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Voltage-induced strain control of the magnetic anisotropy in a Ni thin film onflexible substrate

F. Zighem,a) D. Faurie, S. Mercone, M. Belmeguenai, and H. HaddadiLSPM-CNRS, Universit!e Paris XIII, Villetaneuse, France

(Received 9 June 2013; accepted 22 July 2013; published online 15 August 2013)

Voltage-induced magnetic anisotropy has been quantitatively studied in polycrystalline Ni thin filmdeposited on flexible substrate using microstrip ferromagnetic resonance. This anisotropy is inducedby a piezoelectric actuator on which the film/substrate system was glued. In our work, the control ofthe anisotropy through the applied elastic strains is facilitated by the compliant elastic behavior ofthe substrate. The in-plane strains in the film induced by the piezoelectric actuation have beenmeasured by the digital image correlation technique. Non-linear variation of the resonance field asfunction of the applied voltage is found and well reproduced by taking into account the nonlinear and hysteretic variations of the induced in-plane strains as function of the appliedvoltage. Moreover, we show that initial uniaxial anisotropy attributed to compliant substratecurvature is fully compensated by the voltage induced anisotropy. VC 2013 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4817645]

I. INTRODUCTION

Prospect of controlling local magnetization using elec-tric fields for low power and ultra fast new electronics hasresulted in an amount of new research domains mainlyfocused on artificial engineered materials. Two decades ago,the condensed matter community began studying the interac-tions between a spin polarized current1,2 and magnetic do-main walls in magnetic thin films. Percolation and domainwall excitation (precessional and/or translational) by spinangular momentum transfer from the current to the magneticsystem pushed the study of new magnetic materials andadvanced lithographed magnetic devices.3–5 Since then, newmagnetic configurations have been engineered by properlyshaping magnetic nanostructures (for instance: U-shapednanowires, focused ion beam nanobridges, giant magnetore-sistance spin valve nanowires systems, and magnetic race-track memory devices). Unfortunately, many experimentalstudies have indicated extremely low current-driven domainwall velocity and also non-adiabatic contributions to current-magnetization interaction, which introduce intrinsic thresh-old current for domain wall motion. Clearly, either the maxi-mum possible speed of domain wall based driven recordingand storage systems or power dissipation (directly linked tothe current threshold) is not suitable for ultra-fast futureelectronics.

In order to overcome these important factors limitingthe future miniaturization of integrated recording circuitsbased on simple magnetic nanostructured material, latestapproaches start to involve intrinsic multiferroic and magne-toelectric artificial materials. Natural multiferroics havequite immediately shown a too weak magnetic order at roomtemperature making them useless for applications.6–8 Usingartificial nanostructures combining the two different orders(magnetic and electric one) in a unique system seems to be

the only promising route. The easiest artificial architecturefor a voltage control of the magnetization in those kinds ofmaterials appears to be piezoelectric/magnetostrictivebilayers presenting a good strain-mediated coupling at theinterface.9–11 In order to achieve the highest magnetoelectriccoupling for an efficient voltage manipulation of the magnet-ization, the magnetic device has to be encapsulated inside apiezoelectric environment which leads to two main difficul-ties. First, the deposition of piezoelectric material generallyneeds high temperature and the most of the time also postannealing treatment under severe condition of oxidation.This latter could degrade the good magnetic properties of themagnetic layer. Second, the clamping effect due to the sub-strate limits the stress applicable to the magnetization by thepiezoelectric environment reducing perspective on applica-tions. Indeed, in this kind of bilayers (piezoelectric/magneto-strictive), a significant strained induced magnetoelectriccoupling is obtained only in the presence of non negligiblein-plane strains. In order to avoid both latters’ issues, inversemagnetoelectric effect has been studied by depositing ferro-magnetic thin films on a piezoelectric substrate12–19 or bydirectly gluing (via an epoxy glue) a (thin film/rigid sub-strate) magnetic system onto a piezoelectric actuator.20–23

Noticeably, Brandlmaier et al.20 have shown that filmstrains are much smaller (50%) than the expected values incase of a complete strain transmission through the cementand the rigid substrate.

In this paper, voltage induced in-plane magnetic anisot-ropy has been quantitatively studied in a magnetostrictivefilm deposited on a flexible substrate and glued onto a piezo-electric actuator. For this study, Nickel has been chosen dueto its well-known negative effective magnetostriction coeffi-cient at saturation even in a polycrystalline film with no pre-ferred orientations. Digital image correlation (DIC) andmicro-strip ferromagnetic resonance (MS-FMR) techniqueshave been employed to (i) quantitatively measure thein-plane strains transmitted to the ferromagnetic filma)zighem@univ-paris13.fr

0021-8979/2013/114(7)/073902/6/$30.00 VC 2013 AIP Publishing LLC114, 073902-1

JOURNAL OF APPLIED PHYSICS 114, 073902 (2013)

responsible of the inverse magnetoelectric effect occurringin the fabricated biferroic structure and (ii) experience thevoltage-driven changes of the in-plane magnetic anisotropy.

II. EXPERIMENTAL DETAILS

A 200 nm-thick Nickel film was deposited on a flexible(KaptonVR 24) substrate (125 lm) by radio frequency sputteringat room temperature. The Ni film was found to be polycrystal-line with no strong preferred orientations by x-ray diffraction.After deposition, the film/substrate system was glued onto apiezoelectric actuator. A flexible compliant substrate(Young’s modulus E! 4 GPa) has been chosen in order toavoid clamping effects which can occur with rigid substrates(for example, E! 180 GPa for Silicon) and thus to have maxi-mum strain transmission in between the piezoelectric actuatorand the film.20,21,23 Figure 1 shows a sketch of the Ni thin filmand of the structure allowing voltage-control of the in-planemagnetic anisotropy. Two different axes systems are defined.The first one (x, y, z) is attached to the Ni film, whereas thesecond one (X, Y, Z) describes the piezoelectric actuator ge-ometry. uH (resp. /H) is the angle between x (resp. X) axisand the applied magnetic field (~H); the magnetization (~M) isdefined by its polar angles (h and u) as usual.25

All the measurements presented here were performed atroom temperature using both MS-FMR and DIC technique.MS-FMR was employed to probe the influence of the appliedvoltage on the magnetic properties via the resonance field ofthe uniform precession mode. The DIC was used to quantita-tively measure the in-plane strains (eXX and eYY) induced bythe piezoelectric actuator at the surface of the ferromagneticfilm.

MS-FMR experiments allowed the resonance field Hres

probing by sweeping the applied magnetic field in presence ofa fixed pumping radio frequency (RF) field ~hrf . In this kind ofRF-resonance technique, a weak modulation of the appliedfield ("2–5 Oe at 1480 Hz) is performed in order to optimizethe signal to noise ratio for a better lock-in detection of thesignal. Thus, this technique gives access to the first field deriv-ative of the RF absorption as a function of the applied field. Amore detailed presentation can be found elsewhere.26

DIC is a technique which allows displacement and strainfields measurements on an object surface by capturing

images of the object surface at different states.27,28 One stateis recorded before applying voltage, i.e., the reference image,and the other states are subsequent images of the deformedobject. DIC generally uses random patterns of gray levels ofthe sample surface to measure the displacement via a corre-lation of a pair of digital images. In this study, the film sur-face was spray-painted with a speckle pattern to generate acontrast in the uniform specimen face. Hence, from themeasured strain fields, we can estimate the mean in-planestrains eXX and eYY , that cannot be straightforwardly attainedwith other techniques such as x-ray diffraction.29

III. RESULTS AND DISCUSSION

In Sec. III A, we present the magnetic parameters of theNi film at zero applied voltage. Section III B is devoted to aquantitative measure of the in-plane strains (eXX and eYY) atthe surface of the Ni film using the DIC technique. In Sec.III C, we present the analytical model allowing the conver-sion of the applied voltage into strains, which we developedto analyze the influence of the applied voltage on the mag-netic properties of the film observed by MS-FMR.

A. Magnetic parameters at zero applied voltage

MS-FMR experiments in absence of applied voltagewere performed in order to determine the magnetic parame-ters of the Ni thin film. Indeed, at zero voltage, the frequencyof the uniform mode is expected to only depend on the gyro-magnetic factor c, the magnetization at saturation MS, andthe possible presence of magnetic anisotropies.30 Figure 2(a)shows the frequency variation of the uniform mode as func-tion of the magnetic field applied either along x direction(open symbols) or y direction (filled symbols). The angulardependence of the resonance field of the uniform mode at10 GHz is also presented in Figure 2(b). A non negligibleuniaxial anisotropy of magnitude "310 Oe is observed alongx direction (i. e., uH ! 0) corresponding to a minimum reso-nance field. Since the studied Ni film is polycrystalline withno preferred crystallographic orientations, no macroscopicmagnetocrystalline effect is expected; thus, this uniaxial ani-sotropy should have a magnetoelastic origin. Indeed, as thefilm is deposited on a flexible substrate, a slight curvaturealong a given direction during the elaboration process should

FIG. 1. (a) Sketch of the 200 nm thick Ni thin film deposited onto aKaptonVR substrate (125 lm). (b) Schematic diagram depicting the appliedvoltage within the Piezoelectric/KaptonVR /Ni heterostructure. Note that twodifferent coordinate systems are used; (x, y, z) and (X, Y, Z), respectively,related to the Ni thin film and to the piezoelectric actuator. Thereby, uH isthe angle between the applied magnetic field ~H and x direction and /H is theangle between ~H and X direction.

FIG. 2. (a) Frequency variation of the uniform mode as function of the in-plane applied magnetic field at zero applied voltage. Open symbols areobtained with uH ! 0 #~H k x$ and the filled ones are obtained withuH ! p=2 #~H k y$. (b) In-plane angular dependence of the resonance field at10 GHz. The solid and dashed lines in (a) and (b) are best fits to the experi-mental data using the following parameters: c ! 1:885% 107 Hz:Oe&1; MS

! 480 emu:cm&3; KU ! 7:3% 104 erg:cm&3 and Eq. (1).

073902-2 Zighem et al. J. Appl. Phys. 114, 073902 (2013)

lead to a non zero magnetoelastic anisotropy of the main-tained flat sample during FMR measurements, as suggestedby Zhang et al.31 In this work, this uniaxial anisotropy willbe fitted by using an ad hoc uniaxial anisotropy characterizedby an anisotropy constant KU. From now, easy axis will referto x direction since the angle between x and the uniaxial ani-sotropy is close to zero. Thus, the lines (continuous anddashed) in Figure 2 correspond to fits using the followingexpression obtained with the assumption of an in-plane mag-netization (i.e., h ! p

2):

f 2 ! c2p

! "2

Hres cos#u& uH$ '2KU

MScos2u

! "

% Hres cos#u& uH$ '2KU

MScos2u' 4pMS

! "; (1)

where f is the microwave driven frequency. It results fromthe analysis of the data that the magnetic parameters areclose to the one of bulk Ni.32 A magnetization at saturation(MS) of 480 emu.cm&3 (4pMS ’ 6030 G) with a gyromag-netic factor (c) of 1:885% 107 Hz:Oe&1 is found. The uniax-ial anisotropy constant is estimated to KU ! 7:3%104 erg:cm&3 (we define HU ! 2KU=MS ’ 315 Oe). Thesemeasurements performed at zero voltage will serve as refer-ence in order to evaluate the changes related to the in-planestrains induced by the piezoelectric actuator.

B. Quantitative in-plane strains measurements by DIC

DIC technique has been used to measure the in-planestrains (eXX and eYY) at the surface of the film. The measure-ments have been performed by varying the external voltagefrom 0 V to 100 V (filled symbols) and back to 0 V (opensymbols) with steps of around 5 V. Note that the first 0 Vimage was taken after applying a “saturating” voltage of100 V in order to avoid hysteresis effects which can occur af-ter several hours at zero voltage. The measured eXX and eYY

as function of the applied voltage are shown in Figure 3 and

reach, respectively, 10&3 and &0:5% 10&3 at 100 V. IndeedeXX is found to be positive, whereas eYY is found to be nega-tive with a ratio j eYY

eXXj ’ 0:5. Non linear variations for both

eXX and eYY with the voltage are observed due to the intrinsicproperties of the ferroelectric material used in the fabricationof the actuator.33 This behavior is well reproducible after“saturating” the actuator a first time (at 100 V in this work).It should be noted that these values correspond to mean val-ues calculated in area close to 4 % 4 mm2 (area of the thinfilm). However, the heterogeneities of eXX and eYY can beneglected compared to their “absolute” values and even atthe edge of the 4 % 4 mm2 area. Consequently, the measuredeXX and eYY can be considered as homogeneous in XY plane.Moreover, the estimated in-plane shear strains by DIC werefound to be negligible.

In addition, the analysis of eXX and eYY on an uncoatedarea of the actuator gives same values. Thus, the transmissionof the in-plane strains between the actuator and the surface ofthe film is close to 100%. Therefore, the values of eXX and eYY

shown in Figure 3 should be homogeneous in the thickness,i.e., the strains are well transmitted through the cement andthrough the film/substrate interface. This result is consistentwith previous studies performed on metallic films of compara-ble thicknesses deposited onto flexible substrates and analyzedboth by DIC and x-ray diffraction techniques.28,34

C. Voltage induced magnetic anisotropy probed byMS-FMR

The voltage induced anisotropy has been studied in twodifferent configurations defined by the angle between theeasy axis and X direction (see Figure 4). In those configura-tions, the easy axis is aligned either along Y (first configura-tion, Figure 4(a)) or along X (second configuration, Figure4(b)). As previously mentioned, the Ni film is polycrystallinewith no preferred orientations. This allows to define an effec-tive isotropic magnetostrictive coefficient at saturation k.35

In these conditions and because of the opposite sign of eXX

and eYY values, an additional in-plane anisotropy field paral-lel to Y direction is expected (in the range 0-100 V).Consequently, the initial easy axis is expected to beincreased in the first configuration, while a competitionbetween the initial in-plane anisotropy and the voltageinduced one will take place in the second configuration.

The influence of the applied voltage on the magneticproperties of the thin film has been probed by MS-FMR

FIG. 3. DIC measurements of the mean in-plane strains (eXX and eYY) at thesurface of the Ni film. The circles correspond to eXX while squares corre-spond to eYY . The applied external voltage is ranging from 0 V to 100 V(filled symbols) and back to 0 V (open symbols) with steps of "5 V. The firstmeasurement at 0 V has been performed after “saturating” the actuator at100 V to avoid training effect of the polarization.

FIG. 4. (a), (b) Top view sketches of the two configurations used in the insitu MS-FMR investigations.

073902-3 Zighem et al. J. Appl. Phys. 114, 073902 (2013)

technique. Figures 5(a) and 5(b) show typical MS-FMR ex-perimental spectra recorded at 10 GHz with an applied mag-netic field along the initial hard axis (i.e., /H ! 0 for the firstconfiguration and /H ! p

2 for the second configuration) andfor different applied voltages (0, 30, 60, and 100 V). Notethat the experimental conditions (in term of applied voltage)were same than for the DIC study. Moreover, in order toavoid non linear variations of k as function of the appliedmagnetic field,35 the experimental spectra have beenrecorded at 10 GHz. In these conditions, the deduced reso-nance fields are in a magnetic saturating regime (as shown inFigure 2).

It clearly appears that the resonance field increases(resp. decreases) with the applied voltage in the first (resp.second) configuration. This indicates that the initial uniaxialanisotropy is either reinforced in the first configuration orsoftened in the second one. This is consistent with a negativemagnetostriction coefficient.17 The deduced resonance fieldsas function of the applied voltage are presented in Figures5(c) and 5(d). Here, filled symbols represent the upsweep (0to 100 V) and open symbols represent the downsweep of theapplied voltage (100 to 0 V). The observed non-linear andhysteretic variations of the resonance field are due to the

variations of eXX and eYY as function of the applied voltage(see Figure 3).

In order to quantitatively bind the resonance field varia-tions to the in-plane strains induced by the applied voltage, wecan calculate the uniform precession mode frequency as func-tion of the applied voltage (strain) by adding a magnetoelasticenergy term FME to the total magnetic energy density F of theNi film. In an isotropic case, which is closely ours (non-tex-tured Ni film), FME energy term can be written as:

FME ! &3

2k c2

x &1

3

! "rxx ' c2

y &1

3

! "ryy

! "(2)

rxx and ryy being the in-plane principal stress tensor compo-nents, whereas cx and cy correspond to the direction cosinesof the in-plane magnetization. Moreover, the relationbetween the principal components of stress and strain tensorsis given by the following equations, where E is the Young’smodulus and ! is the Poisson’s ratio:

rxx !E

1' !

! "1

1& !exx '

!

1& !eyy

! "(3)

ryy !E

1' !

! "1

1& !eyy '

!

1& !exx

! "(4)

The voltage dependence of the uniform mode resonancefield is calculated by using the following relation:36

2pfc

# $2! 1#Msinh$2

@2F@h2

@2F@u2 & # @

2F@h@u$

2# $

. Assuming a Young’s

modulus of 2% 1010 dyn.cm&2 (( 200 GPa) and a Poisson’sratio of 0.3,37 the only undetermined parameter is k.Introducing the experimentally found voltage dependence ofeXX and eYY , the best fits of all the experiments performed in

the both studied configurations gives k ! &26% 10&6. Itshould be noted that this value is consistent with commonlyfound values for non-textured polycrystalline Ni film (about–30% 10&6) and validate our overall approach. It should benoted here that the polycrystalline theoretical value can befound by applying an arithmetic average of the analyticalsolutions given by Reuss and Voigt models:38

kReuss ! 2

5k100 '

3

5k111 (5)

kVoigt ! 2

2' 3Ak100 '

3A

2' 3Ak111; (6)

where k100 and k111 are, respectively, the magnetostrictioncoefficients of h100i andh111i directions families (respec-tively, equal to &51% 10&6 and &22.4% 10&6), A is theZener anisotropy index (A ! 2C44=#C11 & C12$ ) 2:6 forNi).35

Note that the hysteretic and non-linear variations of theresonance field as function of the applied voltage are wellreproduced by the analytical model proposed.

Figure 6 shows variations of the resonance field as func-tion of the applied voltage for different uH angles (0; p4 andp2). Here, open squares correspond to experimental dataobtained from the first configuration, while filled circles are

FIG. 5. (a), (b) Experimental spectra recorded at 10 GHz with uH ! 0 at dif-ferent voltages for the first and the second configurations illustrated inFigure 4, respectively. (c), (d) Resonance field variations (at 10 GHz) asfunction of the applied voltage with uH ! 0 for the first and second configu-rations, respectively. The open symbols correspond to upsweep (0 to 100 V),while filled symbols correspond to downsweep (100 to 0 V). The solid anddashed lines are best fits to the experimental data by using an analyticalexpression deduced from equations (2)–(4) An isotropic magnetostrictioncoefficient of &26% 10&6 is deduced.

073902-4 Zighem et al. J. Appl. Phys. 114, 073902 (2013)

obtained from the second configuration. The measurementscoming from the first configuration indicate that the voltageinduced anisotropy is parallel to the initial uniaxial one, andconsequently, the magnitude of the easy axis along Y isincreased. This behavior is observed via the differencebetween the resonance fields measured at uH ! 0 anduH ! p

2, which is roughly 2HU " 600 Oe at zero voltage andaround 1400 Oe at 100 V. Thus, the magnitude of the easyaxis at 100 V is equal to more than twice time the measuredvalue in the absence of voltage. The second configuration ismore interesting since a competition between the initial uni-axial anisotropy and the voltage induced one takes place. Itresults that the initial anisotropy is totally compensated ataround 80 V (i.e., HME ! HU, where HME being the inducedmagnetoelastic anisotropy field) which leads to an isotropicin-plane behavior of the resonance field. Interestingly, at100 V, a non zero easy axis perpendicular to the initial one at0 V is observed.

The solid and dashed lines in Figure 6 are fits to the ex-perimental data calculated by using the parameters previ-ously given. One can note the good agreement between theexperimental measurements and the calculated lines.

Note that a non-negligible overestimation of the magne-tostrictive coefficient can occurs if we neglect the influenceof eYY (i.e., assumption of a uniaxial strain). Indeed, the cal-culated lines (not shown here) in this approximation arequasi similar to the one previously calculated. However, anoverestimation of k is performed (k ! &40% 10&6 insteadof &26% 10&6). Thus, the present study also demonstratesthat a full characterization of the in-plane strains is needed ifwe want to quantitatively analyze the inverse magnetoelec-tric effect occurring inside such structures.

IV. CONCLUSION

• Magnetic anisotropy in Nickel thin films grown onKaptonVR substrate has been studied by microstrip ferro-magnetic resonance. An “initial” uniaxial anisotropy has

been found and is most probably related to the non-flatness of the compliant substrate during deposition.

• Piezo-actuation of Ni/polyimide system has been per-formed allowing a voltage-induced strain control leadingto a change of the total magnetic anisotropy.

• An accurate study by digital image correlation techniqueallowed a good knowledge of in-plane macroscopic strainsat the surface of the film as function of applied voltage tothe piezoelectric actuator. This technique that allows highprecision (about 5% 10&5) is found to be relevant fordetermining in-plane strains in the elastic domain.

• A comparison of strains of the film with that of the piezo-electric actuator demonstrates the full transmission of in-plane elastic strains across the whole system, which is dueto the compliant behavior of the polyimide substrate.

• A simple analytical model taking into account of themeasured strains as function of applied voltage wellmatches the experimental data. The only adjusted parame-ter is the effective magnetostrictive coefficient at magneticsaturation of Ni film and is found to be close to previouslypublished values.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the French ResearchAgency (ANR) for their financial support (project ANR 2010JCJC 090601 entitled “SpinStress”). The authors alsoacknowledge financial support of the CNRS in the frameworkof the “PEPS INSIS” program (FERROFLEX project). Theauthors thank Tarik Sadat (PhD student at Paris 13th univer-sity) for sharing his automatic data analysis program.

1J. C. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996).2S. I. Kiselev, J. C. Sankey, I. N. Krivorotov, N. C. Emley, R. J. Schoelkopf,R. A. Buhrman, and D. C. Ralph, Nature (London) 425, 380 (2003).

3L. Thomas and S. Parkin, “Handbook of magnetism and advanced mag-netic materials,” in Vol. 2: Micromagnetism, edited by Helmut Kronmullerand Stuart Parkin (John Wiley & Sons, 2007).

4S. Mercone, A. Wahl, Ch. Simon, and C. Martin, Phys. Rev. B 65, 214428(2002).

5A. Wahl, S. Mercone, A. Pautrat, M. Pollet, Ch. Simon, and D.Sedmidubsky, Phys. Rev. B 68, 094429 (2003).

6S.-W. Cheong and M. Mostovo, Nature Mater. 6, 13 (2007).7V. Skumryev, V. Laukhin, I. Fina, X. Mart!ı, F. S!anchez, M. Gospodinov,and J. Fontcuberta, Phys. Rev. Lett. 106, 057206 (2011).

8N. A. Spaldin and M. Fiebig, Science 309, 391 (2005).9W. Eerenstein, M. Wiora, J. L. Prieto, J. F. Scott, and N. D. Mathur,Nature Mater. 6, 348 (2007).

10N. Lei, S. Park, P. Lecoeur, D. Ravelosona, and C. Chappert, Phys. Rev B84, 012404 (2011).

11C. A. F. Vaz, J. Hoffman, C. H. Ahn, and R. Ramesh, Adv. Mater. 22,2900 (2010).

12M. Liu, O. Obi, Z. Cai, J. Lou, G. Yang, K. S. Ziemer, and N. X. Sun,J. Appl. Phys. 107, 073916 (2010).

13J. Lou, M. Liu, D. Reed, Y. H. Ren, and N. X. Sun, Adv. Mater. 21, 4711(2009).

14Z. Wang, R. Viswan, B. Hu, J.-F. Li, V. G. Harris, and D. Viehland,J. Appl. Phys. 111, 034108 (2012).

15Z. Li, J. Hu, L. Shu, Y. Gao, Y. Shen, Y. Lin, and C. W. Nan, J. App.Phys. 111, 033918 (2012).

16C. Pettiford, J. Lou, L. Russell, and N. X. Sun, App. Phys. Lett. 92,122506 (2008).

17M. Weiler, A. Brandlmaier, S. Gepr"ags, M. Althammer, M. Opel, C.Bihler, H. Huebl, M. S. Brandt, R. Gross, and S. T. B. Goennenwein, NewJ. Phys. 11, 013021 (2009).

FIG. 6. Resonance field as function of the applied voltage at 10 GHz for dif-ferent uH values (0; p4 and p

2$. Filled symbols correspond to the experimentaldata obtained from the first configuration (Figure 4(a)) while open symbolsare obtained from the second configuration (Figure 4(b)). The dashed andcontinuous lines are fits to the experimental data obtained by using an ana-lytical expression deduced from Eqs. (2)–(4). A magnetostrictive coefficientat saturation of magnitude k ! &26% 10&6 is deduced.

073902-5 Zighem et al. J. Appl. Phys. 114, 073902 (2013)

18A. Brandlmaier, S. Gepr"ags, G. Woltersdorf, R. Gross, and S. T. B.Goennenwein, J. App. Phys. 110, 043913 (2011).

19A. Brandlmaier, M. Brasse, S. Gepr"ags, M. Weiler, R. Gross, and S. T. B.Goennenwein, Eur. Phys. J. B 85, 124 (2012).

20A. Brandlmaier et al., Phys. Rev. B 77, 104445 (2008).21Y. Chen, A. Yang, M. R. Paudel, S. Stadler, C. Vittoria, and V. G. Harris,

Phys. Rev. B 83, 104406 (2011).22Y. Chen, J. Gao, J. Lou, M. Liu, S. D. Yoon, A. L. Geiler, M. Nedoroscik,

D. Heiman, N. X. Sun, C. Vittoria, and V. G. Harris, J. App. Phys. 105,07A510 (2009).

23J. Lou, D. Reed, C. Pettiford, M. Liu, P. Han, S. Dong, and N. X. Sun,App. Phys. Lett. 92, 262502 (2008).

24For more information about the KaptonVR polyimide film, see http://www2.dupont.com/Kapton/en_US/.

25M. Belmeguenai, F. Zighem, Y. Roussign!e, S.-M. Ch!erif, P. Moch, K.Westerholt, G. Woltersdorf, and G. Bayreuther, Phys. Rev. B 79, 024419(2009).

26M. Belmeguenai, H. Tuzcuoglu, M. S. Gabor, T. Petrisor, Jr., C. Tiusan,D. Berling, F. Zighem, T. Chauveau, S. M. Ch!erif, and P. Moch, Phys.Rev. B 87, 184431 (2013).

27H. Haddadi and S. Belhabib, Int. J. Mech. Sci. 62, 47 (2012).28S. Djaziri, P. O. Renault, F. Hild, E. Le Bourhis, P. Goudeau, D.

Thiaudiere, and D. Faurie, J. Appl. Cryst. 44, 1071 (2011).29S. Djaziri, D. Faurie, E. Le Bourhis, Ph. Goudeau, P.-O. Renault,

C. Mocuta, D. Thiaudiere, and F. Hild, Thin Solid Films 530, 30 (2012).30F. Zighem, Y. Roussign!e, S. M. Ch!erif, P. Moch, J. Ben Youssef, and F.

Paumier, J. Phys.: Condens. Matter. 22, 406001 (2010).31X. Zhang, Q. Zhan, G. Dai, Y. Liu, Z. Zuo, H. Yang, B. Chen, and R.-W.

Li, J. App. Phys. 113, 17A901 (2013).32C. A. Neugebauer, Phys. Rev. 116, 1441 (1959).33Details on the piezoelectric actuator structure can be found at http://www.

physikinstrumente.com/.34S. Djaziri, D. Faurie, P. O. Renault, E. Le Bourhis, P. Goudeau, G.

Geandier, and D. Thiaudiere, Acta Mater 61, 5067 (2013).35E. Du Tr!emollet De Lacheisserie, Magnetostriction. Theory and

Application of Magnetoelasticity (Boca Raton, FL: CRC Press, 1993).36U. Netzelmann, J. Appl. Phys. 68, 1800 (1990).37J. C. Smithells, Metals Reference Book, 5th ed. (London: Butterworths,

1976).38H. B. Callen and N. Goldberg, J. Appl. Phys. 36, 976 (1965).

073902-6 Zighem et al. J. Appl. Phys. 114, 073902 (2013)