Voltage controlled inversion of magnetic anisotropy in a ferromagnetic thin film at room temperature

The control of magnetic properties by means of an electric field is an important aspect in magnetism and magnetoelectronics. We here utilize magnetoelastic coupling in ferromagnetic/piezoelectric hybrids to realize a voltage control of magnetization orientation at room temperature. The samples consist of polycrystalline nickel thin films evaporated onto piezoelectric actuators. The magnetic properties of these multifunctional hybrids are investigated at room temperature as a function of the voltage controlled stress exerted by the actuator on the Ni film. Ferromagnetic resonance spectroscopy shows that the magnetic easy axis in the Ni film plane is rotated by 90 degree upon changing the polarity of the voltage Vp applied to the actuator. In other words, the in-plane uniaxial magnetic anisotropy of the Ni film can be inverted via the application of an appropriate voltage Vp. Using SQUID magnetometry, the evolution of the magnetization vector is recorded as a function of Vp and of the external magnetic field. Changing Vp allows to reversibly adjust the magnetization orientation in the Ni film plane within a range of approximately 70 degree. All magnetometry data can be quantitatively understood in terms of the magnetic free energy determined from the ferromagnetic resonance experiments. These results demonstrate that magnetoelastic coupling in hybrid structures indeed is a viable option to control magnetization orientation in technologically relevant ferromagnetic thin films at room temperature.

2 be quantitatively understood in terms of the magnetic free energy determined from the ferromagnetic resonance experiments. These results demonstrate that magnetoelastic coupling in hybrid structures is indeed a viable option to control magnetization orientation in technologically relevant ferromagnetic thin films at room temperature.

Introduction
Multifunctional material systems unite different, e.g. electric and magnetic, functionalities in either a single phase or a heterostructure. They thus are of great fundamental and technological interest. Given that the electric and magnetic properties furthermore are coupled, it becomes possible to control either the magnetization by the application of an electric field or the electric polarization via a magnetic field alone. An electric field control of magnetization is particularly appealing, as it removes the need to generate magnetic fields of sufficient strength for magnetization switching on small length scales-thus enabling novel concepts for high density magnetic data storage applications. Thus, techniques to control the magnetization by means of electric fields or currents have recently been vigorously investigated and several schemes for an electric control of magnetization have been reported. These include the spin-torque effect [1]- [4] in spin-valves and magnetic tunnel junctions and the direct electric field control of magnetization in intrinsically multiferroic materials [5]- [12] or in ferromagnetic/ferroelectric heterostructures [13,14]. A third, very attractive approach for the electric field control of magnetization takes advantage of the elastic channel, i.e. magnetostrictive coupling [15]- [23]. We here show that magnetoelasticity-that is the effect of lattice strain on magnetic anisotropy-in a polycrystalline nickel (Ni) film/piezoelectric actuator hybrid structure can be used to switch the magnetic easy axis in the Ni film by 90 • at room temperature by simply changing the polarity of the voltage V p applied to the actuator. The highly efficient coupling between piezoelectric and magnetic degrees of freedom in the ferromagnet/piezoactuator hybrid furthermore allows to achieve either an irreversible magnetization orientation control of 180 • or a reversible control close to 90 • , depending on whether the magnetization orientation is prepared in a local or global minimum of the free energy via a magnetic field sweep prior to the electric control experiment. We use ferromagnetic resonance (FMR) to quantify the effect of an electric field on magnetic anisotropy, which enables us to calculate the magnetization orientation as a function of V p using a Stoner-Wohlfarth approach [24]. The magnetization orientation as a function of magnetic and electric fields determined in superconducting quantum interference device (SQUID) 3 magnetometry experiments is in full agreement with Stoner-Wohlfarth simulations, even for external magnetic field strengths well below the Ni coercive field. These experiments demonstrate that the strain-mediated electric field control of magnetization is indeed a viable technique in technologically relevant ferromagnetic thin films at room temperature.

Sample preparation and experimental techniques
We fabricated ferromagnetic thin film/piezoelectric actuator structures by depositing Ni thin films onto piezoelectric Pb(Zr x Ti 1−x )O 3 -based actuators [25]. Ni was chosen as the ferromagnetic constituent as it is a prototype 3d itinerant ferromagnet with a Curie temperature T c = 627 K well above room temperature [26], a high bulk saturation magnetization M s = 411 kA m −1 [27] and sizeable volume magnetostriction [28,29]λ = 2 5 λ 100 + 3 5 λ 111 = −32.9 × 10 −6 with λ 100 and λ 111 being the single crystal saturation magnetostriction for a magnetic field applied along a crystalline 100 or 111 axis, respectively. The actuators exhibit a hysteretic mechanical stroke of up to 1.3 × 10 −3 along their dominant elongation axis [cf figure 1(a)] if voltages −30 V V p +150 V are applied. Prior to the deposition of the Ni film, the actuators were mechanically polished to a size of x × y × z = 3 × 2.6 × 2 mm 3 [cf figure 1(a)] to accommodate the size of the sample to the restrictions imposed by the FMR setup. We then used electron beam evaporation at a base pressure of 2.0 × 10 −8 mbar to deposit a 70 nm thick Ni film onto an area of 5mm 2 on thex-ŷ face of the actuators. To prevent oxidation of the Ni film, a 10 nm thick Au film was deposited in situ on top of the Ni layer. The multifunctional hybrid obtained after Ni deposition is sketched schematically in figure 1(a) together with the definition of the angles that describe the orientation of the magnetization M = (M, , ) and the external magnetic field H = (H, θ, φ) in the sample-affixed coordinate system.
To determine the static magnetic response of the ferromagnetic thin film/piezoelectric actuator hybrid we employ SQUID magnetometry. The Quantum Design MPMS-XL-7 SQUID magnetometer is sensitive to the projection m = mĤ of the total magnetic moment m onto the unit vectorĤ = H/H . We corrected m for the paramagnetic contribution of the actuator and used the Ni film volume V = 3.5 × 10 −13 m 3 to calculate the respective projection M = m/V of the magnetization ontoĤ. All magnetometry data shown in the following were recorded at a temperature T = 300 K.
The magnetic anisotropy of the ferromagnetic thin film/piezoelectric actuator hybrid was measured by FMR at room temperature. We use a Bruker ESP 300 spin resonance spectrometer with a TE 102 cavity operating at a constant microwave frequency ν MW = 9.3 GHz. The sample can be rotated in the FMR setup with respect to the external dc magnetic field, so that either θ or φ [cf figure 1(a)] can be adjusted at will. To allow for lock-in detection we use magnetic field modulation at a modulation frequency of 100 kHz with a modulation amplitude of µ 0 H mod = 3.2 mT.

Phenomenology of strain-induced magnetic anisotropy
The piezoelectric actuator deforms upon the application of a voltage V p = 0 V. Due to its elasticity, an elongation (contraction) along one Cartesian direction is always accompanied by a contraction (elongation) in the two orthogonal directions. Therefore, for V p > 0 V, the actuator expands along its dominant elongation axisŷ and contracts along the two orthogonal directions 4 (a) x andẑ. The Ni film affixed to thex-ŷ face of the actuator is hence strained tensilely alongŷ and compressively alongx for V p > 0 V [cf figure 1(b)]. For V p < 0 V the actuator contracts alongŷ and thus expands alongx andẑ and the Ni film thus exhibits a compressive strain alongŷ and a tensile strain alongx [cf figure 1(d)].
To describe the impact of this lattice strain on the Ni magnetization orientation we use a magnetic free energy density approach. The free energy F tot is a measure for the angular dependence of the magnetic hardness, with maxima in F tot corresponding to magnetically hard directions and minima to magnetically easy directions. In equilibrium, the magnetization always 5 resides in a local minimum of F tot . Contrary to single-crystalline films, the evaporated Ni films are polycrystalline and thus show no net crystalline magnetic anisotropy which may compete with strain-induced anisotropies and hereby reduce the achievable magnetization orientation effect [19]. F tot is thus given by The first term F stat = −µ 0 M H (sin sin sin θ sin φ + cos cos θ + sin cos sin θ cos φ) in equation (1) is the Zeemann term and describes the influence of an external magnetic field H on the orientation of M. The uniaxial demagnetization term F demag = (µ 0 /2)M 2 sin 2 cos 2 is the anisotropy caused by the thin-film shape of the sample [30]. The last contribution to equation (1) describes the influence of the lattice strains on the magnetic anisotropy [28]. The strains along thex-,ŷ-andẑ-axis are denoted in Voigt (matrix) notation [31] as ε 1 , ε 2 and ε 3 , respectively. Furthermore, c Ni 11 = 2.5 × 10 11 N m −2 and c Ni 12 = 1.6 × 10 11 N m −2 are the elastic moduli of Ni [29]. The effects of shear strains (ε i , i ∈ {4, 5, 6}) average out in our polycrystalline film and thus are neglected.
Using sin 2 sin 2 + cos 2 + sin 2 cos 2 = 1 and omitting isotropic terms, equation (2) can be rewritten as Due to the elasticity of the actuator and the Ni film, the strains ε i are not independent of each other. The strains ε 1 and ε 2 in thex-ŷ-plane are linked by the Poisson ratio ν = 0.45 of the actuator [25] according to Furthermore, due to the elasticity of the Ni film, the out-of-plane strain ε 3 can be expressed as [19] Assuming a linear expansion of the actuator with lateral dimension L parallel to its dominant elongation axis, we can calculate the strain in the Ni film parallel to the actuator's dominant elongation axis as where δL/L = 1.3 × 10 −3 is the nominal full actuator stroke for the full voltage swing −30V V p +150 V. With equations (5)-(7) all strains in the Ni film can thus directly be calculated for any given voltage V p . This allows to determine the equilibrium orientation of the magnetization as a function of V p by minimizing the total magnetoelastic free energy density F tot [equation (1)].

6
Due to the negative magnetostriction (λ < 0) of Ni and c Ni 11 > c Ni 12 , the in-plane easy axis of F tot is oriented orthogonal to tensile and parallel to compressive strains in the absence of external magnetic fields. Due to the strong uniaxial out-of-plane anisotropy caused by F demag , the in-plane easy axis is the global easy axis. For V p > 0 V, the Ni film exhibits a tensile strain alongŷ (ε 2 > 0) and a compressive strain alongx (ε 1 < 0). The easy axis of F tot is thus oriented along thex-direction [cf figure 1(c)]. Accordingly, for V p < 0 V, the easy axis of F tot is oriented parallel to the compressive strain alongŷ and orthogonal to the tensile strain alongx [cf figure 1(e)]. We thus expect a 90 • rotation of the in-plane easy axis of F tot upon changing the polarity of V p . Note that in the absence of external magnetic fields there are always two energetically equivalent antiparallel orientations of M along the magnetic easy axis. However, for simplicity, we only show one of the two resulting possible in-plane orientations of M in figures 1(b) and (d). Nevertheless, these panels show that it should be possible to change the orientation of M from M x to M ŷ via the application of appropriate voltages V p to the actuator.
The total magnetic free energy density F tot in equation (1) is experimentally accessible by FMR. The FMR equations of motion [32]- [34] ω γ and link the experimentally determined FMR field µ 0 H res to the magnetic free energy density F tot . In equation (8), γ is the gyromagnetic ratio and ω = 2πν MW with the microwave frequency ν MW . The effect of damping is neglected in equation (8), as damping only affects the lineshape which will not be discussed in this article. We note that the FMR resonance field µ 0 H res measured in experiment can be considered as a direct indicator of the relative magnetic hardness along the external dc magnetic field direction. From equations (1) and (8) one finds that smaller resonance fields correspond to magnetically easier directions and larger resonance fields to magnetically harder directions.

FMR
In this section, we quantitatively determine the magnetic anisotropy of our ferromagnetic thin film/piezoelectric actuator hybrid structure using FMR measurements. Figure 2(a) shows four FMR spectra recorded at room temperature with H ŷ and a voltage V p ∈ {−30 V, 0 V, 30 V, 90 V} applied to the actuator, respectively. Each spectrum shows one strong FMR which-due to the magnetic field modulation and lock-in detection-has a lineshape corresponding to the first derivative of a Lorentzian line [35]. The resonance field µ 0 H res of a given FMR line is determined as the arithmetic mean of its maximum and minimum and depicted by the full squares in figure 2(a). The figure shows that, with the external magnetic field H ŷ, µ 0 H res is shifted to higher magnetic fields for increasing V p , while the lineshape is not significantly changed. According to equations (1) and (8), this implies that theŷ-direction becomes increasingly harder as V p is increased.
To determine the evolution of µ 0 H res with V p in more detail, we recorded FMR spectra similar to those shown in figure 2(a) for V p increasing from −30 V to +90 V (upsweep) and decreasing back to −30 V (downsweep) in steps of V p = 10 V. For H ŷ, we obtain the shows that the FMR resonance field for H ŷ increases with increasing V p and decreases with decreasing V p . The small hysteresis between up-and down-sweep is due to the hysteretic expansion of the actuator [25]. Carrying out the same series of FMR measurements with H x yields the resonance fields shown by the triangles in figure 2(b). For this magnetic field orientation, µ 0 H res decreases for increasing V p and vice versa. In terms of magnetic anisotropy we thus can conclude that thex-direction becomes easier for increasing V p while at the same time theŷ-direction simultaneously becomes harder.
For a more quantitative discussion we have also plotted the behaviour expected from equations (1) and (8) as solid lines in figure 2(b). These lines show the resonance fields obtained by assuming a linear, non-hysteretic voltage-strain relation [cf equation (7)] and solving equation (8) with F tot from equation (1). We use a saturation magnetization M s = 370 kA m −1 , as determined by SQUID measurements and a g-factor of 2.165 [36]. Considering the fact that the actuator expansion saturates at high voltages and the data in figure 2(b) only show a minor loop of the full actuator swing, the simulation is in full agreement to the experimental results. This demonstrates that for V p < 0 V theŷ-direction is magnetically easier than thex-direction, while for V p > 0 V thex-direction is easier than theŷ-direction. Moreover, at V p = 0 V, both measurement and simulation yield resonance fields of µ 0 H res ≈ 150 mT for H ŷ as well as H x. Thus, at this voltage, both orientationsx andŷ are equally easy in our sample.
To quantitatively determine the full magnetic anisotropy as a function of V p , we recorded FMR traces at constant V p for several different H orientations. The FMR resonance fields  (1) and (8). The open triangles in figure 3 represent the resonance fields obtained for V p = −30 V and the full circles those obtained for V p = +20 V. Note that in the polar plots in figure 3, the distance of µ 0 H res from the coordinate origin is an indicator of the magnetic hardness, with easy directions corresponding to small distances and hard directions to large distances.
If H is rotated in the film plane [cf figure 3(a), φ = 90 • ], the obtained µ 0 H res (θ) shows minima at θ = 0 • and θ = 180 • for V p = −30 V and at θ = 90 • and θ = 270 • for V p = +20 V, respectively. Thus, a clear 180 • periodicity of the resonance fields and hence a uniaxial magnetic anisotropy is observed for both V p . As the orientations θ corresponding to minima of µ 0 H res for one voltage coincide with maxima for the other voltage, we conclude that the direction of the easy axis is rotated by 90 • if V p is changed from V p = −30 V to V p = +20V. This is exactly the behaviour expected according to figures 1(c) and (e).
If H is rotated from within the film plane (φ = 90 • , θ = 90 • ) to perpendicular to the film plane (φ = 0 • , θ = 90 • ), we obtain the resonance fields shown in figure 3(b). In this case, we observe a strong uniaxial anisotropy with a hard axis perpendicular to the film plane regardless of V p , stemming from the V p -independent contribution F demag to F tot . The inset in figure 3(b) shows that for H in the film plane, the resonance fields for V p = −30 V and V p = +20 V are shifted by approximately 10 mT in full accordance to the data in figure 3(a).

9
As discussed in section 3, the V p dependence of the resonance field is given by a V p dependence of F magel . We thus evaluate the measurement data shown in figures 3(a) and (b) using an iterative fitting procedure of K u,magel,y in equation (1) The resonance fields calculated using these anisotropy fields as well as equations (8) and (1) are depicted by the lines in figure 3. The good agreement between simulation and experiment shows that F tot given by equation (1) is sufficient to describe the magnetic anisotropy of the Ni film.
In summary, the FMR experiments conclusively demonstrate that it is possible to invert the in-plane magnetic anisotropy of our hybrid structure, i.e. to invert the sign of K u,magel,y solely by changing V p . As the FMR experiment furthermore allows to quantitatively determine all contributions to the free energy, equation (1), the orientation of the magnetization vector M in our sample can be calculated a priori for arbitrary H and V p . However, it is not possible to directly measure the magnetization orientation as a function of V p with FMR. To demonstrate that the piezo-voltage control of magnetic anisotropy indeed allows for a voltage control of M, we now turn to magnetometry.

Magnetometry
In this section, we show that it is possible to not only change the magnetic anisotropy but to deliberately irreversibly and/or reversibly rotate M simply by changing V p . To this end, we need to employ an experimental technique that is directly sensitive to the orientation of M rather than to magnetic anisotropies. Here, we used SQUID magnetometry to record the projection m of the total magnetic moment m onto the direction of the external magnetic field H.
In a first series of experiments, we recorded m as a function of the external magnetic field magnitude µ 0 H at fixed orientations of H and fixed voltages V p at T = 300 K. Figure 4 Following the same line of argument we can conclude that thex-direction is magnetically easier for V p = +30 V and harder for V p = −30 V. Altogether these results show that we observe an in-plane anisotropy, the easy axis of which is parallel toŷ for V p = −30 V and parallel tox for V p = +30 V. These observations are fully consistent with the FMR results, and corroborate the simple model shown in figure 1.
Before discussing further experimental magnetometry results, we note that the free energy minima shown in figure 1(c) and (e) as well as the in-plane resonance fields in figure 3(a) (1), only F stat possesses the desirable unidirectional anisotropy. Hence, a small but finite external magnetic field H = 0 can be used to lift the 180 • degeneracy. This approach works for all H orientations, except for H exactly parallel tox orŷ. For H x (with H > 0), the easy axis parallel tox in figure 1(c) is replaced by an easier positivex-direction and a harder negativex-direction, thus the degeneracy is lifted for V p > 0. However, for V p < 0 [cf figure 1(e)] a magnetic field H x is orthogonal to the easy axis which thus remains degenerate. The same consideration holds for H ŷ where we expect degenerate free energy minima for V p > 0 and a preferred M orientation for V p < 0. However, in experiment it is essentially impossible to orient H exactly alongx orŷ; any small misorientation between H andx orŷ is sufficient to lift the degeneracy. We now turn to the experimental measurement of the voltage control of M orientation. To show that M can be rotated by varying V p alone, we change V p at constant external magnetic bias field H. As SQUID magnetometry is limited to recording the projection of M on the direction of the external magnetic field H, it is important to choose appropriate H orientations in the experiments. As evident from figures 1 and 4, H x and H ŷ are the most interesting orientations of the external magnetic field. In view of the circumstance discussed in the previous paragraph, we applied H to within 1 • ofx orŷ, respectively. We still refer to these orientations of H as H x and H ŷ for simplicity, but take into account a misalignment of 1 • in the calculations. As the experimental results and the corresponding simulations will show, this slight misalignment is sufficient to lift the degeneracy in the free energy regardless of V p .
Recording M as a function of V p for two complete voltage cycles −30V V p +120 V with H ŷ and µ 0 H = −3 mT yields the data points shown in figure 5(a). Since H ŷ, M is the projection of M to theŷ-direction in the experiment. Prior to the first voltage sweep starting at point A, the voltage was set to V p = −30 V and the sample was magnetized to a single domain state by applying µ 0 H = +7 T alongŷ which is the easy axis for V p = −30 V. The magnetic field was then swept to µ 0 H = −3 mT which is close to but still below the coercive field of the rectangular loops [cf figure 4] and the acquisition of the M(V p ) data was started. The fact that M is positive at first (starting from point A), while the field is applied along the negativê y-direction, shows that M and H are essentially antiparallel at first. Upon increasing V p in steps of +5 V to V p = +120 V (point B), M vanishes, which indicates an orthogonal orientation of M and H. Upon reducing V p to its initial value of −30 V, M becomes negative (point C), evidencing a parallel orientation of M and H. The V p cycle was then repeated once more, with M now reversibly varying between its negative value at point C and zero at B. Hence the evolution of M is qualitatively different in the first and in the second V p cycle, with an irreversible M rotation in the first cycle and a reversible M rotation in the second cycle. This behaviour is expected from the magnetic free energy [cf equation (1) To complete the picture, we repeated the M(V p ) experiment again, but now applied H x. The magnetic preparation with µ 0 H = 7 T was now performed at V p = +120 V to ensure that the preparation field was again applied along an easy axis. The data recorded subsequently at To quantitatively simulate the evolution of M with V p depicted in figure 5, we again took advantage of the fact that the free energy of the Ni film is known from the FMR experiments. To account for the hysteresis of the actuator expansion which is responsible for hysteresis in the M(V p ) loops in figure 5, we hereby used ε 2 as measured using a Vishay general purpose strain gauge in the voltage range of −30 V V p +120 V. The ε 2 data thus obtained are in accordance with the actuator data sheet. Using ε 2 (V p ) as well as the material constants given above we obtained in-plane free energy contours for each voltage V p . Figure 6 exemplarily shows such free energy contours at the voltages depicted by the capital letters in figure 5. To clearly visualize the effect of H misalignment with respect to the sample coordinate system on F tot , the plots in figure 6 were calculated assuming a misalignment in the in-plane orientation of the external magnetic field θ of 10 • , so that θ = 10 • for H ŷ and θ = 100 • for H x. Figure 6 clearly shows that under these conditions the local minima of F tot are non-degenerate for V p = −30 V and V p = +120 V.
To determine the orientation of M, we traced the minimum of the total free energy F tot as a function of V p . This was done by minimizing equation (1) with respect to the in-plane orientation of M, whilst assuming that = 90 • due to the strong shape anisotropy.
To simulate the experimental M(V p )-loops [cf figure 5], we assume a more realistic misalignment of 1 • in θ and numerically minimize F tot ( ) as a function of V p . For this, we set the initial value of antiparallel to the external magnetic field for µ 0 H = −3 mT and parallel to the external magnetic field for µ 0 H = −5 mT. Minimizing F tot ( ) determines the M orientation which we project onto theŷ-orx-axis to yield M. For this, the magnitude of M is The fact that the experimental results exhibit a more rounded shape than the simulation is attributed to domain formation during the magnetization reorientation, which is neglected in the simulation.
Taken together, the free energy density of equation (1) with the contributions quantitatively determined from FMR and our simple simulation of M(V p ) yield excellent agreement with experiment. In particular, we would like to emphasize that for the experiment and the simulation the application of V p leads to a rotation of M and not to a decay into domains. This is evident from the fact that in figures 5(a) and (b), a large projection of M ontoŷ is accompanied by a small projection ontox and vice versa. Combining FMR and SQUID magnetometry, we thus have unambiguously and quantitatively demonstrated that M can be rotated reversibly by about 70 • at room temperature solely via the application of appropriate voltages V p .

Conclusions and outlook
In conclusion, we have investigated magnetoelastic coupling effects in Ni/piezoactuator hybrids, using both FMR and SQUID magnetometry. The FMR measurements show that the in-plane anisotropy of Ni/piezoactuator hybrids can be inverted if the polarity of the voltage applied to the actuator is changed. Thus, we do not only observe a magnetoelastic contribution to magnetic anisotropy, as one might expect considering the properties of the constituents. Rather, in the hybrid structure, the magnetoelastic coupling is strong enough to dominate over all other contributions to the in-plane magnetic free energy. The magnetometry experiments corroborate this result and furthermore show that it is possible to irreversibly or reversibly rotate M solely by changing V p . For an irreversible M(V p ) rotation, an appropriate preparation of M using a magnetic field sweep is necessary-i.e. M must be aligned in a local free energy minimum. It then can be rotated out of this minimum by changing V p and the corresponding M orientation change can amount to up to 180 • . However, this voltage control of M is irreversible in the sense that M cannot be brought back into the original orientation by changing V p alone. Rather, a second appropriate magnetic field sweep is required to align M into its original orientation. In contrast, the reversible M(V p ) reorientation requires a preparation of M only once. In this case, M is oriented along a global free energy minimum, and can be rotated within up to 70 • (90 • in the ideal case) at will by applying an appropriate V p . The M(V p )-loops simulated by minimizing the single-domain free energy [equation (1)] in a Stoner-Wohlfarth type of approach are in excellent agreement with experiment, showing that the M orientation can be accurately calculated from the free energy determined from FMR as a function of external magnetic and/or electric field strengths. Furthermore, we would like to point out that the hysteretic expansion/contraction of the actuator visible as a hysteresis in M(V p ) [cf figure 5] in particular also leads to distinctly different M(V p = 0), depending on the V p history. Thus, our data also demonstrate that a remanent M control is possible in our ferromagnetic thin film/piezoelectric actuator hybrids. Finally, we note that an electric field control of magnetization orientation via the elastic channel should be possible in any material or hybrid system, given that the magnetoelastic contribution to the magnetic free energy dominates in the plane of interest. In our opinion, this approach thus can be implemented and exploited in a variety of existing spintronic devices, e.g. to control the magnetization orientation in individual magnetic random access memory bits. Additionally, the application of an ac electric field to the actuator will generate a time-dependent strain in the ferromagnet, opening an avenue for the control and investigation of magnetization dynamics.