Inverse magnetoelectric effect in disk samples of ferrite piezoelectric composites

Transcription

1 Science Research ; ( : -8 Published online Aril, (htt:// doi:.648/j.sr.. Inverse agnetoelectric effect in disk sales of ferrite iezoelectric coosites D. A. Filiov, T. A. Galkina, V. M. Laletin Novgorod State University, Russia, Velikii Novgorod Institute of Technical Acoustics, Belarus, Vitebsk Eail address: Ditry.Filiov@novsu.ru (D. A. Filiov, taisiya_galkina@ail.ru (T. A. Galkina, laletin57@rabler.ru (V. M. Laletin To cite this article: D. A. Filiov, T. A. Galkina, V. M. Laletin. Inverse Magnetoelectric Effect in Disk Sales of Ferrite Piezoelectric Coosites. Science Research. Vol., No.,,. -8. doi:.648/j.sr.. Abstract: A theory of the inverse agnetoelectric (ME effect in the region of electroechanical resonance (EMR for the sales in the for of a disk is resented. The exression for the coefficient of inverse ME-conversion on the effective araeter ethod is derived. It is shown that observed the eak increase of effect in the region of electroechanical resonance, resonance frequencies are differed for direct and inverse agnetoelectric effect. Resonance frequencies deendence on ferrite ercentage for ferrite-nickel sinel and lead zirconate titanate sales are investigated exerientally. Keywords: Inverse Magnetoelectric Effect, Electroechanical Resonance. Introduction The agnetoelectric (ME effect is relate to cross effects and consists in that olarization aears in a sale under the action of a agnetic field (direct ME effect and, vice versa, agnetization aears uon the alication of an electric field (inverse ME effect. This effect which was originally redicted by Dzyaloshinskii [] and then observed in exerients [, ], is of interest not only for basic science, but for alications as well, since it coules the values, that has different tensor diensions: olarization (olar vector with agnetizing intensity (axial vector, and, vice versa, agnetization (axial vector with electric intensity (olar vector. Presence of the ME effect in onocrystal directly couled with crystal syetry [4], and its arising is ride by joint action of sin-orbit interaction, odd art of intracrystalline field and external electric field [5]. ME effect in the ferrite iezoelectric coosite is individually absent in ferrite and in iezoelectric hases. Its arising is condition on echanical interaction between agnetostriction and iezoelectric subsystes. In the ferrite coonent, echanical stresses arise due to agnetostriction in a agnetic field, that are transferred to the iezoelectric hase, where occur an electric olarization. And, vice versa, for the inverse effect, deforations induced in the iezoelectric hase under the action of an electric field are transferred to the ferrite hase, where the agnetostriction leads to agnetization of the sale. Presently, the direct ME effect is known in uch detail [6], whereas the inverse effect is still insufficiently studied and even the nuber of ublications on this henoenon is very restricted [7 ]. In this works inverse ME effect investigated exerientally for the sales in the for of a late, where was used lead zirconate titanate (PZT iezoceraic as the iezoelectric, and aterials with large agnetostriction coefficient as the ferrite, to be exact: in [7] D-Terfenol (three-layer structure D-Terfenol-PZT-D- Terfenol, in [8] nickel (three-layer structure PZT-Ni-PZT and in [9,] galfenol (two-ly structure galfenol-pzt. In the resent works realized the easureent of coefficient of inverse ME-conversion frequency deendence and exerientally discovered, that this deendence has resonant nature, in a siilar as ME voltage coefficient frequency deendence for the direct effect. However detailed theoretical descrition of the inverse ME effect it not realized in this works. In work [] it is shown the theoretical descrition of the inverse ME effect for the sales in the for of a late. However the sales in the for of a disk are uch often used in ractice, but not in the for of a late. But data of work [] for the sales in the for of a disk can not be used. Detailed theoretical descrition of the inverse ME effect and exeriental results for the ferrite-nickel sinel and lead zirconate titanate sales in the for of a disk are resented in this work.. Theory of Effect

2 Science Research, ( : -8.. Longitudinal Effect Effective araeter ethod was got wide sread occurrence at the descrition of hysical henoenon in the ferrite iezoelectric coosites [, ]. This ethod consists in that coosition aterial fro the acroscoic oint of view considered as a hoogeneous ediu with soe effective araeters, which are found by cobined solved equations of elasto- and electrodynaics for the ferrite and iezoelectric hases with following averaging. Aarently that this ethod can be used, when the characteristic diensions of coosite building blocks uch saller than sound-wave-length. As the characteristic diensions of the building blocks in the tyical coosition aterials are order the decade of icron, that this descrition ethod can be used as far as frequency order by a hundred MHz. Consider a odel syste corising a sale of the ferrite iezoelectric coosite aterial in the for of a thin disk, with the sale radius R and thickness d. The thin etal electrodes have been alied on the to and on the botto surfaces of the disk, and on which the side face an induction coil, with N nubers of turns (fig.. Let the sale is olarized transversely to contacts lane (axis Z. Direct agnetic field directs either along the sales olarization (longitudinal effect. S + st + st + de qh =, ( S + st + st + de qh =, ( B H + q ( T + = µ. ( T where s ij is the effective coliance of the coosite, d ij and q ij is the effective iezoelectric and iezoagnetic coonents, ε ij is the effective erittivity, E i and H i is the rojections of the tensity vectors of variable electric and agnetic fields. Design rocedure of effective araeters of coosition aterial is resented in [4,5]. It is convenient to used the syetry of a roble and turn to the cylindrical co-ordinates z, r and θ, using the conversions resented in [6] for further calculations. The axial syetry results in nonzero coonents of the ressure and strain tensors T rr, T θθ, S rr and S θθ. Others coonents of the ressure and strain tensors equal to zero. Besides fro the axial syetry results, that the dislaceent coonent u θ equal to zero. We allowance for this, the above exression (- reduces to S rr strr + st + de + qh = θθ, (4 S rr + θθ = st + stθθ + de qh, (5 B = µ H + q( Trr + Tθθ. (6 The equation of otion of the ediu for the radial oscillation reduces to Trr r rr + ( T r Tθθ + ρω ur =, (7 where ρ is the density of coosite. Evaluate fro (4, 5 coonents of stress tensor through coonents of ressure tensor, as result we get: T = ( S S ( ( de qh rr + ν θθ + s ( ν ν, (8 rr + Figure. Scheatic diagra of the structure with: ( sale; ( etal electrodes; ( coil with N nubers of turns. Alternating electric field with frequency ω, that given on the sale, is give rise to oscillation in the sale, which are sread along the sale surface is the radial oscillation, and all along sale thickness is the thicknesses oscillation. In future we will coe to nothing ore than the consideration of the ost low-frequency radial oscillation. Let us assue that the dick is thin, i.e. d<<r.. That the surfaces of the coosite dick are free that is, the noral coonents of the stress tensor on these surfaces are vanishing. Since the dick is thin, we can assue that T = not only on the surface, but in the volue of the dick. Accordingly, the equations for coonents of the strain tensor Si and agnetic induction B can be written as follows: Tθθ = ( νs S ( ( de qh rr + θθ + + s ( ν ν, (9 where ν = s /s is the Poisson's ratio. In order to take the equation for the radial dislaceent, substitute (8, 9 into equation of otion of the ediu (7. After the transforations the equation (7 is reduced to Bessel equation u r r u + r r u r r + k u r r =, ( where k = ρ s ( ν ω. General solution of the ( can be resented as suerosition of the first and second order Bessel functions u r = c kr + cy ( kr. (

3 4 D. A. Filiov et al: Inverse agnetoelectric effect in disk sales of ferrite iezoelectric coosites Constants c and c are defined by the boundary conditions: the dislaceents are lacking in the disk centre, i.e. at r = dislaceent u r =, but the noral strains equal to zero on side surfaces, therefore at r = R strain T rr =. This is give for constants following exressions [7]: ( + ν R c =, c = ( qh + de. ( κj( Here introduced nondiensional variable κ=kr, which values are deends on frequency, disk radius and rate of elastic oscillation roagation. Substituting the values of constants c and c in ( and, exressing the deforation through the ediu dislaceent, we get exressions for the coonents of the strain tensors R ( ( ( κj kr ν J kr T = r ( qh d rr κj( + E ( R ( ( ( νκj kr + ν J kr T = r ( qh de κj( + (4 θθ The agnetization, which is aeared in the sale as a result of agnetostriction as a result of ediu echanical deforation, we define fro Eq. (6. Substituting the exressions ( and (4 in equation (6 we get: where q d ( + ν α B, L =, (7 r r = κj(. (8 The EMF induced in the coil by agnetic flux is ΦL εin = = N α t t π R dθ Brdr = iωnπr B, L E. (9 Suosing, that all absorbed voltage take lace on the easuring volteter, and the electric field strength in sale bound u with the inut voltage by E = Vin d, and for the voltage ratio (transforer coefficient k L = Vout Vin for the longitudinal ME effect is πr ω N αb. ( d k L =, L Accordingly, this structure can be used as a transforer, which has only one winding in contrast to traditional tye transforer... Transverse Effect For the transverse ME effect direct agnetic field H in the sale directs either along the sales olarization P. Alied to the contacts electrical field to rovoke the echanical oscillation in the sale, and change the agnetization in all along sale thickness at the result. For the exeriental investigation of transverse ME effect we use the structure reresented at fig.. q ( + ν κj( kr B = H + ( qh + de s ( J( ( ν κ κ ν κ µ (5 For the exeriental investigation of inverse ME effect, it is easured the EMF of induction, that originated in coil at the agnetic flux easuring, due to the change of the agnetization of caacitor agnetoelectric dielectric. Usually, the volteter resistance in these easureents is uch greater than the coil resistance at the exerient, we can assue that the oen-circuit condition is valid (I = and, hence, H =. We allowance for this, the above exression (5 for the agnetic induction reduces to: B = q d ( + ν κj ( kr κj( E. (6 The inverse ME conversion factor for the longitudinal configuration of fields is defined as α B, L = В Е, where < B > is the average agnetic induction in the sale that R B rdr πr π is deterined as. < B >= d θ Calculating the average agnetic induction and substituting this exression into the above definition, we eventually obtain the following exression: Figure. Scheatic diagra of the structure with: ( sale; ( etal electrodes; ( coil with N nubers of turns, t coil thickness. Equations (- for the ressure tensor Si and for the agnetic induction B for the transverse ME effect takes for: S = st + st + de + qh, ( S = st + st + de + qh, (

4 Science Research, ( : -8 5 B = µ +. ( H + qt qt Coonents of the strain tensors exression are get colicated by the direct agnetic field H break its syste axial syetry at the turn to the cylindrical co-ordinates. However, taking into account, that in the exerient used the oen circuit condition and alternating agnetic field strength equal to zero, the ediu oscillation are rovoke by alternating electric field, directed along axes X, as for the longitudinal effect. Equation of ediu otion for radial oscillation reduced to (, which solution given the coonents of the strain tensors: T rr = R ( ( ( κj kr ν J kr r de, (4 κj( R νκj ( kr + ( J ( kr r θθ = de. (5 κj( T Coonents of the strain tensors T and T connected with coonents T rr and T θθ by: T = Trr cos θ + Tθθ sin θ, (6 T = Trr sin θ + Tθθ cos θ, (7 Using this ratios, for the agnetic induction in the cylindrical co-ordinates we get: B = Trr ( q cos θ + q sin θ + Tθθ ( q sin θ + q cos. (8 θ In a siilar to longitudinal effect, inverse ME conversion factor is defined as α B, T = B E for the transverse effect. Substituting exressions ( and (4 in equation (8, and calculating the average agnetic induction < B >, we obtain the following exression for inverse ME conversion factor: ( q + q d ( + ν α BT, =, (9 r where r defined by (8. For the defined of EMF induced in the coil, we liited by the case, when coil thickness t is saller then disk radius R. At this aroxiation we can take, that agnetic flux, slitting the coil equal to ΦT = N R d and for transforer coefficient: values of iezoelectric d and iezoagnetic q i odules and inversely to coliance odule s value. However for the transverse effect the value of coefficient α B, T is roortional to roduct ( q + qd. And for the longitudinal effect the value α B, L is roortional to roduct q d. As ( q + q > q, that the value of the transverse effect bigger, than of longitudinal. Frequency deendence of the inverse ME conversion factor as the frequency deendence of the ME voltage coefficient α E for the direct effect, has the resonance nature. At the low frequency region, when araeter κ <<, the value of the inverse ME conversion factor ractically is not deend on frequency. However at the frequency, that corresonds to condition r =, it is observe the eak increase of coefficient. Roots of these equation take the nae resonant frequencies f res. The value of lower resonant frequency to average about f res khz for the ferrite-nickel sinel and lead zirconate titanate sales with radius nearly R 5. It should be noted that, in contrast to the inverse ME effect, the resonant growth α E =< E > / H in the direct ME effect is observed at an antiresonance frequency f anres that corresonds to the condition a =, where = / a K + K( + ν r. ( Where K = d ε is the square coefficient of electroechanical couling for radial oscillations. There are inverse ME conversion factor frequency deendences for the ferrite-nickel sinel and lead zirconate titanate sales in the for of a disk calculated by (7 and (9 resulted in the ictures and 4 for the transverse and longitudinal effects. Sale radius R= s. The following quantity values used at the calculations: Ferrite: s =6.8 - /N, s =.4 - /N, q =-88 - /A, q =556 - /A, ρ q = - /A, =5 kg/; Piezoelectric: s =5. - /N, s =5.4 - /N, d =75 - /V, ρ =7 8 kg/. k T ωn R αbt, =. (. Results Discussion Coarison with Exerient As following fro exression (7 and (9 for inverse ME conversion factor its value in roortion to roduct of Figure. Inverse ME conversion factor frequency deendences for longitudinal effects

5 6 D. A. Filiov et al: Inverse agnetoelectric effect in disk sales of ferrite iezoelectric coosites Figure 4. Inverse ME conversion factor frequency deendences for transverse effects Frequencies of resonance and antiresonance has at least the closely values, but they are distinguishable exerientally. Exeriental investigations of effect were realized for the sales of ferrite-nickel sinel and PZT. Sales has a disk for with radius R = Before easureent the sales was olarized by electric field with strength 4 kv/ during two hours at the teerature 8 С. It is used ethod, based on easuring of alternating voltage, that aearing at the suerosition of alternating and slowly changing agnetic field on the sale, for the investigations of direct ME effect. For the investigations of inverse ME effect we used ethod, based on easuring of alternating voltage, that aearing at the easuring coil when it lace in slowly changing agnetic field and when the alternating electric field aly to the sale. At first was investigated the field deendence of low-frequency ME signal. ME effect deendence of bias field strength was easured at the constant value of alternating agnetic field strength Oe. Then was investigated frequency deendence of agnetoelectric coefficient in the electroechanical resonance region at the bias field strength, that agree with a axiu of effect. The oen circuit condition realized very well at the easureent. Exeriental data are shown in table. Table. Table inforation Ferrite ercentage, % exressions (8 and ( for the value r for inverse effect and for the value a for direct effect are equal to zero. For the Poisson s coefficient ν =. 4 the equality to zero of these exressions is haen when value κ =. 74. This ilyies, that the resonant frequency defining by con- dition f res =.74/(π ρ s ( ν R. Piezoceraic density PZT ρ = 78 kg/, coliance odule s = 5. / N, ferrite-nickel sinel density ρ = 5 kg/, its coliance odule s = 6.5 / N. With increase of the ferrite ercentage it is occur of coosite effective density decrease and coosite effective coliance decrease, as result to increase of resonant and antiresonant frequency. Resonant and antiresonant frequency s difference defining by the coefficient of electroechanical couling K, as easily to see by exressions (8 and ( for r and for a. Really, suosing f = f + f and exanding exression anres res for a by sall araeter κ = f π ρ ν R for relative difference of frequencies we get: f ( + ν K. ( f κ ( / κ νj ( κ /( κ J ( κ res Or, substituting the nuerical values ν =. 4 and κ =.74, for relative difference of frequencies we get the resultant exression in the following for: f f res.4 K ( With increase of the ferrite ercentage, the coefficient of electroechanical connection increasing in consequence of coosite effective iezoodule value increase, as a result at the increase of resonant and antiresonant frequency difference. The exeriental and theoretical frequency deendences of inverse ME conversion factor α B for PZT(- 7 ass.%, NiFe,9Co,O4 ass.% structure reresented at fig.5. The exeriental easuring realized when value of bias field H = 8 Oe, that eet the axiu of ME interaction. f res, khz 89,9,4 4,8 59,7 78,8 9, f anres, khz,9 7,9 4,6 6,4 8,5 9,5 f, khz, 4,5,8,7,7,5 α ( = f, G c V 7 49 B, T f res / α E, T( f = fanres, V/( c Oe α ( f = khz, G c V,6,7,94,6,7,65 B, T / α E, T( f = khz, V/( c Oe As following fro exerient, in full accordance with theory, there is a eak increase of effect at the resonant and antiresonant frequency. This frequencies values defining by araeter κ = kr = ω ρ s ( R, at which the values of ν Figure 5. Inverse ME conversion factor B α frequency deendences for transverse effects for PZT(- 7 ass.%, NiFe,9Co,O4 ass.% structure, where the full line is the theoretical deendence, oints are the exeriental data

6 Science Research, ( : -8 7 In this case the inverse ME signal alification occurring at the frequency f res = 5 khz, and the inverse ME conversion factor resonant value three ties as any as its low-frequency value. In coarison with ultilayer coosites, this good quality accounted for the alied of iezoelectric with high good quality (Q and the selection of oerating ractices, that resulting to erforance of the echanical contact between slinters. There is a siilar effect was observed on the sales with other structures, but the resonance frequencies are vary deending on coosite ercentage coosition vary. The exeriental and theoretical resonant frequency deendences of ferrite content in coosite are reresented at fig.6. Figure 8. The difference of resonance and antiresonance frequencies, where the full line is the theoretical deendence, oints are the exeriental data With increase of the ferrite ercentage by iezoodule effective value decrease and decrease of electroechanical couling factor, as a resulted to decrease of resonance and antiresonance frequencies. Effect of coosite structure on the inverse ME conversion factor ( f res = 5 khz reresented at fig.9. We lotting of inverse ME conversion factor deendence of ferrite inclusion volue fraction by using the theoretical odel. Figure 6. Resonance frequency deendences of ferrite content in coosite, where the full line is the theoretical deendence, oints are the exeriental data As aears fro the fig. 6, with increase of ferrite ercentage there is a resonant frequency increase. This account for coosite effective density and effective coliance decrease by ferrite ercentage increase, that resulting in resonant frequency increase. The resonance and antiresonance frequencies deendences of ferrite content in coosite are reresented at fig.7. The difference of resonance and antiresonance frequencies reresented at fig.8. Figure 7. Resonance (the botto characteristic and antiresonance (the uer characteristic frequencies deendences of ferrite content in coosite, where the full line is the theoretical deendence, oints are the exeriental data Figure 9. Deendence of inverse ME conversion factor by ferrite inclusion volue fraction ( f res = 5 khz, where the full line is the theoretical deendence, oints are the exeriental data As can be seen by diagra (fig. 9, the deendence of inverse ME conversion factor by ferrite inclusion volue fraction has a axiu. The inverse ME conversion factor α B is roortional to roduct of effective values of iezoelectric and iezoagnetic odules and inversely roortional to odule of coosite coliance. With ferrite ercentage increase there is iezoodule decrease, that reducing to decrease of α B. As resulting to increase of coefficient with ferrite ercentage increase at first, then coefficient aounting to axiu, and then it has decreased. The inverse ME conversion factor α B is roortional to roduct of iezoelectric and iezoagnetic effective odules and inversely roortional to coosite coliance odule. With increase of the ferrite ercentage, on the one hand, there is increase of the iezoelectric odule s effective value and decrease of the coliance odule, that leading to increase of value α B, on the other hand, with increase of the ferrite ercentage, there is decrease of the iezoodule, that leading to decrease of value α B. As a

7 8 D. A. Filiov et al: Inverse agnetoelectric effect in disk sales of ferrite iezoelectric coosites consequence of that, the value of coefficient is increase at first with increase of the ferrite ercentage, is at the high and then is decrease. Siilarly leading oneself the ME voltage coefficient. Its value also is roortionally to roduct of iezoelectric and iezoagnetic effective odules. However it is inversely not only to coosite coliance odule, but is inversely to roduct of coliance odule and coosite erittivity coefficient, that value also decrease with increase of ferrite concentration. This is leading to that the ME voltage coefficient axiu account to the ost content of ferrite, than the inverse ME conversion factor axiu. References [] I. B. Dzyaloshinskii, Zh. Eks. Teor. Fiz. 7, 88 (959. [] D. N. Astrov, Zh. Eks. Teor. Fiz. 4, 5 (96. [] V.J. Folen, G.T. Rado, E.W. Stalder. Phys. Rev. Lett. 6, 67 (96. [4] Е.А.Turov. Physics-Usekhi 64, 5 (994. [5] Antonenkov O.V., Nikiforov I.S., Filiov D.A. Ferroelectrics. 79, 57 (. [6] M. Fiebig. J. Phys. D: Al. Phys. 8, (5. [7] S. Dong, J.F. Li, D.Viehland, J. Cheng, L.E. Cross. Al. Phys. Lett. 85, 54 (4. [8] Y.K. Fetisov, V.M. Petrov, G. Srinivasan. J. Mater. Res., 74 (7. [9] A. A. Bush, K. E. Kaentsev, V. F. Meshcheryakov, Y. K. Fetisov, D. V. Chashin and L. Y. Fetisov, Zh. Tekh. Fiz. 79 (9, 7 (9. [] Y.K. Fetisov, K.E. Kaentsev, D.V. Chashin, L.Y. Fetisov, G. Srinivasan. J. Al. Phys. 5, 98 (9. [] D.А. Filiov, Т.А. Galkina, G. Srinivasan. Pis a Zh. Tekh. 6,, (. [] G. Harshe, J.O. Dougherty, R. E. Newnha. Int. J. Al. Electroagn. Mater (99. [] G. Harshe, J.P. Dougherty, R.E. Newnha. Int. J. Al. Electroagn. Mater (99. [4] M.I. Bichurin, V.M. Petrov, G. Srinivasan. Phys. Rev. B (. [5] M.I. Bichurin, V.M. Petrov, D.А. Filiov, V.М. Laletin, G. Srinivasan. Persectivnye aterialy 6, 5 (4. [6] W.P. Mazon. Phys. Rev. 74, 4 (948. [7] D.А. Filiov, M.I. Bichurin, V.M. Petrov, V.М. Laletin, G. Srinivasan. FТТ, 46, 9, 6 (4.