Magnetism Basics
Magneti sm 101 : All Ab out Spins
Jeffrey E. Shield
Department of Mechanical Engineering Nebraska Center for Materials and Nanoscience UiUniversit y of fNb Nebrask a Applications of Magnets
Hard (Permanent) Magnets Power generation (DC motors) Hybrid cars All-electric airplanes/ships Microsurgical tools Cordless power tools Wind generators Consumer Electronics Computers (Disk drive voice coil motors) Speakers Magnetic Resonance Imaging Soft Transformer cores Electromagnets Semi-hard Data storage The Markets
Soft Market Hard Market Magnets Share Magnets Share 1980 $1.89 B 70% $0.81 B 30%
1990 $2.69 B 57.4% $2.0 B 42.6%
2000 $3.55 B 44.2% $4.48 B 55.8%
2010 $5.0 B 28.7% $12.44 B 71.3%
th Source: Y. Luo, 18 Workshop on High Performance Magnets and Their Applications, Annecy, France, 2004 Magnetism Basics
Maggpnetism arises from electron spins • electrons rotate about nucleus, creating “magnetic moments” • Sometimes, all of the moments cancel each other, resulting in “diamagnetism” • Here, we will only worry about magnetic moments from at/toms/compoun dthtdtds that do not cance l • Specifically,
UNPAIRED INNER SHELL ELECTRONS Magnetism Basics
• Current (moving electric charge) causes magnetic field
Courtesy Todd Zimmerman Magnetism Basics
Electrons are “spinning” charges→Have magnetic field • Sometimes, all of the moments cancel each other, resulting in “diamagnetism” •Her e, w e will onl y w orr y about m agn eti c m om en ts fr om atom s/com poun ds that do not cancel • Specifically, UNPAIRED INNER SHELL ELECTRONS Courtesy Todd Zimmerman Magnetism Basics
N Atom with a magnetic moment Atom (transition metal, lanthanide, actinide) S
Transition metals
Lanthanides Actinides Magnetism Basics
Periodic array of atoms --“Crystal”
Magnetic moments point in random directions PARAMAGNETIC Magnetic moments align parallel FERROMAGNETIC
Magnetic moments align antiparallel ANTIFERROMAGNETIC
Structure has two magnetic species FERRIMAGNETIC Spontaneous Magnetization
Periodic array of atoms --“Crystal”
Magnetic moments point in random directions PARAMAGNETIC Magnetic moments align parallel FERROMAGNETIC
Magnetic moments align antiparallel ANTIFERROMAGNETIC
Structure has two magnetic species FERRIMAGNETIC Ferromagnetic Elements Paramagnets
M
H H M
H H M
H Ferromagnets
M ? But ferromagnets are not “spontaneously” magnetized H --Think about any steel—screwdriver, automobile body, etc. Flux lines Flux outside a magnet costs energy “Magnetostatic Energy” 2 Ems = ½NdMs Where Nd depends on the shape of the magnet Ferromagnets
The material “self divides” into “MAGNETIC DOMAINS ” --regions with spins pointing in a common direction
Flux lines Increase in magnetization due to domain growth
M
H Ferromagnets
Domain Walls: Thin and Thick
δ = domain wall width = π(A/K)1/2 A = exchange stiffness ~ 10-13 J/m K = Anisotropy constant = 103 – 107 J/m3 So δ ~ 0.1 – 100 nm Ferromagnets
Domain walls can be eliminated by reducing the size of the crystal --Competition between Magnetostatic energy (volume dependent) and domain wall energy (surface area)
γ = domain wall energy = 4(AK)1/2 2 Ems(single domain)= μoMs V/6
Ems(multidomain) = 0.5Ems(single domain) Ems(multidomain) = Edw
1/2 2 Resulting in, for a sphere, RSD = 36(AK) /μoMs
RSD ~ few nm to 1 μm Anisotropy
Anisotropy—Answers the question “How easy is it to rotate a spin away from its preferred direction?”
θ
From 1) Shape 2) Crystal (“Magnetocrystalline”) 3) Stress Shape Anisotropy
⌠ E = -μo H dM ms ⌡
2 Ems = (μo/2) NdM
Since Hd = - NdM is the self de-magnetizing field
M a θ c
2 2 2 Ems = (μo/2) [(Mcos θ) NcM +(Msin θ) Na]
2 2 2 Ems = (μo/2) [M Nc +(Na -Nc)M sin θ]
2 Ks = (μo/2) (Na -Nc)M
Na andNd Nc are dtiiftlddemagnetizing factors along a and c 4 3 When a = c (sphere), Ks = 0; Max Ks~10 J/m Magnetocrystalline Anisotropy
For cubic structures
2 2 2 2 2 2 2 2 2 E = Ko + K1(α1 α2 + α2 α3 + α1 α3 ) + K2(α1 α2 α3 )
Since Ko is angle-independent and K2 is small
2 2 2 2 2 2 E = K1(α1 α2 + α2 α3 + α1 α3 ) For uniaxial structures (hexagonal and tetragonal)
2 4 E = Ko + K1sin θ + K2sin θ
Since Ko is angle-independent and K2 is small
2 E = K1sin θ 3 7 3 K1 = 10 -10 J/m Magnetization
Easy axis M Easy axis Hard axis
H HA
HA = anisotropy field field necessary to saturate in the hard direction
HA = 2K/μοMs Anisotropy and Length Scales
LOW K (“SOFT” MAGNETS) Large domain wall width Small single domain limit
SSamall HA
HIGH K (“HARD MAGNETS”) Small domain wall width Large single domain limit
Large HA Magnetic Properties: Boring Definitions
Saturation Magnetization The maximum obtainable magnetization in a material in response to an applie d magne tic fie ld
Remanent Magnetization (Remanence—Mr)) The magnetization “remaining” in a material after the applied field has been removed
Coercivity (Hc) The magnetic field, applied in the opposite direction, 1 necessary to make the magnetization zero Remanence Anisotropy 0.5 The resistance of a magnetic moment Coercivity s M to point in an unfavorable direction // r 0 M -50 -40 -30 -20 -10 0 10 20 30 40 50 -0.5
-1 Applied Field (kOe) 21 “Hard” v. “Soft” Magnets
Coercivity This (arbitrarily) separates hard (high coercivity) and soft (low coercivity) magnetic materials
Hard 1
Hc > 2000 Oe 0.5
Soft s M // H < 100 Oe r 0
c M -50 -40 -30 -20 -10 0 10 20 30 40 50 -0.5
-1 Applied Field (kOe)
22 Hard (()gPermanent) Magnets
Energy Product The amount of energy stored in a permanent magnet, given by the largest rectangle that can fit in the second quadrant of a B-H graph
Defining property for most applications of permanent magnets
November 16, 2007 23 Full Hysteresis Loops
M Hysteresis loop of a uniililiaxial single- domain particle H along its easy axis
IDEAL LOOP!
Mr = Ms Hci = HA = 2K/μoMs
2 (BH)max = μoMs /4 Full Hysteresis Loops
But a real system has many single-domain particles AthtthdlitdAssume that these are randomly oriented with respect to their easy axis
Stoner-Wohlfarth Model
Mr = ½Ms Hci = 0.48HA
2 (BH)max = μoMs /16 Stoner-Wohlfarth Systems
• Dilute systems of nanocrystalline hard magnetic particles imbedded in a non -magnetic matrix approach the Stoner-Wohlfarth coercivity
Nd-Fe-B Er. Girt, K.M. Krishnan, G. Thomas, E. Girt and Z. Altounian, J. Magn. Magn. MtMater. 231, 219 (2001). FePt in C Yingfan Xu, M. L. Yan, J. Zhou, and D. J. Sellmyy,er, J. App l. Ph ys. 97, 10J320 (2005) 5 nm
FePt C “Real” Magnets
• In a real material, we want a high density of magnetic grains • But then, interactions take over!
•Hci << 0.48HA
•Two basic interactions: •Exchange Interactions--these are short-range 1/2 • lex = (A/K) Exchange-Spring Interactions
• Spins across interfaces influence each other ¾ Interaction length ½ ª lex~ (Α/Κ)
Interface Exchange-Spring Interactions
• Spins across interfaces influence each other ¾ Interaction length ½ ª lex~ (Α/Κ) • Near-interface regions thus have spins influenced by neighboring grains
Interface
lex Exchange-Bias Interactions
Interactions between a ferromagnetic (FM) and antiferromagnetic (AFM) phase
Interface FM Phase AFM Phase
H
The FM spins are “pinned” at the interface ⇒ A (()small) reverse field will not reverse the ferromag net “Real” Magnets
• •Two basic interactions: •Exchange Interactions--these are short-range 1/2 • lex = δ = π(A/K) •Dipolar Interactions--these are long-range and depend on strength of the dipole • ∝1/r3
The reversal looks kind of like:
Strong dipolar, weak exchange Strong dipolar, strong exchange Permanent Magnets
40 ) ee 30
20 vity Hc (kO Hc vity ii 10
Coerc 0 0246
%Additive y (C) Percent Cx in or Sm y 12Co88 32 “Real” Magnets
• Soft Magnetic Materials • Low Coercivity • desire strong interactions • Transformers, AC motors or flux-directors (e.g., write- heads)
•Hard Magnetic Materials (aka Permanent Magnets) • Hig h Coerc iv ity • Desire weaker interactions • DC motors, flux sources (()gMRI), magnetic recordin g Magnetic Materials: Summary
• Important Properties • CiitRCoercivity, Remanence, SttiESaturation, Energy PdtProduct • Important Parameters • Anisotropy • Important Length Scales
•RSD = single domain size ~ nanometers to microns • lex= exchange length ~ a few nanometers • δ = domain wall width ~ a few nanometers • Important Features • Microstructure/nanostructure
So what happens when Important Length Scales meet up with the scale of the Important Features Magnetic Materials: Practical Examples
Low K (soft) materials
Characteristics Low K •Large δ (()domain wall width)
•Small RSD
So,,yy relatively easy reduce microstructure/nanostructure scale so that these converge Nanocrystalline Materials
Hci ∝d6 ∝d-1
0 dsp lex
Grain Size Superparamagnetic Limit:
dsp ~ 25kT/K Nanocrystalline Materials
Grain Boundary Grain Boundary Reduction in Grain Size
lex
lex
Resulting in the anisotropy to be “averaged” over all possible orientations
“Random Anisotropy”—Lowers K (remember that Hc ∝ K)
Material Properties Typical Fe-Si alloys (widely used commercially)
Hc ~ 0.08 Oe Nanocrystalline Materials (Nanoperm or Finemet)
Hc ~ 0.006 Oe Magnetic Materials: Practical Examples
• High K (hard) materials + Low K (soft) materials o“Nanocomposite” magnets Exchange-Spring Interactions
Two-phase Mixtures of Hard and Soft Magnetic Phases • With no exchange coupling, the soft phase reverses easily in an applied magnetic field
Interface HdPhHard Phase SfPhSoft Phase Exchange-Spring Interactions
Two-phase Mixtures of Hard and Soft Magnetic Phases • With no exchange coupling, the soft phase reverses easily in an applied magnetic field Applied Field
Interface HdPhHard Phase SfPhSoft Phase Exchange-Spring Interactions
Two-phase Mixtures of Hard and Soft Magnetic Phases • With exchange coupling, spins within the interaction length remain aligned with the hard magnetic spins
Interface HdPhHard Phase SfPhSoft Phase Exchange-Spring Interactions
Two-phase Mixtures of Hard and Soft Magnetic Phases • With exchange coupling, spins within the interaction length remain aligned with the hard magnetic spins Applied Field Field
Interface HdPhHard Phase SfPhSoft Phase
lex Exchange-Spring Interactions
Two-phase Mixtures of Hard and Soft Magnetic Phases • By reducing the scale of the soft magnetic phase, we can eliminate uncoupled regions Applied Field ¾ improve remanence and coercivity Interface Interface
Hard Phase Soft Phase Hard Phase
2lex Completely coupled Nanocomposite Permanent Magnets
Combine best attributes of each material
Higgyh coercivity Higggh Magnetization Nanocomposite Permanent Magnet
Two-phase: (BH)max = 25 MGOe
Single phase: (BH)max = 12 MGOe Nanocomposite Permanent Magnets
HAADF STEM Image—shows High-Resolution TEM Image— atomic no. contrast Lines are drawn in to show grains Corroborated by x-ray miliicroanalysis
20 nm
5 nm
FePt Fe3Pt Magnetic Materials: Practical Examples
IfInformati on st orage t ech nol ogi es Computer Disk Drive Technology: History
1956—IBM RAMAC •5MB5 MB •0.08 Mb/in2 •$35,000 ($7,000/MB) 1980—First 1GB storage device •Refrigerator-sized (550 lbs.) •$40,000 ($40/MB) 1990—Density of 0.1 Gb/in2 1995—1 GB drive was $625 ($0.76/MB) 2000—20 GB drive was $217 ($0.0125/MB) 2009—Density of 329 Gb/in2 •$0.00014/MB Nanomagnets: Data Storage
How computers remember
Binary Numbers—numbers represented by 1’s and 0’s for example, 3=11, 29=11101 All characters are represented by numbers
Magnets are great to use to store information because they are “binary.”
How so? S N We magnetize different parts of our material in different directions →“”“save” S N We read the different regions as 1’s or 0’s “1” “0” →“open” Each “1” or “0” is a “bit” Nanomagnets: Data Storage
Recording Density: Right now, we can fit about 300 Gbits in a square inch → That’s 1011 little magnets per square inch!! → 500 million could fit on the head of a pin!
At 300 Gb/in2, each bit is approximately 2000 nm2 (they are actually rectangles)
11100 × × × 001 01 Grain (Individual crystal) × × Each bit contains about 20 grains Current Materials
Fundamental issues: SNR ~ 10 log N Need lots of small grains (but V decreases!) KV/k T Thermal Stability τ = 1 e B f0
Current material: Co-Cr-Pt Co w/Pt in solid solution is the magnetic phase Cr segregates to the grain boundaries to magnetically isolate grains
BUT: K ~10 5 J/m3
And KV/kBT must be ~60 for thermal stability
FIND NEW MATERIALS WITH HIGHER K! Nanomagnets: Patterned Media
The Holy Grail of information storage: 1Mk1. Make eac h gra in as sma ll as poss ible 2. Make the grains into a nice pattern 3. Make each grain a single bit The Ultimate in Data Storage
Bit A 6 nm x 6 nm bit would result in a recording density of 20 Tbit/in2 6 nm (20,000 Gbit/in2—or 50 times better than what we have now!) 6 nm Disk Drive Technology: Reading the Data
Another challenge is how we get information from the tiny magnets •“Read” the direction of magnetization
High-sensitivity sensors with high spatial resolution Exchange-bias Applications
Giant Magnetoresistance (GMR) Sensor
Ta Cap Ta FeMn AFM Layer FeMn Co FM Layer Co Cu Spacer Layer Cu NiFe FM layer NiFe Ta Buffer Layer Ta Si Substrate Si
External Field External Field Giant Magnetoresistance
FM Layer i Non-magnetic Layer i
FM Layer
Low Resistance High Resistance Peter Grünberg (Jülich Research Centre) and Albert Fert (University of Paris-Sud) shared the 2007 Nobel Prize in Physics Giant Magnetoresistance
Insulator
With an insulator, electrons now must “tunnel” through the barrier “Magnetic Tunnel Junction” (MTJ) Create “Tunneling MagnetoResistance (TMR) sensor
RhiResearch is: Developing new types of barriers Developing new types of electronic interactions Summary
Interestingggpp things happen when im portant ma gnetic length scales and the scale of the structure converge
Interesting things happen at interfaces between magnetic phases