chapter 11 magnetic materials€¦ · chapter 11 magnetic materials 11.1 3d metals and alloys 11.2...
TRANSCRIPT
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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: [email protected]
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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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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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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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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
(<50,000) and very low coercivity (1 A m-1) are possible.
Permalloy also has useful AMR, ! 3%
Slater-Pauling Curve
Slope -1m µB
Ni80Fe20
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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 + 0.6µB 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$/in 2006
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All three magnets contain ! 70% Fe and store !0.4 J of energy in their stray field
Lodestone1724
Ferrite 1956
Nd-Fe-B 1975
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8 Gbit 1” drivefor cameras 160 Gbit 2.5” perpendicular drive for laptops
Spindle motor
Voice-coil actuator
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Fe4N fcc; a0 = 379 pm
An fcc structure stabilized by N in the body-centeposition.
TC = 767 K
m = 8.8 µB fu1 The moments on the two sites are
quite different; 2.98 µB on 1a and 2.01 µB on 3c.
Js = 1.8 T Ms = 1.5 MA m-1
K1 ! 2 kJ m-3 !s = 100 10-6
This films of "”Fe16N2 with a structure between "Feand Fe4N were claimed to have a polarization of 3.2 Twith K1 ! 10000 kJ m-3 , This exceeds themaximum moment per irom possible from the SlaterPauling curve, and has never been confirmed.
Supersaturated "Fe0.97N0.03 has much reduced K1 andlow magnetostriction in thin films.
11.4 Interstitial compounds
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CrO2 rutile; a = 442 pm, c = 292 pm
The only simple oxide that is a ferromagnetic metal,CrO2 is a black half-metal with a spin gap of about 0.5eV.
The compound is metastable, usually prepared by high-pressure synthesis
Acicular powder with 8:1 aspect ratio and l ! 300 nmhas Hc ! 50 kA/m; it is used as a particulate medium forvideo recording
Js = 0.49 T m0 = 2.0 µB/fu
TC = 396 K
#0 ! 3 µ$ 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 TC
with 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}O4
Often 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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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 <Sz
2> and <Sz>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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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
EF
ib
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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