Electrically Driven Reversible Magnetic Rotation in Nanoscale

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Electrically Driven Reversible Magnetic Rotation in Nanoscale Multiferroic Heterostructures Junxiang Yao, Xiao Song, Xingsen Gao, Guo Tian, Peilian Li, Hua Fan, Zhifeng Huang, wenda yang, Deyang Chen, Zhen Fan, Min Zeng, and Jun-Ming Liu ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b01936 • Publication Date (Web): 29 Jun 2018 Downloaded from http://pubs.acs.org on June 29, 2018

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Electrically Driven Reversible Magnetic Rotation in Nanoscale Multiferroic Heterostructures

Junxiang Yao,† Xiao Song,† Xingsen Gao,†* Guo Tian,† Peilian Li,† Hua Fan,† Zhifeng Huang,† Wenda Yang,† Deyang Chen,† Zhen Fan,† Min Zeng,† and Jun-Ming Liu‡*

†

Institute for Advanced Materials and Guangdong Provincial Key Laboratory of Quantum

Engineering and Quantum Materials, South China Academy of Advanced Optoelectronics, South China Normal University, Guangzhou 510006, China. ‡

Laboratory of Solid State Microstructures and Innovation Center of Advanced Microstructures,

Nanjing University, Nanjing 21009, China. *Correspondence to: [email protected] (X.S.G.) and [email protected] (J.-M.L.)

[Abstract] Electrically driven magnetic switching (EDMS) is highly demanded for next generation advanced memories or spintronic devices. The key challenge is to achieve repeatable and reversible EDMS at sufficiently small scale. In this work, we reported an experimental realization

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of room temperature, electrically driven, reversible and robust 120o magnetic state rotation in nanoscale multiferroic heterostructures consisting of triangular Co nanomagnet array on tetragonal BiFeO3 (BFO) films, which can be directly monitored by MFM imaging. The observed reversible magnetic switching in individual nanomagnet can be triggered by a small electric pulse within 10 V with an ultra-short time of ~10 ns, which also demonstrates sufficient switching cycling and months-long retention lifetime. A mechanism based on synergic effects of interfacial strain and exchange coupling plus shape anisotropy was also proposed, which was also verified by micromagnetic simulations. Our results create an avenue to engineer the nanoscale EDMS for low power-consumption, high-density, nonvolatile magnetoelectric (ME) memories and beyond.

KEYWORDS: Electric driven magnetic switching, magnetoelectric, multiferroic heterostructures, nanomagnets, magnetic random access memory.


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Electro-control of magnetism in multiferroics and magnetoelectric (ME) heterostructures has attracted intensive efforts in recent years,1-8 motivated by their application potentials in low-power consumption, simple device architecture, high-density memory (e.g. magnetoelectric random access memory), and other spintronics devices. In the advanced state-of-the-art spintronic devices, spin-polarized current is normally employed to switch the magnetization (i.e. write a magnetic bit) via e.g. spin-torque driven domain wall motion, while it requires relatively high current density thereby resulting in large energy consumption and heat dissipation.9,10 Instead, based on insulating multiferroic heterostructures, one is able to switch the magnetization merely by electric field rather than electric current, thus dramatically reducing the complexity of device architecture, and consumption energy as well as Joule heat. In the past decade, numerous efforts on electro-control of magnetism have been envisaged, and several interesting physical mechanisms have also been revealed, including the interfacial strain/stress coupling, 11,12 charge mediation,13-15 exchange bias or coupling from ferromagnetic-antiferromagnetic interfaces,16-19 variation of occupation state of magnetic molecular 3d-orbit,20-23 and valley magnetoelectricity in some 2D materials.24,25 These findings have not only enriched our understanding of condensed matters but more importantly made great progresses in realizing future generation electrically driven magnetic switching (EDMS) devices. For EDMS applications in high density devices, the paramount challenge is to achieve a robust and repeatable pure electric driven magnetization reversal at room temperature. Although various roadmaps for electrically driven global or local magnetization reversal in controllable manners have been reported, most of them require an assistance of external (or internal) magnetic field.2628

Recently, Gao et al., reported an in-situ observation of reversible 135o magnetic switching in a

local electric control of small region of NiFe films on piezoelectric Pb(Mg,Nb)O3-PbTiO3 (PMN-


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PT) single crystal.29 A more intriguing achievement is a deterministic and pure voltage-driven 180o net magnetization reversal in micrometer Co0.9Fe0.1 magnets on BiFeO3 (BFO) film by Heron et al.,30 based on the interfacial exchange coupling between BFO and magnets. These important progresses have pushed forward the realization of future magnetoelectric and spintronic devices, nonetheless, a robust and repeated reversible EDMS has not yet been well accomplished, which remains to be one of the major missions for ME researches. Moreover, the magnetic structures in these structures are several micrometers or larger in dimension, with apparent non-uniformities in EDMS in microscopic magnetization, which is certainly a disadvantage for further scaling down for practical application in microelectronic devices. An equally essential but more technologically relevant issue for a device is the ability to scale down to nanometer for practical applications, while this issue has unfortunately received less attention. It is therefore imperative to investigate the EMDS in nanoscale multiferroic heterostructures. Along this line, quite a few experimental and theoretical efforts on electroswitching of nanomagnets driven by piezo-strain, e.g. using PMN-PT substrates, are available, whereas it remains yet unable to realize a repeatable magnetization reversal using single electric pulse.31-34 Although it has been theoretically predicted that the magnetization reversal can be driven by piezo-strain via magnetic moment precession in small single-domain nanomagnets, while the parameter window is extremely narrow (sub-nanosecond switching time),35 making a practical realization challenging. Up to now, an experimental demonstration of robust and reversible EDMS sequence in nanoscale that is suitable for high-density integration still remains elusive, while application appealing for such a technology becomes even more urgent. Without doubt, overcoming these difficulties needs additional mechanism besides the piezo-strain actuation, while several candidates may be explored. One is the interfacial exchange coupling in ME


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heterostructures which may add different symmetry considerations. A combination of the piezostrain and interfacial exchange coupling certainly allows more degenerate energy landscape minima at which a magnetization reversal can be achieved with more possibilities in thermodynamics and more easily in kinetics. Furthermore, another highly promising mechanism can be stemmed from shape anisotropy of magnetism that may be strong in nanoscale soft magnets. Such strong shape-anisotropy can be utilized for tailoring both domain state and style of EDMS. Without surprise, an arbitrary design of multifold shape anisotropy also offers potentials for multistate switching. In this work, we demonstrated a robust yet reversible EDMS in an array of triangular cobalt (Co) nanomagnets on super-tetragonal BiFeO3 (T-BFO) films, as schematically shown in Figure 1A. Here, the triangular shape of nanomagnets was specifically chosen to study the effect of shape anisotropy on both the magnetic domain structures and domain-switching behaviors. On the other hand, the T-BFO films were selected as the active ferroelectric layers, which can not only provide an interfacial exchange coupling between BFO layer and Co nanomagnets,19, 30, 36 but also possibly generate a sizable piezo-strain under an electric field.37,38 The results turned out that the magnetic states of individual nanomagnets in such heterostructures can indeed be driven by a small electric field within 10 V to switch reversibly between two neighboring states of 120o in orientation angle for many cycles. The switching can be actuated as short as ~10 ns and the switched magnetic states can withstand beyond several months. In short, the EDMS sequence facilitates the room temperature operational, electrically driven, reversible and robust, and retention-long 120o magnetic state rotation, promising for high-density energy efficient ME memories or logic devices.


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RESULTS AND DISCUSSION

Nanoscale Co/BFO heterostructures. The multiferroic heterostructure shown in Figure 1A consists of an array of triangular Co nanodots on T-BFO film deposited on (La,Sr)MnO3 (LSMO) buffered (001) LaAlO3 (LAO) substrate. The fabrication process has been described in details in the Materials and Method section. In brief, TBFO and the buffer layer of LSMO film were deposited by pulsed laser deposition, and the triangular Co nanodots were fabricated using the nanosphere lithography with well-ordered polystyrene (PS) nanosphere template (see Materials and Method, and Figure S1). The scanning electron microscopy (SEM) image of the nanodots topology was presented in Figure 1C, revealing well-defined array of Co nanodots with lateral width of ~350 nm and height of ~ 20 nm determined by the AFM topology. The structures and ferroelectric properties of the BFO film on LSMO-buffered LAO substrate were inspected by X-ray diffraction (XRD) and piezoresponse force microscopy (PFM), as shown in Figure S2. The tetragonality of the BFO film was confirmed by the (001) peak in the XRD pattern in Figure S2A, revealing a large c-axis lattice parameter of 0.46 nm, close to the reported value of T-BFO film.39,40 The ferroelectricity and polarization reversibility were confirm by piezoresponse data with well-defined d33-voltage hysteresis shown in Figure S2B. The two abnormal d33 humps right above the coercive field in the hysteresis loop may attribute to the occurrence of intermediate tetragonal/rhombohedral mixed phase (T/R-phase) during the polarization reversal, in agreement with previous reports.38-40 This T/R-phase coexistence was verified by the morphology features on the film surface subjected to different bias voltages, see Figure S2(C to E) for details. The apparent morphology transformation from the initial atomic-flat


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surface (zero bias) to a relatively rough wave-like pattern at a bias voltage of 3.0 V, and then return to flat surface again at a higher bias voltage of 6.0 V, was identified. This corresponds to the phase transformations from the initial pure T-phase to T/R-phase first, and then to reversed T-phase in sequence. The occurrence of intermediate T/R-phase during the polarization reversal may generate sizable interfacial piezo-strain that can functionalize a mediation of the interfacial lattice coupling, in addition to the exchange coupling between BFO film and Co nanodots.19,30,36

Magnetic states of Co nanodots. The macroscopic magnetism of the whole Co nanodots array was characterized by the vibrating sample magnetometer (VSM), showing an in-plane coercive field as small as ~100 Oe (Figure 1B). The magnetic state (or domain structure) of each triangular Co nanodot is shown in Figure 1(D and E). For the virgin sample, a triangular nanodot may show bright contrast in one wing (two wings) and dark contrast in the other two wings (one wing), shown in Figure 1D, ascribed to the stray fields from the in-plane moment alignment. An in-plane magnetic field of ~5 kOe is sufficient to align these moments so that the black contrast appears in the left part and the white contrast in the right part for all nanomagnets (Figure 1E). It should be mentioned that the reliability of the MFM imaging was examined by checking the influence of magnetization state of the MFM probe tip. As shown in Figure S3(A and B), the MFM imaging of the same area using the same tip upon reversed magnetization did give the completely inverted contrast, verifying that the MFM images are not from artifacts. In addition, we also compared the MFM images taken at different lift-height of the MFM probe tip (see Figure S3(E and F)), and no apparent contrast change was observed, indicating that the disturbance of magnetic field from the MFM tip on the magnetic states is negligible if any.


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Upon different treatments using magnetic field, a Co nanodot may prefer one of the six different magnetic states, as evidenced by the MFM images in Figure 1F, noting again that the polycrystalline Co has weak magnetocrystalline anisotropy, thus enabling the existence of shapeanisotropy mediated six magnetic states. To figure out these states, we conducted micromagnetic simulations using the well-known micromagnetic OOMMF software package.41 The six degenerate states at zero-field can be obtained by setting different initial moment configurations, and the simulated configurations are shown in Figure 1G, from which the simulated MFM contrast contours are also given in Figure 1H. These contours are the second-order derivatives of the zcomponent (out-of-plane) stray fields above the simulated configurations calculated by using a MATLAB program, see details in Method section and Supplemental Materias.42,43 Obviously, the measured MFM images match well with the simulated MFM contours one by one, although the formers exhibit blur and distortion to some extent. Such blur and distortion are more or less from the measuring uncertainties, and also due to the approximation that the coarse MFM tip used in experiments was treated as a point magnetic charge in the simulations. The one-to-one correspondence between the MFM image/contour contrasts in Figure 1F/H and magnetic configurations in Figure 1G, indicates that the bright wing has the moment alignment from the triangle corner tip toward the center, while the black wing has the moment alignment from the center toward the corner tip. For convenience of identification, coarse open arrows are added onto the bright and dark wings in Figure 1F to mark the in-plane moment orientations. The color contour shown in Figure 1G scales the local moment orientation with respect to the in-plane (x, y) coordinates given aside. In this sense, in analogue to spin ice classification, here the six magnetic states can be classified into two categories: 1-in-2-out mode (one bright wing and two black wings) and 2-in-1-out mode (two bright wings and one black wing).


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Electrically induced magnetic state rotation Now we inspect the electro-pulse driven evolution of magnetic states for these triangular Co nanodots. We start from the six nanodots shown in Figure 2A for illustration and focus on the three selected nanodots (circle-marked) for detailed investigation. The MFM image of them in the initial state (as-deposited without magnetic field pre-treatment) is given in Figure 2B. A voltage pulse of 8.0 V (with 1.0 ms duration) applied to each dot using the PFM tip probe triggered the switching of some of the six dots and the consequent MFM image is presented in Figure 2C. Subsequently, a voltage pulse of -8.0 V was applied to the three switched dots and the obtained MEM image is shown in Figure 2D. For clearer illustration, the MFM images of the two blue-circled nanodots are zoomed-in and presented in Figure 2(E and F) respectively, together with the simulated MFM contours and magnetic-moment configurations. Several facts upon the electrically switched magnetic structures can be highlighted. First, the first 8.0 V pulse made the magnetic state of the blue-circled nanodot on the left side to rotate anticlockwise for 120o and that of the nanodot on the right side to rotate clockwise for 120o. The subsequent -8.0 V pulse made the magnetic states of the two dots to recover back to the initial states respectively, noting that the 1-in-2-out magnetic mode for the two nanodots remained unchanged. For the red-circled nanodot, the first 8.0 V pulse switched the magnetic state from the 2-in-1-out mode into the 1-in-2-out mode and this mode remained unchanged upon the second 8.0 V pulse. Certainly, the present finding represents a substantial forward step to realize the pure electroswitching of magnetic state in a multiferroic heterostructure. Nevertheless, it should be mentioned that not every Co nanodot in the as-prepared nanodots array enables the magnetic state rotation driven by electrical pulse in the present geometry. The uncertainties are most likely due to the


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existence of inhomogeneities in both the geometries of nanodots and the domain structure of the underneath BFO film, which may be avoided by improving the homogeneities of the whole structure. This issue will no longer be addressed here and our attention goes to the electrically induced magnetic state switching itself by carefully tracking the rotation sequence of the 1-in-2out magnetic mode, noting that this mode can be reversibly switched electrically. First, we look at the intermediate process during the switching for the 1-in-2-out mode. The anticlockwise 120o-rotation by the 8.0 V pulse suggests us to check the magnetic state driven by an intermediate voltage pulse, e.g. 4.0 V pulse. The results are summarized in Figure 3A. At the initial state (E = 0), the net magnetization of a chosen nanodot aligns along the y-axis and this state remained roughly stationary at pulse below 4.0 V. At E > 4.0 V, an intermediate magnetic state with distorted bright-dark contour was reached before the anticlockwise 120o-rotation under a pulse of 8.0 V. This magnetic state was of course stable after the pulse-ending. Subsequently, the negative pulse of -4.0 V distorted the bright-black contour again and the pulse of -8.0 V switched the contour back to the initial state via the clockwise 120o-rotation. The whole magnetic rotation process can be expressed as the schematic magnetization-electric field (M-E) hysteresis, as inserted in Figure 3A. This loop represents a direct demonstration of the pure electro-control of magnetism in the reversible manner, a core target of multiferroic researches. Besides this demonstration, the reversal cycling lifetime, switching speed, state retention, and relevant properties were also checked. First, the above switching sequence was rather repeatable. Figure 3B presents the MFM images of a Co nanodot after various reversal cycles by consecutive switching at electric pulses of  9.0 V and the pulse duration was 1.0 ms. It was seen that the magnetic state upon the back- and forth-rotation for 6 cycles during our observation time was highly reproducible. The detailed data of the 6 cycles are included in Figure S4.


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The switching speed was checked carefully and one set of data are plotted in Figure 4(A and B). Given the pulse height of 10 V, a series of pulses with different durations were taken to trigger the magnetic state switching and the shortest duration for a reliable switching cycle was 10 ns, which is the lowest pulsed width for pulse generator. The reliability was verified by the MFM imaging shown in Figure 4B. Here, the pulse height was far beyond the coercive field (~ 4.0 V), a switching speed as short as 10 ns for BFO film is reasonable, which may be responsible for the ultrafast magnetic switching. However, when the pulse height was reduced, the shortest pulse duration would be seriously elongated and our data showed that a longer duration of 1.0 s for electric pulses of  9.0 V and an even longer duration of ~1.0 ms for  8 V were required, as shown in Figure S5. The variation in switching speed for different pulse voltages implies that the ferroelectric domain switching determines the switching speed of the device.44 For this, we looked into the ferroelectric domain switching behavior for a bare T-BFO film by applying pulsed voltages through AFM probe, and the nucleation and growth of reversed domain were illustrated in Figure S6. It was found that the reversed domain nucleates after applying a short electric pulse, and then becomes more and less stable over a wide range of switching time, and finally it grows up in logarithmic way with further elongation of time. Although the reversed domain shows similar growing behavior for the different voltages (7-10 Vs), while the domain size varies a lot. For a large voltage of -10 V, an ultrashort pulse of 10 ns is sufficient to achieve a sizable reversed domain of ~220 nm in diameter. While it takes a much longer time for a smaller voltage to reach a similar size, e.g. 1 ms for -8 V and 1 s for -6 V. This is in agreement with our experimental observation of the significant difference in switching time of EDMS driven by different pulse voltages (e.g. ~10 ns for -10 V, ~1 ms for -8 V).


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Finally, we come to check the retention of a magnetic state and the results are presented in Figure 4C. It was found that the switched magnetic state can be sustained far longer than several months at room-temperature. The data here show a long retention up to 9 months (6500 hours). In addition, an annealing of the samples at 100 oC for one hour did not damage the magnetic state. More detailed MFM imaging for the retention at various durations can be found in Figure S7. These switched magnetic states may be protected by the large shape anisotropy against thermal fluctuations and other disturbances, even though the ferroelectric domains may undergo some extent of relaxations.

Micromagnetic simulation and discussion The driving force for the electrically driven in-plane 120o magnetic state rotation, includes several ingredients. Our micromagnetic simulations unveiled that a combination of two ingredients is sufficient to reproduce the observed behaviors in a semi-quantitative sense. They are the interfacial exchange coupling and piezo-strain mediated coupling. The interfacial exchange coupling deals with the interface between the magnetically soft Co nanodot and the underlying BFO film, noting that BFO has a weakly canted moment (Mc) that is strongly coupled with the electric polarization P via the Dzyaloshinskii-Moriya (DM) interaction.19,30,36 This coupling enables possibly an electro-control of Mc and consequently a control of magnetic state in the Co layer. Usually it is insignificant and inefficient unless the magnetic layer is ultrathin (< 3 nm). In the present work, the Co nanodots are relatively thick (> 10 nm) considering the robustness of magnetic state, while this coupling alone is insufficient to drive the EDMS process due to its short-range nature. The second ingredient is the relatively long-range piezo-strain mediated coupling, generated as a consequence of electrically induced transient T/R-phase transformation during polarization


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switching of the underneath BFO film that is initially in the T-phase. Our finding is that a proper out-of-plane electric field pulse imposed by the tip could trigger a transient T/R-phase, as shown in Figure S2 and to be discussed below. It is known that R-phase has a much larger in-plane lattice constant (a ~ 0.40 nm) than that of T-phase (a ~ 0.3665 nm).38,39 The appearance of this transient state in the region underneath a Co nanodot must be accompanied with an in-plane tensile strain pulse, thus producing a magnetoelastic anisotropy in this Co nanodot that favors the out-of-plane easy-axis. Besides, the surface of this T/R-coexisting region must be much rougher, which enlarges the effective BFO/Co interfacial contact area bringing about an extra tensile strain. This enhanced interface roughness also gives rise to an effective perpendicular anisotropy in association with the change of demagnetization, which cannot be neglected in our case.45 In short, the consequence of the electrical pulse imposed on the BFO region under a Co nanodot is the appearance of a transient T/R-phase region and thus the emergence of a perpendicular magnetoanisotropy pulse on the Co nanodot. Such emerging synergic effect of the piezo-strain mediated coupling plus interfacial coupling seems to enable a reversible EDMS sequence. Certainly, one needs a more comprehensive understanding of such synergic effect which is nevertheless quite complicated. In proceeding, we proposed a simplified model taking into account of the above consideration and then performed the micromagnetic simulations. In this model, an electrically modulated anisotropy (Kz) from the piezo-strain mediated coupling and an effective coupling field (hDM) from the interfacial coupling are considered in addition to the general magnetic Hamiltonian. The simulation details can be found in the Method and Supplementary Materials. In the simulation, we use an electrically modulated anisotropy pulse to mimic the effect of piezostrain. In details, a dynamic magneto-anisotropy pulse (Kz, see Method and Figure S8) along the


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out-of-plane easy axis is generated in accompanying with the occurrence of transient T/R-phase region, as schematically shown in Figure 5A where two BFO lattice units on the film surface are drawn for a guide of eyes. On the other hand, an effective field hDM arising from the DM interaction has the same orientation as the canted moment Mc and is perpendicular to both polarization P and antiferromagnetic moment L in the BFO film, i.e. hDM ~ Mc ~ PL.30,36 Certainly, a polarization reversal leads to a switching of Mc, and thus the switching of hDM (the non-uniform spatial distribution of hDM at different states can be found at Figure S9). This sequence is also schematically illustrated in Figure 5A. In the initial state (left) where the BFO region underneath the Co nanodot is in the T-phase with the indicated P, Mc, and L. One has Kz = 0 and net hDM < 0 since no electric pulse is applied in this state. When an electric pulse is applied, the polarization switches and the BFO region underneath the Co nanodot transits into the T/R-state (middle, where Kz > 0 and net hDM > 0), which will trigger the moment switching of the Co nanodot to the outof-plane direction. When the electrical pulse is ended, this BFO region is changed to the reversed T-phase (right) with Kz = 0 and net hDM > 0, and the magnetic moments of the Co nanodot will switch from the out-of-plane alignment to the in-plane alignment, and simultaneously rotate the in-plane magnetization. The results of micromagnetic simulations using the OOMMF software package41 are presented in Figure 5C. The time (t)-sequences of Kz and net hDM associated with the electrical pulse are plotted in Figure 5B where the initial state covers t = 0 ~ 3.0 ns, the electrical pulse ranges over t = 3.0 ~ 23.0 ns, and the end state is stabilized after t = 20 ns. The estimation of these parameters is given in the Supplementary section S3. The simulated in-plane moment M (two components Mx, My) in time sequence is plotted in Figure 5C too (bottom row). It is seen that the two components slightly fluctuate immediately after the pulse front-edge before tending to stable values which are


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both close to zero, indicating an out-of-plane flipping of the Co moments. This is an intermediate state. Similarly, fluctuations of these components immediately after the pulse back-edge are seen before tending to different values, corresponding to the flipping of the out-of-plane moments onto the in-plane alignment. This process can be shown illustratively by the evolution of magnetic states for the initial state, two intermediate states, and reversed state in the top row of Figure 5C . It was found that upon applying the electric pulse, the magnetic moment first reorientates towards outof-plane direction, while there still have some small in-plane components left (see the first intermediate state in Figure 5C). At the same time, the net hDM was also switched by the electric pulse, and the reversed hDM-field tends to drive the x-component of magnetization from –x to +x direction. The switching of in-plane component of magnetization occurs nearly at the ending of strain pulse, passing through a transient vortex state (see second intermediate state). After the electric pulse stops, the magnetic moments relax back to the in-plane orientation, and the xcomponent of magnetization completely reverses while keeping the y-component almost unchanged, resulting a flipping of the total net magnetization from one corner (left) to the opposite corner (right) of the triangular nanodot. It is noted that the initial and reversed states both take the 2-in-1-out mode, corresponding to a clockwise 120o rotation of the magnetic state. It should be mentioned that the reversed state can also be switched back to the initial state by a negative electrical pulse, indicating that the observed magnetic state rotation is reversible. To further understand the effects of Kz and hDM-field, a magnetic switching diagram was also calculated by micromagnetic simulation and illustrated in Figure S10. It was found that for small strain mediate coupling (ΔKz), there occurs a none-switching region over a wide hDM range up to 600 Oe. While for small hDM-fields (100-400 Oe), in additional to the none-witching region, an uncontrollable switching region (e.g. irreversible or random switching) also arise at relative low


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ΔKz region, hence a rather large ΔKz is required to achieve a reversible 120o switching. The simulations thus confirmed that the effective field (hDM) alone is insufficient to switch the magnetization, and the piezo-strain can greatly reduce the magnetic switching energy barriers. Similarly, we have also confirmed by simulation that the strain coupling itself is also unable to drive the reversible magnetic state rotation. Therefore, the observed EDMS is more likely due to a synergic effect of both couplings. It is also worth noted that our simulation is based on a rather simplified model which is not able to exactly quantify the individual contribution from different factors, nevertheless, the simulation can still provide us a good insight into the complicated switching process. On the other hand, it is possible that other factors like current induced magnetic field may also contribute to the observed magnetic switching, in our case however the current is too small (10 nm) as well as the use of relatively oxidation resistive Co. Second, our nanoscale heterostructures are based on perpendicular architecture, compatible with advanced semiconductor technologies and large scale integration. We have already obtained a pixel density of >1.0 Gbit/in2 for the nanodots array in the present work, and it also has the capability of scaling to a higher density. Third, the devices can be operated at an ultrahigh speed as fast as 10 ns at relatively small voltage (~10 V), which is probably the fastest switching speed for EDMS devices, to the best of our knowledge. Fourth and more interestingly, the individual nanomagnets in our work have six stable equivalent states, which may


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provide further opportunities to create multi-state memory devices. In fact, occasionally we have succeeded in visiting each of the six magnetic states one by one using the electrical pulse driving, as shown in Figure S12. In a word, we have demonstrated in this work that this nanostructured multiferroic array is promising for low energy consumption, low operation voltage, ultrafast, and high density nonvolatile memory or logic devices.

CONCLUSION In summary, we have demonstrated the observation of reversible 120o magnetic state rotation driven by electric field in the triangular Co nanomagnets arrayed on the T-BFO film. This can be interpreted based on the synergic effects of piezo-strain and exchange coupling, which may also modulated by the shape anisotropy, as supported by the micromagnetic simulations. The accessed magnetic states are rather robust, which can be reversely switched for many cycles and each state shows its retention as long as several months within our experimental access. Moreover, the magnetic state rotation can be achieved by one electric pulse as short as ~10 ns at a low voltage of 10 V. These excellent merits of the devices may push forward the realization of high density, low operation voltage, ultrafast and low power consuming magnetoelectric nonvolatile memory (e.g. MERAM) or other spintronic devices.

MATERIALS AND METHODS Preparation of BFO thin films The T-phase BFO films with LSMO bottom electrode layers were prepared by PLD. First, the LSMO bottom electrode layers were pre-deposited on (001)-oriented LAO substrates by PLD using a KrF excimer laser (=248 nm) at an ambient temperature of 600 oC and an oxygen pressure


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of 20 Pa. Then, the T-BFO layers (~ 30 nm in thickness) were sequentially deposited by PLD in a low oxygen pressure of ~1.4 Pa at an elevated temperature of 650 oC. A series of microstructural characterizations have been carried out, confirming that the as-prepared BFO films are epitaxial and have the pure T-phase with the (001) out-of-plane orientation.

Patterning of Co nanodot array The Co nanodot array on the T-BFO film was fabricated by a nanosphere lithography technique using closely packed PS nanosphere arrays as template, as detailed in Figure S1. In brief, the nanosphere template with dot diameter of ~1.0 m was first transferred onto the previously deposited T-BFO film in a liquid environment. Subsequently, the Co nanodots covered with an ultrathin Au protective layer were deposited by thermal evaporation at a high vacuum of 3×10-4 Pa. Finally, the mask was lifted-off in methylene chloride, and thus an ordered triangular Co nanodot array attached to the BFO film was obtained.

Microstructural characterizations The crystallinity of BFO films was characterized by X-ray diffraction (PANalytical X′Pert PRO), and the well epitaxial super-tetragonal BFO structure was reflected by the -2 scan. The top view surface morphologies were obtained by scanning electron microscopy (SEM, Zeise Ultra 55), atomic force microscopy (Asylum Cypher AFM), which show well-defined array of triangular Co nanomagnets.


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Magnetic and electric characterizations The piezoresponse force microscopy (PFM) and magnetic force microscopy (MFM) observations were conducted by a scanning probe microscopy (Cypher, Asylum Research). To improve the PFM sensitivity, we adopted a dual frequency resonant-tracking technique (DART) provided by Asylum Research Company. The local piezoresponse loop measurements were carried out by fixing the PFM probe on a selected nanodot, and then applying a triangle-square waveform bias voltage accompanying with an ac driving voltage of 1.5 V, via the conductive PFM probe (BRUKER, PMV-PT). For characterization of electric control of magnetization, we first imaged the MFM micrographs of the initial magnetic states using the MFM probes (Multi75M-C), Budget Sensors, and then applied the dc scanning bias voltages or voltage pulses on the nanomagnets through the MFM tips, and finally the MFM images were taken again to see the evolution of magnetic states driven by electric field. Besides, the magnetization loop of the whole sample was measured by a vibrating sample magnetometer (VSM) imbedded inside a physical property measurement system (PPMS-9), Quantum design.

Micromagnetic simulation We utilize the three-dimensional OOMMF software package,41 in which the time-dependent evolution of magnetization is obtained by solving the well-established Landau-Lifshitz-Gilbert (LLG) ordinary differential equation. The parameters used in the simulations include the spontaneous magnetization MS = 1.4  106 A/m, exchange constant A = 30  10-12 J/m, damping coefficient  = 0.05, and effective anisotropy factors. The anisotropy factors include the static magnetoanisotropy factor K0 originated from the residual strain in the as-deposited states, and the


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dynamic anisotropy pulse K from the piezo-strain pulse due to the electrically induced transient T/R coexisting state, as well as the shape anisotropy Kshape. A detailed discussion on these anisotropy factors can be found in Calculation of anisotropy section in Supplementary Text, where the overall effective anisotropy was derived by using the area enclosed in the measured virgin magnetization curves between in-plane and out-of-pane directions (see Figure S8).45 The cell size for the simulations is 5×5×2.5 nm3. The effective field hDM due to the interfacial coupling from the BFO film was calculated following the method proposed by Wang et al.,46 and the distribution state of hDM can be found in the Figure S9. The choice of the simulation parameters is also described in the Supplementary Text. The simulated MFM contours were calculated based on the second-order derivative of the outof-plane component of the stray field distributions at certain height above the simulated magnetic states.42,43 In this work, a Green function method proposed by Saito et al.42 and a MATLAB program developed in our group were employed to derive the simulated MFM contours. More details can be found in Supplementary Text and reference 42.

ASSOCIATED CONTENT Supporting Information Available: Some additional data about (1) nanostructure fabrication procedures, (2) micromagnetic simulation procedure and parameters, (3) structure and morphologies of BFO films, (4) MFM images regarding switching reversibility, speed and stability, (4) M-H loops and magnetization curves, (5) distribution of polarization domains and local canted magnetic moments, (6) simulated phase-diagram for EDMS, (7) magnetic switching driven by scanning bias voltages, (7) switching among six magnetic states triggered by electric field. This supporting information is available free of charge via the Internet at http://pubs.acs.org.


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AUTHOR INFORMATION Corresponding Authors *Email: [email protected] (X.S.G). *Email: [email protected] (J.-M.L).

Author Contributions X.S.G. conceived and designed the experiments. J.X.Y. conducted the main experiments. H.F., J.X.Y, G.T., Z.F.H, D.Y.C. M.Z. and Z.F. contributed to the sample fabrications and XRD measurements. P.L.L. and W.D.Y carried out the PFM measurements. X.S. conducted the micromagnetic simulations. X.S.G. & J.-M.L. conducted the data interpretation and co-wrote the article. All authors discussed the results and commented on the manuscript. The authors declare no competing financial interests.

ACKNOWLEDGMENT The authors thank for the financial supports from the National Key Research and Development Program of China (Nos. 2016YFA0201002, 2016YFA0300101, 2016YFA0201004), the State Key Program for Basic Researches of China (No. 2015CB921202), the Natural Science Foundation of China (Nos. 11674108, 51272078), the Project for Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme (2014), Science and Technology Planning Project of Guangdong Province (No. 2015B090927006), the Natural Science Foundation of Guangdong Province (No. 2016A030308019). D.F.Z was also acknowledged for assist on PFM testing.


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Figure 1. The magnetic states for the Co/BFO/LSMO/LAO heterostructure with triangular Co nanodot array on epitaxial BFO thin films deposited on LSMO-buffered LAO substrates. (A) Schematic of the multiferroic heterostructure. (B) Measured in-plane and out-of-plane M-H hysteresis loops. (C) SEM image of seven triangular Co nanodots. (D and E) MFM images of the seven Co nanodots shown in C, before (D) and after (E) alignment by an in-plane magnetic field of 5000 Oe. The scale bars in (C-E) are 500 nm. (F and G) High-resolution MFM images of six magnetic states (F) for a chosen Co nanodot magnet and their corresponding magnetization vector maps by simulations (G). The open dashed coarse arrows shown on the MFM images in F mark the average magnetization vectors of the three triangle wings. (H) Calculated MFM contours from the simulated configurations in (G).


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Figure 2. Electric field driven reversible magnetic state rotation in individual Co nanodots. (A to D) Magnetic state rotations triggered by electric pulses applied onto specific Co nanodots: (A) AFM topology of six Co nanodots on BFO film; (B to D) the MFM images of the six nanodots by sequence, for the initial magnetic state without any pre-treatment (B), then upon an electric pulse of +8 V (C), and then upon second electric pulse of -8 V onto the circled nanodots (D). (E and F) Enlarged MFM images of the two blue-cycled nanodots, I & II, in the three magnetic states, respectively, in the top row, together with the simulated MFM contours in the middle row, and the simulated magnetization vector maps in the bottom row. The open dashed coarse arrows marking the average magnetization vectors for the three triangle wings given on MFM images, indicating that the magnetic states upon the rotations in this Figure are all in the 1-in-2-out mode.


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Figure 3. The reversible magnetic state rotations triggered by a set of electric pulses on a selected Co nanodot. (A) The sequential MFM images of the nanodot upon a set of sequential electric pulses at a duration of 1 ms: 0 V (starting state)  4 V  8 V  0 V  -4 V  -8 V  0 V (end state). The open dashed coarse arrows marking the average magnetization vectors for the tree triangle wings given on MFM images. This sequence constitutes a hysteresis loop in the magnetization (M) versus electric field (E) plane schematically shown in the middle region, indicating clearly the electrically driven magnetic switching (magnetic state rotation) of the nanodot. (B) MFM images of the nanodot upon multi-cycled magnetic state rotations, triggered by two sequential electric pulses of 9 V and – 9 V with a duration of 1 ms. All the MFM images have the same scale bar of 200 nm.


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Figure 4. Ultrafast magnetic state switching and long-time retention behaviors. (A) The wave forms of two ultrashort electric pulses (10 ns at 10 V) applied onto a selected Co nanodot. (B) MFM images of this nanodot in the initial state, after the first electric pulse of 10 V for 10 ns, and after the second pulse of –10 V for 10 ns. (C) MFM images demonstrating the retention property of the magnetic state in a “written” Co nanodot as red-cycled. The series read: initial state, switched state after subjected to an electric pulse of 8 V for 1.0 ms, this switched state after heating at 100 o

C for one hour, and this switched state after retention duration of nine months (6500 hours).


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Figure 5. Micromagnetic simulations of electrically driven magnetic state rotation for a triangular nanomagnet. (A) Schematics of phase evolution of the BFO film upon applying an electric pulse to switch the polarization, which is in accompanied with changes in strain and interfacial coupling. P: polarization, AFM: antiferromagnetic order, Mc: canted magnetic moment; Kz: transient anisotropy pulse, hDM: effective interfacial magnetic field. (B) Evaluated electric pulse induced variation of Kz and hDM. (C) Simulated magnetization vector map contours for the four magnetic states according to the time series (top row), and the simulated x- and y-components of the in-plane net magnetization before, within, and after the electric pulse. The electric pulse duration is artificially set in this figure.


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Electrically Driven Reversible Magnetic Rotation in Nanoscale

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