Strain-controlled magnetic domain wall propagation in hybrid piezoelectric/ferromagnetic structures

Abstract

The control of magnetic order in nanoscale devices underpins many proposals for integrating spintronics concepts into conventional electronics. A key challenge lies in finding an energy-efficient means of control, as power dissipation remains an important factor limiting future miniaturization of integrated circuits. One promising approach involves magnetoelectric coupling in magnetostrictive/piezoelectric systems, where induced strains can bear directly on the magnetic anisotropy. While such processes have been demonstrated in several multiferroic heterostructures, the incorporation of such complex materials into practical geometries has been lacking. Here we demonstrate the possibility of generating sizeable anisotropy changes, through induced strains driven by applied electric fields, in hybrid piezoelectric/spin-valve nanowires. By combining magneto-optical Kerr effect and magnetoresistance measurements, we show that domain wall propagation fields can be doubled under locally applied strains. These results highlight the prospect of constructing low-power domain wall gates for magnetic logic devices.

ARTICLE

Received 23 Apr 2012 | Accepted 14 Dec 2012 | Published 22 Jan 2013

Na Lei1,2, Thibaut Devolder1,2, Guillaume Agnus1,2, Pascal Aubert1,2, Laurent Daniel3, Joo-Von Kim1,2, Weisheng Zhao1,2, Theodossis Trypiniotis4, Russell P. Cowburn4, Claude Chappert1,2, Dan Ravelosona1,2 & Philippe Lecoeur1,2

The control of magnetic order in nanoscale devices underpins many proposals for integrating spintronics concepts into conventional electronics. A key challenge lies in nding an energy-efcient means of control, as power dissipation remains an important factor limiting future miniaturization of integrated circuits. One promising approach involves magnetoelectric coupling in magnetostrictive/piezoelectric systems, where induced strains can bear directly on the magnetic anisotropy. While such processes have been demonstrated in several multiferroic heterostructures, the incorporation of such complex materials into practical geometries has been lacking. Here we demonstrate the possibility of generating sizeable anisotropy changes, through induced strains driven by applied electric elds, in hybrid piezoelectric/spin-valve nanowires. By combining magneto-optical Kerr effect and magnetoresistance measurements, we show that domain wall propagation elds can be doubled under locally applied strains. These results highlight the prospect of constructing low-power domain wall gates for magnetic logic devices.

1 Institut dElectronique Fondamentale, Universit Paris-Sud, 91405 Orsay, France. 2 UMR 8622, CNRS, 91405 Orsay, France. 3 Laboratoire de Gnie Electrique de Paris, CNRS, UMR8507/SUPELEC/UPMC/Univ Paris-Sud, 91192 Gif-sur-Yvette, France. 4 Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, UK. Correspondence and requests for materials should be addressed to N.L. (email: mailto:[email protected]

Web End [email protected] ).

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DOI: 10.1038/ncomms2386 OPEN

Strain-controlled magnetic domain wall propagation in hybrid piezoelectric/ferromagnetic structures

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms2386

The prospect of controlling local magnetization using electric elds for ultra-low-power spintronics has resulted in a new research direction that involves multiferroic and

magnetoelectric materials16. However, existing approaches involving natural multiferroics are either limited by weak ferromagnetism at room temperature7 or are effective only at low temperatures8,9. One promising avenue to circumvent such issues concerns the use of strain-mediated coupling in piezoelectric/magnetostrictive bilayer structures1016. In such structures, the applied voltage across the lm thickness generates a uniaxial strain in the piezoelectric layer that is transferred to the magnetostrictive nanomagnet, resulting in a change in its magnetic properties. It has been shown theoretically that this can form the basis of ultra-low-power computing and signal processing towards possible applications for energy harvesting17,18. In this context, rst investigations of individual switching events under applied voltages have been reported in thin-lm FeGa/BaTiO3 bilayer structures19. However, the difculty to integrate such complex heterostructures into electrically controlled nanoscale devices has precluded the demonstration of local manipulation of single nanomagnet that would be an essential step towards the magnetoelectric control of spintronic devices.

A promising approach towards high-density magnetic memories20,21 and spin logic elements22 involves the propagation of domain walls (DWs) in magnetic nanowires. In this work, we demonstrate that DW motion can be electrically controlled at room temperature using strain-mediated magnetoelectric coupling in piezoelectric/ferromagnetic nanostructures. We rst describe a device geometry that allows for an efcient transfer of a strong local strain to the ferromagnetic stripe. By using conventional three-dimensional ferromagnetic spin valves (SVs), in conjunction with the commonly used piezoelectric material PbZr0.5Ti0.5O3 (PZT), we show that the energy barrier for DW motion can be doubled under reasonable applied electric elds. We show how such functionality can be exploited in a DW gate, which could serve to generate Boolean logic functions or stabilize DWs in memory applications.

ResultsHybrid PZT/ferromagnetic device structure and transport measurements. A straightforward means of obtaining high magnetoelectric coupling involves encapsulating the magnetic nanodevice inside a piezoelectric environment23. However, two important hurdles must be overcome to achieve this goal. First, ceramic piezoelectric layers, like PZT, require high temperature deposition or post annealing (4400 1C) under severe oxidation conditions24, which inevitably degrade the magnetic properties. Second, the clamping effect from the substrate limits the crystal stress in any solid-state device. In order to avoid these issues, we have focused on an approach based on the lateral geometry seen in Fig. 1, which allows for memory and logic functions to be constructed using magnetic DWs in nanowires (see Supplementary Discussion). The sides of the piezoelectric bar are free to move but its bottom surface is clamped by the substrate, which does not allow for any global longitudinal compression. By applying a voltage, the electrical polarization rotates away from the growth direction25, which induces a strain exx40 corresponding to an elongation in the bar width, particularly near the top surface where the magnetic wire is located. In addition, this geometry leads to a large accumulated strain eyy at both longitudinal ends of electrodes. The induced strains along the x and y directions result in a local pinning potential for a DW, irrespective of the sign of the magnetostriction.

In addition to the strain being transferred to the ferromagnetic nanowire, it is a desirable for magnetization reversal to be detected using a transport-based method, such as giant magnetoresistance (GMR), which would allow for such a device to be integrated into micro- and nanoelectronic components26. For this purpose, we used magnetic wires based on in-plane magnetized spin valves with composition free layer (FL)/Cu/Co, where two different FL materials were studied: a 5-nm-thick CoFeB layer and a 10-nm-thick composite permalloy/CoFeB layer. For a given lateral wire width of 700 nm, the different aspect ratio of the two systems gives rise to two distinct DW types: an asymmetric transverse DW conguration for the CoFeB system and a vortex wall for the permalloy/CoFeB system. The complete device structure is shown in Fig. 2a.

Transport measurements were rst performed on the devices without any applied voltage, as shown in Fig. 2b. The typical GMR ratio is about 0.4% in the set of samples with 5 nm CoFeB as free layer, which is sufciently high to detect DW motion with good precision in the free layer. The presence of an asymmetric high resistance state results from the pinned-layer (PL) magnetization that starts to reverse before the FL magnetization is fully reversed. The magnetization reversal of the PL is shifted to positive elds, owing to the presence of an exchange bias eld

U+

Ti/Au

PZT

PZT

+ Ti/Au

Ti/Au

U

Ti/Au

H

Pt

PZT Spin valve

IrMn

Co

I

Cu

CoFeB

Pinned layer

Free layer

U+

MgO

z

U

Ti/Au V

+ Ti/Au

x y

Figure 1 | Lateral approach used to manipulate magnetic domain wall through magnetoelectric coupling. (a) In the absence of applied voltages on the piezoelectric layer, the domain wall (DW) propagates freely in the magnetic stripe. (b) DW propagation in magnetic stripe can be controlled by voltages through lateral magnetoelectric coupling device. By applying a voltage onto the piezoelectric layer, a local stress is induced, followed by DW blockade. (c) Measurement conguration with hybrid PZT and spin-valve (SV) hall bar-shaped device, a single DW is injected from a large reservoir. The position of the DW is monitored by measuring the GMR between two electrodes. By applying a voltage on PZT, an induced stress results in a local modication of the domain wall dynamics. The SV multilayer structure is shown on the right.

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SV

Applied V

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Ti/Au

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+

1 m

0.4

GMR ratio (%)

0.2

0.0

40 20 40

20

0 [afii9839]0H (mT)

Figure 2 | Fabricated device structure and magnetic transport property of SV stripe. (a) Cross section of the device measured by scanning electron microscopy. SV stripe is located in the middle of PZT, and side electrodes are in a good contact with PZTside walls. (b) GMR loops of SV stripe, which is measured by sweeping an external magnetic eld H along easy axis. The free-layer and pinned-layer magnetization reversal with applied eld are shown with solid black squares and open black squares, respectively.

m0Hex 15 mT resulting from a coupling with the

antiferromagnetic IrMn layer. For the FL, a slight shift towards positive elds (around 0.6 mT) can also be observed, which originates from an interlayer coupling between the two ferromagnetic layers27. The angular dependence of the coercive eld of the free layer is consistent with the propagation of a single DW in the nanowire after being injected from a reservoir (see Supplementary Fig. S1). The hysteresis loop branch that corresponds to the reversal of the free layer can be then explained as follows: (1) injection of the DW at the rst GMR electrode at HN, (2) propagation towards the PZT bars (bottom part of the branch), (3) propagation along the PZT bars (centre part of the branch) and then (4) propagation towards the second GMR electrode. Thus the coercive eld here corresponds to the average propagation eld along the PZT bar, which is about 6 mT at zero voltage. It is important to note that sharp steps in the GMR signal, which are typically associated with domain wall pinning and depinning, are not present in our samples for a number of reasons. First, there are potential contributions to the magnetoresistance from the Hall crosses. These structures consist of additional arms perpendicular to the wire in which wall

propagation takes place. As a result, the MR curves contain an irreversible (sharp) component owing to wall propagation and a reversible (coherent rotation) part owing to magnetization rotation in the arms. Second, magnetization processes in the PL also contribute to the overall magnetoresistance signal. While the FL and PL loops are well separated in the full spin-valve lms before patterning (as determined from magneto-optical Kerr effect measurements), the separation becomes less pronounced in the wire structures after patterning. As a result, the measured magnetoresistance signal contains both FL and PL reversal processes.

Magneto-optical Kerr effect measurements of DW propagation. In order to provide further evidence of DW propagation in our system, we performed spatially resolved magneto-optical Kerr effect (MOKE) measurements to study magnetization reversal at different regions along the magnetic wire. The experiments were conducted on samples with a 10-nm-thick permalloy/CoFeB free layer. The spatial resolution of the focused beams used is B2 mm, which is sufcient to detect magnetization reversal inside and outside of the strained regions associated with the PZT electrodes.

The experimental results are shown in Fig. 3. We note that MOKE measurements for the patterned wires always show sharp hysteresis loops for the free layer, which is a key signature of magnetization reversal by DW propagation. When the spot is focused on the wire under unstrained PZT area (Fig. 3a), the coercive eld is measured to be 7.5 mT. In contrast, the same measurement for a spot focused in the region in between the electrodes gives a coercive eld of 11 mT, as shown in Fig. 3b. The coercive elds under strained PZT area are always larger than those under non-strained PZT area. The origin for a larger coercive eld within the strained PZT region is unclear at this stage. We suspect that the coupling between the ferroelectric domains and the ferromagnetic domains may result in such an increase. The domain structure of the PZT areas covered by the gold electrode is also expected to be different from the uncovered areas. Furthermore, when the laser beam is focused in the unstrained area, the measured coercive elds show almost no variation with the applied voltage (see Supplementary Fig. S2b, the red stars).

From these data, we can conrm with a greater degree of certainty that domain nucleation occurs within the non-strained PZT area, as the coercive eld is lower. Furthermore, the sharpness of the hysteresis loops indicates that magnetization reversal occurs through DW propagation. This lends further support to the physical picture we present here, that is, the magnetization reversal is initiated by domain nucleation and proceeds by DW propagation along the wire.

However, MOKE measurements for our system in the strained area prove to be unreliable for studying DW propagation under applied voltages in detail for the following reasons. First, ferro-electric materials, like PZT, normally exhibit a hysteretic change of the birefringence with applied electric eld based on their value of the remanent polarization28. The MOKE measurement of the strained PZT area under applied voltage contains a large background from the ferroelectric signal, which is not trivial to correct for. Second, the reection of the laser beam from the two gold electrodes gives rise to an important source of additional noise. Third, the STO substrate used is transparent at a thickness of 1 mm, which means that the Faraday effect in the STO layer also contributes to total signal of the MOKE. As the longitudinal MOKE signal from the buried free layer of the nanowire is small, the MOKE measurements can only give qualitative information about changes in the coercive eld Hc under applied voltages.

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0 V10 V20 V50 V

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0 V to 50 V

0 V to 50 V

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50 25 50

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[afii9839]0H (mT)

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Figure 3 | Magneto-optical Kerr effect measurements of domain wall propagation. (a) Hysteresis loop determined from a spatially resolved MOKE measurement when the spot falls in a region outside of the PZT electrodes, which indicates a coercive eld of 7.5 mT. (b) Hysteresis loop determined from a spatially resolved MOKE measurement when the spot falls in a region in between of the PZTelectrodes, which indicates a coercive eld of 11 mT. Insets: illustration of the position of the laser spot used in the spatially resolved MOKE measurement.

17.58

Propogation field

([afii9839] 0H p, mT)

10

8

Capacitance (pF)

17.5

Given these difculties, we choose to rely on magnetoresistance measurements to characterize DW propagation under applied voltages in our samples.

Inuence of induced strain on DW propagation. The inuence of the gate voltages on the DW propagation is illustrated in Fig. 4a. The initial state consists of an in-plane depolarized state of the PZT bar. The GMR ratio change with applied voltage is due to the PL magnetization reversal that occurs before the FL magnetization is fully reversed. The striking feature seen in Fig. 4a is a large increase of the coercivity of the free layer under stress. Following the magnetization reversal with magnetic eld under voltage (see Supplementary Fig. S2a), we observe rst a change of slope of the ascending branch, showing a modication of the dynamics of DW motion only along the PZT bars. Note also that HN is not modied under voltage (see Supplementary Fig.

S2b, black squares, which is consistent with MOKE measurements, red stars in Supplementary Fig. S2b), which is consistent with the injection of the DW outside of the strained PZT area.

The average propagation eld Hp as a function of applied voltage from 50 to 50 V (100 kV cm 1) was extracted at 50% of the total

GMR (Fig. 4b). Note that the propagation eld of the FL doubles for an applied voltage of VPZT 50 V.

17.0

16.5 50 25 50

0

Applied PZT voltage (V)

25

Figure 4 | GMR measurements of domain wall propagation in the free layer of 5 nm CoFeB. (a) Giant magnetoresistance loops with different applied voltages, which starts from a depolarized state of the PZT layer. (b) Propagation eld in the free layer as a function of the voltage applied on the PZT layer. (c) Propagation eld of free layer as measured by scanning the voltage applied on the PZT layer starting from 50 V (top panel) and

C V measurement of the PZT layer, starting from 20 V (bottom panel).

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To further conrm that the change of Hp is owing to the inverse magnetostrictive effect, the propagation eld was directly compared with the capacitance of PZT under applied voltages. The Hp was determined by scanning the voltage applied on the

PZT layer as shown in the top panel of Fig. 4c. We clearly observe a buttery shape as expected for a ferroelectric-related effect. The propagation eld at 0 V is higher than in Fig. 4b, which is an indication of a remnant in-plane polarization of the PZT layer. CV measurements of the PZT layer were performed at 1 MHz, as seen in the bottom panel of Fig. 4c. A buttery shape is also clearly evidenced with a typical coercivity Ec of about 3 V (6 kV cm 1). The observed asymmetrical switching is presumably linked to the asymmetric interface side contact generated from fabrication. We observe also that the hysteretic change of Hp with voltage is linked to the switching of the two polarizations of the PZT layer, which is a clear indication of magnetoelectric coupling in our hybrid piezoelectric/ferromagnetic nanodevice. Note that any Joule heating can be excluded as the leakage current through the PZT layer is in the range of nA, Hp increases with voltage and no increase in the spin-valve resistance is seen with applied voltages.

These measurements were repeated for the 10-nm-thick permalloy/CoFeB FL system, in which a different DW structure is expected. Furthermore, the GMR ratio of 1.4% for this system is greater than the ratio for the 5-nm-thick CoFeB system, which allows for greater sensitivity for localizing the DW along the wire. The hysteresis curves obtained from magnetoresistance measurements are presented in Fig. 5. In contrast to the rst system, we observe clear plateaus in the FL switching under different applied voltages, while no plateaus are seen in the absence of applied voltages. The plateaus occur at positions representing 1520% of the total MR variation, and are more obvious at higher voltages with larger strain, while independent of the sign of the applied voltage. These levels are consistent with DW pinning at the edges of the PZT electrodes, which is expected from electrical and micromagnetic modelling (see Supplementary Fig. S3 and Supplementary Discussion). The observation of plateaus in this particular system may be owing to two reasons. First, the permalloy/CoFeB FL system exhibits larger GMR value (that is, 1.4%, as opposed to 0.3% for the pure CoFeB FL system). Second, the vortex wall present is expected to be more sensitive to local pinning sites, owing to the compact nature of the wall structure. As such, it follows that the vortex wall will be more greatly affected by changes in these pinning sites owing to the applied strains. In Fig. 5c, one can observe that the change in the coercive eld with applied voltage is less signicant in comparison with the pure CoFeB system, as magnetostrictive effects are smaller in permalloy. Spatially resolved magneto-optical Kerr measurements conrm that magnetization reversal occurs by DW propagation through the strained PZT area in these samples (see Fig. 3).

DiscussionWe propose that our structure, which functions like a magnetic DW gate, can form the building block for generating Boolean logic functions. An example for a NOR gate is given in Fig. 6a. The principle is very similar to the concept of the magnetic shift register based on moving DWs in a racetrack geometry with spin-polarized currents20,21. The elementary logic device consists of a DW nanowire on top of a PZT bar, with a writing line to nucleate DWs, an electrical control A for injecting spin-polarized currents into the wire, two inputs B0 and B1 that involve applied electric elds to the PZT layer and an output C that involves detecting the local magnetization with a magnetic tunnel junction (MTJ). We point out that this system can be easily recongured to supply a logical NAND operation by simply

starting the output C in a 1 initial state with an antiparallel magnetization conguration in the MTJ. As the two inputs B0

and B1 are identical, it is possible to construct as many of these

1.014

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Normalized MR

1.008

1.002

18 12 6

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0 V 10 V 20 V 30 V

1.005

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14

12

[afii9839] 0H c(mT)

10

0 V to 30 V

0 V to 30 V

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30 15 0 15 30

Applied PZT voltage (V)

Figure 5 | GMR measurements of domain wall propagation in the free layer of 10 nm permalloy/CoFeB. (a) Zoom of giant magnetoresistance (GMR) loops with different applied voltages, which starts from a depolarized state of the PZT layer to 30 V, two clear plateaus are observed. (b) Zoom of GMR loops with different applied voltages, which starts from 0 to 30 V, two clear plateaus are also observed. (c) Propagation eld in the

free layer as a function of the voltage applied on the PZT layer.

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B0

B1

C

0

0

1

0

1

0

1

0

0

1

1

0

C = B0 NOR B1

Writing driver

Vout

Writing driver

Vout

Figure 6 | Proposal of domain wall logic and domain wall memory.(a) Design of a multi-input NOR logic function by using voltage controlof elementary DW gates. Control A is used for current-driven DW motion, and the writing line is used to generate a domain wall. Inputs B0 and B1 are piezoelectric-controlled DW gates, and output C serves as read out for the magnetization direction in the wire through the tunnelling magnetoresistance effect. The device functions as follows. First, a domain wall is nucleated in the wire with the Oersted eld generated by the current owing through the write line, with the output C set to the low resistance state 0 (parallel magnetization state of the MTJ). If either or both of the gate voltages B0 and B1 are applied (that is, in the 1 state), then the induced anisotropy change at the gates concerned lead to a local pinning of the domain wall, which leaves the output C in the 0 state. However, if both gate voltages are off (inputs B0 and B1 set to 0), then the generated domain wall can propagate free along the wire, driven by the spin-polarized currents controlled by A, leading to magnetization reversal at the output C and thereby switching this state to 1. This scheme corresponds to a logical NOR operation and NOR table is shown on top. (b) Design of a racetrack memory using voltage control of a DW gate. Proposed device scheme in which individual PZTelectrodes supplement pinning sites dened by articial notches. These electrodes act as bit lines (BL), as they allow individual domain walls to be pinned on demand by applied voltages, thereby allowing a content-addressable function to conventional racetrack memories. For example, in order to write the current state 1 0 1 0 to nal state 1 0 0 0, the voltages on BL0 and BL2 are on and voltage on BL1 is off, by sending the domain wall-driven current (control A), the nal state can be achieved.

as desired to obtain a multi-input (for example, eight bits) logic device.

The scheme described above could provide additional functionality to the racetrack memory device20,21, as shown in Fig. 6b. For the racetrack device, articial constrictions are required to stabilize DWs against thermal uctuations, but further downscaling of such geometries represents a technological

challenge. Furthermore, high current densities are required to induce DW motion because of the strong pinning as a result of these constrictions. A possible solution to these issues could involve using voltage-induced strains to assist DW pinning at each of the constrictions in a racetrack device. When DW shifting is required, the voltages at all constrictions concerned can be set to zero, thereby leading to a reduced propagation eld and therefore the requirement for lower current densities. The inclusion of the PZT electrodes would also endow the additional function of addressable content, as DWs in parts of the racetrack could be clamped by applied electric elds, while walls in other parts could continue to be shifted along the wire. In the conventional racetrack memory, the storage is programmed strip-by-strip or word-by-word. This represents a serious drawback in comparison with random access memory in which each bit or storage element can be addressed individually. By combining with the read heads implemented on each individual information bit29, such a scheme could allow for each data in the magnetic stripe to be accessed for write and read operations, as in traditional random access memory30, where the PZT electrodes and magnetic nanowires are addressed, respectively, by bit lines and word lines. This additional functionality overcomes one of the key limitations of the conventional racetrack design, where DWs are driven in unison under applied currents without the storage being addressable individually20.

Methods

Fabrication. The devices consist of a PZT lm with a lateral spin valve grown on top, and they were fabricated on vicinal SrTiO3 (001) single-crystal substrates. The 400 nm PZT was rst grown by pulsed laser deposition at 580 1C under 120 mTorr O2 atmosphere3133. It was then patterned into a 5-mm-wide Hall bar by optical lithography and ion milling using Ar and O2. The 700-nm-wide spin-valve stripe and the side gate electrodes in the middle part of the bar are fabricated by two steps of electron beam lithography and a subsequent lift-off process. The spin valves consisting 2(nm) MgO/FL/4 Cu/4 Co/0.3 Cu/8 IrMn/4 Pt, where the free layer (FL) is either 5 Co40Fe40B20 or 5 permalloy/5 Co40Fe40B20, were grown by magnetron sputtering at 5.8 10 4 mbar Ar under an in-plane bias eld of 100 mT. The

width of 700 nm for the spin-valve stripe was chosen to promote easy DW propagation by minimizing pinning owing to rough edges. For the spin-valve structure, a 2 nm MgO buffer was used to reduce the electrical eld screening effect and domain coupling between the ferroelectric and ferromagnetic layers. A 0.3 nm layer of Cu was inserted between Co and IrMn to enhance the magnetic coupling34. The side gate electrodes (5 nm Ti/150 nm Au) were grown by e-beam evaporation and patterned to 4 mm (w) 400 mm (l). Finally, contact electrodes with 10 nm Ti/

300 nm Au were deposited using a lift-off process after optical lithography.

Transport measurements. An a.c. (10 mA) lock-in technique was used to obtain the GMR signal at room temperature under an applied voltage on the PZT. The hysteresis loops of GMR were measured by sweeping the magnetic eld at a rate of 4 mT min 1. Owing to the nature of ferroelectric domain structure, the voltages on

PZT were applied in two ways. The rst concerns the initial polarizing scan, which involves ramping the voltage from 0 V with an in-plane depolarized state to polarized states at high voltages (50 or 50 V). The second concerns the loop scan, which involves sweeping the voltage from an in-plane polarized state ( 50 V) to

50 V and back to 50 V. The leakage currents measured during the voltage scans

were measured to be in the nA range.

Spatially resolved magneto-optical Kerr effect measurements. A 2 mm-diameter-focused laser spot (thermally stabilized solid-state laser source at 660 nm with a power of about 100 mW) was placed on the spin-valve nanowire with an incidence angle of 451 in longitudinal MOKE geometry. The sinusoidal in-plane magnetic eld along the nanowire is generated by a quadrupole electromagnet at a frequency of 3 Hz and an amplitude of 25 mT.

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Acknowledgements

We acknowledge invaluable support from V. Pillard and S. Eimer for the lm preparation, L. Santandrea for the nite-element simulations and fruitful discussions withE. Fullerton, Edwin Fohtung and Oleg Sphyrko. This work was partially supported by the European Communities FP7 programme, through contract NAMASTE number 214499 and contract MAGWIRE number 257707, and the ANR-NSF project Friends. N.L. also acknowledges nancial support from CNano IDF.

Author contributions

N.L. designed the experiment, fabricated the device and performed the measurement. N.L. and G.A. did the lithography. N.L. and T.T. did the magneto-optical measurements, under the supervision of R.P.C. N.L. and T.D. analysed and interpreted the data. P.A. andL.D. did the strain simulation. J.-V.K. performed analytical and micromagnetic modelling. W.Z. designed logic function and memory architecture. N.L., T.D., L.D., J.-V.K. and D.R. edited and commented on the manuscript. C.C., D.R. and P.L. planned and supervised the project.

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How to cite this article: Lei, N. et al. Strain-controlled magnetic domain wall propagation in hybrid piezoelectric/ferromagnetic structures. Nat. Commun. 4:1378 doi: 10.1038/ncomms2386 (2013).

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