Moulson A.J., Herbert J.M. Electroceramics: Materials, Properties, Applications

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In the case of ferromagnetic and ferrimagnetic materials the spins are strongly

coupled over the region of a domain, but when a suﬃciently strong magnetic

ﬁeld is applied the domain structure disappears and the material possesses a

magnetization vector M

which precesses around H with the Larmor frequency.

Because of the spin–orbit lattice coupling the precessional energy is steadily

dissipated, and in consequence M

gradually spirals in towards the H direction as

indicated in Fig. 9.38(a). A measure of the time taken for the energy transfer to

occur is the relaxation time t.

The precessional motion can be maintained by a suitable radio frequency ﬁeld

superimposed on the steady ﬁeld. For example, in Fig. 9.38(b), when a steady

ﬁeld H

is applied along the z axis and a radiofrequency ﬁeld H

is applied in the

x–y plane and rotates in the same sense and at the same frequency as the

precession, resonance occurs. ‘Gyromagnetic resonance’ as outlined above is in

principle the same as ‘ferrimagnetic resonance’ referred to earlier (Section 9.3.1),

except that in the former case the material is magnetically saturated by a strong

applied ﬁeld. In practice the steady ﬁeld, which determines the Larmor

frequency, is made up of the externally applied ﬁeld, the demagnetizing ﬁeld

and the anisotropy ﬁeld, and is termed the eﬀective ﬁeld H

. Figure 9.39 shows

the H

values at which resonance occurs in some of the important communica-

tions and radar frequency bands.

At low applied ﬁelds, when the ferrite is magnetically unsaturated, broad-band

losses occur, the so-called ‘low-ﬁeld losses’, and the increasing loss as H

decreases can be identiﬁed with that occurring on the high-frequency side of

the peaks in Figs 9.29 and 9.31. Low-ﬁeld losses arise because the radio-

frequency ﬁeld resonates with the magnetization in individual domains which

precesses around the anisotropy ﬁeld H

. It can be shown that this resonance

occurs over a range of frequencies between m

and m

gðH

þ M

Þ; thus, to

512 MAGNETIC CERAMICS

Fig. 9.38 Precessional motion of magnetization: (a) M

spiralling into line with H as the

precessional energy is dissipated; (b) precession maintained by an applied radio frequency

ﬁeld.

TEAMFLY

Team-Fly

avoid the onset of low-ﬁeld losses in low-frequency applications, it is necessary

for H

and M

to be as small as possible.

To understand the principle of operation of important ‘non-reciprocal’ (see

below) microwave devices, consider what occurs when a plane-polarized

microwave is propagated through a ferrite in the direction of a saturating ﬁeld

. The wave can be resolved into two components of equal amplitude

but circularly polarized in opposite senses, i.e. into a ‘right-polarized’ and a

‘left-polarized’ component. These two components interact very diﬀerently with

the material, leading to diﬀerent complex relative permeabilities

¼ m

 jm@

and m*



¼ m



 jm @



, as shown in Fig. 9.40. Because of the

PROPERTIES INFLUENCING MAGNETIC BEHAVIOUR 513

Fig. 9.39 Eﬀective ﬁeld values H

at which resonance occurs in some important frequency

bands.

Fig. 9.40 Dependence of the permeability on H

for ‘right’ and ‘left’ circularly polarized

components of a plane-polarized microwave of frequency o ¼ gm

diﬀerent permeabilities, the phase velocities of the two components diﬀer, so that

the negative, or left, component is retarded relative to the positive, or right,

component, causing a clockwise rotation of the plane of polarization. The sense

of the rotation relative to H

does not depend on the direction of propagation.

Thus, if a plane wave is rotated 458 in the clockwise sense during its passage

through a saturated ferrite, then if it were to be reﬂected back, it would suﬀer a

further 458 rotation. Because of this the process is said to be ‘non-reciprocal’.

A rigorous analysis of the interaction of the microwave ﬁeld with the

precessing magnetization involves the tensor permeability and is beyond the

scope of the present text. For the case of a plane-polarized wave of angular

frequency o propagating through a magnetically saturated ferrite in the direction

of the saturating ﬁeld, such an analysis yields

¼ 1 þ

 o

ð9:36Þ

and



¼ 1 þ

þ o

ð9:37Þ

in which m

and m



are the relative permeability values for the right and left

circularly polarized components respectively, o

¼ m

and o

¼ m

, H

the resonance ﬁeld and M

is the saturation magnetization.

Because the wave velocities

and v



of the two components diﬀer, a phase

diﬀerence f develops between them as they propagate. The plane of polarization

is thus rotated by an angle y ¼ f=2. The angular rotation y=L of the plane of

polarization per unit path length can be estimated as follows. Suppose that the

plane-polarized wave travels a distance L through a medium of relative

permittivity e

and relative permeabilities m

and m



. If the average velocity is

v, then the fast and slow components travel distances of ðL=vÞv

and ðL=vÞv



respectively, where v

and v



are the fast and slow speeds. The path diﬀerence is

D ¼

ðv

 v



Þð9:38Þ

and the phase diﬀerence is

f ¼

ðv

 v



ð9:39Þ

where l is the average wavelength. The plane of polarization is therefore rotated

through y where y ¼ f/2

y ¼

 v



and

514 MAGNETIC CERAMICS

 v



Þð9:40Þ

Since

 v









¼ p f







ð9:41Þ

where f is the frequency of the wave. Because



ðm



1=2

and v

ðm

1=2

ð9:42Þ

where c is the velocity of light in a vacuum,

1=2

ðm

1=2



 m

1=2

Þð9:43Þ

For a device operating below resonance the applied ﬁeld is small compared

with H

, although suﬃciently strong for the ferrite to be magnetically saturated.

Under these conditions o

 o and o

5o, and therefore it follows from Eqs

(9.36) and (9.37) that

1=2

 1 

ð9:44Þ

and

1=2



 1 þ

ð9:45Þ

Therefore Eq. (9.43) becomes

1=2

ð9:46Þ

In a typical case where e

¼ 10 and M

¼ 170 kA m

, y=L ¼ 108 mm

The width DH

of the resonance absorption curve measured at half peak

power – the ‘3 dB resonance line width’ – should in general be as small as

possible since this implies a narrow range of frequencies over which strong

interaction with the ferrite can occur; however, there are certain broad-band

applications where this would not be the requirement. There are two main

contributions to the linewidth:

1. the intrinsic linewidth characteristic of the single crystal and

2. additional eﬀects arising in the case of polycrystalline materials and inﬂuenced

by magnetic anisotropy and microstructural features.

PROPERTIES INFLUENCING MAGNETIC BEHAVIOUR 515

The intrinsic single-crystal linewidth can be shown to be inversely proportional

to the relaxation time.

In a polycrystalline material each crystallite experiences its own eﬀective ﬁeld,

which is determined in part by magnetic anisotropy. Therefore, because of the

diﬀerent orientations of the crystallites, there will be a distribution of resonant

frequencies; in consequence, narrow linewidths are associated with low

anisotropies. Magnetic inhomogeneities – inclusions and pores – also disturb

the local eﬀective ﬁelds and so lead to line broadening. The eﬀect of porosity on

resonance linewidth can be expressed by the relationship

¼ 1.5M

pð1  pÞð9:47Þ

where p is the fractional volume porosity. Thus it is evident that a pore-free

single-phase microstructure is necessary for minimum linewidth.

There is also a strong dependence of resonance linewidth on surface ﬁnish,

which is exempliﬁed by the following data for small (0.35 mm diameter) YIG

spheres in a resonant cavity. The linewidths for surfaces ﬁnished with 15 mm grit,

5 mm grit and ‘highly polished’ were 560 A m

, 240 A m

and 40 A m

respectively.

At high microwave powers ‘spin waves’ may be excited rather than the

uniform precession discussed so far. Power from the radiofrequency ﬁeld is then

coupled into the spin-wave system and the energy dissipation shows a higher

than proportional increase with increasing power. The power threshold P

which spin-wave resonance sets in is measured in terms of a material parameter

, the spin-wave linewidth, which is a measure of the damping of the spin

waves. There are two approaches to increasing DH

and thus the microwave

power-handling capability of the ferrite – tailoring the composition or tailoring

the microstructure. For example, the substitution of holmium and dysprosium

for gadolinium in Y

2.9

0.1

leads to an approximately tenfold increase in

516 MAGNETIC CERAMICS

Fig. 9.41 Dependence of the spin-wave linewidth DH

on grain size.

. In addition, the spin waves can be strongly damped if the grain size of a

polycrystalline ceramic is kept small. For example, Fig. 9.41 shows that a

reduction in grain size from 30 mmto1mm increases D H

by a factor of

approximately 30 and thus, because P

/ DH

, increases the power-handling

capability by a few orders of magnitude. Therefore, although single crystals oﬀer

the optimum microwave properties at low ﬁelds, a ﬁne-grained material performs

more satisfactorily at high power levels.

9.4 Preparation of Ferrites

The choice of composition of a soft ferrite is made to achieve one or more of the

following properties:

1. maximum permeability;

2. minimum losses;

3. temperature variation of properties between prescribed limits;

4. adequate saturation magnetization;

5. satisfactory behaviour over the required frequency band;

6. ﬁnally but by no means the least important, minimum cost.

The basic choice of composition for the great majority of applications lies

between MnZn and NiZn ferrites. The former have a lower material cost and are

superior in all the above properties except 5 and the latter are more suitable for

operation at higher frequencies. (MnZn)Fe

has the disadvantage of requiring

a low oxygen pressure atmosphere during sintering so that its manufacture

necessitates a special kiln with a supply of suitable gas for the atmosphere.

(NiZn)Fe

can be ﬁred in air. Fabrication generally follows the lines described

in Chapter 3. Features unique to ferrites are outlined below.

9.4.1 Raw materials

The raw materials can be minerals that have only been puriﬁed by mechanical

methods or the purer products of chemical processes. Both haematite (Fe

)

and magnetite (Fe

) occur in large deposits of better than 90% purity that, for

some ferrites, require little more than grinding before use. A purer grade of

can be obtained from the pickle liquor that results from the removal of

oxide crusts during steel fabrication. The liquor contains iron chlorides and can

be converted into oxide by spraying into heated air in an apparatus similar to

that used in spray drying but operated at a higher temperature.

PREPARATION OF FERRITES 517

High-purity oxides can be obtained by calcining oxalates in an atmosphere

with a controlled oxygen content:

FeðCO

! Fe þ2CO

2Fe þ 3O

! 2Fe

The product consists of very small crystals that need little grinding. Co-

precipitation of mixed oxalates can also give intimate mixing.

Most transition elements are available in a pure state as metals which can be

dissolved in acids. A mixture of nitrates can be evaporated to dryness and

calcined to form precursor oxide mixtures for the preparation of spinel and

garnet ferrites. Alternatively, mixed oxides, carbonates or oxalates can be

precipitated. Microwave ferrites that are required to be of high purity can be

prepared by one of these chemical routes.

Barium ferrite adequate for certain permanent magnet applications can be

prepared from crude mineral iron oxide. A past interest in the material for

perpendicular magnetic recording stimulated studies of a variety of chemical

routes, including hydrothermal synthesis, to produce powders [12].

9.4.2 Mixing, calcining and milling

Mixing is usually carried out in a ceramic ball mill with steel balls. The inevitable

attrition of the mill balls leads to an addition of 0.5–1 wt% to the iron content

for which allowance must be made. Care must be taken to maintain the quantity

and size distribution of the mill balls and to remove those that have become so

small that they cannot be separated from the slip or powder on sieving.

Calcination (typically at temperatures in the range 1000 8–1100 8C, depending

on composition) is carried out in saggars or continuously in a rotating tube kiln.

An air atmosphere is used even though this results in a high Mn

content in

MnZn ferrites, but the state of oxidation is rapidly rectiﬁed during sintering. A

low Mn

content can be a disadvantage during the early stages of sintering

since, at about 430 8C, MnZn ferrites take up oxygen, converting Mn

to Mn

with a resulting lattice shrinkage. The temperature gradients within a furnace are

often considerable at this stage in ﬁring and the pressings are weak. One part of a

large piece may be shrinking while another part is expanding, resulting in the

formation of cracks. At temperatures above 700 8C the thermal gradients are

greatly reduced because of the rapid interchange of radiant energy so that eﬀects

of this type are less likely to cause problems.

9.4.3 Sintering

If a low oxygen pressure is required during sintering nitrogen is injected at a

point in the tunnel kiln where the temperature is approximately 1000 8C, and the

518 MAGNETIC CERAMICS

air is eﬀectively displaced at a position where the temperature is 1300 8C. The

composition of the atmosphere is monitored by passing samples from the hot

zone through a paramagnetic oxygen meter or by using a zirconia solid state

electrolytic device (see Section 4.6.1) within the furnace. The low oxygen pressure

(around 1 kPa (7.5 Torr)) is maintained until the pieces have cooled to around

500 8C. A controlled atmosphere can also be obtained by burning methane or

town gas in a limited supply of air. The large-scale process in a continuous kiln

does not allow full atmosphere control because the extent to which oxygen gains

access to the hot zone is governed by so many variables, one of which is the

packing of the work on the trolleys which inevitably varies with the sizes and

shapes of the pieces concerned. Where close control is essential, as with pot

cores, the pieces are ﬁred in well sealed batch kilns. In this case the oxygen

pressure can be programmed to correspond to the equilibrium pressure of the

desired balance of oxidation states at both the maximum temperature and as it

falls to around 900 8C. Below 900 8C the rate at which oxygen is exchanged

between the ferrite and the atmosphere is suﬃciently slow that, provided that the

cooling is rapid, there is no need to maintain tight control. Means are often

provided for moving the sintered material into a cooled compartment when the

temperature has fallen suﬃciently.

In the cases of NiFe

and the rare earth garnets for microwave use, in which

the losses due to conductivity must be minimized, an oxygen atmosphere may be

required for sintering so that the concentration of Fe

ions is reduced to a very

low level.

9.4.4 Single-crystal ferrites

The growth of single crystals is discussed in Section 3.10. Because of a

combination of high permeability and abrasion-resistance single crystal Mn–Zn

ferrites are used for the read-out heads in VCRs. The crystals can be grown by

the Bridgman–Stockbarger method. Garnet ferrite crystals are required for many

microwave applications and as thin layers for magneto-optical devices. Since

these compounds melt incongruently they are grown from solutions based on

lead oxide. The gadolinium gallium garnet crystals melt congruently and can be

grown directly from the melt.

9.4.5 Magnets with oriented microstructures

For hard ferrites for use as permanent magnets relative permeability is

unimportant and is usually near to unity in the magnetized state. The important

parameters are a high coercive ﬁeld, a high remanent magnetization and the

maintenance of a suitable combination of these properties over the operational

PREPARATION OF FERRITES 519

temperature range. Only ferrites with the hexagonal magneto-plumbite structure

with compositions close to MO6Fe

, where M is Ba or Sr, are used.

Somewhat better properties can be obtained with strontium, but the cost of the

raw material usually determines which is used at a particular time. In what

follows, barium ferrite only is referred to on the understanding that either

barium or strontium may be involved.

Production processes are broadly similar to those used for soft ferrites, but

various techniques can be introduced to orient the easy axes of magnetization of

the crystals in the sintered ceramics. Since all the iron is in the Fe

state,

sintering can be carried out in air. Simple shapes can be pressed from a mixture

of Fe

and BaCO

and sintered at 1300 8C to form permanent magnets of

suﬃcient quality for some applications. More commonly a mixture of BaCO

and Fe

is calcined and treated in the way described for soft ferrites. The

milling of the calcine may be more prolonged since the coercive ﬁeld is increased

by having a smaller crystal size. The calcination is often carried out in rotary

calciners (Fig. 3.1) on a continuous basis yielding the fully formed ferrite. When

milled this calcine forms tabular particles with the easy direction of magnetiza-

tion normal to their larger surfaces. These features permit some degree of particle

orientation during pressing.

Orientation of the single-crystal powder particles by an applied ﬁeld

requires that they should be able to rotate relative to one another so that, on

average, their easy directions of magnetization are aligned. Only a limited

extent of alignment can be obtained using dry powders, and it is more

eﬀective to make the ferrite powder into a slurry with water which is removed

during pressing through a specially designed die. Demagnetizing and static

ﬁelds are applied in rapid succession from coils round the die, the water is

sucked out of the slurry while the static ﬁeld is still applied and pressure is

exerted by a top punch (Fig. 9.42(a)). If suitable deﬂocculants are used, a

high degree of dispersion can be obtained in the slurry so that the particles

can be oriented eﬀectively. The ﬁlter cake is subjected to moderate pressure

(15 MPa, 1 tonf in

) to compact it and remove excess water. It is usually

necessary to apply a demagnetizing ﬁeld before the compact can be removed

from the die without the risk of its breaking. The direction of magnetization

required is usually normal to the major surfaces of the pressed piece so that

the magnetizing coils can be placed round the die to give a ﬁeld parallel to

the motion of the punches. The process is slow compared with normal die

pressing, and the consequent higher cost can only be justiﬁed when the

improved energy product is needed in the intended application. A complex die

for producing small motor magnets is shown in Fig. 9.42(b) and a production

press in Fig. 9.43.

Some degree of anisotropy can also be achieved by applying a ﬁeld during the

extrusion of a paste formed from barium ferrite powder and a viscous ﬂuid

medium. In this case the plate-like shape of the particles also assists orientation

520 MAGNETIC CERAMICS

since the plane of the plates tends to align parallel to the direction of extrusion

(Fig. 9.44).

Barium ferrite powder is also incorporated in rubber or polymer matrices to

make, for instance, the familiar magnetic gaskets used to latch refrigerator doors.

In this case the particle size must be adjusted to an optimum of around 1 mm

since this gives maximum coercive ﬁeld. The powder can be incorporated by

PREPARATION OF FERRITES 521

Fig. 9.42 (a) Diagram of the pressing cycle: M, Die; S,S

, punches; P, injection pump; F,

suspension; C, magnet coil. The punches contain ﬁlters and drainage channels for the water. (i)

Before and (ii) after the material is injected into the compression space; the slurry is densiﬁed

from 40% to 13% water content, and the particles are oriented by the magnetic ﬁeld; (iii) after

densiﬁcation by slight upward movement of the lower punch, the amount of the movement

depending on the thickness of the product; demagnetization; (iv) removal of the compacted

product. (b) Die for simultaneous pressing of eight oriented magnet segments. (Courtesy of

Philips Technical Review.)