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

Transcription

1 9/8/9 Alexandru Ioan Cuza UNIVERSITY Centre for Applied Research in Physics and Advanced Technologies Center of Excellence in Scientific Research (6-11) of The Romanian National Commission for Scientific Research in Universities IASI - ROMANIA Preisach model of hysteresis in magnetic materials and FORC based identification techniques Alexandru STANCU Professor, Director Alexandru Ioan Cuza University, Faculty of Physics, Department of Physics & Centre for Applied Research in Physics and Advanced Tecnologies () Iasi, ROMANIA European School on Magnetism 9: Models in magnetism : from basic aspects to practical uses September 1-1th 9, Timisoara, Romania 1 Outline Introduction about hysteresis Scalar Preisach model FORC identification technique Examples ferromagnetic systems ysteretic processes in spin-transition materials Conclusions 1

2 9/8/9 Which hysteresis model we choose in a given situation? ow 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 ysteresis Loop? 3 Identical ML for essentially different systems 1. Normalized moment Applied field 15-1.E E-1.94E-9.95E E E E E-9 β E E E-8 β E-8 1.5E-8 1.8E-8-1.1E E E-8.73E E-8.74E E E-8 α α 4

3 9/8/9 To understand Preisach model I i I m /m s c Stoner Wohlfarth model +1 B( β,) A( α,) 1 S( s,) F. Preisach 1935 M.A. Krasnoselskii & A.V. Pokrovskii 1983, 1989 I.D. Mayergoyz 1986 z θ ϕ ϕ x Ps y θ 5 Preisach plane β T( α1, β1 ) Q Q O P α P(α,β) M( α1, β1 ) hs α β c P T ( m, m ) m /m s M ( m, m ) h i O hc=const. hc +1 h i =const. B( β1,) A( α1,) 1 6 3

4 9/8/9 β Q ML O m α + 1. ML(+) ML( ) β Q P β - m M Q Normalised Magnetic Moment O α L(t) O m α Applied Magnetic Field (Oe) P + M P - m + M 7 Magnetization processes β L 1 ( α =) Q β L1 ( α=) Q L α = β O M α L (β=) O I P II III α M β L1 ( α=) P M L ( β=) II Q O α I III P M 8 4

5 9/8/9 For more examples ystersoft Univ. of Florida - Iasi University Technical Univ. Wien Petru Andrei Department of Electrical and Computer Engineering Florida State University and Florida A&M University 9 Generalized use of FORCs Conclusion: FORC diagram can be calculated for ANY hysteretic system. 1 5

6 9/8/9 Conclusion FORC distribution and FORC diagram can be obtained from experimental data. Problems: ow we decode the information contained in an experimental FORC diagram? Does it contain sufficient information to identify ANY hysteresis model? T B (K) 13 1 Ni Fe pure 11 Co Zn T A (K) µ 1.6µ 1.4µ 1.µ 1.µ 8.n 6.n 4.n.n. -.n 1 5 i (Oe) c (Oe) 5 i (Oe) 1.8µ 1.6µ 1.4µ 1.µ 1.µ 8.n 6.n 4.n.n. -.n 7 θ r (deg) θ (deg)

7 9/8/9 Normalized magnetic moment FORC diagram method ML - ML + r m - (,) FORC r -3 3 Applied magnetic field (Oe) 1. P(α,β) ρ (, ) r (, ) 1 mforc r = Preisach plane T( α1, β1) Q O P r β P T ( m, m) m /m s Q α M( α1, β1) M ( m, m).5 hs α +1 m. -.5 β O c hc=const. B( β1,) A( α1,) hi hc hi=const. 1 Rectangular hysteron 13 FORC distribution 1..5 r = β B(+d, r +d r ) A(, r ). = α Normalized magnetic moment A B Case A ρ =. d r =d β d=d α β A B Case B ρ < α B Case C ρ > A 14 7

8 (arb. units) (arb. units) 9/8/9 Symmetry.. β α.. β α r (arb. units) m r (arb. units) (arb.units) 15 Magnetic characterization of samples using FORC diagrams Main problems State dependent interaction field distribution Reversible magnetization processes 16 8

9 9/8/9 Mean field interactions 1 m -1. α -4-4 Normalized magnetic moment m( appl +αm) Magnetic field (Oe) ( ) m= f = + αm 17 Preisach singular distributions α= 18 9

10 9/8/9 Preisach singular distributions α< i (a. u.) c (a. u.) 19 Preisach singular distributions α> 1

11 9/8/9 Operative plane.. β α.. β -. Normalized magnetic moment m( appl +αm) -4-4 Magnetic field (Oe) α 1 FORC patterned medium i (a. u.) i (a. u.) i (a. u.) c (a. u.) c (a. u.) c (a. u.) 11

12 9/8/9 Magnetizing mean field interactions m Alpha =

13 9/8/9 Alpha = Alpha =

14 9/8/9 Alpha = Alpha =

15 9/8/9 Operative plane 5 imax imax alpha 7 6 imed isig 5 4 imed, isig c 9 Compare the results

16 9/8/9 Reversible vs. irreversible magnetization processes Normalized magnetic moment ML - ML + r m - (,) FORC r -3 3 Applied magnetic field (Oe) 31 Relation with deltam measurement 1. Normalized Magnetic Moment Applied Magnetic Field (Oe) Normalized Magnetic Moment Normalized Magnetic Moment IRM DCD ML deltam Applied Magnetic Field (Oe) IRM DCD ML deltam Applied Magnetic Field (Oe) Stancu A., Bissell PR, Chantrell RW, JAP,

17 9/8/9 Problems with deltam/enkel plots 1. Sensitive to the quality of the demagnetization state in IRM process Negative (demagnetizing-like) deltam is compatible with statistical interactions (no preference to demagnetizing interactions) Normalized Magnetic Moment IRM DCD ML deltam Applied Magnetic Field (Oe) BaFe (oriented sample)-positive deltam m Normalized Magnetic Moment IRM DCD ML deltam Applied Magnetic Field (Oe) Stancu A., Bissell PR, Chantrell RW, JAP,

18 9/8/9 BaFe (random sample) 1. m Normalized Magnetic Moment IRM DCD ML deltam Applied Magnetic Field (Oe) -1-1 Stancu A., Bissell PR, Chantrell RW, JAP, 1 35 Video magnetic tape Normalized Magnetic Moment IRM DCD ML deltam Applied Magnetic Field (Oe) Stancu A., Bissell PR, Chantrell RW, JAP,

19 9/8/9 Experimental procedure - SORC Order Order Order 1 Normalized Magnetic Moment Applied Magnetic Field (Oe) 37 Second-Order Reversal Curves m/m s A p p l i e d f i e ld ( a. u. ) A p p l i e d f i e l d ( a. u. ) r r..3 r FORC SORC FORC-SORC Error evaluation!!! Stancu A., Andrei P., JAP,

20 9/8/9 Experimental data m. m. m 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 4

21 9/8/9 FORC FORC distribution gives a static, average image of the interactions while the interaction field distribution is changing during the magnetization processes Without a proper model the dynamics can t be observed and evaluated 41 FORC technique applied to other systems Preisach and FORC identification technique can be applied to ANY hysteretic system 4 1

22 9/8/9 Spin crossover systems e g tg Δ e g t g Energy LS S E a Δ Low spin state igh spin state Diamagnetic S= Paramagnetic S= Fe(II) d 6 n S Metal-ligand distance 1. n S Different colors T[K] Pressure[bar] Different volumes K n S.4 5 K Different vibrational properties. 55 K temps(sec) 43 Thermal hysteresis in spin transition materials T 1 T 1 n S.4 n S.4 fast 3 T 3 T 1. a T(K) T(K) b energy 514 nm fast fast slow S 1 A k L 1 Δ 5 T LIESST.8.8 LS metal-ligand distance.6.6 n S.4 n S.4. c T(K) T(K) d The LIESST Effect (Light Induced Excited Spin State Trapping) 44

23 9/8/9 Preisach model for thermal hysteresis 1. n S Normalized sample temperature n S /N T[K] T r =T β T=T T=T α P(T,T r ).. T/T T β 1.4 T α =T β P'(T α,t β ) T α Tanasa et al, PRB 5; Enachescu et al, PRB 5 45 Thermal hysteresis. Effect of impurities T B (K) 13 1 Ni Fe pure b(k) Co Zn T A (K) c(k) 46 3

24 9/8/9 Pressure & temperature hysteresis 1..8 p Δp=18bar 1..8 n S.6.4 n S.6.4 ΔT=K Multi-ferroic materials.. p p(bar) T (K) p(bar) initial state final state p(bar) n S n S T (K) n S pression p(bar) temperature T(K) 47 Elastic model of hysteresis Low spin state igh spin state Molecular volume change during transition elastic interactions appear inside the sample System shape and volume change during transition L. Stoleriu, C. Enachescu, A. Stancu, A. auser, IEEE Trans. Magn., 8 C. Enachescu L. Stoleriu, A. Stancu, A. auser, PRL

25 9/8/9 Elastic model of hysteresis and relaxation Low spin state igh spin state For every particle the following differential system is solved at every step: d xi dxi m = F xi μ dt dt d yi dyi m = F yi μ dt dt F xi are the algebraic sums of forces acting on particule on the two directions µ is the damping constant 49 Cooperativity effect ralaxation process 1, igh spin fraction,8,6,4,, Monte Carlo time 5 5

26 9/8/9 Size effects in nanoparticulate spin transition materials A. Rotaru, Ph.D. Thesis, 9 51 Conclusions The extensive use of the FORC technique induced a new interest in the Preisach model Unfortunately, in many cases the analysis is not complete We recommend at least a mean field analysis / work in the operative plane All FORC analysis should be coupled with a statistical model specific to the physical system analyzed 5 6

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