Dionne G.F. Magnetic Oxides

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170 4 Ferrimagnetism

Table 4.2 Molecular ﬁeld coefﬁcients of nickel and manganese spinel ferrite (determined

semiempirically)





0:8

0:2



0:2

1:8



Fe–Fe Fe–Ni Ni–Ni Fe–Fe Fe–Mn Mn–Mn



mol=cm



mol=cm



mol=cm



mol=cm



mol=cm



mol=cm



–200 – – 200 180 160

–60 –58 –60 60 59 58

312 276 – 312 187 62

Table 4.3 Magnetic parameters of common spinel and garnet cubic ferrites

4M

300 K

exp:

Compound n

tet

oct

(theor.) (G) (G) (K)

SPINEL

5 5 C 4 4 6,400 6,000 858

”Fe

58.33.3 5;000 4;500 948

ZnFe

0 5  5 0 (antiferro) paramag paramag –

CdFe

0 5  5 0 (antiferro) paramag paramag –

MnFe

5 5 C 5 5 7,000 5,000 573

CoFe

5 5 C 3 3 6,000 5,300 793

NiFe

5 5 C 2 2 3,800 3,400 858

CuFe

5 5 C 1 5 7,000 5,000 728

MgFe

5 5 C 0 0 1,800 1,500 713

0:5

1:5

5 5 C 2:5 2.5 4,200 3,900 943

GARNET

15 10 5 2,400 1,800 560

Typical spinel lattice parameter a

 8:4

A; density  4:5–5:5 gm=cm

; typical garnet (YIG)

lattice parameter a

 12:4

A; density  5:17 gm=cm

A defect spinel structure that is called maghemite and written as Fe



1=3

2=3

,where

 represents a cation site vacancy. A more common antiferromagnetic nonspinel form is known

as hematite with designation ’Fe

ions occupy the tetrahedral sublattice in the amount of 20%. The anomalously low Curie

temperature is caused by very weak

interaction involving Mn

The experimentally observed magnetic moment is attributed to upwards of 10% of the Mg

ions

occupying the tetrahedral sublattice thereby placing more Fe

in the octahedral sublattice

based on the experimental parameter values listed in Tables 4.2 and 4.3.InFig.4.10,

thermomagnetization characteristics from measurements are compared with the re-

sults of computations in which the molecular orbital exchange concepts developed

in Sect. 3.1 were applied to the spinel ferrite family [32]. The corresponding param-

eter values used for the calculations are listed in Table 4.4.

Magnetite (lodestone) is a naturally occurring normal spinel of chemical formula





. Because the electrical conductivity introduced by the full

complement of octahedral-site Fe

ions that can transfer electrons among the Fe

neighbors (a process called polaronic electron hopping), magnetite is more a vehicle

for studying the electrical properties of oxides than a practical magnetic insulator

4.3 Ferrimagnetic Oxides 171

Fig. 4.10 Thermomagnetism characteristics of basic spinel ferrites: (a) measured curves inspired

by Fig. 32.7 in reference [24], and (b) computations by a molecular-orbital model [32]

Table 4.4 Spinel ferrite molecular ﬁeld coefﬁcients (determined from molecular-orbital theory)

B-site Ion-S



mol=cm





mol=cm





mol=cm



5=2 150 60 C273

5=2 200 60 C300

”-Fe

5=2 170 60 C282

5=2

135 51 C178

5=2

200 32 C222

2 200 25

C240

3=2 200 58

C269

1 200 90

C330

Standard site distribution Fe

0:2

0:8



0:2

1:8



Fully inverted site distribution Fe





Values are corrected for t

–t

ferromagnetic direct exchange which decreases monotonically as

the shell ﬁlls with paired spins. For Fe





(magnetite), N

was adjusted to 25

from 44 mol=cm

to account for ferromagnetic double exchange

[33]. It is also one of the best hosts for studying the magnetic contribution of the

ion, which can cause important magnetoelastic and dielectric effects. One in-

teresting feature of this compound is the order-disorder transition of Fe

–Fe

ions in the B sublattice that occurs at T  120 K. Below this temperature, the crys-

tal structure undergoes a phase transition from cubic to orthorhombic symmetry,

lending further credence to the proposition that the magnetoelastic Fe





ions

undergo a J–T or S–O condensation that stabilizes the transfer electrons in their po-

laronic traps and causes an anomalous decrease in conductivity. This general subject

is discussed further in Chap. 8.

Lithium ferrite contains the most iron ions next to magnetite and is the ferrite

compound with the largest Curie temperature .T

 940 K/. As can be recognized

immediately from the chemical formula Fe ŒLi

0:5

1:5

 O

, 25% of the B sublat-

tice is diluted by the Li

ions. Nonetheless, the net number of Bohr magnetons

is 2.5, which is sufﬁcient to produce a room-temperature 4M  3;500 G. To

lower the moment, magnetic dilution can be accomplished by direct Al

in the

B sublattice or more commonly by substitutions of 0:5Li

C Ti

! 1:5Fe

with chemical formula Fe

1t=2

t=2

ŒLi

0:5

1:5t

 O

. As the site distributions

172 4 Ferrimagnetism

Fig. 4.11 Calculated lithium-zinc ferrite thermomagnetization curves

indicate, when the B sublattice is diluted with Ti

ions, the extra Li

ions

required for electrical charge neutralization replace Fe

ions in the A sites. To in-

crease the moment, Zn

! 0:5Fe

C0:5Li

are substituted into the A sublattice

according to Fe

1z



0:5z=2

1:5Cz=2



. This modiﬁcation also increases the

content of the B sublattice, producing the initial rise in magnetization shown

in Fig. 4.4, but it also causes a reduction in T

because of the decreased net num-

ber of Fe

–Fe

interactions shown in the curves of Fig. 4.11. The results are

from a molecular ﬁeld analysis [23] and are also listed in Table 4.1 and discussed

in Appendix 4A. The uses of Li ferrite have become mainly in microwave appli-

cations because of its high T

made possible by the larger amounts of Fe

both sublattices and generally good dielectric properties in the microwave bands.

Its higher 4M capabilities make it particularly attractive in the millimeter-wave

bands (above 35-GHz frequencies). The development of Li ferrite of good ceramic

quality was delayed by the high volatility of Li. When these materials are subjected

to temperatures above 1;000

C, Li

O is lost and the compound becomes iron-rich

with the result that diamagnetic ’-Fe

hematite phase precipitates and Fe

reduced to Fe

in the B sublattice, causing charge transfer that lowers the resistiv-

ity. To make dense microwave-quality Li ferrite, bismuth oxide .Bi

/ is added as

a ﬂux to lower sintering temperatures [34]. Unfortunately, the tendency of Bi

segregate along grain boundaries also causes a deterioration in mechanical integrity.

4.3 Ferrimagnetic Oxides 173

Nickel ferrite Fe





is an inverted and generally well-behaved

spinel with Ni

occupying almost half of the octahedral B sublattice. A small

amount .<5%/ can be expected to ﬁnd its way into the tetrahedral A sites under

thermal equilibrium conditions, causing magnetoelastic and spin–lattice relaxation

effects. Because Ni

carries a spin value S D 1 in addition to an effective Land´e

g factor greater than 2 (see Sect. 5.1) nickel ferrite can offer higher magnetizations.

Since Ni

occurs only occasionally and in special situations (e.g., Li

-substituted

NiO) [35, 36], the incidence of Fe

is usually negligible, and dielectric prop-

erties are excellent for microwave applications. Because the e

orbitals are half

ﬁlled, this ion presents a signiﬁcant covalent transfer integral b and consequently

a strong superexchange coupling to neighbors of its own kind and to the adja-

cent Fe

ions of both sublattices. Similar to Li ferrite its magnetic moment can

be reduced, in this case typically by direct substitutions of Al

for Fe

ions,

which initially favor B-site dilution according to the theoretical analysis reported by

Borghese [12].

The magnetic moment can also be raised by the Zn

ions diluting the A sublat-

tice (similar to the LiZn ferrite case shown in Fig. 4.4, with the attendant increase in

the sensitivity of 4M to temperature resulting from the decrease in T

,asshownin

Fig. 4.12 [37]. The peak maximum magnetization of 5;000 G at room temperature

can be obtained with Zn replacing Ni, but occupying 35% of the tetrahedral sites,

i.e., Fe

0:65

0:35



0:65

1:35



. An additional beneﬁt of Zn for ma-

terials preparation is a reduction in the solid-state reaction (sintering) temperature.

As examined in Chap. 5, a drawback to nickel ferrite can be the large negative 

100

magnetostriction constant that renders the anisotropy and hysteresis-loop properties

Fig. 4.12 Thermomagnetism curves of nickel-zinc spinel ferrite, showing the effects of Zn

dilution of the minority tetrahedral A sublattice. Note decrease in Curie temperatures. Data are

from Pauthenet [37]

174 4 Ferrimagnetism

of the material highly stress-sensitive. The origin of this property could be the

unquenched orbital momentum of the A-sublattice Ni

ground state, which is dis-

cussed in Sect. 5.3. Manganese in the 3C state helps to compensate magnetostriction

through its local Jahn-Teller <100> axial expansion effect [38], and should be used

as an additive where square hysteresis loops are desired. Although the Curie tem-

perature of Ni ferrite is not as high as that of Li ferrite, the material in ceramic

form is generally considered to be of better quality in a microstructural sense, i.e.,

it is denser and has more uniform grain size. Because of these properties, as well

as because of its wide range of magnetization values, Ni ferrite ranks as one of the

most-used ferrite families.

Manganese ferrites are mainly normal with site distributions indicated by the

formula Mn

0:8

0:2



0:2

1:8



.TheMn

ion has a larger radius

than most of the ions of the 3d

series, 0.80

A instead of 0:65

A. To accommo-

date this larger cation, the lattice parameter is increased with the result that some

of the b

=U factors of the covalent bonding are reduced, thereby increasing the

coefﬁcient leading to a Curie temperature that is the lowest of all of the basic

spinel ferrite families, as shown in Fig. 4.10. This effect is reﬂected in the values of

the molecular ﬁeld coefﬁcients N

, which reveal weaker interactions that involve

, as shown in Table 4.2 where large reductions occur in the N

coefﬁcients

for Fe-Mn and Mn-Mn [24]. These results support the conclusions of Simsa and

Brabers [39] that a canting angle of 54

among the Mn

ions in the B sublattice

accounts for an initial deﬁciency in the magnetic moment at T D 0 K.

For microwave applications, dielectric losses due to poor dielectric properties

stem from the charge transfer mechanism that stabilizes Fe

in B sites, i.e.,

C Mn

! Fe

C Mn

. There are also two possible polaronic conduc-

tion opportunities here: Fe

$ Fe

C e



and Mn

$ Mn

 e



. In general,

the Curie temperatures of this family are unacceptably low for applications with

power dissipation effects that are likely to increase the temperature. Similar to Li

and Ni ferrites, T

is reduced further when Zn

is added to increase 4M .

Magnesium ferrite is mainly inverted with a typical formula Mg

0:1

0:9



0:9

1:1



. The magnetization and permeability are too low for most

low frequency applications, but the family has proven to be useful for certain mi-

crowave regimes in situations where the high temperature sensitivity is tolerable. In

these cases, manganese is added for the purpose of suppressing any formation of

through the charge transfer equation Fe

CMn

! Fe

CMn

[40,41].

As a consequence, this family is usually referred to as the magnesium-manganese

ferrites. Final properties of ceramic versions are sensitive to the ﬁring schedule be-

cause of the uncertain ionic site dispositions. The principal virtues of this hybrid

family are its square hysteresis loops and insensitivity to stress made possible by the

presence of Mn

ions. The compensation of magnetostriction is believed to result

from a combination of J–T effects in B sites and a minority of S–O effects in A sites.

Cobalt ferrite is also an inverted spinel of formula Fe





, with

Co occupying the B sites. For reasons that will be explained in subsequent chapters,

this compound is of interest primarily for its magnetoelastic properties from which

the phenomena of magnetocrystalline anisotropy and magnetostriction arise. Like

, it can also feature a g factor greater than 2 in octahedral sites. Divalent cobalt

4.3 Ferrimagnetic Oxides 175

in a B site is a classic spin-orbit stabilized ion that favors a compressive distortion

along the c axis of the ligand octahedron, analogous to Ni

in tetrahedral sites.

Unfortunately, these properties are generally undesirable for many conventional ap-

plications. Moreover, the strong coupling of Co

orbital states to the lattice is

responsible for large power losses when this ferrite is used as a microwave propaga-

tion medium. In small amounts, however, Co

ions can be beneﬁcial for adjusting

anisotropy and magnetostriction, and in controlling relaxation effects that inﬂuence

peak power limits.

Copper ferrite is another spinel that features a magnetoelastically active con-

stituent Cu

, which like Mn

is a classic Jahn-Teller ion in an octahedral site.

Also similar to Mn

, magnetoelastic and relaxation effects from a small fraction of

in tetrahedral sites would also be expected from unquenched L in the upper T

triplet. The formula is generally inverted, in the form of Fe





,but

can in theory assume a monovalent state in Cu

0:5

2:5

analogous to Li fer-

rite, but with part of the Cu

ions occupying tetrahedral A sites [31]. As in the case

of Ni

and Co

in octahedral sites, the g factor of the Cu

ion can be greater

than 2, but because of its low spin value S D 1=2, Cu ferrites are not of high perme-

ability and are rarely considered for microwave applications because their chemistry

and microstructure in ceramic form are difﬁcult to control. At high temperatures

copper has a volatility comparable to that of lithium. Sintering temperatures are

lower than typical for spinels, and the attainment of good stoichiometry is a chal-

lenge. Furthermore, because of the strong Jahn-Teller tendencies, the Cu

ion can

drive the lattice symmetry tetragonal, as it does in Fe





(and also

the superconducting cuprate perovskite host compounds such as La

and will also produce strong positive magnetostrictive effects when used as an ad-

ditive to cubic lattices. Another drawback is the polaronic conduction mechanisms

similar to those of Mn ferrite (Cu

$ Cu

C e



and Cu

$ Cu

 e



)

[42]. One interesting possibility is the use of monovalent copper in A sites to pro-

duce higher magnetization compounds for microwave applications. This subject

is discussed in Appendix 4B. Table 4.5 lists a qualitative summary of spinel fer-

rite magnetization properties as well as magnetoelastic effects that are discussed in

Chap. 5.

4.3.2 Garnet Ferrites fc

.

The garnet family is the best-behaved chemically and structurally of all ferrimag-

netic oxides. From a magnetic standpoint, it is also the most thoroughly investigated.

Following the ﬁrst synthesis of the iron garnets by Bertaut and Forrat [43], care-

ful analysis of the crystal structure was carried out by Geller and Gilleo [44, 45].

The three cation sites dodecahedral c, octahedral a, and tetrahedral d are shown in

relation to a section of the crystallographic unit cell in Fig. 4.13. It can be readily

seen that the principal symmetry axes of the a and d sites do not conform to the cu-

bic cell axes <100>, <111>,and<110>, in marked contrast to the spinels which

have the A and B sites neatly packed into the cubic cell. Only the octahedral site

176 4 Ferrimagnetism

Table 4.5 Initial effects of dilutant ions in inverted spinel ferrite A





Ions Site M

jjK

jj

,Ga

3C a

++ ––

2C b

B ++ ––

C 2Ti

4C c

A C 2B ++ ––

A * – + –

2C d

B – +

3C e

B –– – +

2C f

B – ** ** –

and Ga

occupy both octahedral and tetrahedral sites, but opposite to the garnets, they

initially have strong preference for the octahedral sites in the inverted spinels

is the divalent-ion basis for the magnesium ferrite family

C2Ti

combination is used in Li ferrite. The added Li

replaces Fe

in the tetrahedral

sites, but the net result is a lowering of M

by the 2Ti

ions diluting the octahedral sublattice

is used in very small amounts to compensate K

. It will cause K

to pass from negative

to positive at about 0.01–0.02 ions per formula unit. Because it is spin-orbit stabilized, it is also a

fast-relaxing ion

is a Jahn-Teller ion that inﬂuences magnetostriction by adding a positive contribution to

the large 

100

constant that makes the average value 

pass through zero at a concentration of

about 0.2 ions per formula unit

is a spin-orbit stabilized ion that is a natural constituent of spinel ferrites. It enhances the

negative anisotropy constant by favoring the h111i-axis extensions, and thereby increases the 

111

magnetostriction constant. In combination with host Fe

ions, it can provide a hopping electron

conduction mechanism that is detrimental to high-frequency applications

has one of its trigonal axes aligned with a lattice <111> direction [46]. An even

more important difference is that the tetrahedral sites are more numerous than the

octahedral sites in the ratio of 3:2, thereby making the d sublattice dominant in con-

tributing to the magnetization. As will be shown in Chap. 5, this feature allows the

magnetoelastic properties to be varied over a wider range.

Dielectric properties of the garnets are generally superior to those of the spinels,

due in part because all of the cations are naturally in the 3C state, thereby affording

less opportunity for Fe

to form. Magnetocrystalline anisotropy and magnetostric-

tion are also manageable quantities. Moreover, there are a plethora of substitutions

available for all three sites that may be used to tailor magnetic, microwave, and op-

tical properties. Because the system is more refractory than the spinels, chemical

stability is generally higher among conventional compounds, i.e., those based on yt-

trium or lanthanum series ions in the c sublattice. Garnet systems with lower sinter-

ing temperatures are the families with cation combinations

Y; Ca

ŒFe; Zr.Fe; V/

and

Bi; Ca

ŒFe; Zr.Fe; V/, and are used where lower magnetizations are accept-

able and the high sublimation rate of Bi at solid reaction or sintering temperatures

can be tolerated.

Yttrium iron garnet is the basic magnetic host of this family, and can be altered by

a variety of substitutions. Al

and Ga

ions are used to reduce the magnetization

by forming solid solutions of Y

(YIG) with either Y

(YAG) or

(YGG). With these two ions, the dilution begins in the d sublattice and

gradually spills over to the a sites [47,48]. For this reason Al

(or Ga

)areused

to reduce the magnetization, as shown in Gilleo’s data [16]ofFig.4.14. To increase

4.3 Ferrimagnetic Oxides 177

Fig. 4.13 Garnet crystal structure with bond angle diagrams, below and above the compensation

temperature T

comp

that occurs when the c-sublattice is occupied by heavy rare-earth ions of the

series

Fig. 4.14 Thermomagnetism

curves of yttrium aluminum

iron garnet ferrite, showing

the effects of Al

net

dilution of the majority

tetrahedral d sublattice. Data

are from Gilleo and Geller

[16]

178 4 Ferrimagnetism

Fig. 4.15 Thermomagnetism curves of yttrium indium iron garnet ferrite, showing the effects of

dilution of the minority octahedral a sublattice. Compare with Fig. 4.14. Data are from Gilleo

and Geller [16]

magnetization, the larger ions In

(or Sc

) can be used up to a concentration level

of about 0.5 per formula unit because they occupy a sites almost exclusively. With

the greater reduction in the number of J

exchange couplings by a-site dilution;

however, the Curie temperature drops quickly with dilution, similar to the case of

Zn in the A sites of spinels. Examples of these effects are shown in the data of

Fig. 4.15.

Yttrium-calcium iron garnet is a common modiﬁcation of the basic YIG compo-

sition that has been considered for use in special microwave and magneto-optical

applications with vanadium diluting d sites or zirconium a sites. The advantages of

this family lie in two features: (1) V

and Zr

occupy exclusively their respective

sites, which means that the adjustments in magnetization can be achieved without

unwanted dilution of the opposite sublattice that would cause a further decrease in

Curie temperature; and (2) calcium, vanadium, and zirconium are less expensive

chemicals than the alternative yttrium, lanthanum, indium, or scandium. A further

beneﬁt of the use of calcium actually comes from the reduced amounts of yttrium

4.3 Ferrimagnetic Oxides 179

Table 4.6 Initial effects of dilutant ions in garnet ferrites

i



Ions Site M

jjK

jj

,Ga

3C a

++ +, * –

2Ca

C V

5C b

2c C d ++ + –

C Ge

4C b

c C d ++ + –

C Si

4C b

c C d ++ + –

,Sc

3C b

C Zr

4C b

c C a *+ ++ *

C Sn

4C b

c C a *+ ++ *

C Si

4C c

a C d *+ ++ *

3C d

a –– – +

,Pb

2C e

c – +

2C f

a ** ** – **

and Ga

occupy both octahedral and tetrahedral sites, but initially have strong preference

for the tetrahedral sites in the garnets. Ga

reduces M

more efﬁciently and can raise K

can be used instead of Ca

in c sites, as well as La

instead of Y

for lattice parameter

adjustments

is used in very small amounts to compensate K

. It will cause K

to pass from negative

to positive at about 0.02 ions per formula unit. Because it is spin-orbit stabilized, it is also a fast-

relaxing ion

causes a Jahn-Teller distortion that adds a positive contribution to the magnetostriction

constants and makes the average value pass through zero at a concentration between 0.05 and 0.1

ions per garnet formula unit

and Pb

are important for magnetooptical applications but can increase microwave losses

is a spin-orbit stabilized ion that occurs as a natural impurity. It enhances the negative

anisotropy constant by favoring the h111i-axis extensions, and thereby increases the 

111

mag-

netostriction constant. In combination with host Fe

ions, it can provide a hopping electron

conduction mechanism that is detrimental to high-frequency applications

or lanthanum because these rare-earth elements can contain fast-relaxing impurities

that are magnetically lossy to microwaves. One other ion that is used particularly for

magneto-optical application is Bi

for reasons that will be explained in Chap. 7.

This ion, however, is extremely large and does not freely substitute for Y

over

the full range. In fact, the compound Bi

(BIG) may exist only as ﬁlms of

submicron thickness scale [49].

Table 4.6 presents a qualitative summary of magnetic and magnetoelastic prop-

erties of YIG-based garnets similar to that given for the spinels in Table 4.5.Itis

appropriate to mention at this point that in all of the magnetic garnets and spinels,

magnetoelastic properties can be tailored by select ions identiﬁed previously. To re-

duce the negative anisotropy, very small amounts of Co

paired with a tetravalent

diamagnetic ion can be substituted. To offset the negative magnetostriction, Mn

ions can be substituted directly for Fe

. This subject will be discussed in Chap. 5.

Other ions of the lanthanide group can be used generously in the c sublattice to

form what amounts to a distinct set of ferrimagnetic compounds. Because the ionic

spins that are introduced to the c sublattice exchange couple to the iron in the d and

a sublattices, a wide variety of thermomagnetic, magnetoelastic, microwave, and

optical properties can be created in these rare-earth iron garnets.