

difﬁcult to distinguish between changes in the intrin-

sic and extrinsic properties.

432

Magnetic Fi lms: Hard

Adding a paramagnetic component such as

neodymium in NdFeB forms a neodymium-rich

intergranular paramagnetic phase decoupling the

ferromagnetic Nd

B grains. The decoupling pre-

vents domain nucleation induced by neighboring

grains and increases the coercivity. With increasing

neodymium content the c-axis texture is lost but

the grain size is reduced and the energy product

can be optimized with neodymium concentrations

slightly higher than the stoichiometric composition

(Piramanayagam et al. 1998).

It has been observed that increasing boron content

up to 17 at.% leads to an increase in the c-axis texture

and increases the perpendicular coercivity signiﬁcant-

ly (Araki et al. 1999). Due to the excess boron a soft

magnetic amorphous phase is formed between the

columnar Nd

B grains. This ﬁne microstructure

should be exchange coupled and the authors suggest

that the observed sharp interfaces prevent domain

nucleation. Boron contents above 17 at.% reduce the

coercivity as the amount of the soft magnetic amor-

phous phase increases.

Of different intention is the addition of a second

phase with a higher saturation magnetization M

increasing the iron content above the stoichiometric

value. Such a composite material can possess a higher

saturation magnetization and also a higher remanent

magnetization, provided the soft iron phase is cou-

pled to the hard magnetic Nd

B phase. Accord-

ingly, in NdFeB ﬁlms an increase in M

with the iron

content has been observed (Piramanayagam et al.

1998). Additionally, the iron content can improve the

c-axis texture. Both factors should contribute to the

observed increase in remanence.

However, as large soft iron grains can act as a nu-

cleus during the magnetic reversal and significantly

reduce the coercivity, it is important for a composite

ﬁlm to limit the iron grain size so that the complete

iron grains are coupled to the hard Nd

B grains

(grain size less than B10 nm—twice the Bloch wall

width). Films sputtered at 650 1C show iron grain

sizes of B10 nm, and up to 17 vol. % Fe the co-

ercivity decreases only slowly (Tsai et al. 1999b).

6. Multilayers

The well-deﬁned preparation of alternating soft and

hard magnetic layers should enable the testing of

the micromagnetic models of exchange coupling

(see Magnets: Remanence-enhanced). Parhofer et al.

(1996) showed that iron layers below 30 nm are fully

coupled to the Nd

B layers and the reduced re-

manence R ¼J

increases significantly when the

iron thickness is reduced to this value. He conﬁrmed

that the saturation magnetization can be calculated

from the volume-weighted sum of both magnetiza-

tions, indicating that at the interface no significant

structural deterioration occurs.

In nanocomposite magnets, for optimum BH

max

the following considerations hold: To make use of

the high M

of the soft magnetic phase, its fraction

should be increased. On the other hand the nucle-

ation ﬁeld for magnetization reversal (and conse-

quently H

) is lowered as the thickness of the soft

magnetic phase becomes larger. So in order to keep

a high fraction of the soft phase, also the thickness

of the hard phase must be reduced. But this reduc-

tion is limited as the coercivity of the hard magnetic

phase is lost if its thickness reaches the same order

of magnitude as the domain wall width. Shindo

et al. (1997) conﬁrmed this trend in experiment

and found a good agreement with a micromagnetic

calculation when using an interlayer exchange-

coupling strength of about 10% of the intralayer

couplings. They also conﬁrmed the exchange-spring

effect by measuring reversible minor magnetization

curves.

In spite of these advantages, such multilayers tend

to lose the c-axis texture (Parhofer 1997), their crys-

tallinity can be reduced, they show a significant

increase in roughness, and intermixing in the range of

10 nm can occur (Shindo et al. 1997).

Multilayers of Nd

B and a nonmagnetic ma-

terial should also allow decoupling of the magnetic

layers. While experiments with silver failed due to

the reaction to form NdAg (Aylesworth et al. 1989),

multilayers with tunsgten (Panagiotopoulos et al.

1997) only break their layered structure during an-

nealing. With an appropriate Nd

B thickness of

about 5 nm, the resulting microstructure consists of

separated isotropic Nd

B grains (grain size

B10 nm) in a tungsten matrix and H

is improved

up to 20 kOe.

7. Texture

The aim of having a textured ﬁlm is to use the micro-

scopic anisotropy for an application with a macro-

scopic anisotropy and to increase M

above the

limit of 0.5 for a randomly-oriented ﬁlm. While ﬁlms

deposited at room temperature and subsequently an-

nealed are isotropic, ﬁlms on heated substrates can be

grown with a c-axis texture, so that the hard magnetic

axis is oriented perpendicular to the substrate. (In

contrast to CoSm, the substrate temperature is usu-

ally above T

, therefore no stray ﬁeld forces the

c-axis to lie within the ﬁlm surface.) As an explana-

tion for the c-axis texture, Cadieu (1987) suggested

that a high ion ﬂux onto the substrate (usually ob-

tained at low deposition rates during sputtering)

should prevent the formation of long ordered repeat

distances parallel to the substrate plane, and mate-

rials having a longer c-axis (as Nd

B) should,

therefore, favor a c-axis texture. In agreement with

this, he observed a decrease in the c-axis texture with

increasing deposition rate.

433

Magnetic Films: Hard

Another reason for this texture can be the aniso-

tropic growth velocity known from bulk material,

which forms longer c-surfaces than a and b. Starting

with an isotropic texture, the c-axis oriented grains

grow faster and cover more and more of the substrate

resulting in c-axis texture. In agreement with this,

ﬁlms with a rough surface and grown at higher tem-

peratures above 650–700 1C (leading to a stronger

reaction with the substrate) lose the c-axis texture.

Also the ﬁlm composition can inﬂuence the texture: a

high iron content (Piramanayagam et al. 1998) or

boron content (Araki et al. 1999) improves the c-axis

texture.

A buffer also provides the possibility to modify

ﬁlm texture. While ﬁlms on tantalum and titanium

generally obtain a (001) c-axis texture, a tungsten or

molybdenum buffer can change the texture towards

(105), whereas on platinum no texture was observed.

With a chromium buffer different textures were ob-

served. Also the grain size and roughness is inﬂu-

enced by different buffers (Piramanayagam et al.

1998, Shima et al. 1998, Shindo et al. 1997, Tsai et al.

1998, Tsai et al. 1999c, Parhofer et al. 1998).

In spite of the reactivity with a silicon substrate, it

seems to be possible to deposit epitaxial Nd

ﬁlms on Si(111) with the c-axis lying in plane

(Kruusing 1999), while approaches to prepare epi-

taxial ﬁlms on Mo(001) with the c-axis perpendicular

to the substrate have not been successful: here a dif-

ferent, unidentiﬁed, phase grows epitaxially at the

beginning (Keavney et al. 1997).

Since in all the experiments the texture could not be

controlled without changing other parameters such as

the grain size or composition, it is difﬁcult to deduce

the effect of texture on the magnetic properties.

However, it occurs, as a general tendency, that the

ﬁlms with the best magnetic properties do not possess

the best c-axis texture (Parhofer 1998). With a strong

c-axis texture the angle between the spins in neigh-

boring grains is small and the grain boundaries seem

not to provide effective pinning. This effect is de-

scribed by the coercivity model of Kronmu

ller (see

Coercivity Mechanisms) where the microstructural

parameter for pinning efﬁciency increases with

stronger grain misalignment. Here it would be use-

ful to separate the grains magnetically while retaining

the c-axis texture.

8. Roughness

Films grown at higher temperatures show an in-

creased ﬁlm roughness. In general, ﬁlms with a rough

surface exhibit a higher H

than smooth ﬁlms. This is

attributed to pinning of the magnetic domains at the

asperities. But since applications such as microstruc-

turing or hard disks need a smooth surface (danger of

head crashes or a too large read/write distance), an

increased roughness is not suitable.

9. Stability and Thickness

Oxide and silicon substrates react strongly with

NdFeB and destroy the magnetic properties—a gen-

eral problem with rare earth components. Also some

metals show interdiffusion: silver (Aylesworth et al.

1989); molybdenum (Tsai et al. 1999c), tungsten (Tsai

et al. 1999c, Panagiotopoulos et al. 1997). In order to

keep the intrinsic properties, inert substrates or buff-

ers such as chromium (Parhofer et al . 1998), platinum

(Tsai et al. 1999c) or tantalum (Piramanayagam et al.

1998, Aylesworth et al. 1989) can be used.

Though Parhofer et al. (1998) showed that a chro-

mium protection layer of 20 nm can limit the decay of

below about 10% per year, this is not sufﬁcient

for a device lifetime of 10 years and also for use in a

hard disk the protection layer thickness must be sig-

nificantly reduced. Therefore long-term stability will

remain a challenge for this material.

With decreasing thickness also the grain size can

decrease and a two-fold increase in H

has been ob-

served when reducing the thickness from some

100 nm to 25 nm (Parhofer et al. 1998), a thickness

appropriate for a storage material. It should be noted

that for NdFeB ﬁlms deposited directly on quartz

(without a chromium buffer) H

vanishes below 100

nm, interdiffusion seems to destroy the intrinsic

properties. Otherwise ﬁlms on tantalum show an in-

crease of H

up to a thickness of 500 nm (Pi-

ramanayagam et al. 1997).

10. Conclusions and Perspectives

B thin ﬁlms show a good example of the ap-

plication of hard magnetic concepts in thin ﬁlms and

of the possibilities of thin ﬁlm methods to inﬂuence

the microstructure. As in bulk material, controlling

the microstructure is the key to optimizing the mag-

netic properties. For thin ﬁlms an appropriate buffer

can control the microstructure in addition to inter-

diffusion or texture. As a growing ﬁlm tends to rep-

licate the grain size of the existing ﬁlm, for example

the selection of a binary system (NiAl) instead of

chromium could cut the grain size of the buffer and

of the conventional magnetic ﬁlm in half (Feng et al.

1994). Another approach is to use the chemical seg-

regation observed for instance in the Cr–Co system.

In this system chromium segregates into the grain

boundaries which reduce the exchange-coupling

between the cobalt-rich grains (Wittig et al. 1998).

Using similar systems as buffer and replicating this

microstructure should allow modiﬁcation of the

microstructure while conserving the intrinsic proper-

ties of Nd

B. These two examples show the

potential of binary buffers and their application.

Structuring the ﬁlms to prepare separate magnetic

dots is a potential path for producing magnetic

434

Magnetic Fi lms: Hard

recording media. The achieved structural size of

0.5 0.5 mm (Kubota et al. 2000) opens the perspec-

tive that the noise caused by a statistical grain en-

semble is reduced by a structured media.

See also: Magnetic Films: Anisotropy; Magnetic

Layers: Anisotropy

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1989 Growth and control of the microstruture and magnetic

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S. Fa

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IFW Dresden, Germany

Magnetic Force Microscopy

Magnetic force microscopy (MFM) (Martin and

Wickramasinghe 1987, Gru

tter et al. 1992) is a

slow-scan, raster-type imaging technique that maps

a signal issued from the interaction of a tiny magnetic

probe, or tip, with the magnetization distribution

within the observed sample. The technique has been

demonstrated to yield a resolution below some 20 nm

in favorable cases with minimal or even no sample

preparation. A magnetic force microscope may be

435

Magnetic For ce Microscopy

operated under ambient conditions or ultrahigh vac-

uum, allowing the study of clean magnetic surfaces

and the link between growth and magnetic properties.

Static magnetic ﬁelds may be applied to the sample

during image acquisition, a necessary condition for

correlating magnetic microstructures and hysteresis

cycles. Because MFM relies on the interaction of two

magnetic bodies, the probe and the sample, MFM is

an indirect imaging method. It is potentially perturb-

ative and, thus, may not be termed noninvasive.

1. Operation Principle

A magnetic force microscope (Fig. 1) may be de-

scribed as composed of a force transducer, a micro-

fabricated cantilever coated with a magnetic thin

layer (Gru

tter et al. 1990), an x,y,z set of translation

actuators, and a signal processing and feedback unit.

Various types of forces may act on the tip located at

the extremity of the cantilever, among them van der

Waals forces when the tip and sample surfaces are

brought into close contact, capillary forces owing to

an adsorbed water layer when the microscope is op-

erated under ambient conditions, electrostatic forces,

and magnetostatic forces if both the probing tip and

sample are magnetic. Magnetostatic forces are those

forces that govern the interactions of, for example,

two bar magnets or allow a hard magnetic material

body to attract soft magnetic elements. A magnetic

force microscope should be operated under such con-

ditions that long-range dipolar-type forces become

prominent (Scho

nenberger et al. 1990).

In the static mode or force detection scheme, the

restoring force constant of the cantilever opposes

the magnetically induced cantilever deﬂection, thus

establishing equilibrium. Although different methods

have been developed to monitor the cantilever de-

ﬂection, optical means now dominate. Interferomet-

ric techniques have been used to measure precisely

the distance between the cantilever end and a ﬁxed

point in space (e.g., Rugar et al. 1988). In Fig. 1 a

laser beam is reﬂected from the upper surface of the

cantilever into a quadrant detector. Signal combi-

nations (A þB)(C þD) and (A þD)(B þC) are

proportional to the deﬂection and torsion of the can-

tilever, respectively (Meyer and Amer 1990).

In a second operating mode, the dynamic or a.c.

mode (Martin and Wickramasinghe 1987, Hobbs

et al. 1989), a piezoactuator induces forced oscilla-

tions of the cantilever. In the limit of small amplitude

oscillations along the z direction and an assumed

harmonic oscillator behavior, the resonance frequency

of the cantilever varies with the force gradient as

o ¼ o

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1 

ð1Þ

where o

is the free oscillation cantilever resonance

frequency and k is the cantilever restoring force con-

stant. It has been recognized (Albrecht et al. 1991)

that frequency detection is preferable to amplitude

detection because of the long characteristic response

time of the latter to a pulse-like change in the force

gradient.

An MFM image is therefore a mapping of the po-

sition-dependent force or force gradient exerted by the

sample on a magnetic tip moving at a given distance

from the sample surface. If the distance is too short,

van der Waals-type forces may dominate, whereas

spatial resolution is bound to decrease with increasing

distance. In practice, working (often referred to as

‘‘lift’’) distances between a few nanometers and a few

tens of nanometers are used. Since the strength of the

force and/or force gradient rapidly decays with dis-

tance from the surface, surface relief needs to be

compensated for (Scho

nenberger et al. 1990). This

may be achieved through three point landmark inter-

polation for smooth surfaces (Hug et al. 1993) or a

more advanced protocol including topography mon-

itoring followed by force or force gradient detection at

a preset lift height z

lift

(Fig. 2) (Babcock et al. 1995).

Whereas forces as low as 1 pN (10

12

N) may be de-

tected with a good signal-to-noise ratio (SNR) in

state-of-the-art static experiments (Hug et al. 1998),

the minimal detectable force gradient against thermal

noise (Albrecht et al. 1991) is given by

min



¼ 2k

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

TDn

ð2Þ

where A, k

, T, Dn,andQ are the cantilever oscilla-

tion amplitude, Boltzmann constant, temperature,

detector bandwidth, and cantilever resonance qual-

ity factor, respectively. Under ambient conditions

Figure 1

Schematic representation of a force microscope (not to

scale). S is the sample.

436

Magnetic For ce Microscopy

(QB100–150), force gradients as low as 10

5

1

are routinely measured.

2. Image Formation

Central to the understanding of MFM is the magne-

tostatic equivalent to Coulomb’s law expressing the

force between two magnetic ‘‘monopoles’’ (Fig. 3):

¼F

4pm



7r  r

ðr

 r

Þð3Þ

In a ferro- or ferrimagnetic body, magnetic charge

densities may be deﬁned and related to the magnet-

ization distribution

r) ¼M

r), m

¼1, through

the relationships

¼m

div ðm

Þ in the volume

¼þm

ðm

 n

Þ at free surfaces

ð4Þ

It follows that MFM neither directly maps the

magnetization distribution (the unknown in a mag-

netic imaging experiment) nor the magnetic induction.

In order to improve understanding of image for-

mation processes, the demagnetizing or stray ﬁeld

Figure 2

MFM operating mode: the inﬂuence of the sample topography (here, grains in a NiFe thin ﬁlm deposited on a sputter

deposited NiO underlayer (courtesy of P. Gogol)) is minimized by measuring the frequency shift due to the interaction

between the magnetized probe and the sample at a ﬁxed ‘‘lift’’ height above the sample along each line scan. Usual

‘‘lift’’ heights are in the range 20–50 nm.

Figure 3

(Central) forces between two magnetic point-like

charges.

437

Magnetic For ce Microscopy

r) arising from volume or surface charge densities

located at

is introduced. According to standard

electromagnetic theory, it derives from the scalar

potential F

r ) owing to:

ðr

Þ¼grad½F

ðr

Þ ð5Þ

with

ðr

Þ¼

4pm



ZZZ

ðr

-0

7 r

r

-0

ðr

-0

7 r

r

-0



ð6Þ

For instance, volume and surface charges pertain-

ing to the tip are the source of a demagnetizing ﬁeld

inside the tip itself and a (localized) stray ﬁeld

tip

acting on the sample. It proves convenient at this

point to assume that the magnetization distribution

within the tip remains ﬁxed (say pinned) during im-

age acquisition. Let the magnetization within the

sample reach its equilibrium conﬁguration as the re-

sult of exchange interactions, anisotropy, demagnet-

izing ﬁeld distribution (represented by the constants

A, K, and vector ﬁeld

sample

, respectively), and tip-

induced stray ﬁeld

tip

for a given lift height:

sample

¼ m

½A; K; H

sample

; H

tip

ðr

; z

lift

Þ ð7Þ

Now assume an inﬁnitesimal variation dz of the tip to

sample distance. Precisely because

m has reached its

equilibrium conﬁguration, the virtual work done by

m simply reads

dE ¼m

sample



ZZZ

sample

½gradðH

tip

Þm

sample

d

rdz

lift

ð8Þ

It follows directly that the force acting on the tip is

given by

¼ m

sample

ZZZ

sample

@ H

tip

 m

sample

r ð9Þ

Similarly, the force gradient reads

lift

¼m

ZZZ

sample

tip

 m

sample

(

ZZZ

sample

@ H

tip



d m

-sample

lift

)

ð10Þ

In Eqns. (9) and (10), the ﬁrst and second derivatives

of the tip stray ﬁeld may, for a given tip, be exper-

imentally determined. In view of Eqn. (5), integration

by parts of Eqn. (9) leads to the following important

result:

¼

ZZZ

tip

r þ

tip

ZZZ

tip

D;z

r þ

tip

D;z

r ð11Þ

Equation (11) shows that the force acting on the tip

is the convolution product of the charge distribution

and the component along the tip displacement direc-

tion of the tip stray ﬁeld. In this sense, MFM may be

viewed as a microscopy of the charge distribution

within and at the free surfaces of the sample, a result

ﬁrst established by experiments (Rave et al. 1994) and

derived in the case of the tip stray ﬁeld not inﬂuenc-

ing the magnetization distribution in the sample

(Hubert et al. 1997). It ought to be stressed that the

charge densities in Eqn. (11) do include potential

perturbations of the sample charge distribution under

the inﬂuence of the tip stray ﬁeld.

Since the force exerted by the sample on the tip is

necessarily equal and opposite to the force exerted by

the tip on the sample, the subscripts ‘‘sample’’ and

‘‘tip’’ may be interchanged in Eqns. (9)–(11). If the tip

is to be viewed as a monopole or a point dipole, then

the force and force derivative read

Monopole : F

¼ r

tip

sample

D;Z

;

¼ r

tip

sample

D;Z

Point dipole : F

¼ m

tip



@ H

sample

;

¼ m

tip



sample

ð12Þ

where r

tip

and



tip

are the monopole strength and tip

moment, respectively. Equations (12), neglecting al-

together perturbations, have provided and still pro-

vide a simple although inaccurate interpretation tool

for MFM image analysis.

In spite of their concise form, neither Eqn. (9) nor

Eqn. (11), notwithstanding Eqns. (12), provide any

means of solving the inverse problem, namely ﬁnding

the magnetization distribution knowing the force

map, except if accepting extremely constraining as-

sumptions such as the existence of only two magnet-

ization directions, say, up and down (Hug et al.

1998). Rather, MFM image interpretation will in

most cases need to rely on a highest likelihood basis

and/or estimation of a magnetization distribution

and, knowing tip characteristics, simulating the

MFM image. Several iterations might prove neces-

sary before a reasonable agreement between experi-

mental data and simulations is achieved.

3. Probes

Integrated silicon cantilever and pyramid assemblies

(Gru

tter et al. 1990) now form the largest basis for

438

Magnetic For ce Microscopy

MFM probes. The pyramid (and cantilever, usually)

is sputter coated with a suitable magnetic alloy (e.g.,

CoCr) with thickness up to a few tens of nanometers

(Fig. 4). Tip stray ﬁelds are by no means small

(Thiaville et al. 1997, McVitie et al. 1997, Lohau

et al . 1999), typically ranging from 10 mT to 50 mT

(Fig. 5). If uniform, such high-amplitude external

ﬁelds would prove sufﬁcient to saturate low to me-

dium coercivity samples. MFM thus relies on the fact

that the lateral extension of the tip stray ﬁeld remains

small. The aspect ratio of tips may be improved either

via the growth of carbon needles at the extremity of

standard silicon pyramids (Ru

hrig et al. 1994) or via

micromachining techniques such as focused ion beam

etching. Through directional evaporation and shad-

owing, the amount of magnetic material deposited on

the tips may be greatly reduced. The stray ﬁeld, how-

ever, cannot be reduced beyond ﬁgures quoted above

Figure 4

Scanning electron microscopy images of microfabricated cantilever tip assemblies (NANOSENSORS) (a, b) prior to

magnetic ﬁlm deposition, and (c, d) after deposition and intensive MFM imaging. Note the sharpened pyramid apex

in (b) and a similar proﬁle in (d) in spite of a 35 nm CoCr layer sputter coated on the silicon tip and the collection of

nanometer debris after use.

439

Magnetic For ce Microscopy