ElectromagneticsElectromagnetics(ENGR 367)(ENGR 367)
Magnetic Materials & Magnetic Materials & MagnetizationMagnetization
IntroductionIntroduction
►Question: Why do some materials Question: Why do some materials respond respond to magnetic fields, while to magnetic fields, while others do not?others do not?
►Answer: Magnetic materials have a Answer: Magnetic materials have a property known as Magnetization property known as Magnetization
as as quantified in the relative quantified in the relative permeability permeability constant (constant (rr).).
Description of Magnetic Material Description of Magnetic Material PropertiesProperties
►For accurate quantitative prediction: For accurate quantitative prediction: Quantum Theory is requiredQuantum Theory is required
►For qualitative description: For qualitative description:
Orbital Mechanics Model sufficesOrbital Mechanics Model suffices
Orbital Mechanics ModelOrbital Mechanics Model
► AtomAtom has electrons that has electrons that orbit around its nucleus orbit around its nucleus making a miniature making a miniature current loop that results current loop that results in an in an orbital magnetic orbital magnetic momentmoment
► Electron spins around Electron spins around its own axis to produce its own axis to produce a significant a significant spin spin magnetic momentmagnetic moment
Orbital Mechanics ModelOrbital Mechanics Model► The relative contribution of the magnetic The relative contribution of the magnetic
moments of each atom and the molecular moments of each atom and the molecular makeup of a material classifies it asmakeup of a material classifies it as DiamagneticDiamagnetic ParamagneticParamagnetic FerromagneticFerromagnetic AntiferromagneticAntiferromagnetic FerrimagneticFerrimagnetic SuperparamagneticSuperparamagnetic
► Any atom with a magnetic moment in the Any atom with a magnetic moment in the presence of an applied magnetic field will presence of an applied magnetic field will experience a torque that tends to align itexperience a torque that tends to align it
DomainDomain►Definition:Definition:
a a regionregion within a ferromagnetic within a ferromagnetic material material having a having a large dipole momentlarge dipole moment due to due to collections of associated atoms collections of associated atoms with with uncompensated spin momentsuncompensated spin moments
► Shape, size & direction of moment: Shape, size & direction of moment:
varies between neighboring regions varies between neighboring regions within a within a crudecrude sample that cancels the sample that cancels the effect overalleffect overall
See also magnetic dipole moments and domains of ferromagnetic materials as illustrated in Fig. 3.36 WW pp. 139, 140.
Alignment of Magnetic Alignment of Magnetic DomainsDomains
► Alignment: Alignment: may be achieved by an applied magnetic may be achieved by an applied magnetic
fieldfield► Upon removal of the external magnetic field, Upon removal of the external magnetic field,
domains do not all return to their original state domains do not all return to their original state and thus exhibit a magnetic history known and thus exhibit a magnetic history known
as as hysteresishysteresis (an interesting & practical effect (an interesting & practical effect unique to ferromagnetic materials)unique to ferromagnetic materials)
► Examples: Ferromagnetic elements & compoundsExamples: Ferromagnetic elements & compounds
Fe, Ni, Co, BiMn, CuMnSnFe, Ni, Co, BiMn, CuMnSn, etc., etc.
See also nonlinear Magnetization curve in Fig. 3.37 WW p. 141
Other Examples Other Examples of Magnetic Materials Each Classof Magnetic Materials Each ClassClass of Magnetic MaterialClass of Magnetic Material Ex’s: Elements & Ex’s: Elements &
CompoundsCompounds
DiamagneticDiamagnetic Bi, H, He, NaCl, Au, Cu, Si, Bi, H, He, NaCl, Au, Cu, Si, GeGe, etc., etc.
ParamagneticParamagnetic K, O, etc.K, O, etc.
AntiferromagneticAntiferromagnetic MnO, NiO, FeS, CoClMnO, NiO, FeS, CoCl22, etc., etc.
FerrimagneticFerrimagnetic FeFe33OO44 (iron oxide (iron oxide magnetite),magnetite),
NiFeNiFe22OO44 (nickel ferrite), (nickel ferrite), etc.etc.
SuperparamagneticSuperparamagnetic Ferromagnetic particles in Ferromagnetic particles in a nonferromagnetic a nonferromagnetic matrixmatrix
Qualitative Summary Qualitative Summary of Magnetic Material Properties of Magnetic Material Properties
ClassClass mmorborbvsvs. . mmspinspin BBintint vs. vs. BBapplappl
CommentsComments
Dia-Dia- mmorb orb = -= -mmspinspin << weak weak effecteffect
Para-Para- mmorborb++mmspin spin smallsmall
>> weak weak effecteffect
Antiferro-Antiferro- <<<< int. canc.int. canc.
Ferro-Ferro- <<<< >>>> Domains!Domains!
Ferri-Ferri- <<<< >> High High resist.resist.
SuperparaSuperpara--
<<<< >> MatrixMatrix
Applications of Magnetic Applications of Magnetic MaterialsMaterials
► Ferromagnetic Materials: Permanent Ferromagnetic Materials: Permanent Magnets, Magnetic Data Storage, Magnets, Magnetic Data Storage,
etc.etc.
► Ferrimagnetic Materials: Ferrites commonly Ferrimagnetic Materials: Ferrites commonly used used for transformer and/or toroid cores for transformer and/or toroid cores due to due to their higher resistance that reduces their higher resistance that reduces eddy eddy currents that cause ohmic losscurrents that cause ohmic loss
► Superparamagnetic: used to create recording Superparamagnetic: used to create recording tape tape for audio or video applicationfor audio or video application
Magnetization QuantifiedMagnetization Quantified► Approach: define Amperian (bound) currentApproach: define Amperian (bound) current
1)1) Associated with bound charges of electrons in atoms Associated with bound charges of electrons in atoms locked into lattice structure of a materiallocked into lattice structure of a material
2)2) Magnetic dipole moment of each individual chargeMagnetic dipole moment of each individual charge
3)3) For n dipoles per unit volumeFor n dipoles per unit volume
4)4) Magnetization: magnetic dipole moment per unitMagnetization: magnetic dipole moment per unit vol.vol.
2[A m ]i bm I dS
2
1
[A m ]n
total ii
m m
V
0
1lim ( ) [A/m]totalM m
V V
Bound versus Free Current Bound versus Free Current Forms of A.C.L.Forms of A.C.L.
►Mathematic Expressions:Mathematic Expressions:
BoundBound versus versus FreeFree
►Note: Note:
IIbb depends on the number and alignment of depends on the number and alignment of the miniature magnetic dipoles along the the miniature magnetic dipoles along the closed pathclosed path
[A]
where bound current
b
b
I M dL
I
[A]
where free current
I H dL
I
Bound & Free Currents Bound & Free Currents CombinedCombined
► Total CurrentTotal Current
► Free CurrentFree Current
►General Relation for General Relation for BB versus versus HH
0( total)=(bound)+(free) (since H=B/ in free space)
0( / ) (A.C.L.)T bI I I B dL
0
0 0
( / )
( / ) / [A/m]
T bI I I B dL M dL
I B M dL H B M
0 ( ) [A/m]B H M
Linear Isotropic Magnetic MediaLinear Isotropic Magnetic Media(e.g., paramagnetic, (e.g., paramagnetic,
diamagnetic)diamagnetic)►MagnetizationMagnetization
►Magnetic Flux Magnetic Flux DensityDensity
0
0 0
0
( )
( ) (1 )m m
r
B H M
H H H
H H
where magnetic susceptibility [unitless constant]m
m
M H
0
where 1
relative permeability
and permeability [H/m]
r m
r
Nonlinear & Anisotropic Nonlinear & Anisotropic MaterialsMaterials
(e.g., ferromagnetic)(e.g., ferromagnetic)► If magnetization (If magnetization (MM) responds nonlinearly to ) responds nonlinearly to
an an imposed magnetic field (imposed magnetic field (HH) such ) such as for a as for a ferromagnetic polycrystalline ferromagnetic polycrystalline materialmaterial relationrelation still applies, but. . .still applies, but. . . the parameters the parameters mm and and rr will not be constant will not be constant
material properties since material properties since HH vs. vs. MM is nonlinear is nonlinear
► If linear and homogeneous, but anisotropic If linear and homogeneous, but anisotropic as for as for a ferromagnetic single crystal a ferromagnetic single crystal thenthen
0 ( )B H M
[ ] where [ ] is a 3 3 matrixxx xy xz
yx yy yx
zx zy zz
B H
Example of Magnetization Example of Magnetization CalculationCalculation
►Exercise 3 (D9.6, Hayt & Buck, 7/e,Exercise 3 (D9.6, Hayt & Buck, 7/e, p. p. 281):281): FindFind:: GivenGiven::
a)a)
?M
5
5
70
1.8 10 H/m and 120 A/m
here we have ( 1)
1.8 10 H/mwhere 14.3
4 10 H/m
(13.3)(120 A/m) 1600 A/m
m r
r
H
M H H
M
Example of Magnetization Example of Magnetization CalculationCalculation
►Exercise 3 (continued)Exercise 3 (continued) FindFind:: GivenGiven::
b)b)
?M
28 3
27 2
28 27
22 and 8.3 10 atoms/m
where 4.5 10 A m /atom
so here we have
(8.3 10 )(4.5 10 ) 374 A/m
r
i
i
n
m
M nm
Example of Magnetization Example of Magnetization CalculationCalculation
►Exercise 3 (continued)Exercise 3 (continued) FindFind:: GivenGiven::
c)c)
?M
0 0
6
-70
300 T and 15
where we have (1 )
(15)(300 10 T)so
(1 ) (16)(4 10 H/m)
224 A/m
m
r m
mm
m
B
B B BH
BM H
M
SummarySummary
►Forces on moving charge in a magnetic Forces on moving charge in a magnetic field field may result inmay result in Forces on current carrying conductorsForces on current carrying conductors Torques on current loopsTorques on current loops
►Magnetization results from miniature Magnetization results from miniature bound bound current loops of electrons withcurrent loops of electrons with Orbital magnetic momentsOrbital magnetic moments Spin magnetic momentsSpin magnetic moments
SummarySummary
► Different classes of materials exist, some Different classes of materials exist, some have have weaker and some stronger weaker and some stronger magnetic effectsmagnetic effects
► The permeability constant (The permeability constant () indicates the ) indicates the magnetization and magnetic effects of a magnetization and magnetic effects of a linear, linear, isotropic materialisotropic material
► Some ferromagnetic materials have practical Some ferromagnetic materials have practical nonlinear or anisotropic effectsnonlinear or anisotropic effects
► Applications of magnetic materials include: Applications of magnetic materials include: permanent magnets, data storage, motors, permanent magnets, data storage, motors, generators, transformer/toroid cores, etc.generators, transformer/toroid cores, etc.
ReferencesReferences
►Hayt & Buck, Hayt & Buck, Engineering Engineering ElectromagneticsElectromagnetics, 7th edition, McGraw , 7th edition, McGraw Hill: New York, 2006.Hill: New York, 2006.
►Wentworth, Wentworth, Fundamentals of Fundamentals of Electromagnetics with Engineering Electromagnetics with Engineering ApplicationsApplications, John Wiley & Sons: 2005. , John Wiley & Sons: 2005.
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