ATOMIC ORIGINS OF MAGNETISM

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ATOMIC ORIGINS OF MAGNETISM ELECTRICITY AND
MAGNETISM ARE TIED TOGETHER. ELECTRIC FIELD OR
ELECTRICITY OCCURS SPONTANEOUSLY FROM ELECTRONIC
CHARGES. MAGNETIC FIELD OR MAGNETISM IS A RESULT
OF MOVING CHARGES. FROM AN ATOMIC VIEW OF
MATTER, WE HAVE ORBITAL MOTION OF THE
ELECTRON, SPIN MOTION OF THE ELECTRON. THESE TWO
ELECTRON MOTIONS ARE THE SOURCE OF MACROSCOPIC
MAGNETIC PHENOMENA IN MATERIALS.
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MAGNETIC VARIABLES MAGNETIC FIELD STRENGTH
(INTENSITY) IS REPRESENTED BY H (FIELD THAT
RESULTS SOLELY FROM FREE CURRENT). MAGNETIC
MOMENT PER VOLUME IS MEASURED BY M
(MAGNETIZATION). M RESULTS FROM THE TWO ATOMIC
MOTIONS ORBITAL AND SPIN MOTION OF THE
ELECTRON. B H 4pM (CGS)
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MAGNETIC SUSCEPTIBILITY AND PERMEABILITY THE
MOST COMMON MAGNETIC EXPERIMENT IS TO APPLY A
MAGNETIC FIELD TO A MATERIAL AND MEASURE THE
MAGNETIZATION INDUCED BY THE FIELD. SUSCEPTIBILT
Y k M/H PERMEABILITY m
B/H m 1 4 p k
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MAGNETIC MATERIALS FERROMAGNETISM
INTERACTION IS STRONGLY ATTRACTIVE TOWARD A
MAGNETIC POLE, PARAMAGNETISM INTERACTION IS
WEAKLY ATTRACTIVE, DIAMAGNETISM INTERACTION
IS WEAKLY REPULSIVE.
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MAGNETIC DOMAINS AN ORDINARY PIECE OF IRON BELOW
ITS CURIE TEMPERATURE YIELDS A MACROSCOPIC TOTAL
MOMENT. HOW IS IT THAT THIS PIECE OF IRON HAS NO
MAGENTIC MOMENT? A MACROSCOPIC MAGNETIC MATERIAL
WILL BREAK UP INTO DOMAINS. AN OPTIMAL WALL
THICKNESS l (kTc / Ka)1/2 WITH A SURFACE
ENERGY OF g (kTcK / a)1/2 a - THE LATTICE
SPACING, l - A FEW TENS OF
NANOMETER, g - 1 erg / cm2.
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HYSTERESIS WHEN A FERROMAGNETIC MATERIAL IS
MAGNETIZED BY AN INCREASING APPLIED FIELD AND
THEN THE FIELD IS DECREASED, THE MAGNETIZATION
DOES NOT FOLLOW THE INITIAL MAGNETIZATION CURVE
OBTAINED DURING THE INCREASE. THIS
IRREVERSIBILITY IS CALLED HYSTERESIS (DUE TO
INTERNAL FRICTION). PERMANENT MAGNETS (SUCH AS
REFRIGERATOR MAGNETS) REQUIRE LARGE Ms, Mr, AND
Hc. HARD MAGNETS - Hc gt 100 Oe (MOTORS,
GENERATORS), SOFT MAGENTS - Hc lt 10 Oe
(TRANSFORMER CORES, ELECTRONIC
CIRCUITS)
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THE INITIAL MAGNETIZATION CURVE MAY BE DIVIDED
INTO TWO REGIMES RAYLEIGH LAW REGIME,
MAGNETIZATION ROTATION. THE LOW-FIELD BEHAVIOR
OF THE INITIAL MAGNETIZATION IS GIVEN BY THE
RAYLEIGH LAW, µ µo nH (B µH) WHERE µo AND
n ARE THE RAYLEIGH CONSTANTS OF THE MATERIAL 30
lt µo lt 105 0.5 lt n lt 1.2 x 107 AND B µoH
nH2 HENCE THE PARABOLIC NATURE OF M VS. H AT LOW
H.
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THE BARKHAUSEN EFFECT IS DUE TO THE DOMAIN WALLS
STICKING AT INCLUSIONS AS THEY ATTEMPT TO MOVE
WITH CHANGING H. AT LARGE FIELDS, M(H) Ms (1 -
a / H)
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SMALL PARTICLE MAGNETISM (1 µm OR
LESS) MAGNETISM OF SMALL FERROMAGNETIC PARTICLES
IS DOMINATED BY TWO KEY FEATURES - THERE IS
SIZE UPPER LIMIT FOR SINGLE DOMAIN, - THERMAL
ENERGY CAN DECOUPLE THE MAGNETIZATION FROM THE
PARTICLE ITSELF TO GIVE RISE TO THE PHENOMENON OF
SUPERPARAMAGNETISM. TWO CRITICAL SIZES ARISE
FROM IT - SINGLE DOMAIN SIZE, - SUPERPARAM
AGNETIC SIZE.
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SINGLE-DOMAIN PARTICLES OF SIZE D
(DIAMETER) THE ENERGY COST OF DOMAIN FORMATION
EXCEEDS THE BENEFITS FROM DECREASING THE
MAGNETOSTATIC ENERGY. THE MAGNETOSTATIC ENERGY
Ms2D3 THE TOTAL DOMAIN WALL ENERGY gD2 SINGLE
DOMAIN SIZE Ds g / Ms2
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COERCIVITY OF SINGLE-DOMAIN PARTICLES MAGNETIZATI
ON REVERSAL IN SINGLE-DOMAIN PARTICLES OCCUR VIA
ROTATION. IT PRODUCES A LARGE COERCIVITY IN
COMPARISON TO MULTIDOMAIN SYSTEM. MAGNETIZATION
CAN ROTATE BY COHERENT MOTION OF THE ATOMIC
SPINS, BUT OTHER MOTIONS FANNING AND CURLING
CAN OCCUR. THE RESPONSE OF Ms TO AN APPLIED FIELD
IS HINDERED BY THE ANISOTROPY (CRYSTALLINE,
SHAPE, STRESS) Ea K sin2q THE APPLIED FIELD
SUPPLIES A POTENTIAL ENERGY OF Ef - Ms H THE
EQUILIBRIUM DIRECTION OF Ms RESULTS FROM THE
MINIMUM OF THE TOTAL ENERGY ETOTAL Ea Ef.
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CONSIDER THE SITUATION IN WHICH THE APPLIED FIELD
IS PERPENDICULAR TO THE EASY AXIS. THEN
ETOTAL - MsH sinq k
sin2q sinq MsH / 2K ETOTALMI
N - (MsH)2 / 2K (MsH)2 / 4K -
(MsH)2 / 4K AND Hc (2K) /
Ms COERCIVITY
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THE TWO CASES WE HAVE CONSIDERED REPRESENT
EXTREMES OF THE POSSIBLE HYSTERESIS CURVES,
TOTALLY CLOSED (NO HYSTERESIS) AND TOTALLY OPEN
(SQUARE). VERY OFTEN WHEN DEALING WITH
NANOPARTICLES, THE EASY AXIS ARE RANDOMLY
ORIENTED. THE HYSTERESIS CURVE IS AN AVERAGE
OVER ALL ORIENTATION. SOURCE OF THE ANISOTROPY
K CRYSTALLINE ANISOTROPY, SHAPE,
STRESS, SURFACE
ANISOTROPY. SHAPE ANISOTROPY FOR NANOPARTICLES
IS VERY LARGE EVEN FOR MODEST SHAPE RATIOS, c / a.
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IT IS EASIER TO INDUCE A MAGNETIZATION ALONG A
LONG DIRECTION OF A NONSPHERICAL NANOPARTICLE
THAN ALONG A SHORT SINCE THE DEMAGNETIZING FIELD
IS LESS IN THE LONG DIRECTION. FOR A PROLATE
SPHEROID WITH MAJOR AXIS c GREATER THAN THE
OTHER TWO AND EQUAL AXES OF LENGTH a, THE SHAPE
ANISOTROPY IS Ks (1/2) (Na Nc) Ms2 WHERE Nc
2Na 4p SPHERE - Na Nc, Ks
0 PROLATE SPHEROID (c gtgt a) - Nc 0, Na 2p,
Ks 2p Ms2 THUS A LONG ROD OF IRON WITH Ms
1714 emu / cm2 WOULD HAVE A SHAPE ANISOTROPY
CONSTANT OF Ks 1.85 x 107 erg / cm3 THIS IS
SIGNIFICANTLY GREATER THAN CRYSTAL ANISOTROPY.
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THE TOTAL MAGNETIZATION OF A FERROMAGNET Ms WILL
PREFER TO LIE ALONG A SPECIAL DIRECTION CALLED
THE EASY AXIS. THE ENERGY ASSOCIATED WITH THIS
ALIGNMENT IS CALLED THE ANISOTROPY ENERGY Ea K
sin2q THERE ARE SEVERAL REASONS THAT ANISOTROPY
MAY OCCUR STRESS OR SHAPE (INDUCED) AND
MAGENTOCRYSTALLINE ANISOTROPY (INTRINSIC).
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MAGNETOCRYSTALLINE ANISOTROPY THE EASE OF
OBTAINING SATURATION MAGNETIZATION IS DIFFERENT
FOR DIFFERENT CRYSTALLOGRAPHIC DIRECTIONS. AN
EXAMPLE IS A SINGLE CRYSTAL OF IRON FOR WHICH Ms
IS MOST EASILY OBTAINED IN THE 100 DIRECTION,
THEN LESS EASY FOR THE 110 DIRECTION, AND MOST
DIFFICULT FOR THE 111 DIRECTIONS. THE 100
DIRECTION IS CALLED THE EASY DIRECTION WHICH IS
IN THE DIRECTION OF SPONTANEOUS MAGNETIZATION
WHEN BELOW Tc. FOR A UNIAXIAL MATERIAL WITH ONLY
K1, IT CAN BE SHOWN THAT THE FIELD NECESSARY TO
ROTATE THE MAGNETIZATION 90 AWAY FROM THE EASY
AXIS IS H 2K1 / Ms
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THE PHYSICAL ORIGIN OF THE MAGNETOCRYSTALLINE
ANISOTROPY IS THE COUPLING OF THE ELECTRON
SPINS, TO THE ELECTRON ORBIT, WHICH IN TURN ARE
COUPLED TO THE LATTICE.
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FANNING MAGNETIZATION REVERSAL BY THE FANNING
MECHANISM IS RELEVANT IN CHAINS OF NANOPARTICLES
OR HIGHLY ELONGATED NANOPARTICLES. IN A CHAIN THE
Ms VECTOR OF EACH NANOPARTICLE INTERACTS WITH ITS
NEIGHBORS VIA THE MAGNETIC DIPOLAR
INTERACTION. THUS THE DIPOLES LINE UP, NORTH TO
SOUTH, AND LIKE TO REMAIN IN ALIGNMENT, HENCE
CAUSING AN ANISOTROPY EVEN IF NO OTHERS
EXIST. THIS IS CALLED AN INTERACTION
ANISOTROPY. THE INCOHERENT REALIGNMENT IS CALLED
FANNING. FANNING REVERSAL LEADS TO A SQUARE
HYSTERESIS LOOP. THE Hc IS ONE-THIRD AS LARGE AS
FOR A COHERENT REVERSAL Hc (FANNING) p Ms / 6
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CURLING IF THE ATOMIC SPINS ARE ALWAYS
PERPENDICULAR TO A RADIUS VECTOR IN THE XY-PLANE,
THIS IS CALLED CURLING. INFINITELY LONG
NANOPARTICLES NO MAGNETOSTATIC ENERGY IS
INVOLVED. THE REVERSAL VIA CURLING TAKES
PLACE. FINITE NANOPARTICLES THE EXCHANGE
INTERACTION IS MORE EFFECTIVE IN RESISTING THE
REVERSAL, HENCE THE SMALL PARTICLES REVERSE
COHERENTLY. THE CROSSOVER BETWEEN CURLING AND
COHERENT ROTATION OCCURS AT ROUGHLY 15 nm FOR
IRON NANOPARTICLES.
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SUPERPARAMAGNETISM A LARGE TOTAL MOMENT IS BOUND
RIGIDLY TO THE PARTICLE BELOW THE CURIE
TEMPERATURE BY ONE OR MORE OF THE VARIETY OF
ANISOTROPIES. THE ENERGY OF THIS BOND IS KV.
WITH DECREASING PARTICLE SIZE, KV DECREASES UNTIL
THE THERMAL ENERGY kT CAN DISRUPT BONDING OF THE
TOTAL MOMENT TO THE PARTICLE. THEN THIS MOMENT IS
FREE TO MOVE AND RESPOND TO AN APPLIED FIELD
INDEPENDENT OF THE PARTICLE. µp Ms V AN APPLIED
FIELD WOULD TEND TO ALIGN THIS GIANT MOMENT (OR
SUPERMOMENT) BUT kT WOULD FIGHT THE ALIGNMENT
JUST AS IT DOES IN A PARAMAGNET.
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SUPERPARAMAGNETISM HAS TWO KEY QUALITIES - LACK
OF HYSTERESIS, - UNIVERSAL CURVE OF M VS. H /
T. THE ANISOTROPY ENERGY KV REPRESENTS AN
ENERGY BARRIER TO THE TOTAL SPIN REORIENTATION
HENCE THE PROBABILITY FOR JUMPING THIS BARRIER IS
exp(-KV / kT) THE TIMESCALE FOR A SUCCESSFUL
JUMP IS t to exp(-KV / kT) WHERE to - ATTEMPT
TIMESCALE 10-9 s. IF Ms REVERSES AT TIMES
SHORTER THAN THE EXPERIMENTAL TIMESCALES (10 s lt
t lt 100 s), THE SYSTEM APPEARS SUPERPARAMAGNETIC.
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THE CRITICAL VOLUME Vsp 25 kT / K BY USING t
100 s AND to 10-9 s. E.G. Co - Dsp 7.6
nm (Ds 70 nm) Fe - Dsp 16 nm AT 300
K. TB KV / 25k, BLOCKING TEMPERATURE T lt TB -
FREE MOVEMENT OF µp MsV IS BLOCKED BY THE
ANISOTROPY T gt TB - SYSTEM APPEARS
SUPERPARAMAGNETIC
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THE COERCIVITY OF SMALL PARTICLES AT LARGE SIZE,
THE PARTICLES HAVE MANY DOMAINS, THUS
MAGNETIZATION REVERSAL IS DOMINATED BY DOMAIN
WALL MOTION, WHICH IS RELATIVELY EASY, HENCE THE
COERCIVITY IS LOW. HOWEVER, AS PARTICLE SIZE
DECREASES, THE COERCIVITY IS FOUND EMPIRICALLY TO
FOLLOW Hc a (b / D) UNTIL SINGLE DOMAIN IS
REACHED. THE LARGEST COERCIVITIES OCCUR AT THE
SINGLE-DOMAIN SIZE. BELOW THIS, Hc FALLS OFF DUE
TO THERMAL ACTIVATION OVER THE ANISOTROPY
BARRIERS, LEADING TO Hc (2K / Ms) 1 - (Dsp /
D)3/2 AND SUPERPARAMAGNETISM AT THE
SUPERPARAMAGNETIC SIZE FOR WHICH Hc 0.
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MAGNETORESISTANCE THE CHANGE IN RESISTANCE R
OF A MATERIAL UNDER AN APPLIED MAGNETIC FIELD H
IS KNOWN AS MAGNETO-RESISTANCE. (Dr / r) R(H)
R(0) / R(0) KELVIN EXAMINED THE RESISTANCE OF
AN IRON SAMPLE. HE FOUND 0.2 INCREASE IN THE
RESISTANCE FOR LONGITUDINAL FIELD, 0.4 DECREASE
IN THE RESISTANCE FOR TRANSVERSE FIELD.
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GIANT AND COLOSSAL MAGNETORESISTANCE GIANT
MAGNETORESISTANCE WAS DISCOVERED IN MATERIALS
FABRICATED BY DEPOSITING ON A SUBSTRATE ALTERNATE
LAYERS OF NANOMETER THICKNESS OF A FERROMAGNETIC
MATERIAL AND A NONFERROMAGNETIC METAL. THE
ELECTRON SCATTERING DEPENDS ON THE ORIENTATION OF
THE ELECTRON SPIN WITH RESPECT TO THE DIRECTION
OF MAGNETIZATION
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THE MAGNETORESISTANCE EFFECT IN THESE LAYERED
MATERIALS IS A SENSITIVE DETECTOR OF DC MAGNETIC
FIELDS AND ALREADY USED AS READING HEAD FOR
MAGNETIC DISKS (MAGNETIC STORAGE DEVICES OR
SENSING ELEMENTS IN MAGNETOMETERS). MATERIALS
MADE OF SINGLE-DOMAIN FERROMAGNETIC NANOPARTICLES
WITH RANDOMLY ORIENTED MAGNETIZATIONS EMBEDDED IN
A NONMAGNETIC MATRIX DISPLAY GIANT
MAGNETORESISTANCE. MIXED VALENCE SYSTEM
EXHIBITS VERY LARGE (COLOSSAL) MAGNETORESISTIVE
EFFECTS. La0.67Ca0.33Mn Ox DISPLAYS MORE THAN A
THOUSANDFOLD CHANGE IN RESISTANCE WITH 6-T DC
MAGNETIC FIELD.
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NANOCARBON FERROMAGNETS IRON AND COBALT
NANOPARTICLES ARE NECESSARY FOR THE NUCLEATION
AND GROWTH OF CARBON NANOTUBES. NANOTUBE GROWTH
INVOLVES TWO IRON NANOPARTICLES. A SMALL IRON
PARTICLE SERVES AS A NUCLEUS AND A LARGER
PARTICLE ENHANCES THE GROWTH. THE CORECIVE
FIELD INCREASES THREE TIMES WHEN TEMPERATURE IS
REDUCED TO 4.2 K.
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