Jounl of Optoelectonics d Advced Mteils Vol. 6, No. 3, Septeme 2004, p. 1059-1063 FIRST ORDER REVERSAL CURVES AND HYSTERESIS LOOPS OF FERROELECTRIC FILMS DESCRIBED BY PHENOMENOLOGICAL MODELS M. Feciou-Moiu *, D. Ricinschi, P. Postolche, C. E. Ciomg, A. Stcu, L. Mitoseiu,c Dept. of Electicity, Al. I. Cuz Univesity, Isi 700506, Romi Gdute School of Eng. Science, Osk Univesity, Toyonk, Osk 560-8531, Jp c Dept. of Chem. of Pocess Eng. DICheP, Univesity of Geno, I-16129, Itly The incesing pts of the non-symmetic P(E) hysteesis loops of PZT feoelectic films (Fist Ode Revesl Cuves - FORC), wee used in ode to clculte the FORC distiution in which seption of the evesile d ievesile contiutions to the poliztion ws otined. The ole of the fequency of the pplied field on the switching popeties of the feoelectic films wee lyzed y this method. A phenomenologicl model ws used to descie the P(E) hysteesis loops. Using the model pmetes detemined fom the fit of P(E) mjo loops, mino loops d the FORCs wee simulted, t vious fequencies d mplitudes of the pplied field. The clculted FORC digm ws comped with the expeimentl one d the limits of the model wee discussed. (Received Apil 19, 2004; ccepted June 22, 2004) Keywods: Feoelectic switching, Fist ode evesl cuves, Phenomenologicl model 1. Intoduction The method of investigtion of hysteetic systems y mes of Fist Ode Revesl Cuves (FORC) digms initilly poposed fo geologicl feomgnetic systems d ltely fo ecoding medi, spin glsses d feofluids [1-3] ws ecently pplied fo feoelectic films [4-5]. The method involves the mesuement of mino hysteesis loops otined y cycling the smple etween stution d vile evesl field. Being sensitive to vious pmetes, including chcteistics of the feoelectic system ut lso chcteistics of the field histoy d chcteistics, the expeimentl FORC digms contin ich infomtion. In ode to disclose the infomtion contined in these digms, modelling tools e used d the ole of the model pmetes on the FORC digms e septely investigted [6-8]. Vious techniques hve een employed fo desciing the hysteetic ehviou of feoelectics [9-11]. Among them, the semimcoscopic theoies comining the phenomenologicl ppoch with enegy eltions give esonle esults d hve smll nume of effective model pmetes. The phenomenologicl ppoch initilly poposed fo soft mgnetic mteils y Jiles d Atheton [12] ws successfully pplied fo desciing the hysteesis loops of PMN feoelectic elxos [13]. In this ppe, the expeimentl FORC digms otined fo P(Z,Ti)O 3 (PZT) thin films e comped with the ones simulted on the sis of the phenomenologicl model of Jiles-Atheton, with the ppoximtion of Dee [14]. An intepettion of the mechisms involved in the oseved pttens is poposed. 2. Expeiment d definition of the FORC digms P(Z,Ti)O 3 (PZT) films otined y Rf - sputteing technique hving Pt electodes wee used fo expeiments [15]. Single pulse hysteesis mesuements in 500Hz tigul signl with * Coesponding utho: mfeciou@stone.phys.uic.o
1060 M. Feciou Moiu, D. Ricinschi, P. Postolche, C. E. Ciomg, A. Stcu, L. Mitoseiu 10V mximum mplitude hve een pefomed using FCE feoelectic teste (Toyotechnic) ccoding to the sequence: (i) stution unde positive field E Est =400kV/cm; (ii) mping the field down to evesl vlue E, when the poliztion follows the descending ch of the Mjo Hysteesis Loop (MHL); (iii) incesing the field ck to the positive stution, when the poliztion is function of oth the ctul field E d of the evesl field E [4-5]. The FORC fmily stting on the descending MHL ch is denoted s p (E,E), similly, the FORCs + pforc (E,E) c e otined using the scending ch of the MHL [4]. The FORC digm epesents contou plot of the FORC distiution, defined s the mixed second deivtive of poliztion with espect to E d E [2]: 2 FORC [ χ (E,E)] 1 pforc (E,E) 1 ρ ( E,E) = = FORC, (1) 2 E E 2 E in which χ E, E) e the diffeentil susceptiilities mesued long the FORCs. The FORC ( ( E, E distiution ρ ) desciing the vition of poliztion with espect to chges in oth the evesl field E d the ctul electic field E d it ws detemined using the numeicl method poposed in [2]. By chging the coodintes of the FORC distiution fom (E,E) to {E c =(E-E )/2, E i =(E+E )/2}, whee E c d E i ply the ole of locl coecive d intection field espectively, ρ E,E ) ecomes identicl with the Peisch distiution [16] fo systems stisfying the clssicl ( c i Peisch model conditions [17]. The expeimentl FORC digms otined fo PZT film t the fequencies f = 5 Hz d f = 500 Hz e pesented in Fig. 1 (-). They clely show evesile d ievesile components with mximum t E M =-0.3E mx, E M =0.1E mx which hs the meing of the fields fo the highest nume of switchle units cusing the min contiution to the poliztion. An symmety of the of the ievesile FORC long E M =0.2E mx ws explined s due to selfpolizing effect in the film [4-5]. A highe speding d diffusion of the ievesile pt of the FORC distiution is found fo highe fequency togethe with incesing of the evesile component. The position of the mximum of the ievesile pt is slightly shifted towds highe fields fo f = 500 Hz. In the pesent ppe, the est fit pmetes of the phenomenologicl model Jiles-Atheton [12], with the ppoximtion of Dee wee used fo simulting the FORC poliztion d FORC digms t the two fequencies. Nomlized E /E mx 2E-8 1.9E-8 1.6E-8 1.3E-8 9.7E-9 6.8E-9 3.9E-9 Nomlized E /E mx 1.4E-8 1.3E-8 1.1E-8 8.7E-9 6.5E-9 4.4E-9 2.3E-9 1.3E-1-2E-9-9.3E-10-2E-9 - Fig. 1. Expeimentl FORC digms of PZT films t fequencies: () 5 Hz d () 500 Hz. 3. Theoy In the Jiles-Atheton ppoch [12] the P(E) hysteesis loops ws modeled in two steps [12]. Fistly, the idel hysteetic poliztion is clculted y consideing clssicl Boltzmn sttistics fo the poility of dipoles to occupy specific enegy sttes. The hysteetic effect is lte
Fist ode evesl cuves d hysteesis loops of feoelectic films 1061 dded y consideing the devitions fom the hysteetic stte due to the estiction of domin wll movement y pinning sites in the feoelectic. In the pesence of scling poliztion P 1, the ssumption tht dipoles c oient in y diection yields the Lgevin fomul: P E e = P1 + PS coth (2) Ee whee P S is the stution poliztion, is constt d E e is the effective field consideed s: E e ( E E ) + ( P ) = α (3) 0 P 0 in which αp qutifies the field contiutions due to the intedomin coupling d stess effects d (E 0, P 0 ) e the is field d espective poliztion consideed to ccount fo the symmeties of the hysteesis loops. The hysteesis cuve P(E) is otined y including the evesile P ev d ievesile poliztion P iev esulting fom the tsltion d ending of domin wlls pinned t the inclusions of mteil: iev de = P ~ δ iev (4) kδ α P ( P P ) iev whee, within the ppoximtion poposed y Dee [14]: { de > 0 d P > P } o { de < 0 d P P } ~ 1, < δ = (5) 0, othewise. The pmete k qutifies the vege enegy equied to eoient the domins d it is ssimptoticlly ppoximted y the coecive field in the soft mteils. In ou simultions, k pmete ws chosen s Gussi function of the vlues of the electic field. The totl poliztion is thus: P P ev + P iev =, in which: P c( P P ) ev = (6) iev The finl eqution of Jiles-Atheton model used y us in ou simultion ws: de ~ = δ δk ( 1 c)( P P) + c ( 1 c) α( P P) de (7) whee = 1 on the scendent d = -1 on the descendt ch of the hysteesis loop. 4. Results d discussion The expeimentl MHL loops of PZT films t the two fequencies hve een fistly fitted with the pesent model. A good fit ws otined fo f=500hz (Fig. 2 ) d esonle one fo f=5hz (Fig. 2 ), due to the spce chge effects lteing the switching poliztion d mifesting in the mesued P(E) loops minly t low-fequency.
1062 M. Feciou Moiu, D. Ricinschi, P. Postolche, C. E. Ciomg, A. Stcu, L. Mitoseiu - - simulted dt expeimentl dt -400-300 -200-100 0 100 200 300 400 Electic Field (kv/cm) simulted dt expeimentl dt Electic Field (kv/cm) - - Electic Field (kv/cm) c Electic Field (kv/cm) d Fig. 2. Expeimentl, est-fit MHL t () 5 Hz d () 500 Hz fequency of electic field d computed FORCs on the sis of phenomenologicl model t: (c) 5 Hz d (d) 500 Hz. Using the est fit vlues detemined fom the MHL, the FORCs wee simulted (Fig. 2 c, d). The computed FORC digms (Fig. 3, ). show simil ehviou with the expeimentl ones: evesile component with mximum t E=0 d ievesile pt locted t the sme field vlues s the expeimentl ones. The model is lso le to descie the symmety of the FORC digms long the E xis which peviously ws consideed s coming fom the pefeentil poliztion of the switching units locted t the ottom electode film intefce which c esily switch in one diection, ut they need highe d distiuted fields fo switching in the opposite one [4]. This effect, ecently found in ulk mteils d descied within Ldu models seems to e moe elted to intinsic chcteistics of the switchle system th to intefce effect [18]. The model is lso le to descie the effect of incesing fequency on the FORCs cusing shift of the mximum towds highe fields d speding of the distiution. Due to the fct tht the switchle dipoles e not le to follow the fst vition of the pplied fields t highe fequency, ppent highe coecivity is found in the simulted FORCs, like in the expeimentl digms (Fig. 1 ). -5.000 000 6.000-5.000 0.3846 11.50 Nomlized E /E mx 17.00 22.50 28.00 33.50 39.00 Nomlized E /E mx 5.769 11.15 16.54 21.92 44.50 27.31 50 30 - - Fig. 3. FORC digms computed on the sis of the phenomenologicl model t () 5 Hz d () 500 Hz.
Fist ode evesl cuves d hysteesis loops of feoelectic films 1063 5. Conclusions The expeimentl FORC distiution otined fo PZT films t diffeent fequencies wee comped with ones computed on the sis of phenomenologicl model. The Jiles-Atheton theoy in the vesion poposed y De ws used fo the fitting of the MHL. Using the est vlues fits, the FORCs wee simulted. The computed FORC digms show simil ehvio with the expeimentl ones. The model is le to descie coectly the evesile d ievesile components on the P(E) loops, the symmety of the FORC digms long the E xis d the effect of incesing fequency on the FORC digms. Refeences [1] I. Myegoyz, Mthemticl Models of Hysteesis, Spinge, New Yok, 1991. [2] C. R. Pike, A. P. Roets, K. L. Veosu, J. Appl. Phys. 85, 6640 (1999); Geophys. J. Int. 145, 721 (2001). [3] H. G. Ktzge, F. Pzmdi, C. R. Pike, K. Liu, R. T. Sclett, K. L. Veosu, G. T. Zimyi, Phys. Rev. Lett. 89, 257202 (2002). [4] A. Stcu, D. Ricinschi, L. Mitoseiu, P. Postolche, M. Okuym, Appl. Phys. Lett. 83, 3767 (2003). [5] D. Ricinschi, A. Stcu, L. Mitoseiu, P. Postolche d M. Okuym, J. Optoelecton. Adv. Mte. (to e pulished). [6] C. R. Pike, A. P. Roets, M. J. Dekkes, K. L. Veosu, Phys. Eth d Plety Inteios 126, 11 (2001). [7] A. Stcu, C. Pike, L. Stoleiu, P. Postolche, D. Cimpoesu, J. Appl. Phys. 93, 6620 (2003) [8] C. Enchescu, PhD Thesis, Univ. of Vesilles, Fce, (2003). [9] I. W. Chen, Y. Wg, Feoelectics 206, 245 (1998). [10] W. Chen, C. S. Lynch, J. Int. Mte. Systems d Stuctues 9, 427 (1998). [11] P. Ge, M. Joueh, Pecision Eng. 17, 211 (1995). [12] D. C. Jiles, D. L. Atheton, J. Mgn. Mgn. Mte. 61, 48 (1986). [13] R. C. Smith, C. L. Hom, SPIE Vol. 3667, Newpot Bech, CA, Mch 1-4, 150 (1999). [14] J. H. B.Dee, IEEE Ts. Mgn. 30, 5 (1994). [15] D. Ricinschi, M. Okuym, Appl. Phys. Lett. 81, 4040 (2002); Integ. Feoel. 50, 149 (2002). [16] F. Peisch, Z. Phys. 94, 277 (1935). [17] A. Stcu, C. Pike, L. Stoleiu, P. Postolche, D. Cimpoesu, J. Appl. Phys. 93, 6620 (2003) [18] D. Ricinschi, L. Mitoseiu, A. Stcu, P. Postolche, M. Okuym, The 16 th Intentionl Symposium of Integ. Feoel. ISIF 2004, 5-8 Ap. 2004, Koe.