Improved Preisach -DOK Modeling on the Henkel Plot of A Longitudinal Barium Ferrite

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1 Poeedings of te 01 nd Intenational Confeene on Compute and Infomation Appliation (ICCIA 01) Impoved Peisa -DOK odeling on te Henkel Plot of A Longitudinal Baium Feite Zao Jing, Xue Fang, Han Ning Depatment of Pysis and Eletial Engineeing Handan College Handan, , Cina @qq.om Abstat Te Henkel plot and te Δm plot of a longitudinal baium feite ad disk and γ-feo3 flexible disk wee simulated by te impoved Peisa-DOK model.te study esults sow tat te baium feite exibit lage positive inteations, as sown by lage positive in te Δm plot, and tend to esist demagnetization, leading te oiented baium feite possess te unusual emanene aateisti. Keywods-Peisa model, suseptibility, emanene I. INTRODUCTION In eent yeas, te aeal density of ad disk dives as doubled evey yea [1, ]. In geneal, te magneti popeties usually ae deived fom te odinay ysteesis loop of te media, but tis an lead to inonsistent esults beause te odinay ysteesis loop inludes bot te evesible and te ievesible omponents of magnetization evesal, weeas te eoding poess depends only on te ievesible omponents, wi ae efleted only in te emanene loops. Refeene [3] popose tat te emanene loop paametes ae moe elevant to te magneti eoding poess tan te ysteesis loop paametes. At pesent, te development of te γ - FeO3 media and te CoFe media ave been estited beause of tei bad emanene, temal stability and oosion esistane. etal magneti patiles possessed of te lage eoding potential sine tey ave te ige oeivity and emanene, but tee ae two sotomings: obvious oosion esistane and te onditionality of patile dimension. Te Baium feite media wee studied fo ig density magneti eoding media, sine tey ave good emial stability and meanial popeties. In addition, tei lage magnetoystalline anisotopy and lowmedia noise aateistis make it attative fo igdensity magneti eoding appliations [4]. Espeially, te Baium feite media ave te moe pefetly emanene aateisti so tat tey ae appliable not only te oating vetial magneti eoding media but also te longitudinal eoding media and te abitay oiented media. Refeene [5] epoted tat tey wee studying te expeiment of te oating vetial baium feite ad disk sample, oweve, tis sample was not applied widely owing to te poo emanene aateisti. In tis study, we simulated te ysteesis loop and te Henkel plot and te Δ m plot of te BaFe and te γ - FeO3, and alulated te emanene popeties. II. THE IPOVED DOK ODEL Te lassial Peisa model an simulate only an ievesible magnetization [6], oweve, fo te ealisti media, te Peisa model must be impoved so tat it an simulate not only te ievesible magnetization but also te evesible magnetization. Te E. D. Toe, J. Oti and G. Kàdà (DOK) model [7] stats wit a moving Peisa model and adds a magnetization-dependent alulation of evesible magnetization as well. Taditionally, te ievesible magnetization is alulated by integating ove te entie Peisa model plane. In tis pape, an altenative metod is to use a diffeential equation appoa, woking wit suseptibility dietly [8, 9]. In te model, te magnetization of a mateial give te applied field H. Te opeative field wi is defined as H + α, (1) wee α is te expeimentally detemined moving paamete. Te total magnetization is alulated by simultaneously solving te equations below: d (,, m l ) d, () dmi I (,, mi ) d. (3) In tese equations, is te total suseptibility, I is te ievesible suseptibility, mi is te nomalized ievesible magnetization. If we onside te evesible magnetization, te total magnetization is te sum of its ievesible and evesible pats mi + ) mr, (4) wee is te satuation magnetization, is te squaeness of a media, m R is te nomalized evesible magnetization, espetively. Taking te deivative wit espet to te opeative field d d I + ) R (5) 1781

2 Poeedings of te 01 nd Intenational Confeene on Compute and Infomation Appliation (ICCIA 01) wee R is te evesible suseptibility. Fo magneti eoding media, te Peisa distibution funtion is Gaussian and an be expessed as ( ) ( ) ( ) 1 1 i i p i, exp + π i i (6) i wee is te aveage itial field, is te inteation field, is te itial field, i and ae te standad deviations of te inteation field and itial field, espetively. In tis model, te ievesible suseptibility is diffeent wen te opeative field is ineasing o deeasing. Wen is ineasing, we obtain te ievesible suseptibility ( ) i ( 1+ λ) + i λ) I, in exp ef π τ (7) wee i k +, τ, i k ( ) k i λ and i κ 1 λ. (8) Fo small values of, wen i is mu lage tan, as is te ase in eoding media, we ave ( 1+ λ) + i λ) ef 1 τ (9) giving ( ) i I, in ( ) exp π (10) Wen is deeasing, we may ewite equation (7) as ( + ) i I, de ( ) exp π (11) Fo a state dependent te model, te evesible magnetization is mr a f ( H ) a f ( H ) + (1) wee a good appoximation is made by γh f ( H ) 1 e. (13) Aoding to te DOK model 1+ mi 1 mi a+ a and (14) Te paamete γ is anote expeimental-detemined paamete elated to te magneti suseptibility. Te use of tis expession in equation (5) yields a full expession fo te total opeative suseptibility 1 I ( f ( H ) + f ( H )) ) + + ) ( a+ f ( H ) a f ( H )) [ 1+ α ) ( a+ f ( H ) a- f ( H ))]. (15) i By te same token we an get system initial emanene magneti suseptibility ( ) + + ( ) + ( ) i i λ i i λ i v exp π ef ef τ τ (16) o te system magneti suseptibility of initial magnetization uve is 1 v ( f ( H ) + f ( H )) ) + + ) ( a+ f ( H ) a f ( H )) ini [ 1+ α ) ( a+ f ( H ) a- f ( H ))] (17) Te total magnetization fo input sequene of opeative field an be omputed at ea step as ( + Δ) m( ) + Δ (18) wee Δ is te ange in opeative field at ea step. Te algoitm to alulate te total magnetization esulting fom an input sequene of applied field using te fast DOK model is desibed in Table 1. TABLE I. tep CALCULATING PROCEDURE OF IPROVED DOK ODEL. Algoitm 1 et k1, 1 0, 1H 1+α 1 and te onvegene toleaneε et kk+1, k k-1 3 Calulate k H k +α k Calulate Δ k k - k-1 Calulate Ik using equation (10) o (11) Calulate k using equation (15) Calulate new value of Compute E k step, otewise set III. k using equation (18) k, if E ε, ten go to k k and go to step 3. REULT AND DICUION Fig. 1 sows te simulated ysteesis loop, wi was ompaed wit a measued ysteesis loop of te baium feite ad disk(bafe) [10] and γ -FeO3 flexible disk. Te applied field sequene fo BaFe was as following: tating fom Oe, wi is suffiient to satuate te sample, te applied field was edued to -100 Oe. At -100 Oe te field was evesed and ineased to Oe, taning a fist-ode evesal uve. At Oe te field was again evesed and edued to Oe, taing a seond-ode evesal uve. Te applied field sequene fo γ - FeO3 was as following: tating fom Oe, wi is suffiient to satuate te sample, te applied field was edued to -400 Oe. At -400 Oe te field was evesed and ineased to +600 Oe, taning a fist-ode evesal 178

3 Poeedings of te 01 nd Intenational Confeene on Compute and Infomation Appliation (ICCIA 01) uve. At +600 Oe te field was again evesed and edued to -000 Oe, taing a seond-ode evesal uve. As sown in Fig. 1, te model is in exellent ageement wit te measued esults tougout te poess, inluding te seond-ode evesal uve, illustating tat te impoved DOK model is appliable to a vaiety of magneti eoding media. Te best-fit paametes ae list in Table. α (Oe/emu) i (Oe) i (Oe) agnetization,,emu agnetization,,emu easuement imulation Applied field, H,Oe (a) Applied field,h,oe (b) easuement imulation Figue 1. easued(dot line)and simulated (solid line) ysteesis loop of te longitudinal BaFe ad disk sample (a) and te γ -FeO3 flexible disk sample (b) using te impoved DOK model. TABLE II. ODELING PARAETER OF THE LONGITUDINAL BAFE HARD DIK APLE AND THE γ -FEO3 FLEXIBLE DIK APLE. odeling paametes BaFe ad disk γ -Fe O 3 flexible disk (emu) γ (Oe) agneti inteations between patiles play an impotant ole in te popeties of magneti eoding media and ae evident in te emanent poesses. Compaison of te emanene poesses sows small diffeenes dependent on te initial magnetization state wi an be dietly attibuted to inteation. Fist, stating fom positive satuation, te field is emoved and te media is bougt to te satuation emanene. Te negative field -H is ten applied and emoved, and te emanene d is measued. On te ote and, te system is initially in te demagnetized state, te positive field H is applied and ten emoved, and te emanene is measued. In te absene of inteations, by onsideing te switing field distibution of te patiles in te Peisa model, it an be sow tat d and ae elated by [11] d 1 (19) Te igt of te equation is te Wolfat elation tat it is expeted to old fo an assembly of independent, singledomain, uniaxial patles. Te plot of d as a funtion of is known as te Henkel plot, and povides a ommon way to epesent emanene popeties. Te vaious esults obtained ae patly modified by te pesene of inteations. Fo any abitay Peisa distibution, te Henkel plot bounds is d 1 (0) Beause of te Peisa distibution wit te fatoized f ( ) ( ) fom f i in tis pape, te Henkel plot yield te following emanene law: d 1 (1) Tis emakably simple law is ompletely independent ( ) of f x. Patile-patile o wall-wall inteation effets an be put in evidene by plotting d vs (Henkel plot) and by looking at any depatue fom te Wolfat elation. Deviations of te measued Henkel plots fom te staigt line epesenting Eq. ( 19) ave been intepeted as indiations of positive and negative inteations depending on wete te measued 1783

4 Poeedings of te 01 nd Intenational Confeene on Compute and Infomation Appliation (ICCIA 01) vaiation is above o below te line epesenting te Wolfat elation. Te diffeene between te uves an be measued by Δm d ( H ) ( H )) () Plots of Δm vs H ave ome to be known as Δ m plots. Δ m plots as well as Henkel plots an eflet te inteation effet among neigboing patiles. Δm > 0, it ow tat fo positive inteation; Δm < 0, ow tat fo negative inteation. Fo eseaing te inteations between patiles of te BaFe, we simulated te Isotemal emanent magnetization uve, and ten obtained te Henkel plot wit te BaFe and te γ -FeO3, sown in Fig.. Aoding to te Eq. ( ), we dawed te Δ m plots, sown in Fig. 3. d / Wolfat elation BaFe γ -Fe O / Figue. Henkel plots fo te γ -FeO3 flexible disk sample(das dot line)and longitudinal BaFe ad disk sample (solid line). Δ Figue Applied field,h,oe BaFe γ -Fe O 3 Δ m plots fo te γ -FeO3 flexible disk sample(das dot line)and longitudinal BaFe ad disk sample (solid line). We obseved te Henkel plot and te Δ m plots of te BaFe as lage depatue fom te Wolfat elation and tee is a big positive peak in te Δ m plots, in ote wods, te inteations between patiles of te BaFe ae stonge tan of te γ -FeO3, making fo te BaFe ave te moe pefetly emanene aateisti. Te BaFe as te lage magnetoystalline anisotopy and its patile sape as not many avities and banes so tat it is moe pefet tan of te aiula γ -FeO3. One of te possible easons tat te emanene popeties of te BaFe ae bette tan of te γ - FeO3 is tat te oeivity of aiula γ -FeO3 magneti patile is lie on te sape anisotopy. Wit te fineness and unifomity of patiles, we an enane its oeivity. Te BaFe as te lage magnetoystalline anisotopy and its patile sape as not many avities and banes so tat it is moe pefet tan of te aiula γ -FeO3, leading te oiented Bafe possess te unusual emanene aateisti. IV. CONCLUION We apply a impoved DOK model of ysteesis to te emanene popeties of a longitudinal baium feite ad disk and a γ -FeO3 flexible disk. Te Peisa model deomposes te magnetization poess into evesible and ievesible pats, and deomposes te ievesible pat into μ many magneti units wit moment 0, oeivity and bias field i. In te impoved DOK model, it is neessay to model te evesible omponent sepaately and add it popotionally to te ievesible omponent in ode to alulate te total magnetization. any magneti poesses of a magneti mateial ae simulated by diffeent suseptibility funtions. Te evesal uve, te ysteesis loop, te evesible uve, te Henkel plot and te Δ m plot of a longitudinal baium feite ad disk and γ -FeO3 flexible disk wee simulated by te impoved DOK model, and we get some paametes. Te study esults sow tat te paametes not only embody te vaied magneti poesses but also eflet te emanene popeties of te two samples. In te study of te longitudinal baium feite ad disk and γ -FeO3 flexible disk, te oeivity of te baium feite deided by te magnetoystalline anisotopy is lage tan tat of te aiula γ -FeO3 detemined by te sape anisotopy. By te analysis of te Henkel plot and te Δ m plot, te baium feite exibit lage positive inteations, as sown by lage positive in te Δ m plot, and tend to esist demagnetization, leading te oiented baium feite possess te unusual emanene aateisti. REFERENCE [1] Coffey K R, Tomson T, Tiele J U. J. Appl. Pys., 00; 9(8): 4553 [] peliotis D E. J. ag. ag. ate., 1999; 193: 9 [3] peliotis D E. J. Appl. Pys., 1990; 67:

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