6/4/2013

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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.

OED

Hysteresis Loop

Hysteresis ParametersSaturation Magnetization :    Ms, JsSaturation Remanence:     Mrs, JrsCoercivity:   HcCoercivity of Remanence:  HcrInitial Susceptibility:  k0

Dunlop and Özdemir, 2007

For (Dilute) Pure MaterialsComposition dependent: Mrs, Ms, k0 , Hc, HcrConcentration dependent: Mrs, Ms, k0Grain size/microstructure: Mrs/Ms, Mrs/k0, 

k0/Ms, Hc, Hcr, Hcr/Hc

For Magnetic MixturesIndividual parameters and ratios all varyaccording to component propertiesand relative proportions

For (Dilute) Pure MaterialsComposition dependent: Mrs, Ms, k0 , Hc, HcrConcentration dependent: Mrs, Ms, k0Grain size/microstructure: Mrs/Ms, Mrs/k0, k0/Ms, Hc, Hcr, Hcr/Hc

Dunlop and Ozdemir, 1997

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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.

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.

M

H

0 30 60 90 120 150 180

ener

gy g

radi

ent

ener

gy

theta

EanisoEhEtotdE/dtheta

0

0

phi=15°

Magnetite (Ms=480 kA/m) SD needles (Hk=240 kA/m = 302 mT), Bapp=160 mTM

H

Magnetite (Ms=480 kA/m) SD needles (Hk=240 kA/m = 302 mT), Bapp=160 mT

0 30 60 90 120 150 180

ener

gy g

radi

ent

ener

gy

theta

EanisoEhEtotdE/dtheta

00

phi=45°

M

H

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Angular dependence of switching fields for uniaxial SD particles (Stoner – Wohlfarth)

phi

M

H

s

uk M

KH

0

2

(a) H0 aligned with easy axis (φ=0)

Hc=Hk = (Nb-Na)MsMr/Ms=1.0

(b) H0 perpendicular to easy axis (φ=π/2)Reversible magnetizationMr/Ms=0, Hc=0i=Ms/HK

(c) for all φ (randomly oriented array of SD particles)

Mr/Ms=0.5Hc= 0.479 HK(φ=0) = 0.479 (Nb‐Na)Ms

Ha Ms

Ha

Ms

Dunlop and Ozdemir, 1997

Magnetization process in SD GrainsRotation of MomentsResponse of a random assemblage of uniaxial single domain (SD) particles during hysteresis cycle

Tauxe, 2008

Magnetization process in PSD GrainsNonuniform Magnetization States

flower state

vortex state

Dunlop and Ozdemir, 1997

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O’Reilly, 1984

Magnetization process in MD grain

Remanent state (Mr) is near zero with low Hc.Hysteresis Parameters for MD grains

Mr/Ms <0.1Hc(MD) << Hc(SD)

Wall translation Domain rotation Domain nucleation

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

SD/SP magnetite Small SP particles

(Housen, 1992)

shear zone mylonite

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Applied field [T]

M n

orm

aliz

ed

0

1

-1

-10 1

SD magnetite

fine hematite

‐1

0

1

‐1 0 1

M/Ms

Bapp [T]

‐1

0

1

‐1 0 1

M/Ms

Bapp [T]

‐1

0

1

‐1 0 1

M/Ms

Bapp [T]

‐1

0

1

‐1 0 1

M/Ms

Bapp [T]

SSD+SP (4 nm)

0% SP 25% SP 50% SP 100% SP

‐1

0

1

‐1 0 1

M/Ms

Bapp [T]

‐1

0

1

‐1 0 1

M/Ms

Bapp [T]

‐1

0

1

‐1 0 1

M/Ms

Bapp [T]

SSD+SP (8 nm)

‐1

0

1

‐1 0 1

M/Ms

Bapp [T]

0% SP 25% SP 50% SP 100% SP

MMfMp

09-27

Field [T]0

M [A

m2/

kg]

-26.0 x10 -25.0 x10 -24.0 x10 -23.0 x10 -22.0 x10 -21.0 x10

-17-1.0 x10 -2-1.0 x10 -2-2.0 x10 -2-3.0 x10 -2-4.0 x10 -2-5.0 x10 -2-6.0 x10

Unmixing Hysteresis Loops1. M(H)=Mf(H)+Mp(H)+Md(H)+Maf(H)=Mf(H)+Mlin(H)

Additional hysteresis measurements and parameters

-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

1

-1000 -800 -600 -400 -200 0 200 400 600 800 1000

M/Ms

Bapp (mT)

Stoner-Wohlfarth Modelrandomly-oriented

elongate uniaxial SD grains

M+(Bapp)

M-(Bapp)

Mrh(Bapp)

Mih(Bapp)

Bc

Mrs

Brh

Mrh(B): “remanent hystereticmagnetization” – irreversiblemagnetization changesBrh: median field of Mrh,~Bcr

Mih(B): “induced hystereticmagnetization” – reversiblemagnetization changes

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Unmixing Loops2. Coercivity classes

Additional hysteresis measurements and parameters

Msi(B): initial magnetization curvefrom saturation remanence

Et: transient energy dissipationEhys: hysteretic energy lossEt / Ehys : TED ratioMrh(B): remanent hysteretic curve=(M+(B)‐M‐(B))/2

Brh: Mrh median field 

Additional hysteresis measurements and parameters

“wasp‐waisted”: Ehys>(4MsBc),>0

“rectangular”: Ehys=(4MsBc),=0

“pot‐bellied”: Ehys<(4MsBc),<0

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M_initialM_loop_rawMfM_gridMrhMihMf_fitM_errMbf_dot

SJ059-vsm

Field [T]10-1

M [A

m2/

kg]

6.0e-2

5.0e-2

4.0e-2

3.0e-2

2.0e-2

1.0e-2

-1.0e-17

-1.0e-2

-2.0e-2

-3.0e-2

-4.0e-2

-5.0e-2

-6.0e-2

Sigma=0.64 (“wasp-waisted”)Backfield remanence and HCR in SD Grains

Tauxe, 2008

2. (Ms)

3. (Mrs)

5->1. DCD (Mr=0)

+ - +

HCR =0.524HK;Angular dependence ofswitching field forrandomly-orienteduniaxial SD grains(Stoner-Wohlfarth)

5

moment ODs

The “Day Plot”

TM0, TM20, TM40, TM60, with a range of grain sizes

“Day plot”:Grain size / domain state

“Squareness-coercivity plot”:Grain size / domain state, composition

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Day Plots: Behavior of mixtures

Theoretical Day Plots for Magnetite (Dunlop, 2002)

coercivity ratio Hcr/Hcbecomes large for mixtures of hard and soft materials(e.g., mgt-hmt, SP-SD)

for magnetite, SD-MD mixtures are indistinguishablefrom discrete PSD sizes

Day Plots: Behavior of mixtures

Theoretical Day Plots for Magnetite (Dunlop, 2002)

for TM60, SD-MD mixtures are quite differentfrom discrete PSD sizes

Day Plots: Behavior of mixtures

Theoretical Day Plots for Magnetite (Dunlop, 2002)

for TM60, SD-MD mixtures are quite differentfrom discrete PSD sizes

CS914.001

Field [T]10.90.80.70.60.50.40.30.20.10

mom

ent [

Am

2]

2.20e-52.00e-51.80e-51.60e-51.40e-51.20e-51.00e-58.00e-66.00e-64.00e-62.00e-6

-6.78e-21-2.00e-6-4.00e-6-6.00e-6-8.00e-6-1.00e-5-1.20e-5-1.40e-5-1.60e-5-1.80e-5-2.00e-5-2.20e-5

Magnetization [A

m2/kg]

1.6e-1

1.4e-1

1.2e-1

1.0e-1

8.0e-2

6.0e-2

4.0e-2

2.0e-2

-6.9e-18

-2.0e-2

-4.0e-2

-6.0e-2

-8.0e-2

-1.0e-1

-1.2e-1

-1.4e-1

-1.6e-1

satu

rate

d:M

(H)=

M+

HS

HF

appr

oach

to s

atur

atio

n:M

(H)=

M+

H+

HS

HF

irrev

ersi

ble

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Questions

• How can we tell if M is saturated?• What are the uncertainties in MS and HF?

tc04-01-000

3.80E-06

3.85E-06

3.90E-06

3.95E-06

4.00E-06

4.05E-06

0.70 0.75 0.80 0.85 0.90 0.95 1.00

Bapplied [T]

m [A

m2 ]

datalinear fitpoly fit

ms [nAm2] hf [nAm2/T] 3376±3 659±3 R2=0.996 3940 331 R2=0.999

M(H)=Ms(1-a/H-b/H2)+hfH

Analysis of Variance and F tests

sum‐squared deviations (variance) from best‐fit model

=  noise variance (pure error)+  misfit variance (model error)

F = (misfit variance)/(noise variance)= (total variance – noise variance)/(noise variance)

high values of F ‐> reject model

How do we calculate noise variance?

Inversion Symmetry through origin: M(H)=‐M(‐H)

Wright 5000 (3/4 micron magnetite)

-90

-75

-60

-45

-30

-15

0

15

30

45

60

75

90

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Bapp [T]

M [A

m2/

kg]

M(Bapp)

-M(-Bapp)

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Inversion Symmetry through origin: M(H) = -M(-H)

1. Quantify noise variance (“pure error”):i = Mi(Hi) – ( -M(-H))interpolated2=(i)2 / N

2. Quantify signal/noise ratio:m

2=(Mi)2 / Ns/n = m / Q=log10(s/n)

Wright 5000 (3/4 micron magnetite)

0

15

30

-0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0

Bapp [T]

M [A

m2/

kg]

M(Bapp)

-M(-Bapp)

synthetic ferrihydrite

2.6E-04

2.7E-04

2.8E-04

2.9E-04

3.0E-04

3.1E-04

3.2E-04

3.3E-04

1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5field [T]

M [A

m2/

kg]

measured M(H)inverted -M(-H)Linear (measured M(H))

F test for lack of fitFLF = (misfit variance)/

(“pure error” variance)= (Mfit,i – Mi)2/(M+

i – M‐inv,i)2

Fnl70~13000

B>0.98 Bmaxexcluded

Real and Imaginary Susceptibility

H(t)=H0cos(t)

in-phase (“real”):M’(t)=k’ H(t)= k’ H0cos(t)

out-of-phase (“imaginary” or“quadrature”):M”(t)= k” H0sin(t)

(conductivity, viscosity,hysteresis)

H, M

time

HM'M"Mtot

1. Applied FieldH( t) = Ho cos(t)

-1000 0 10000

0.001

0.002

0.003

0.004

0.005

0.006time t

H( t) , A/ m

3. M agnetic Response

-15000

-10000

-5000

0

5000

10000

15000

0 0.002 0.004 0.006time t

M , A/ m

AC Rayleigh Loops:Rayleigh Magnetization Law

2. Low-Field Hysteresis Behavior

-15000

-10000

-5000

0

5000

10000

15000

-1000 0 1000

M , A/ m

H, A/ m

RayleighLaw :

M= kH

Weak‐field hysteresis

M vs. H NonlinearIrreversible 

2 20 0 0( ) ( ) / 2M H H H H

0 0

0

0

0

0

43

434

3 (ln )

HH

H ddHd

d H

For H < 0/dM/dH = constant

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Low‐field hysteresis (Rayleigh) loop for basalt sampleJackson et al., 199

7

H = 1000 A/mB =0H = 1.26 mT

Dunlop and Özdemir. 1997

Synthetic TM spheres

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

0.1 1 10 100 1000 10000

HAC [A/m]

k [S

I]

TM0 k'TM0 k"TM05 k'TM05 k"TM28 k'TM28 k"TM41 k'TM41 k"TM55 k'TM55 k"

Amplitude Dependence of Susceptibility

TM0

TM55

TM41

TM28

TM05

synthetic TM spheres

Synthetic TM spheres

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.1 1 10 100 1000

HAC [A/m]

k [S

I]

TM0 k"TM05 k"TM28 k"TM41 k"TM55 k"

Rayleigh Relationship0

43 (ln )

dd H

Synthetic TM spheres

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.1 1 10 100 1000

HAC [A/m]

k [S

I]

TM0 k"TM0 dk'/dln(Ho)TM05 k"TM05 dk'/dln(Ho)TM28 k"TM28 dk'/dln(Ho)TM41 k"TM41 dk'/dln(Ho)TM55 k"TM55 dk'/dln(Ho)

Rayleigh Relationship0

43 (ln )

dd H

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For materials that undergo hysteresis in weak fields

1. Susceptibility increases with field amplitude

2. Out‐of‐phase susceptibility increases with field amplitude

MD TM above 100K,MD pyrrhotite above 34KMD hematite above 250K

hematite: 1000 micron, 100 Hzcourtesy of Gunther Kletetschka

0.00E+00

2.00E-06

4.00E-06

6.00E-06

8.00E-06

1.00E-05

1.20E-05

1.40E-05

1.60E-05

1.80E-05

0 50 100 150 200 250 300Temperature [K]

[m3 /k

g]

X' 16 A/mX" 16 A/mX' 24 A/mX" 24 A/mX' 80 A/mX" 80 A/mX' 160 A/mX" 160 A/mX' 240 A/mX" 240 A/m

pyrrhotite EOR

0.00E+00

5.00E-07

1.00E-06

1.50E-06

2.00E-06

2.50E-06

3.00E-06

3.50E-06

4.00E-06

0 50 100 150 200 250 300 350

Temperature [K]

[m3 /k

g]

k' 30 A/mk'' 30 A/mk' 100 A/mk'' 100 A/mk' 300 A/mk'' 300 A/mk' 1000 A/mk'' 1000 A/mk' 2000 A/mk'' 2000 A/m

Ikon magnetite 02

field [T]0.150.10.050-0.05-0.1-0.15

field [mT]0.150.10.050-0.05-0.1-0.15

Mag

netiz

atio

n [A

m2/

kg]

9.00e18.00e17.00e16.00e15.00e14.00e13.00e12.00e11.00e10.00e0

-1.00e1-2.00e1-3.00e1-4.00e1-5.00e1-6.00e1-7.00e1-8.00e1-9.00e1

mom

ent [Am2]

9.00e18.00e17.00e16.00e15.00e14.00e13.00e12.00e11.00e10.00e0-1.00e1-2.00e1-3.00e1-4.00e1-5.00e1-6.00e1-7.00e1-8.00e1-9.00e1

Ikon magnetite 02

Temperature [Kelvin]300.00250.00200.00150.00100.0050.00

Temperature [C]0-50-100-150-200-250

Bc[

mT]

3.803.603.403.203.002.802.602.402.202.001.801.601.401.201.000.800.600.40

Bc[T]

0.0040.0040.0030.0030.0030.0030.0030.0020.0020.0020.0020.0020.0010.0010.0010.0010.0010.000

TV~120K

TI~130K

Temperature-dependent hysteresis:phase changes, order-disorder transitions, blocking/unblocking

CS914.001

field [T]0.20.10-0.1-0.2-0.3

field [mT]0.20.10-0.1-0.2-0.3

Mag

netiz

atio

n [A

m2/

kg]

1.60e-11.40e-1

1.20e-11.00e-18.00e-26.00e-2

4.00e-22.00e-20.00e0

-2.00e-2-4.00e-2

-6.00e-2-8.00e-2-1.00e-1-1.20e-1

-1.40e-1-1.60e-1

mom

ent [Am

2]

1.60e-11.40e-1

1.20e-11.00e-18.00e-26.00e-2

4.00e-22.00e-20.00e0-2.00e-2-4.00e-2

-6.00e-2-8.00e-2-1.00e-1-1.20e-1

-1.40e-1-1.60e-1

CS914.001

Temperature [Kelvin]300.00250.00200.00150.00100.0050.00

Temperature [C]0-50-100-150-200-250

Bc[

mT]

55.00

50.00

45.00

40.00

35.00

30.00

25.00

20.00

15.00

10.00

5.00

Bc[T]

0.055

0.050

0.045

0.040

0.035

0.030

0.025

0.020

0.015

0.010

0.005

Temperature-dependent hysteresis:phase changes, order-disorder transitions, blocking/unblocking

MP101-9.6a

field [T]1.000.00-1.00

field [mT]1,5001,0005000-500-1,000-1,500

Mag

netiz

atio

n [A

m2/

kg]

4.00e03.50e0

3.00e02.50e02.00e01.50e0

1.00e05.00e-10.00e0

-5.00e-1-1.00e0

-1.50e0-2.00e0-2.50e0-3.00e0

-3.50e0-4.00e0

mom

ent [Am

2]

7.00e-5

6.00e-5

5.00e-5

4.00e-5

3.00e-5

2.00e-5

1.00e-5

0.00e0

-1.00e-5

-2.00e-5

-3.00e-5

-4.00e-5

-5.00e-5

-6.00e-5

-7.00e-5

MP101-9.6a

Temperature [Kelvin]900.00800.00700.00600.00500.00400.00300.00

Temperature [C]65060055050045040035030025020015010050

Ms[

Am

2/kg

]

4.0e03.8e03.6e03.4e03.2e03.0e02.8e02.6e02.4e02.2e02.0e01.8e01.6e01.4e01.2e01.0e0

8.0e-16.0e-14.0e-12.0e-10.0e0

ms[A

m2]

7.0e-5

6.5e-5

6.0e-5

5.5e-5

5.0e-5

4.5e-5

4.0e-5

3.5e-5

3.0e-5

2.5e-5

2.0e-5

1.5e-5

1.0e-5

5.0e-6

0.0e0

MP101-9.6a

Temperature [Kelvin]800.00700.00600.00500.00400.00300.00

Temperature [C]55050045040035030025020015010050

Bc[m

T]

6.00

5.50

5.00

4.50

4.00

3.50

3.00

2.50

2.00

1.50

1.00

0.50

0.00

Bc[T]

0.0140.012

0.010

0.0080.006

0.0040.002

0.000-0.002

-0.004

-0.006-0.008

-0.010-0.012

-0.014

-0.016

MP101-9.6a

Temperature [Kelvin]900.00800.00700.00600.00500.00400.00300.00

Temperature [C]65060055050045040035030025020015010050

Xhf

[m3/

kg]

1.80e-71.70e-71.60e-71.50e-71.40e-71.30e-71.20e-71.10e-71.00e-79.00e-88.00e-87.00e-86.00e-85.00e-84.00e-83.00e-82.00e-81.00e-80.00e0

-1.00e-8

Temperature-dependent hysteresis:phase changes, order-disorder transitions, blocking/unblocking

Tc

Tc Tb

6/4/2013

13

Thermal fluctuation tomography

hysteresis/backfield measurements over a range of T ‐> distribution of V, Hk (grain size and shape)

20

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

6/4/2013

14

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

6/4/2013

15

-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

6/4/2013

16

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)

6/4/2013

17

Egli, 2005 (Environmental Magnetism Workshop) http://www.irm.umn.edu/Misc/soils_case_study.pdf

Coercivity Deconvolution

Egli, 2004

Natural sediments

ARM/SIRMNon‐interacting SD > 1.5 mm/A

Magnetic Components

Cubo‐octahedral elongated

MTB

First-order reversal curve (FORC)

FORC distribution

Field [T]0.40.30.20.10-0.1-0.2-0.3-0.4

mom

ent [

Am

2]

1.0e-4

5.0e-5

0.0e0

-5.0e-5

-1.0e-4

-10x10-3

-5

0

5

10

Hu (T)

0.140.120.100.080.060.040.020.00

Hc (T)

100

50

0200150100500

100

50

0200150100500

Rev

ersa

l fie

ld M(Brev,Bmeas)

dM/dBmeas

Measurement field

FORC model: aligned uniaxial SDgrain(s), no bias, Bc=100 mT

Hu

(T)

6/4/2013

18

100

50

020 01 501 00500

Field [T]0.40.30.20.10-0.1-0.2-0.3-0.4

Field [mT]4003002001000-100-200-300-400

mom

ent [

Am

2]

1.0e-4

5.0e-5

0.0e0

-5.0e-5

-1.0e-4

-20x10-3

-10

0

10

20

Hu (T)

0.140.120.100.080.060.040.020.00

Hc (T)

100

50

020 01 501 00500

100

50

020 01 501 00500

Measurement field

Rev

ersa

l fie

ld

FORC model: aligned uniaxial SDgrain(s), 15 mT bias, Bc=100 mT

Hu

(T)

M(Brev,Bmeas)

dM/dBmeas

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.

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

6/4/2013

19

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

Wall translation Domain rotation Domain nucleation

Jiles, 1991

Magnetization curves from Stoner‐Wohlfarth Model for various angles between the direction of magnetic field and easy axis

Stoner‐Wohlfarth (ideal noninteracting uniaxial SD) FORC behavior

hysterons with small bias fields and a range of coercivity extending up to Hk