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Chapter 11Magnetic Materials

11.1 3d metals and alloys

11.2 Intermetallic compounds

11.3 Interstitial compounds

11.4 Ferromagnetic oxides

11.5 Antiferromagnetic and ferrimagnetic oxides

11.6 Amorphous materials

11.7 Rare earths

11.8 Miscellaneous materials

Comments and corrections please: jcoey@tcd.ie

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Ubiquity of Oxides

Earth’s crust is composed almost entirely of oxides — rocks, economic minerals, water.

Composition in atomic %

Oxygen (O2-) is most abundantfollowed by silicon (Si4+) andaluminium (Al3+).

Crust is mostly composed ofaluminosilicates.

Iron (Fe2+/Fe3+) is mostabundant magnetic element. It is40 times as abundant as allother magnetic elementstogether.

Si4+O2-

Al3+

Fe

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Electronic configuration of 92% of the ions in the crust is the same 2p6 !

The 2p6 closed shell is very stable.

1s1 2.1H+

2p620.4Si4+

3p6 1.5K+

2p6 1.8Mg2+

3p6 1.9Ca2+

3d6/5 2.5Fe2+/3+

2p6 2.6Na+

2p6 6.0Al3+

2p660.7O2-

ConfigurationAbundance (at%)Ion

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Abundances of magnetic elements

Price scales roughly inversely with abundance. 1 atom in 40 in the crust is iron, and iron is about40 times as abundant as all other elements put together.

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Cobalt price fluctuations 1970 - 2006

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Metals. Metallic structures are more or less dense packed arrays. Z = 8 - 12. ABABAB (hcp) or

ADCADCADC (fcc)

Atomic radii: 3d atoms;r = 125 pm

4f atoms; r = 180 pm

Rare earth volume is 3x the 3d volume.

The 3d and 4f atoms form intermetallic compounds.

Oxides. Many oxide structures have structures based on dense-packed oxygen arrays (fcc or hcp)

with cations in the octahedral and sometimes in the tetrahedral interstices.

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Metals

Metals have densely-packed structures with high coordination number Z = 8 - 12: fcc,hcp, bcc …. The 3d metallic radii are ! 0.125 nm. 4f metallic radii are ! 0.180. i.e theirvolumes are 3 times greater.

177Dy128Cu

180Gd124Ni

180Sm125Co

182Nd126Fe

187La127Mn

181Y128Cr

r(pm)Metalr(pm)MetalMetals of the same size form disordered alloys(solid solutions)

Metals of quite different sizes may formintermetallic compounds of definite stoichiometry.

The 3d metals can accommodate small, lightelements (C, N) in interstitial sites.

71N

77C

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Co2+

Co0 Gd

Gd Co Gd Co

As metallic atoms, thetransition metals occupy onethird of the volume of therare earths. As ions theyoccupy less than one tenth.

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bcc fcc

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L20 FeCo L10 CoPt

1:1 Superstructures

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hcp ordered

1:1 Superstructures

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L12 Ni3Fe

3:1 Superstructures

DO3 Fe3Al

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C1 NiMnSb

Ternary Superstructures

L21 Co2MnSi

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Roct = (21/2 -1)rO = 58 pm Rtet = ((3/2)

1/2 - 1)rO = 0.32 pm

Oxides

Oxides are usuallyinsulating.Structures arebased on dense-packed O2- arrays,with cations ininterstitial sites.

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122Gd3+60Ni3+ 3d769Ni2+ 3d8

136La3+61 (56)Co3+ 3d675 (65)Co2+ 3d7

119Y3+64Fe3+ 3d578 (61)Fe2+ 3d6

149Pb2+65Mn3+ 3d483Mn2+ 3d552Fe3+ 3d5

161Ba2+62Cr3+ 3d342Al3+

144Sr2+64V3+ 3d253Mn4+ 3d360Zn2+

134Ca2+67Ti3+ 3d155Cr4+ 3d253Mg2+

pm12-foldsubstitutional

pm6-foldoctahedral

pm6-foldoctahedral

pm4-fold

tetrahedral

Cation radii in oxides: low spin values are in parentheses.

The radius of the O2- anion is 140 pm

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Iron Fe bcc; a0 = 287 pm

The most important ferromagnetic material.

Main constituent of the whole Earth, 5 wt % of crust.

Usually alloyed with 6 at% Si and fabricated in

300 µm rolled laminations (isotropic or grain

oriented), castings or reduced powder,

Mainly used in electrical machines (motors, transformers)and magnetic circuits.

Production 5 Mt/yr for magnetic purposes (8 B¤)

Js = 2.0 T (Si-Fe) Ms = 1.78 MA m-1 (Fe)

TC = 1044 K (Fe)

K1 = 48 kJ m-3 (Fe)

!s = -8 10-6

11.1 3d metals and alloys

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-5 0 -5 0 eV

3d- holes

bccfcc

Phases in iron; 0 TC Tm

fcc iron is a weak ferromagnet; fcc iron is nonmagnetic

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Fe65Co35 (Permendur) bcc; a0 = 286 pm

The ferromagnet with the highest polarization

Random bcc solid solution, sometimes alloyed with V.

Castings, reduced powder,

Spinodal nanostructure of acicular grains in a nonmagneticAl-Ni matrix in Alnicos

Used in for electromagnet pole pieces and in othermagnetic circuits, thin films, permanent magnets (Alnico)

Js = 2.45 T Ms = 1.95 MA m-1

K1 = 20 kJ m-3

TC = 1210 K

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Slater-Pauling Curve

Slope -1

m µB

Fe65Co35

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Permalloy Fe20Ni80 fcc; a0 = 324 pm

Multipurpose soft magnetic material, withnear-zero anisotropy and magnetostriction

Sometimes alloyed with Mo, Cu …

Sputtered or electrodeposited films, sheet,powder.

Uses: magnetic recording; write heads, readheads (AMR), magnetic shields, transformecores

Js = 1.0 T Ms = 0.8 MA m-1

K1 ! 2 kJ m-3 !s = 2 10

-6

TC = 843 K

Compositions near Fe50Ni50 have larger Js butgreater anisotropy

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The end-members of the solid solution Fe and Ni have opposite signs of magnetostriction!s and of magnetocrystallijne anisotropy K1c.

By good luck, they both cross zero close to the Ni80Fe20 composition. Hence permalloy isan ideal soft magnetic material. It is very easily magnetized to saturation, even in thin filmform (K1c ! 0), and it is practically insensitive to strain (!s ! 0). Very high permeability

(

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Cobalt Co hcp; a = 251 pm, c = 407 pm

Highest-TC ferromagnet, anisotropic,expensive ("50 /kg), strategic.

Useful alloying addition

Sputtered nanocrystalline thin films(with Cr, Pt, B additions) are used asmedia for hard discs

Js = 1.8 T Ms = 1.43 MA m-1

K1 = 530 kJ m-3

TC = 1388 K

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Magnetic ordering temperature of >2000 materials

"Fe2O3 Co

Highest Curie temperatureHighest Néel temperature

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Cobalt price fluctuations

1.3 Mt/yr

15 $/kg

Ni

55,000t/yr

50 $/kg

Co

1100 Mt/yr0.6$/kg

Fe

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Dysprosium Dy hcp; a = 359 pm, c = 565 pm

Dy3+ m = 10.6 µB per atom

(10 µB from the 4f10 6H15/2 term + 0.6

µB from the spin polarized 5d6s band)

Largest low-temperature magnetizationof any element Ms(0) = 2.4 MA m

-1

TN = 179 K (Helical structure)

TC = 89 K

11.2 Rare earths

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Samarium-cobalt SmCo5 hexagonal; a=499 pm c= 398 pm

Versatile, high-temperature permanent magnet.

Cellular intergrowth with Sm2Co17 in

Sm(Co, Fe, Zr, Cu)7.6 alloys provides

domain-wall pinning

Dense sinterered oriented material.

Uses: specialised electrical drives

Expensive (!150 ¤/kg)

Jr = 1.0 T (BH)max = 200 kJ/m3

K1 = 17 MJ m-3 Ba

= 30 T

TC = 1020 K

R-T exchange is direct, between the 5d and 3d shells

This is antiferromagnetic; on-site coupling of 5d and 4fspins is ferromagnetic, hence moments couple parallelfor light rare earths (J = L - S) and antiparallel for heavyrare earths (J = L + S).

Useful alloys are of Pr, Nd, Sm with Fe, Co, Ni

11.3 Intermetallic compounds

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Typical cellular precipitation structure

of Sm(Co0.71Fe0.14Cu0.13Zr0.02)8.3

Reversal mechanisms:

A Nucleation in the bulk

B Nucleation at a defect

C Pinning at extended defects

M

H

nucleation-type magne

pinning-type magnet

Hdepinning

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Neomax, Nd2Fe14B tetragonal; a = 879 pm, c = 1218 pm

The highest-performance permanent magnet.

Discovered in 1983 by Sagawa (sintered) and byCroat and Herbst (melt spun)

Dy, Co .. substitutions

Dense sinterered oriented material, melt-spunisotropic flakes.

Voice-coil actuators, spindle motors, nmr imaging,flux sources ….

Cost ! 30 ¤/kg, Production 10 kT/yr (1 B¤)

Jr = 1.4 T (BH)max = 200-400 kJ/m3

K1 = 4.9 MJ m-3 Ba

= 7.7 T

TC = 878 K

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O

Si

Al

Fe

Mg

Ca

K

Na

H

Others

Si4+ O2-

Al3+

Fe

Crustal abundances (top 9) All magnetic elements

Global production ~50,002/3 in China. Nd priceincreased from 8$ to 25$/in 2006

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All three magnets contain ! 70% Fe and store !0.4 J of energy in their stray field

Lodestone1724

Ferrite 1956

Nd-Fe-B 1975

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8 Gbit 1” drivefor cameras 160 Gbit 2.5” perpendicular drive for laptops

Spindle motor

Voice-coil actuator

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Fe4N fcc; a0 = 379 pm

An fcc structure stabilized by N in the body-centeposition.

TC = 767 K

m = 8.8 µB fu1 The moments on the two sites are

quite different; 2.98 µB on 1a and 2.01 µB on 3c.

Js = 1.8 T Ms = 1.5 MA m-1

K1 ! 2 kJ m-3 !s = 100 10

-6

This films of "”Fe16N2 with a structure between "Feand Fe4N were claimed to have a polarization of 3.2 Twith K1 ! 10000 kJ m

-3 , This exceeds themaximum moment per irom possible from the SlaterPauling curve, and has never been confirmed.

Supersaturated "Fe0.97N0.03 has much reduced K1 and

low magnetostriction in thin films.

11.4 Interstitial compounds

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CrO2 rutile; a = 442 pm, c = 292 pm

The only simple oxide that is a ferromagnetic metal,CrO2 is a black half-metal with a spin gap of about 0.5eV.

The compound is metastable, usually prepared by high-pressure synthesis

Acicular powder with 8:1 aspect ratio and l ! 300 nmhas Hc ! 50 kA/m; it is used as a particulate medium forvideo recording

Js = 0.49 T m0 = 2.0 µB/fu

TC = 396 K

#0 ! 3 µ$ cm

11.5 Ferromagnetic oxides

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• A magnetically-ordered metalwith a fully spin-polarisedconduction band

• P = (N% -N &)/ (N % +N &) = 100%

• Metallic for % electrons butsemiconducting for & electrons.Spin gap '& ! 1 eV.

• Integral spin moment 2 µ(

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EuO NaCl; a0 = 516 pm

A black insulator. When oxygen deficient it is metallicbelow TC and exhibits a metal insulator transition at TCwith colossal magnetoresistance.

Eu2+ is in a 8S term , 4f7. m0 = 2.0 µB/atom

Ferromagnetic Tc = 69 K. Heisenberg ferromagnet

M0 = 1.69 MA m-1

•

J1

J2

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NiO NaCl; a0 = 418 pm

A green Mott insulator.

Ni2+ is in a 3F term. m0 = 2.0 µB/atom

Antiferromagnetic TN = 525 K

Was used as an exchange bias layer in spin valves.

•

J1

J2

418

426

431

445

a0 (pm)

1

3/2

2

5/2

S

-85-50-13105253d8NiO

-21.5-6.9-3302913d7CoO

-8.2-7.8-5701983d6FeO

-3.5-7.2-6101173d5MnO

J2(K)J1(K))p (K)TN(K)

11.6 Antiferromagnetic and ferrimagnetic oxides

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Magnetite, Fe3O4 spinel; a0 = 839 pm

Most common magnetic mineral, source of rockmagnetism, main constituent of lodestones..

A ferrimagnet. with Fe2+ and Fe3+ disordered on B -sitesabove the Verwey transition at Tv = 120 K, orderedbelow; A-B superexchange is the main magnetic inter-action

[Fe3+]tett {Fe2+ Fe3+}oct O4

& % % -5 µB + 4 µB +5 µB = 4 µB

A half-metal. Fe(B); & electrons hop in a t2g band

Used as toner, and in ferrofluids.

Potential for spin electronics..

Js = 0.6 T m0 = 4.0 µB / fu

K1 = -13 kJ m-3 !s = 40 10

-6

TC = 843 K

[A]{B2}O4

AB

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Magnetite is the prototype for afamily of spinel ferrites, whichincludes Ni-Zn ferrite for rfapplications and *Fe2O3 i.e. [Fe]{Fe5/3!1/3}O4 for magnetic recording.

4s

3d

2p

% &

EF

'%Eµ

heavy electrons

Fe3O4 B-sites The B sites are populated by a mixture ofFe3+(3d5) and Fe2 +(3d6) ions. At RT the t2g&

electrons hop in a narrow polaron band.Resistivity is ! 50 µ$ m.

At the Verwey transition TV = 119 K, theinteratomic Coulomb interactions lead tocharge ordering – ‘Wigner crystallization’Resistivity increases by 100x. Symmetry isreduced to monoclinic; details of charge orderare still controversial

JAB = -28 K JAA = -18 K JBB = +3 K

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Maghemite, *Fe2O3 spinel; a0 = 834 pm

Ferrimagnet with disordered B-site vacancies:

[Fe3+]{Fe3+1.67!0.33}O4Often Co surface-doped for increased

anisotropy.

Metastable acicular or equiaxed powder.

Particulate recording media; ferrofluids

Js = 0.49 T m0 = 3.3µB / fu

K1 = -3 kJ m-3

TC ! 1020 K,

but it reverts to "Fe2O3 around 800 K

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Magnetite Fe3O4 Maghemite *Fe2O3

[Fe3+]{Fe2+ Fe3+}O4 [Fe3+]{Fe3+5/3

!1/3}O4

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Hematite, Fe2O3 corundum; a = 504 pm, c = 1375 pm

Most common iron oxide mineral.

hcp oxygen array with Fe3+ in 2/3 of octahedralinterstices..

Red insulator with localized d electrons.

3d5 6A1 state.

Antiferromagnetic, but sublattices are

slightly canted above the Morin

transition by D-M interaction

TN = 960 K.

J1 = 6.0 K, J2 = 1.6K

J3 = -29.7 K, J4 = -23.2 K.

Js = 2.8 10=3 T m0 = 0.002 µB / fu

K1 = 23 kJ m-3 Ba = 2µ0K1/Js = 20 T

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% &

4s

3d5 6A1

2p

'&

"Fe2O3

Ar room temperature there is a weakferromagnetic moment caused by canting of thesublattice magnetizations by the Dzialoshinski-Moria (D-M) interaction HDM = D.Si x Si .

Below 260 K there is a spin reorientation tothe c-axis. D is then zero by symmetry, and the

weak interaction disappears.

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What causes the spin reorientation ?

The spin direction is set by competing cf and dipoledipole interactions, which vary as and 2

respectively. Bdip = µ0/4#[3(m.r)r/r5 - m/r3]

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"FeOOH; Goethite Goethite; a = 995 pm ,b = 301 pm c =462 pm

A brown antiferromagnetic insulator named forGoethe!

The magnetic structure consists of double zig-zagchains ordered antiferromagnetically

TN ! 460 K.

The main constituent of rust,

also found in tropical soils.

Often superparamagnetic

when well crystallized.

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BaFe12O19; Hexaferrite magnetoplumbite; a = 589 pm c = 2319 pm

An hcp lattice of oxygen and Ba, with iron inoctahedral (12k, 4f2 , 2a) tetrahedral (4f1) and trigonalbipyramidal (2b) sites.

Brown ferrimagnetic insulator. All magnetic ions areFe3+. Also SrFe12O19 and La/Co substitution.

Structure is 12k%2a%2b%4f1&4f2&

TC = 740 K.

Low-cost permanent magnet, the first magnet tobreak the ‘shape barrier’. 98% of all permanentmagnets by mass are Ba or Sr ferrite. Found on everyfridge door and in innumerable catches, dc motors,microwave magnetrons, …

80g manufactured per year for everyone on earth

Js = 0.48 T . K1 = 450 kJ m-3

. Ba = 1.7 T

m0 = 20 µB / fu

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What is the source of the anisotropy ?

Fe3+ is an S-state ion.

The 2b site has noncubic symmetry, and the cf mixes anexcited term 4G (t2

4e) into the ground state.

Hcf = DSz2

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Jr (BH)max

(T) (kJ/m3)

Intrinsic (crystal) 0.48 [46]

Oriented sintered 0.41 34

Isotropic sintered 0.23 9

Oriented bonded 0.30 16

Isotropic bonded 0.13 5

Polarization and energy product ofdifferent forms of BaFe12O19

Sintered magnets

Bonded magnets

Ferrite magnets are made from powderplatelets, with a particle size of about 2 µm.

The powder may be sintered or bonded inplastic or rubber

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Y2Fe5O12; YIG Garnet; a0 = 1238 pm,

A synthetic garnet, with iron in tetrahedral (24d) andoctahedral (16a) sites. The Y and O form a ! close-packed array..

YIG – Yttrium Iron Garnet is a green ferrimagneticinsulator.The magnetic structure is e24d %, 16a&

TC =560 K

Js = 0.18 T m0 = 5.0 µB/fu

YIG is an insulator with excellent high-frequencymagnetic properties., and a very narrowferromagnetic resonance linewidth. It is used formicrowave components.

Also useful as a magneto-optic material when dopedwith Bi

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Compensation points in rare-earth garnets. The R moment for heavy rare earths isweakly coupled, antiparallel to the net iron moment. It falls rapidly with temperature.

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11.7 Amorphous and miscellaneous materials

a-FeF3

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a-Gd0.27 Co0.75

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Compensation point in a-GdCo3

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a-FeF3

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Magnetic semiconductors

We would like a ferromagnetic semiconductor which could be used at roomtemperature and doped p or n type. This would be ideal for spin electronics, butsuch a material does not yet exist!

0.2860Fe3O4

1.4392CrO2Half Metals

16628Ni

121380Co

201044Fe

48-Au

44-CuMetals

180000-Bi

2000-GraphiteSemimetals

10170(GaMn)As

8000-GaAs

30000-InSb

1400-SiSemiconductors

Mobility (cm2V-1s-1)Curie Point (K)

% &

cb5d/6s

vb

EF

Magnetic semiconductors; n-typeMagnetic semiconductors; n-type

Spin-polarized conduction band; n-type S!c Example EuO

Eu 4f7

Magnetic semiconductors; p-typeMagnetic semiconductors; p-type

b)% &

cb

vb

EF

Spin-polarized valence band; p-type S!v Example (Ga1-xMnx)As

Mn 3d5

Spin-split impurity bandSpin-split impurity band

Spin-polarized impurity band S"i

c) % &

cb

vb

EFib

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Ordered diamond structure

Mn2+ d5 e2t3

TC for 5% Mn is 160 K

Moment is 4µB/Mn

3d5% + 4p hole&

Jsd = 0.2 eV

Jpd = 2.0 eV

Antisite defects pin EF

(GaMn)As Zinc blende; a = 566 pm

4s

3d5 6A1

4p

1.4 eV

0.1 eV

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SG P63mc O (1/3,2/3,3/8); Zn (1/3,2/3,0)

A structure of corner-sharing tetrahedra;

4 - 4 coordination..

Zn- O, 4 bonds, 0.204 nmZn-O-Zn 6 bonds 109°, 6 bonds 110°

Band gap 3.3 eV

Impurity configurations.

Mn2+ d5 e2t3 Fe2+ d6 e3t3 (J-T); Co2+ d7 e4t3

Zincite, ZnO wurstite; a = 335 pm, c = 523 pm

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Magnetic ordering temperature of >2000 materials

"Fe2O3 Co

Highest Curie temperatureHighest Néel temperature

ZnO doped with a few percent, 1 - 5% of Co, Fe, V … is reported to beferromagnetic with Tc > 300 K.

This contradicts everything we know about magnetism in oxides!