CARPATH ESM 2009 - Timisoara 2 - Magnetism

9/8/2009

1

ESM 2009 - Timisoara 1CARPATH

Alexandru STANCU

Professor, Director CARPATH

“Alexandru Ioan Cuza” University, Faculty of Physics, Department of Physics &Centre for Applied Research in Physics and Advanced TecHnologies (CARPATH)

Iasi, ROMANIA

“Alexandru Ioan Cuza” UNIVERSITY

IASI - ROMANIA

Centre for Applied Research in Physics and Advanced Technologies

Center of Excellence in Scientific Research (2006-2011) of The Romanian National Commission for Scientific Research in Universities

Preisach model of hysteresis in magnetic materials and FORC based identification techniques

European School on Magnetism 2009:Models in magnetism : from basic aspects to practical uses

September 1-10th 2009, Timisoara, Romania


Outline

Introduction – about hysteresisScalar Preisach modelFORC identification techniqueExamples – ferromagnetic systemsHysteretic processes in spin-transition materialsConclusions

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2


Which hysteresis model we choose in a given situation ?

How we choose ?Criteria ? To simulate correctly high order magnetization curves ?Identification methodologies …In many papers the identification is made using an arbitrary selection of

magnetization processes. Is it OK?

Can we use for identification only the Major Hysteresis Loop ?


Identical MHL for essentially different systems

-20000 -10000 0 10000 20000

-1.0

-0.5

0.0

0.5

1.0

Nor

mal

ized

mom

ent

Applied field

-20000 -15000 -10000 -5000 0 5000 10000 15000 20000-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

Hα

Hβ

-1.00E-10

2.94E-9

5.98E-9

9.02E-9

1.21E-8

1.51E-8

1.81E-8

2.12E-8

2.42E-8

2.73E-8

3.03E-8-20000 -15000 -10000 -5000 0 5000 10000 15000 20000

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

Hα

Hβ

-1.00E-10

2.95E-9

6.00E-9

9.05E-9

1.21E-8

1.52E-8

1.82E-8

2.13E-8

2.43E-8

2.74E-8

3.04E-8

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To understand … Preisach model

m0/m0s

H

+1

–1

A(Hα,0)B(Hβ,0)

Hc

S(Hs,0)

IHiI

F. Preisach 1935M.A. Krasnoselskii & A.V. Pokrovskii 1983, 1989I.D. Mayergoyz 1986

Ps

H0

x

y

z

ϕ0

ϕ

θθ0

Stoner Wohlfarth model


Preisach plane

T(Hα1,Hβ1)

Hα

Hβ

M(Hα1,Hβ1)

m0/m0s

H

+1

–1

A(Hα1,0)B(Hβ1,0)

O

T0(Hm,–Hm)

M(Hα1,Hβ1)

M0(Hm,−Hm)

Q

Q0

P

P0

P(Hα,Hβ)

Hα

Hβ Hc0

O

hs

hchi

hc=const.

hi=const.

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MHL

Hα

Hβ

O

Q0

P0

+

–

M0

L(t)

Hα

Hβ

O

Q0

P0

+

–

M0

H

-Hm

Hm

Hα

Hβ

O

Q0

P0

+ –

M0

H

-Hm

Hm

-3000 -2000 -1000 0 1000 2000 3000

-1.0

-0.5

0.0

0.5

1.0

H

MHL(+) MHL(–)

Nor

mal

ised

Mag

netic

Mom

ent

Applied Magnetic Field (Oe)


Magnetization processes

Hα

Hβ

O

Q0

P0

M

L1 (Hα=H)

L2

M0

Hα=Hβ

Hα

Hβ

O

Q0

P0

I

II

III

L1 (Hα=H)

L2 (Hβ=H)

M0

Hα

Hβ

O

Q0

P0

I

II

III

L1 (Hα=H)

L2 (Hβ=H)

M0

H

H

H

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For more examples … Hystersoft

http://www.eng.fsu.edu/~pandrei/HysterSoft/index1.html

Petru AndreiDepartment of Electrical and Computer EngineeringFlorida State University and Florida A&M University

Univ. of Florida - Iasi University – Technical Univ. Wien


Generalized use of FORCs

Conclusion: FORC diagram can be calculated for ANY hysteretic system.

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Conclusion …

FORC distribution and FORC diagram can be obtained from experimental data.

Problems:How we “decode” the information contained in an experimental FORC diagram ? Does it contain sufficient information to identify ANY hysteresis model ?


-200.0n0.0200.0n400.0n

600.0n800.0n1.0µ1.2µ1.4µ1.6µ1.8µ

-1000

-500

0

500

-200.0n0.0

200.0n400.0n600.0n800.0n

1.0µ1.2µ1.4µ1.6µ1.8µ

-1000

-500

0

5000 1000 2000

Hi (Oe) Hi (Oe)

Hc (Oe)

0 90 180 270 3600

90

180

270

360

θ (deg)

θ r (deg

)

100 110 120 130 140 150100

110

120

130

140

150

TA(K)

T B(K

)

Ni

Co

Zn

Fe pure

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FORC diagram method.

-3000 0 3000

-0.7

0.0

0.7MHL+

MHL-

m-FORC

(Hr,H)

Hr

Nor

mal

ized

mag

netic

mom

ent

Applied magnetic field (Oe)

H

( ) ( )2 ,1,2

FORC rr

r

m H HH H

H Hρ

−∂= −

∂ ∂

T(Hα1,Hβ1)

Hα

Hβ

M(Hα1,Hβ1)

m0/m0s

H

+1

–1

A(Hα1,0)B(Hβ1,0)

O

T0(Hm,–Hm)

M(Hα1,Hβ1)

M0(Hm,−Hm)

Q

Q0

P

P0

Rectangular hysteron

Preisach plane

P(Hα,Hβ)

Hα

Hβ Hc0

O

hs

hchi

hc=const.

hi=const.-3000 -2000 -1000 0 1000 2000 3000

-1.0

-0.5

0.0

0.5

1.0

m

H


FORC distribution

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0dH=dH

αdHr=dH

β

B(H+dH,Hr+dHr)A(H,Hr)

Hβ

Hα

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0-1.0

-0.5

0.0

0.5

1.0

H=Hα

Hr=Hβ

Nor

mal

ized

mag

netic

mom

ent

A

B

A

B

A

B

Case A ρ = 0

Case B ρ < 0

Case C ρ > 0

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Symmetry

-0.2 0.0 0.2 0.4

-0.4

-0.2

0.0

0.2

Hα

Hβ

-0.2 0.0 0.2 0.4

-0.4

-0.2

0.0

0.2

Hα

Hβ

-8 -4 0 4 8-1.0

-0.5

0.0

0.5

1.0

m

H (arb.units)

-2 0 2 4 6-6

-4

-2

0

2

H (arb. units)

Hr (

arb.

uni

ts)

-2 0 2 4 6-6

-4

-2

0

2

H (arb. units)

Hr (

arb.

uni

ts)


Magnetic characterization of samples using FORC diagrams

Main problemsState dependent interaction field distributionReversible magnetization processes

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Mean field interactions

( )0

m f HH H mα

⎧ =⎨

= +⎩

H

m 1

α

-4000 -2000 0 2000 4000

-1.0

-0.5

0.0

0.5

1.0 m(Happl+αm)

Magnetic field (Oe)

Nor

mal

ized

mag

netic

mom

ent


Preisach – singular distributions

α=0

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α<0

0 2 4 6 8 10 12

-6

-4

-2

0

2

4

6

Hc (a. u.)

Hi (

a. u

.)



α>0

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Operative plane

-4000 -2000 0 2000 4000

-1.0

-0.5

0.0

0.5

1.0 m(Happl+αm)

Magnetic field (Oe)

Nor

mal

ized

mag

netic

mom

ent

-0.2 0.0 0.2 0.4

-0.4

-0.2

0.0

0.2

Hα

Hβ

-0.2 0.0 0.2 0.4

-0.4

-0.2

0.0

0.2

Hα

Hβ


FORC – patterned medium

0 2 4 6 8 10 12

-6

-4

-2

0

2

4

6

Hc (a. u.)

Hi (

a. u

.)

0 2 4 6 8 10 12

-6

-4

-2

0

2

4

6

Hc (a. u.)

Hi (a

. u.)

0 2 4 6 8 10 12

-6

-4

-2

0

2

4

6

Hc (a. u.)

Hi (a

. u.)

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Magnetizing mean field interactions

-3000 -2000 -1000 0 1000 2000 3000

-1.0

-0.5

0.0

0.5

1.0

m

H

-0.0000010.0000000.0000010.0000020.0000030.0000040.0000050.000006

0

-0.0000010.0000000.0000010.0000020.0000030.0000040.0000050.000006

0

0 1000 2000


Alpha = 0

-0.0000010.0000000.0000010.0000020.0000030.0000040.0000050.000006

0

-0.0000010.0000000.0000010.0000020.0000030.0000040.0000050.000006

0

0 1000 2000 3000 4000

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Alpha = 300

0.0000000

0.0000005

0.0000010

0.0000015

0.0000020

0

0.0000000

0.0000005

0.0000010

0.0000015

0.0000020

0

0 1000 2000 3000 4000


Alpha = 500

0.00000000.00000020.00000040.00000060.00000080.00000100.0000012

0

1000

0.00000000.00000020.00000040.00000060.00000080.00000100.0000012

0

10000 1000 2000 3000 4000

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Alpha = 600

0.0000000

0.0000002

0.0000004

0.0000006

0.0000008

-1000

0

1000

0.0000000

0.0000002

0.0000004

0.0000006

0.0000008

-1000

0

1000

0 1000 2000 3000 4000


Alpha = 1000

0.0000000

0.0000001

0.0000002

0.0000003

0.0000004

-1000

0

1000

0.0000000

0.0000001

0.0000002

0.0000003

0.0000004

-1000

0

1000

0 1000 2000 3000 4000

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Operative plane

0 200 400 600 800 1000

-100

-50

0

50

100

150

200

250H

iMax

alpha

HiMax

0.00000000.00000020.00000040.00000060.00000080.0000010

0

0.0000000

0.0000002

0.0000004

0.0000006

0.0000008

0.0000010

0

0 1000 2000 3000 4000

200 400 600 800 1000 1200 1400 1600 1800 2000 2200

-100

0

100

200

300

400

500

600

700

HiM

ed, H

iSig

Hc

HiMed HiSig


0.00000000.00000020.00000040.00000060.00000080.0000010

0

0.0000000

0.0000002

0.0000004

0.0000006

0.0000008

0.0000010

0

0 1000 2000 3000 4000

-0.0000010.0000000.0000010.0000020.0000030.0000040.0000050.000006

0

-0.0000010.0000000.0000010.0000020.0000030.0000040.0000050.000006

0

0 1000 2000 3000 4000

Compare the results…

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Reversible vs. irreversible magnetization processes

-3000 0 3000

-0.7

0.0

0.7MHL+

MHL-

m-FORC(Hr,H)

Hr

Nor

mal

ized

mag

netic

mom

ent

Applied magnetic field (Oe)

H


Relation with deltaM measurement

-2000 -1000 0 1000 2000-1.0

-0.5

0.0

0.5

1.0

IRM DCD MHL deltaM

Nor

mal

ized

Mag

netic

Mom

ent


-2000 -1000 0 1000 2000-1.0

-0.5

0.0

0.5

1.0

IRM DCD MHL deltaM

Nor

mal

ized

Mag

netic

Mom

ent


-1000 0 1000

-0.5

0.0

0.5

Nor

mal

ized

Mag

netic

Mom

ent


Stancu A., Bissell PR, Chantrell RW, JAP, 2001

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Problems with deltaM/Henkel plots

Sensitive to the quality of the demagnetization state in IRM processNegative (demagnetizing-like) deltaM is compatible with statistical interactions (no preference to demagnetizing interactions)

-2000 -1000 0 1000 2000-1.0

-0.5

0.0

0.5

1.0

IRM DCD MHL deltaM

Nor

mal

ized

Mag

netic

Mom

ent


-2000 -1000 0 1000 2000 3000

-3000

-2000

-1000

0

1000

2000--3

2234567899

2


BaFe (oriented sample)-positive deltaM

-3000 -2000 -1000 0 1000 2000 3000

-1.0

-0.5

0.0

0.5

1.0

m

H

-0.0000010.0000000.0000010.0000020.0000030.0000040.0000050.000006

-1000

0

1000

-0.0000010.0000000.0000010.0000020.0000030.0000040.0000050.000006

-1000

0

10000 1000 2000

-2000 -1000 0 1000 2000-1.0

-0.5

0.0

0.5

1.0

IRM DCD MHL deltaM

Nor

mal

ized

Mag

netic

Mom

ent



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BaFe (random sample)

-4000 -2000 0 2000 4000

-1.0

-0.5

0.0

0.5

1.0

m

H

-0.00000020.00000000.00000020.00000040.00000060.00000080.00000100.00000120.00000140.00000160.0000018

-1000

0

1000

-0.00000020.00000000.00000020.00000040.00000060.00000080.00000100.00000120.00000140.00000160.0000018

-1000

0

1000

0 1000 2000 3000

-2000 -1000 0 1000 2000-1.0

-0.5

0.0

0.5

1.0

IRM DCD MHL deltaM

Nor

mal

ized

Mag

netic

Mom

ent




Video magnetic tape

-2000 -1000 0 1000 2000-1.0

-0.5

0.0

0.5

1.0

IRM DCD MHL deltaM

Nor

mal

ized

Mag

netic

Mom

ent


0.0000000

0.0000005

0.0000010

0.0000015

0.0000020

-1000

0

1000

0.0000000

0.0000005

0.0000010

0.0000015

0.0000020

-1000

0

1000

0 2000


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Experimental procedure - SORC

Order “0”

Order “1”

Order “2”

-1000 0 1000

-0.5

0.0

0.5

Nor

mal

ized

Mag

netic

Mom

ent



Second-Order Reversal Curves

- 8 - 6 - 4 - 2 0 2 4 6 8- 1 . 0

- 0 . 8

- 0 . 6

- 0 . 4

- 0 . 2

0 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

m/m

s

A p p l i e d f i e l d ( a . u . )- 8 - 6 - 4 - 2 0 2 4 6 8

- 1 . 0

- 0 . 8

- 0 . 6

- 0 . 4

- 0 . 2

0 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

A p p l i e d f i e l d ( a . u . )

-4 -2 0 2 4-4

-2

0

2

4

H

Hr

-4 -2 0 2 4-4

-2

0

2

4

H

Hr

-0.20

-0.10

0

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80-4 -2 0 2 4

-4

-2

0

2

4

H

Hr

-0.050

-0.040

-0.030

-0.020

-0.010

0

0.010

0.020

0.030

0.040

0.050

0.060

0.070

0.080

0.090

0.10

FORC SORC FORC-SORC

Stancu A., Andrei P., JAP, 2005

Error evaluation !!!

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Experimental data

-5000 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 5000-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

m

H -5000 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 5000-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

m

H-5000 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 5000

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

m

H

0 1000 2000 3000 4000 5000-5000

-4000

-3000

-2000

-1000

0

0 1000 2000 3000 4000 5000-5000

-4000

-3000

-2000

-1000

0

0 1000 2000 3000 4000 5000-5000

-4000

-3000

-2000

-1000

0


FORC-Preisach distributions

The distribution of the interaction fields is NOT stable. It depends on the magnetic state. Preisach distribution is moving and has variable variance.Reversible magnetization processes are coupled with the irreversible ones

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FORC …

FORC distribution gives a static, average image of the interactions while the interaction field distribution is changing during the magnetization processesWithout a proper model the dynamics can’t be observed and evaluated


FORC technique applied to other systems

Preisach and FORC identification technique can be applied to ANY hysteretic system …

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Spin crossover systems

Fe(II)d6

Low spin state

Diamagnetic S=0 Paramagnetic S=2

Different colors

Different volumes

High spin state

Different vibrational properties

Δ0 t2g

eg egt2g

Ea

Ener

gy

Metal-ligand distance

LS HS Δ

0 200 400 600 800 10000.0

0.2

0.4

0.6

0.8

1.0

nHS

Pressure[bar]

110 120 130 140 150 1600.0

0.2

0.4

0.6

0.8

1.0

nHS

T[K]

0 10000 20000 30000 40000 50000 60000 700000.0

0.2

0.4

0.6

0.8

1.0

55 K

50 K

45 K

nHS

temps(sec)


Thermal hysteresis in spin transition materials

115 120 125 130 135 140 145 1500.0

0.2

0.4

0.6

0.8

1.0

n HS

T(K)

a

110 115 120 125 130 135 1400.0

0.2

0.4

0.6

0.8

1.0

b

n HS

T(K)

100 105 110 115 120 125 1300.0

0.2

0.4

0.6

0.8

1.0

n HS

T(K)

c

95 100 105 110 1150.0

0.2

0.4

0.6

0.8

1.0

n HS

T(K)

d

fast

514 nm

3T2

1T2

slow

fast

fast

kHL

1A1

5T2

3T1

1T1

ΔHS

LSmetal-ligand distance

ener

gy LIESST

The LIESST Effect (Light Induced Excited Spin State Trapping)

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Preisach model for thermal hysteresis

0.4 0.6 0.8 1.0 1.2 1.4 1.6

0.4

0.6

0.8

1.0

1.2

1.4

1.6

P'(Tα,T

β)

Tα=T

β

Tβ

Tα

0.4 0.6 0.8 1.0 1.2 1.4 1.6

0.4 0.6 0.8 1.0 1.2 1.4 1.6

0.0

0.2

0.4

0.6

0.8

1.0

P(T,Tr)

T/T0

T=T0

nHS

/NT=T

α

Tr=T

β

Normalized sample temperature

90 100 110 120 1300.0

0.2

0.4

0.6

0.8

1.0

nH

S

T[K]

Tanasa et al, PRB 2005; Enachescu et al, PRB 2005


Thermal hysteresis. Effect of impurities

100 110 120 130 140 150100

110

120

130

140

150

TA(K)

T B(K

)

Ni

Co

Zn

Fe pure

0 5 10 15 20 25105

110

115

120

125

130

135

140

c(K)

b(K

)

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Pressure & temperature hysteresis

0 200 400 600 800 1000 12000.0

0.2

0.4

0.6

0.8

1.0

p2n H

S

p(bar)

Δp=180bar

p1

168 170 172 174 176 178 180 1820.0

0.2

0.4

0.6

0.8

1.0

n HS

T (K)

ΔT=2K

600 750 900

0.0

0.2

0.4

0.6

0.8

1.0

170 175 180 1850.0

0.2

0.4

0.6

0.8

1.0600 750 900

p(bar)3

T (K)

2

1

12

34

4

5 6

5

6

7

7

8

9

9

8

p(bar)

initial statefinal state

nHSn

HS

0400

8001200

1600

0.0

0.2

0.4

0.6

0.8

1.0

160165

170175

180185

n HS

tempe

ratur

e T(K

)

pression p(bar)

Multi-ferroic materials


Elastic model of hysteresis

Low spin state

High spin state

Molecular volume change during transitionelastic interactions appear inside the sample

System shape and volume change during transition

L. Stoleriu, C. Enachescu, A. Stancu, A. Hauser, IEEE Trans. Magn., 2008C. Enachescu L. Stoleriu, A. Stancu, A. Hauser, PRL 2009

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25


Elastic model of hysteresis and relaxation

Low spin state

High spin state

For every particle the following differential system is solved at every step:

2

2

2

2

⎧= −⎪⎪

⎨⎪ = −⎪⎩

i ixi

i iyi

d x dxm F

dtdtd y dy

m Fdtdt

μ

μ

Fxi are the algebraic sums of forces acting on particule on the two directionsµ is the damping constant


Cooperativity effect – ralaxation process

0 2 4 6 8 10

0,0

0,2

0,4

0,6

0,8

1,0

Hig

h sp

in fr

actio

n

Monte Carlo time

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26


Size effects in nanoparticulate spin transition materials

A. Rotaru, Ph.D. Thesis, 2009


ConclusionsThe extensive use of the FORC technique induced a new interest in the Preisach modelUnfortunately, in many cases the analysis is not completeWe recommend at least a mean field analysis / work in the operative planeAll FORC analysis should be coupled with a statistical model specific to the physical system analyzed

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Documents

CARPATH ESM 2009 - Timisoara 2 - Magnetism