6/4/2013 1 Rock-Magnetic Experimentation, Data Analysis and Sample Characterization Thermomagnetic methods: M(T meas , T trt , t…) in fixed field •M S (T meas ) - mineral composition and concentration, independent of grain size, microstructures… • k(T meas , f, Hac,…) – composition, grain size… •M R (T meas ) for different initial remanent states – history-dependent behavior, wide range of experiments possible •M R (T trt, H) - TRM acquisition, thermal demagnetization Isothermal methods: M(H meas , H trt , t…) at constant T • M(H meas ) – hysteresis, FORC analysis •M R (H trt ) – IRM, ARM acquisition, AF demagnetization, coercivity spectrum analysis Composite methods: field- and temperature-dependent M Thermal fluctuation tomography: f(V,H k ) for SP/SSD populations hysteresis, n. Etymology: < Greek ὑστέρησις a coming short, deficiency, < ὑστερεῖν to be behind, come late, etc., < ὕστερος late. A phenomenon observed in some physical systems, by which changes in a property (e.g. magnetization, or length) lag behind changes in an agent on which they depend (e.g. magnetizing force, or stress); any dependence of the value of a property on the past history of the system to which it pertains. 1881 Proc. Royal Soc. 33 22 The change of polarisation lags behind the change of torsion. To this action‥the author [J. A. Ewing] now gives the name Hysteresis. OED Hysteresis Loop Hysteresis Parameters Saturation Magnetization : M s ,J s Saturation Remanence: M rs, J rs Coercivity: H c Coercivity of Remanence: H cr Initial Susceptibility: k 0 Dunlop and Özdemir, 2007 For (Dilute) Pure Materials Composition dependent: M rs ,M s ,k 0 ,H c ,H cr Concentration dependent: M rs ,M s ,k 0 Grain size/microstructure: M rs /M s ,M rs /k 0 , k 0 /Ms, H c ,H cr, H cr /H c For Magnetic Mixtures Individual parameters and ratios all vary according to component properties and relative proportions For (Dilute) Pure Materials Composition dependent: M rs ,M s ,k 0 ,H c ,H cr Concentration dependent: M rs ,M s ,k 0 Grain size/microstructure: M rs /M s ,M rs /k 0 ,k 0 /Ms, H c ,H cr, H cr /H c Dunlop and Ozdemir, 1997
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Rock-Magnetic Experimentation, Data Analysis and Sample Characterization
Thermomagnetic methods: M(Tmeas, Ttrt, t…) in fixed field• MS(Tmeas) - mineral composition and concentration, independent of grain size, microstructures…• k(Tmeas, f, Hac,…) – composition, grain size…• MR(Tmeas) for different initial remanent states – history-dependent behavior, wide range of experiments possible• MR(Ttrt, H) - TRM acquisition, thermal demagnetization
Isothermal methods: M(Hmeas, Htrt, t…) at constant T• M(Hmeas) – hysteresis, FORC analysis• MR(Htrt) – IRM, ARM acquisition, AF demagnetization, coercivity spectrum analysis
Composite methods: field- and temperature-dependent MThermal fluctuation tomography: f(V,Hk) for SP/SSD populations
hysteresis, n.Etymology: < Greek ὑστέρησις a coming short, deficiency, < ὑστερεῖν to be behind, come late, etc., < ὕστερος late.
A phenomenon observed in some physical systems, by which changes in a property (e.g. magnetization, or length) lag behind changes in an agent on which they depend (e.g. magnetizing force, or stress); any dependence of the value of a property on the past history of the system to which it pertains.1881 Proc. Royal Soc. 33 22 The change of polarisation lags behind the change of torsion. To this action‥the author [J. A. Ewing] now gives the name Hysteresis.
v=volumeMs=saturation magnetizationKu=anisotropy constantH0=applied field
Stoner-Wohlfarth Model (1948)
Non-interacting particlesCoherent rotation without thermal effectsUniaxial anisotropy
Total magnetic energy of particle consists of field interaction energy (EH) and the uniaxial shape anisotropy energy (Ea)
aH EEE ),(
0 02
v cos( )
vsinH s
a u
E M H
E K
2
021 )( sabu MNNK
Stoner EC and Wohlfarth EP (1948) A mechanism of magnetic hysteresis in heterogeneous alloys. Philosophical Transactions of the Royal Society of London A 240: 599–642.
Hysteresis in Single Domain Particles
v=volumeMs=saturation magnetizationKu=anisotropy constantH0=applied field
Stoner-Wohlfarth Model (1948)
Non-interacting particlesCoherent rotation without thermal effectsUniaxial anisotropy
Total magnetic energy of particle consists of field interaction energy (EH) and the uniaxial shape anisotropy energy (Ea)
aH EEE ),(
0 02
v cos( )
vsinH s
a u
E M H
E K
2
021 )( sabu MNNK
Stoner EC and Wohlfarth EP (1948) A mechanism of magnetic hysteresis in heterogeneous alloys. Philosophical Transactions of the Royal Society of London A 240: 599–642.
Nucleation, displacement, denucleation of DW with changing field
Wall Energy is a function of position in a crystal due to the crystal defects
Demagnetizing field is strong enough to drive walls backs towards M~0
a) Demagnetized stateb) In the presence of a saturating
field, c) Field lowered to +3 mTd) Remanent state, e) back field of -3
mT,
Inset shows detail of domain walls moving by small increments called Barkhausen jumps.
(Domain wall observations from Halgedahl and Fuller, J. Geophys. Res., 88, 6505-6522, 1983)
Magnetization process in MD grainsTranslation of domain walls
Taux
e, 2
008
Halgedahl, S. Bitter patterns vs. hysteresis behavior in small particles of hematite.JGR, 100, 353-364. 1995
Single grain of Hematite
Barkhausen jumps
Single grain of TM60
Room temperature saturation remanence (Mrs) and Coercivity (Hc) as a function of grain size for magnetite (Dunlop and Özdemir 2007)
Rather than the rather abrupt decrease at the SD threshold predicted theoretically,gradual decreases in properties are observed over several decades of grain diameter
Magnetite hysteresisproperties: f(d)
Distorted Loops
Mixtures of Magnetic PhasesComposition and Grain Size
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ (Tauxe et al. 1996) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐
Magnetite + Hematite SD/SP magnetite Large SP particles
hysteresis/backfield measurements over a range of T ‐> distribution of V, Hk (grain size and shape)
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0 0( ) ( ) (1 / ( ))( , , , , ) exp
2S K K
S KVM T H T H H TV M H T H
kT
( ) ( ) ( )K b a SH T N N M T For shape anisotropy:
->0 as V->0, Ms->0, Hk->0, and/or H0->Hk
20
0 0( ) (1 / ( ))( , , , , ) exp
2( ) K KS
S KV H T H H TV H T M TH
kM
T
)( ( () )K b Sa TH N N MT For shape anisotropy:
Relaxation time is governed by:
* Intrinsic Mineral PropertiesMS(T)
00
2
0( ) ( ) (1 / ( ))( , , , , ) exp
2S K K
S KVM HT T H TT HV M H
kH
T
( ) ( ) ( )K b a S TH N N MT For shape anisotropy:
Relaxation time is governed by:
* Intrinsic Mineral PropertiesMS(T)
* Experimental/Natural ConditionsH0, T
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20
0 0( ) ( ) (1 / ( ))( , , , , ) exp
2S K K
S KM T H T H H TM H T H
kTVV
(( ()) )b aK SH TN NT MFor shape anisotropy:
Relaxation time is governed by:
* Intrinsic Mineral PropertiesMS(T)
* Experimental/Natural ConditionsH0, T
* Grain CharacteristicsV, shape (Nb-Na)
for >m: stable SD, blockedfor <m: SP, unblocked
STABLE Blocked
SUPERPARA-MAGNETIC Unblocked
T T T1 3 4
Tempe
rature
or tim
e
H(t,h,T)
Coercivity (HK)
volume
for H0=0, blocking contoursare curves of constant VHk
for H0>0, blocking contoursshift to right
-25
-24
-23
-22
-21
0 0.05 0.1 0.15 0.2
0Hk0 [T]
Log 1
0(V
[m3 ])
-1-0.8-0.6-0.4-0.2
00.20.40.60.8
1
0 50 100 150 200
DC backfield [mT]
M/M
0
DC demagnetizationof IRM (constant T=T1)
Blocking countours (H,T1)
0( , )KArea
M f V H dA -25
-24
-23
-22
-21
0 0.05 0.1 0.15 0.2
-1-0.8-0.6-0.4-0.2
00.20.40.60.8
1
0 50 100 150 200
DC backfield [mT]
M/M
00Hk0 [T]
Log 1
0(V
[m3 ])
DC demagnetizationof IRM (constant T=T1)
Blocking countours (H,T1)
0( , )KArea
M f V H dA
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-25
-24
-23
-22
-21
0 0.05 0.1 0.15 0.2
0Hk0 [T]
Log 1
0(V
[m3 ])
-1-0.8-0.6-0.4-0.2
00.20.40.60.8
1
0 50 100 150 200
DC backfield [mT]
M/M
0
DC demagnetizationof IRM (constant T=T1)
Blocking countours (H,T1)
0( , )KArea
M f V H dA 0.0
2.0
4.0
6.0
8.0
10.0
0.00 0.05 0.10 0.15 0.20
DC backfield [T]
dm/d
H [a
rb]
r
CS91410-300K, T = 10º
H = 5 mT
0
-25
-24
-23
-22
-21
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Log 1
0(V
[m3 ])
0Hk0 [T]
-2.6e+01
-2.5e+01
-2.4e+01
-2.3e+01
-2.2e+01
-2.1e+01
0.00 0.10 0.20 0.30 0.40 0.50 0.60mu0Hk0 [T]
log1
0(V
[m3]
)
100 nm
CS914
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1.0e+00
1.5e+00
2.0e+00
2.5e+00
3.0e+00
0.00 0.20 0.40 0.60 0.80 1.00width/length
log1
0(le
ngth
[nm
])
-2.6e+01
-2.5e+01
-2.4e+01
-2.3e+01
-2.2e+01
-2.1e+01
0.00 0.10 0.20 0.30 0.40 0.50 0.60mu0Hk0 [T]
log1
0(V
[m3]
)
100 nm
CS914
Rock-Magnetic Experimentation, Data Analysis and Sample Characterization
Thermomagnetic methods: M(Tmeas, Ttrt, t, ,…) in fixed field• MS(Tmeas) - mineral composition and concentration, independent of grain size, microstructures…• k(Tmeas, f, Hac,…) – composition, grain size…• MR(Tmeas) for different initial remanent states – history-dependent behavior, wide range of experiments possible• MR(Ttrt, H) - TRM acquisition, thermal demagnetization
Isothermal methods: M(Hmeas, Htrt, t, ,…) at constant T• M(Hmeas) – hysteresis, FORC analysis• MR(Htrt) – IRM, ARM acquisition, AF demagnetization, coercivity spectrum analysis
Composite methods: field- and temperature-dependent MThermal fluctuation tomography: f(V,Hk) for SP/SSD populations
Coercivity Component Analysis of Remanent Magnetization Curves
[Egli, MAG‐MIX, 2005]
Different phasesDifferent grain sizesDifferent anisotropiesDifferent sources
dM/dlog(H)
Decomposition of IRM acquisition/demagnetization curves into several components with the use of model functions (e.g. , log‐Gaussian coercivity distributions)
Magnetic hysteresis of real samples can be represented as the superposition of a large number of elemental “hysterons” – square loops which each have a coercivity (half width) and bias field.
Each point in the FORC/Preisach space has a specific coercivity and bias, and the FORC/Preisach function represents the relative number or strength of hysterons with those characteristics.
field
mom
ent
Positive bias(loop shifted to right)
field
mom
ent
Negative bias(loop shifted to left),Same coercivity
field
mom
ent
Sum of two hysteronswith equal and opposite bias,same coercivity
mom
ent
field
mom
ent
field
mom
ent
field
zero biasLow coercivity
zero biasHigher coercivity
Sum of two hysteronswith zero bias,different coercivity
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FORC Analysis / Preisach Theory
Magnetic hysteresis of real samples can be represented as the superposition of a large number of elemental “hysterons” – square loops which each have a coercivity (half width) and bias field.
Each point in the FORC/Preisach space has a specific coercivity and bias, and the FORC/Preisach function represents the relative number or strength of hysterons with those characteristics.
O’Reilly, 1984
Magnetization process in MD grain
MD FORC distribution: lots of hysterons with low coercivity and a wide range of positive and negative bias fields