Towards magnonic devices based on voltage-controlled magnetic anisotropy

Despite significant technological advances in miniaturization and operational speed, modern electronic devices suffer from unescapably increasing rates of Joule heating and power consumption. Avoiding these limitations sparked the quest to identify alternative, charge-neutral information carriers. Thus, spin waves, the collective precessional motion of spins in permanent magnets, were proposed as a promising alternative system for encoding information. In order to surpass the speed, efficiency, functionality and integration density of current electronic devices, magnonic devices should be driven by electric-field induced methods. This review highlights recent progress in the development of electric-field-controlled magnonic devices, including present challenges, future perspectives and the scope for further improvement. Magnonics involves the manipulation of spin waves in order to develop more energy efficient spintronics devices which do not rely on the movement of electronic charge. Here, the authors review the various methods designed to control magnonics with particular focus on voltage i.e. electric-field.

velocity and attenuation length as compared with light waves (i.e. photons) inside optical fiber, shorter wavelength of SWs in nanometer scale makes them compatible with nanoscale magnonic devices as opposed to microscale photonic devices. Figure 1b shows schematic illustration of a magnonic device. It mainly consists of four elementary components: (1) a spin wave waveguide (SWWG), (2) a microwave source for excitation, (3) a detector, and (4) some functional elements for SW manipulation, channeling, and amplification. Generally, thin films made of ordered magnetic materials are used as SWWGs. Later in this article, we shall describe various methods of SW excitation 1,12-15 , manipulation [16][17][18][19] , channeling 17,[20][21][22] , amplification 2,23-25 , and detection 14,15,26 . Although different kinds of methods are available for all the above-mentioned operations, all-electrical methods are preferable for application of magnonics into onchip-integrated devices. However, charge current-based electrical methods, which are most commonly found in the literatures for operating magnonic devices, cannot be used because of high power consumption due to Joule heating, which becomes more severe for nanoscale devices. For successful implementation of magnonic devices into future technology, we need to find out energetically efficient alternative method for their operation, which must be compatible with nanoscale microwave devices. This can be achieved if magnonic devices are operated by voltage i.e., electric field instead of charge current. Magnetoelectric (ME) effect allows us to control magnetic properties by electric field. Multiferroic materials show strong ME effect due to presence of magnetic and electrical ordering, simultaneously 27,28 . The strong coupling between magnetic and electric polarization allows to control magnetic properties by electric field and vice versa. However, multiferroic materials generally have low saturation magnetization, low spin polarization and there are only few single-phase multiferroic materials available at room temperature as opposed to FM materials 29 . Although, ferromagnetic semiconductors 30 , such as (In, Mn)As, (Ga, Mn)As, also offer electric field modulation of magnetic anisotropy and exchange interaction via electric-field-controlled carrier density, room temperature operation has not been demonstrated yet. Alternatively, ME effect can be observed when a magnetostrictive film (e.g. Ni) is placed on a piezoelectric substrate (e.g. Pb(Mg 1/3 Nb 2/3 )O 3 -PbTiO 3 , LiNbO 3 ) 31 . The electric field-induced strain in the piezoelectric substrate is transferred to adjacent FM film, in which the magnetic properties are modulated through magnetostriction. For practical applications, piezoelectric thin films are required instead of the piezoelectric substrate. However, there is no report on piezoelectric films with strong ME effect until now. Another alternative method would be recently discovered voltage (i.e., electric field) controlled magnetic anisotropy (VCMA), which is generally observed at the interface between ultrathin 3d transition ferromagnetic metals (e.g., Fe, CoFeB) and nonmagnetic insulators (e.g. MgO, Al 2 O 3 ) 32 . This VCMA is believed to be occurred due to relative changes of electronic occupation state in 3d orbitals of FM 33,34 by applied electric field.
In this article, we review the recent progress of electric-fieldcontrolled magnonic devices based on propagating SWs in ferromagnetic thin films. After a brief historical background about various methods for excitation, manipulation, channeling, amplification of SWs, and development of magnonic crystals and logic gates, we highlight recent reports on the operation of various functions of magnonic devices by voltage i.e., electric field, in particular, through modulation of perpendicular magnetic anisotropy at ferromagnetic metal and oxide interface. Finally, we describe the future perspectives, challenges, and further scopes to improve the efficiency of magnonic devices.
Origin of VCMA and VCMA coefficient Perpendicular magnetic anisotropy (PMA) is essential to enhance the thermal stability of nanomagnets at room temperature. Generally, strong PMA is observed at the interfaces between 3d transition metal FMs (e.g., Co) and heavy nonmagnetic metals (e.g., Pt, Pd, W, Au) 35 . However, Co-Pt, Co-Pd, and Co-Au heterostructures also show relatively high Gilbert damping, which is not desirable for current-induced magnetization switching and other magnonics applications. Moreover, interfacial PMA (iPMA) cannot be modulated by electric field in these systems due to the absence of oxide or dielectric layer at the interface. PMA can also be observed at the interfaces between 3d-FMs (e.g,. Co, Fe, and their alloys) and MO x (M = Mg, Al, Ta, and Ru). Among them, the heterostructures made from CoFeB and MgO draw particular attention due to lower damping constant of CoFeB 36 and high tunneling magnetoresistance (TMR) ratio of CoFeB/MgO/CoFeB at room temperature 37 . At CoFeB/MgO interface, the out-ofplane (OOP) 3d z 2 -orbitals of Fe strongly bond with OOP 2p z -orbitals of O resulting in a significant charge transfer from 3d z 2 -orbitals to 2p z -orbitals. Therefore, the number of electrons in b Schematic illustration shows the basic components of a typical magnonic device. Thin films made of ferromagnetic metals, ferrimagnetic insulators, and antiferromagnets are generally used as SW waveguide, where SWs can be excited by microwave field, spin-orbit torque, pulsed laser beam, and thermal agitation. Those SWs can be detected by various optical or electrical methods. Manipulation and control of SW properties such as frequency, wavevector, phase, group velocity, dispersion character, and guiding SWs through reconfigurable nanochannels are the keys for the development of magnonic devices. SWs can be amplified by compensating damping torque through spin current-induced anti-damping torque OOP orbitals is reduced as compared with the number of electrons in in-plane (IP) orbitals, which in fact introduces a sizeable PMA through spin-orbit coupling (SOC) of FM. When electric field is applied at FM/oxide interface, the number of electrons in OOP 3d-orbitals of Fe is changed with respect to IP orbitals as shown from first-principle calculations 33,38 (Fig. 2a). This affects the bonding strength between 3d-and 2p-orbitals resulting in a substantial change of iPMA. Since the penetration depth of electric field in metal is only few Amstrong, therefore VCMA effect is only limited to ultrathin FM films. Although, electric field control of electronic occupation state is believed to be the main mechanism behind VCMA, several alternative theories are also found in the literature. One of the interesting theories says that the inhomogeneous electric field at the metal/oxide interface couples to the quadrupole of electronic orbital in FM 39 . This electric quadrupole again couples to the magnetic dipoles and controls iPMA. Another theory says that Rashba SOC at FM/ oxide interface can generate iPMA 40 . The applied electric field at the interface modifies Rashba SOC, which in fact modulates iPMA. Naik et al. experimentally demonstrated the development of tensile and compressive strain in nanometer thick MgO layer due to the application of electric field with opposite polarity at FM/oxide interface 41 . Therefore, it is possible that the iPMA is modulated by the piezoelectric property of MgO through magneto-elastic coupling. In reality, all the above mechanisms may be present and contribute simultaneously to the modulation of iPMA. Moreover, these mechanisms neither require atomic movement nor require any chemical reaction, which enables high-speed operation of VCMA magnonics devices with highcycling endurance.
First-principle calculation shows that the change in the number of electrons in 3d-orbitals of Fe is linearly proportional to the applied electric field (E) at FM/oxide interface 34 . Therefore, change in the magnetic moment and iPMA should also be linearly proportional to electric field 33 i.e,. ΔK S ¼ βE, where ΔK S is the change in iPMA and β is known as magnetoelectric or VCMA coefficient. Several experimental reports show this linear variation of iPMA with electric field [45][46][47] . However, the magnitude and sign of β depend upon several factors. For instance, VCMA coefficient and its sign can be same or different for opposite polarity of electric field 46-49 . Xiang et al. reported nonlinear variation of iPMA with electric field for Cr/Fe/MgO heterostructure 42 with a local minima of iPMA at E ¼ þ100mV nm À1 (Fig. 2b). The iPMA increases linearly with E above and below the local minima. Although minimal point is independent of annealing and measurement temperature, β and iPMA strongly depend upon them. These behaviors can be attributed to have intrinsic origin due to electronic band structure at the FM/oxide interface. Some additional reports show that β also depends upon the underlayer material 45,50 , substrate 51 , temperature 52 , FM layer 44 , and MgO overlayer thickness 53 . This is worth to mention here that only first-order anisotropy varies with electric field, whereas second-order anisotropy remains unchanged 43,44 (Fig. 2c). That means only first-order anisotropy has interfacial origin. Interestingly, the electric field applied at the FM/oxide interface not only changes the iPMA but also modulates Gilbert damping parameter (Fig. 2d) as demonstrated by Okada et al. 44 . This is because iPMA and Gilbert damping, both, are originated from SOC. Surprisingly, any correlation between VCMA coefficient and electric field variation of Gilbert damping was not observed.
The reported value of β is up to few tens of fJ V À1 m À1 for CoFeB/MgO interface 44,47,50 . One of the challenges is to increase the value of β in order to further improve the efficiency of magnonic devices. This can be done by engineering FM/oxide interface. Theoretical reports 54 predict that the insertion of the ultrathin heavy metallic layer in between FM and oxide layer could significantly enhance the value of β. Later on a number of experimental reports came out to show the enhancement β by inserting even relatively lighter materials, such as Hf, Mg 55 , and heavy materials, such as Ta, Pt 55 , W, and Ir 56 . The possible reason behind this is the suppression of surface oxidization of FM   57 and Cr 49 at the FM/oxide interface can significantly enhance, both, iPMA and β. The VCMA coefficient over few hundreds of fJ V À1 m À1 can be achieved by this method due to the diffusion of Ir, Cr into the FM layer. VCMA coefficient can be further increased up to few pJ V À1 m À1 by using voltage-controlled electromigration 58 , redox reactions 59 , charge trapping 60 , and magnetostriction 61 . Unfortunately, these methods of VCMA are not suitable for high-frequency applications due to lower speed of operation and poor cycling endurance. Therefore, engineering the electronic bands at FM/oxide interface is more desirable for microwave magnonic devices.

VCMA-induced ferromagnetic resonance (VCMA-FMR)
As VCMA at FM/oxide interfaces relies upon the modification of electronic occupation states in 3d orbitals of FM, it is suitable for microwave applications, such as excitation of ferromagnetic resonance (FMR) and SWs in the gigahertz regime. There are several important characteristics of VCMA excitation of FMR (VCMA-FMR). One of the most promising and sensitive methods for electrical detection of VCMA-FMR is the homodyne detection technique by using TMR effect 47,62,63 (Fig. 3a). A magnetic tunnel junction (MTJ) composed of a free magnetic layer and a reference or pinned magnetic layer is used for this purpose. Microwave voltage is applied across the MTJ to periodically modulate the iPMA of free layer. At resonance, a finite dc voltage V rec (called rectified voltage) is produced across the MTJ due to mixing of time varying TMR and small radio frequency (rf) current across the junction. One of the basic differences between spin-transfertorque (STT) excitation and VCMA excitation is that the STT is proportional to sin θ, whereas VCMA-torque is proportional to sin θ cos θ, where θ is the elevation angle of magnetization 63 . Therefore, V rec becomes proportional to sin 2 θ for STT excitation and sin 2 θ cos θ for VCMA excitation when measured by MTJ, as the sensitivity of TMR detection is proportional to sin θ. Hence, VCMA-FMR signal measured by MTJ becomes maximum at θ ¼ 55 o (Fig. 3b). It is important to mention here that the pinned layer does not have any role for VCMA excitation, it is used only for detection. In absence of STT and/or field-like torque (FLT), the lineshape of the VCMA-FMR spectra should be purely antisymmetric Lorentzian. However, as the homodyne detection signal is sensitive to the relative phase between rf current through the MTJ and time varying TMR due to FMR, the lineshape can be changed from anti-symmetric Lorentzian to symmetric Lorentzian depending upon the relative orientation of magnetizations in two layers of MTJ 64 and DC bias voltage 43 (Fig. 3c). Moreover, the sign of the anti-symmetric Lorentzian signal can be reversed by reversing the direction of bias magnetic field 62 .
Most important advantage of VCMA-FMR is ultralow power consumption. Nozaki et al. 63 have shown that the power consumption for VCMA excitation can be at least two orders of magnitude lower than the current induced STT excitation. It is worth to mention here that this is not the fundamental limit of power consumption for VCMA-FMR. The power consumption can be further reduced by increasing VCMA coefficient through engineering of FM/oxide interface. At lower excitation power or in the linear regime of excitation, V rec is proportional to applied rf power (P rf ) 63 , whereas cone angle of magnetization precession is linearly proportional to applied rf voltage (V rf ) 47 . Moreover, the lineshape, linewidth, and resonance frequency of VCMA-FMR remain independent of P rf . However, with the increase of P rf , the V rec , and cone angle of precession deviate from their linear increment with P rf and V rf , respectively, due to the nonlinear FMR 47,65 (Fig. 3d, e). Therefore, the lineshape is distorted from anti-symmetric Lorentzian, linewidth is broadened, and resonance frequency is decreased (Fig. 3d). Rana et al. 47 have shown that the coherent FMR becomes incoherent above a threshold excitation power (Fig. 3f), which in fact distorts the lineshape and increases the linewidth. Cone angle of magnetization precession monotonically increases with P rf and eventually becomes saturated. In the nonlinear regime, FMR is basically governed by four magnon scattering, which creates two k≠0 ( + k and −k) magnons by annihilating two k ¼ 0 magnons 66 . As a result, coherent FMR becomes incoherent.
Nonlinear parametric excitation of SWs by VCMA Uniform FMR and also coherent SWs cannot be excited by VCMA when the static magnetization of FM film is aligned either perpendicular to the film plane (θ ¼ 90 o ) or in the film plane (θ ¼ 0 o ) (Fig. 3b). However, by performing theoretical analysis 67,68 and numerical simulations 69 , Verba et al. have shown that these special magnetization configurations are suitable for nonlinear parametric excitation of SWs, where frequency of applied rf electric field (E rf ) i.e., VCMA is twice larger than the SW frequency. Later on it has been experimentally demonstrated by Chen et al. 70 . The magnetization vectors of a FM film generally precess randomly around its equilibrium direction due to the thermal fluctuation (thermally generated magnons). When the oscillation trajectory becomes elliptical due to presence of either shape anisotropy or magnetocrystalline anisotropy of the FM film, the z-component of dynamic magnetization oscillates in a frequency twice larger than the magnetization vector oscillation 67 . The time varying VCMA efficiently couples to the z-component of dynamic magnetization when the frequency of applied E rf becomes twice larger than the SW frequency. The main advantage of parametric excitation is that it can efficiently excite and selectively amplify even shorter wavelength SWs as compared with linear excitation, where the wavelength of excitation is limited by the dimension of gate electrode and excitation efficiency drastically decreases for shorter wavelengths 1 . Of course this limitation of linear excitation may be overcome by the methods mentioned in ref. 71 . Interestingly, parametric SWs with relatively large amplitude and much narrower linewidth can be excited by VCMA 69 , as compared with Oersted field. The disadvantage of parametric excitation, as opposed to linear excitation, is that it is not energy efficient as high-threshold power of microwave field is required for the excitation. The threshold power strongly depends upon the width of waveguide (WG), width of gate electrode, excitation frequency, and SW wavevector 67,68 . Nevertheless, the threshold power can be significantly reduced by replacing microwave field by VCMA 70 . For OOP orientation of magnetization, the lower threshold value of excitation is obtained for long wavelength dipolar dominated SWs in narrow WG with width about few tens of nanometer 67 (Fig. 4a). For IP orientation of magnetization, the SW with much shorter wavelength (dominated by exchange interaction) can be excited very efficiently by VCMA (Fig. 4b), as the efficiency of parametric interaction between excited SWs and VCMA is proportional to OOP component of dynamic magnetization in this case 68 . Herein lies the advantage of VCMA excitation over Oersted field excitation, as this is only the inherent property of VCMA excitation. In all the cases, the threshold power can even be reduced by choosing a FM/oxide heterostructures with higher VCMA coefficient. Another important characteristic of parametric excitation is that the resonance frequency shifts toward the lower frequency with the increase of excitation power due to nonlinear effect 70 (Fig. 4c).

Excitation of coherent propagating SWs
There are several ways available for the excitation of SWs, such as rf current-induced Oersted fields 14,19 (Fig. 5a), spin-transfertorques (STT) 12,13 (Fig. 5b), femtosecond pulsed laser beams 11,15,[72][73][74] (Fig. 5c), and thermal energy 75 . Oersted fields are not suitable for nanoscale spintronics devices due to their spatially nonlocalized nature. However, there are some alternative ways which even enable spatially uniform microwave Oersted fields to excite SWs with shorter wavelength without localizing it. For instance, SWs with shorter wavelength can be excited by creating magnetic nonuniformities either naturally or artificially. Au et al. have shown that localized dynamic dipolar field created by the FMR of a rod-like magnetic nanostructure on top of a SWWG can excite shorter wavelength SWs 76 . Even smooth interface between two magnetic films can also excite shortwavelength coherent SWs very efficiently 71 . All these abovementioned methods either need to create nonuniformities in magnetic film or need two magnetic layers, which may increase the complexity of device fabrication. The STT, on the other hand, can be easily localized in nanoscale area. However, these currentinduced methods suffer from huge power consumption due to inherent Joule heating. Another efficient way to excite coherent SWs is femtosecond pulsed laser beam 11,15 . But this method is suitable only for scientific studies, and may be difficult to implement in practical magnonic devices. Thermal excitations are also not suitable for practical purposes due to its incoherent nature of excitation. As an alternative VCMA promises to be a very efficient way to excite FMR and SWs at ultralow power consumptions. The key advantage of VCMA is that the excitation area can be localized without creating nonuniformities in magnetic structure or using a second magnetic layer, unlike Oersted field excitation.
Although parametrically excited nonlinear SWs have several advantages, linear or coherent propagating SWs are required for the development of magnonic logic devices. This is because the linear relationship of SW amplitude with rf voltage (V rf ) of excitation makes it easier to control SW amplitude and phase for logic operation. Rana et al. 1 have experimentally demonstrated that coherent propagating SWs can be excited in ultrathin FM films by VCMA. In this case, a metal gate electrode is placed on the top of the oxide layer (Fig. 5d). V rf is applied across gate electrode and WG for periodically modulating iPMA of WG underneath gate electrode. At resonance frequency, the coherent SWs with frequency same as V rf are excited and propagate along the WG. The lateral width (w) of the gate electrode decides the range of wavevectors, which can be excited by V rf . The excitation efficiency as a function of wavevector can be found by performing the Fourier transform of spatial distribution of electric field at the FM/oxide interface. In this case, the dependence of excitation efficiency with wavevector is given by square of sinc function, which says that the SWs with wavevector (k) up to 2π=w can be excited 1 . Therefore, in order to excite SWs with high k (i.e., shorter wavelength), the width w of gate electrode needs to be reduced. Nevertheless, this is technically possible as nanometerscale gate electrode can be fabricated and electric field can be, in principle, localized within few tens of nanometer underneath gate electrode.
The SW propagation length in metallic FM films is limited to few micrometer to few tens of micrometer due to higher Gilbert damping as opposed to ferrimagnetic insulators (e.g., Yttrium iron garnet (YIG)) and Heusler alloys. The SW propagation length for ultrathin FM films possessing iPMA is further reduced to about a micrometer due to lower group velocity and higher Gilbert damping parameter. Therefore, one of the challenges of magnonics is to increase the propagation length of SWs in ultrathin FM films. Although, several charge current-induced SW amplification methods 2,3,23,24,77 are available, the main drawback of these methods is, again, Joule heating and higher power consumption. Alternatively, this problem can be solved by reducing the overall dimension of the device below SW propagation length. One necessary condition for this is that the excitation area should be strictly localized within nanometer dimension in order to fit with nanoscale devices. Herein lies the advantage of VCMA excitation of SWs over microwave antenna-induced Oersted field excitation. Rana et al. have shown that amplitude of VCMAinduced SWs decay exponentially as a function of propagation distance due to localized nature of electric field underneath the gate electrode 1 . On the other hand, antenna-induced SWs do not exactly follow exponential decay function, specially, first couple of points, due to nonlocalized nature of antenna-induced Oersted field (Fig. 5e). This proves that VCMA-induced excitation (linear and nonlinear) will be more suitable for nanoscale magnonic devices, especially, for ultrathin FM films. The amplitude of VCMA-induced coherent SWs also vary linearly with V rf (Fig. 5f) 1 . Also, there is not any threshold power of linear coherent excitation unlike nonlinear parametric excitation. That means coherent SWs can be excited even at ultralow microwave power like uniform FMR, with a scope of further reduction by increasing VCMA coefficient.

Formation of reconfigurable SW nanochannels
After excitation, the SWs propagate along the surface of WG. For practical application, it is necessary to guide the SWs through channels so that they can reach to a targeted position for next operation. One of the popular methods is geometrically patterning the WG either into stripe or wire 78 . In this case, the SW path is basically decided by the shape of the WG, which cannot be further manipulated. Second method is the confinement of SWs by internal demagnetizing field of WG 79 (Fig. 6a). The SW path can be moved from the edge to the center of WG and vice versa simply by tuning the excitation frequency. When the magnetostatic SWs propagate from a narrow WG to a wider WG, it does not propagate along a straight line. Instead, SWs are bended and propagate like a beam along well-defined directions due to the anisotropic nature of dipolar interaction (Fig. 6b). This is called SW caustic. The direction of SW propagation can be controlled by changing the orientation of in-plane bias magnetic field 20 . The situation becomes even more interesting in the presence of nonuniform magnetization i.e,. nonuniform effective magnetic field inside the WG, which behaves like a graded refractive index for the propagation of magnetostatic SWs. The SWs, passing through the nonuniformly magnetized area, can be steered toward preferred direction by tuning nonuniformity of internal magnetic field with an external magnetic field 80 . In principle, any patterned magnetic micro-or-nanostructure shows nonuniformity in magnetization. However, the desired nonuniformity in magnetization can be created through proper design of sample structure by using single or multiple magnetic materials, and can be controlled through dynamic demagnetizing field with the help of an external magnetic field 81 . Very recently, the theoretical work by Krivoruchko et al. have shown that an external electric field, applied along a direction perpendicular to SW wavevector and magnetization, can induce Dzyaloshinskii-Moriya-like (DM-like) interaction 82 , known as Aharanov-Casher effect. This electric field-induced DM-like interaction makes SWdispersion anisotropic and nonreciprocal, which also promises to be a potential method to create caustic-like SW beam excited from a point source in a FM thin film. Another interesting method is the confinement and channeling SWs along magnetic domain walls of nanometer width. Domain walls can be created either by shape anisotropy of thin film 21 (Fig. 6c) or by heatassisted magnetic scanning probe lithography technique 22 . The SW path can be moved along the width of WG by shifting the domain wall by changing bias magnetic field magnitude. Very recently, it has been proposed that by controlling the phase of an array of antenna, the excited SWs can be sent toward any direction and even can be focused at a specific point 83 . Here, the directional propagation of SWs is achieved by utilizing SW interference phenomena. Alternatively, directional propagation of SWs may also be achieved by tuning propagating SW phase by VCMA (Fig. 6d).
By performing micromagnetic simulations Rana et al. have proposed that propagating SWs can also be confined and guided through virtual nanochannels formed by VCMA 17 . This can be done by placing a metallic gate electrode, with width smaller than that of the WG, on top of the WG. When DC voltage is applied across the gate electrode and WG, the electric field at the FM/ oxide interface modulates iPMA of WG underneath the gate electrode (Fig. 6e). This creates a virtual channel on the WG with different anisotropy energy than that of the WG. The SWs can propagate along these channels provided that SW resonance condition is satisfied only inside the channels, whereas outside of channels SWs are prohibited at the excitation frequency. The width and shape of the channel is decided by the width and shape of gate electrode. SW nanochannels with width down to few tens of nanometer can be formed by this method (Fig. 6f). The key advantage is that the nanochannels formed by VCMA are reconfigurable. It means a number of channels can be formed simultaneously for parallel data processing, and SWs can be selectively sent through any single channel or any combination of channels. Moreover, the SWs with different wavevector can be sent through different channels when the channels are formed by applying different gate voltages. Sadovnikov et al. have demonstrated that the SWs propagating along a stripe-like WG can be transferred to an identical adjacent magnetic stripe through dynamic dipolar coupling between the stripes 84 . By controlling the internal magnetic field of stripes through voltage-induced strain, one can tune the dipolar interaction between the SWs propagating along bilateral magnonic stripes. In that way, the channeling of SWs through magnonic stripe and transfer of SW signals from one magnonic stripe to other one can be reconfigured by gate voltage. One of the main sources of power consumption in magnonic devices is bias magnetic field, which is generally created by sending current through the coil. This problem can be solved if ultrathin FM films with relatively high iPMA are used. The iPMA helps to align magnetization perpendicular to the plane of the film even in absence of bias magnetic field. Therefore, the nanochannels can be formed even in absence of bias magnetic field. It is worth to mention here that magnetostatic forward volume spin waves (MSFVWs) are excited when the magnetization of thin film is aligned perpendicular to the plane, and this MSFVWs can easily propagate through a curved path due to their isotropic dispersion character as opposed to other magnetostatic waves excited for in-plane orientation of magnetization 85 26 . If magnetostatically coupled arrays of nanomagnets, which have well-defined orientation of magnetization at remanence due to shape anisotropy, are used as WGs, the SWs can propagate along straight as well as curved path even in absence of bias magnetic field.   Fig. 5 Excitation of coherent propagating spin waves (SWs). Schematic diagrams show SW excitation by various means. a When radio frequency (rf) current is sent through a microwave antenna, the generated Oersted field inductively couples to the SWs having same frequency (ω) as the rf current. The wavelengths of the SWs are decided by the periodicity of nonuniform Oersted field. b When an unpolarized current is sent through a ferromagnetic layer (fixed layer), the current is spin-polarized due to the exchange interaction of moving electron spins with the localized magnetic spins in ferromagnet. If this spin-polarized current enters into a second ferromagnetic layer (free layer) through a nanocontact, it locally introduces a torque (known as spin-transfer torque) into the magnetic moments and excites SWs, which can propagate along the ferromagnetic layer 13  Reconfigurable magnonic crystals Manipulation of SW properties such as SW frequency, wavevector, phase, group velocity, amplitude, attenuation length, and magnonic band structure are essential for the development of magnonic logic devices, filters, attenuators, and amplifiers. Charge current-induced Oersted field has been one of the most commonly used techniques for modulation of SW frequency, wavevector, and phase. Nagaoka et al. 18 have shown that the frequency of propagating SWs in FM films possessing iPMA can be modulated by VCMA without charge current. Although there are some reports about the electric-field modulation of SWs in multiferroic materials 27,28 and ferrimagnetic insulators (e.g. YIG) 82,86 , the VCMA modulation of SWs in metallic FMs has several advantages over them as already discussed.
Magnonic crystals (MCs) are the artificial crystals, which are formed by periodic spatial variation of magnetic parameters of a magnetic thin film. MCs are used to manipulate the magnonic band structure and/or to create and tune magnonic band gaps of a magnonic WG with respect to the magnonic band structure of a plain WG 87 (Fig. 7a). This is essential in order to develop various magnonic filters, attenuators, and logic devices. There are several ways to create MCs as described in an interesting review article by Chumak et al. 88 . Static MCs can be created by periodic variation of film thickness, width, and shape of WG 89 , saturation magnetization, and anisotropy 90 . Arrays of magnetic dots 72,91 and antidots 87,92 are examples of static MCs. The magnonic zone boundaries and band gaps of static MCs can be tuned only by external bias magnetic field 89 , which is not very easy to utilize in practical devices. Dynamic MCs can be created by periodic arrays of stripe domain structures at the remanence state 93 , laserinduced periodic heating 94 (which modifies saturation magnetization), current-induced periodic Oersted field 95 (Fig. 7b), and travelling surface acoustic wave-induced periodic strain 96 (Doppler shift of SW frequency). The magnonic bands of dynamic MCs can be reconfigured easily as compared with static MCs. Moreover, same dynamic MC can be used for multi-purposes, such as logic operations, magnonic conduits, reconfigurable filters, and data reversers. Wang et al. recently proposed reconfigurable MCs created by VCMA 97 . MCs can be created artificially by placing periodic arrays of stripe-like metal gate electrodes on top of an ultrathin FM film (Fig. 7c). When DC voltage is applied across gate electrodes and WG, the iPMA of FM, only underneath the gate electrodes, is modulated by static electric field applied at FM/oxide interface. As a result, MC is developed with a lattice constant same as the spatial periodicity of gate electrodes. The Brillouin zone boundary of this MC, which is decided by the periodicity (P) of modulated iPMA, can be shifted by changing the periodicity of applied gate voltage. This voltage-controlled MC can open a magnonic band gap at Brillouin zone boundary, where propagation of SWs is prohibited due to reflection from zone boundary (Fig. 7d). The key advantage of VCMA-controlled MCs is that the width of the band gap and transmission of SWs at Brillouin zone boundary can be tuned by varying gate voltage magnitude (Fig. 7e). This shows the reconfigurable character of these MCs. Moreover, the MC and corresponding band gap at zone boundary can be turned on and off in nanosecond time scale at a very low power consumption.

VCMA-controlled magnonic interferometers for logic operations
In electronics, the digital operations are performed by using various kinds of logic gates made of transistors. Likewise, the digital operations in magnonics can be performed by using magnonic logic gates made of magnonic interferometers and magnonic transistors. Magnonic interferometers are based on the wave characters of SWs, whereas magnonic transistors are based on the particles characters of magnons. Mach-Zehnder interferometer (MZI) is widely used for SW interference operations. Two SWWGs are used as two arms of MZI. The SWs in these two arms are launched either from a single source or from two independent sources, and then the SWs are interfered either physically 98 or electronically 19 . The SW amplitude and/or phase in these two arms are manipulated by external perturbations to control the output interference signal 7 . Anything which can modulate SW properties can be used as external perturbations, such as current-induced Oersted field 16,19,98 , heat 94 , and VCMA 17 . In logic operation, the external perturbations are used as logic inputs, and interference signal is used as logic output. For example, logic inputs may be defined to be "1" when perturbations are "on" (i.e. current through conductor or voltage across the gates are applied) and "0" when perturbations are "off". Likewise, logic output may be defined to be "1" when large SW signal is obtained due to constructive interference, and "0" when minimal SW signal is obtained due to destructive interference. In another approach, SW phase itself is used as logic inputs 99 . For instance, SW phase "0" and "π" can be used as logic inputs "0" and "1", respectively. All kinds of logic gates such as NOT, AND, OR, NOR, XNOR, NAND, and majority gate can be realized by using single or multiple SW interferometers. The main drawbacks of Oersted field-controlled MZIs are higher power consumption and difficulty to implement in nanoscale magnonic devices due to nonlocalized nature of Oersted field. These two problems can be resolved if the interferometer is operated by VCMA. Rana et al. have proposed VCMA-controlled XNOR, universal NAND logic gates 17 . Interfacial PMA of the two WGs, used as the arms of MZI, are locally modulated by applying voltage across metal gate and WG (Fig. 8a). The applied gate voltage either modulates SW phase or stop SW propagation depending upon its sign and magnitude. The XNOR gate can be developed by modulating SW phase (Fig. 8b), whereas universal NAND gate can be developed by stopping SW propagation. In addition, universal NAND gate can also be formed by using VCMA-controlled SW nanochannels. Chumak et al. reported all-magnon-based logic devices, where it has been shown that the source-to-drain magnon current (i.e., SWs) in a magnon transistor can be controlled by launching additional magnons from an intermediate gate 100 . The high density of magnons confined in gate area ensures nonlinear four magnon scattering. Therefore, the magnon current at the output of drain is dramatically reduced with the injection of gate magnons. The advantage of this magnon transistor is that the SWs are not controlled by charge current induced methods. If the source and gate magnons are generated by VCMA 1,70 , the power consumption may be drastically reduced. The XOR (Fig. 8c) and universal NAND gates can be formed by combining two such magnon transistors in parallel. Another component of magnonic logic devices is SW multiplexer and de-multiplexer, which are basically used to send SW signal from one of the many input channels to one of the many output channels via a combiner. These devices can also be formed by either Oersted field 78 or VCMA 17 . results are reported on the various functions of magnonic devices by VCMA, the experimental demonstration and study for most of them are still lacking. As the theoretical and simulations results do not take into account electrical losses due to leakage current and impedance mismatch, experimental studies are essential to figure out and minimize the electrical losses by proper engineering of magnonic devices. For instance, Nozaki et al. have reported that majority of microwave power is reflected from a MTJ due to impedance mismatch 63 . A major bottleneck in practical realization of electric-field-controlled magnonic devices is low value of VCMA coefficient. Therefore, increasing VCMA coefficient up to pJ V À1 m À1 by engineering FM/oxide interface is of high priority. Another bottleneck is to find out FM materials with low damping parameter in order to reduce energy loss of SWs. Ferrimagnetic insulators and Heusler alloys can be the alternatives. Experimental report shows that a direct electric field coupling to propagating SWs is possible even in a centrosymmetric ferrimagnetic insulators, like YIG, via Aharanov-Casher effect. This provides an efficient way to modulate SW frequency, phase 86 , and propagation direction 82 . Although, Heusler alloys, like Co 2 FeAl, show iPMA 101 and high TMR 102 , demonstration of electric-field control of iPMA is still lacking. As a matter of fact, FMs are suitable for applying VCMA. Therefore, use of SW amplifier is essential in magnonic devices to compensate the energy losses of SWs during propagation. There are several wellknown charge current induced methods available for SW amplification. For instance, the SWs can be amplified by passing current through conducting WG 77 , by microwave magnetic field through parametric pumping 24 , by modulating Gilbert damping through spin-orbit torque (SOT) 2,3,23 , which can be even modulated by electric field 103 . Alternatively, VCMA can be used for SWs amplification in order to design low power magnonic devices. Microwave magnetic field can be replaced by VCMAtorque to build up energy-efficient parametric amplifier. Although magnetoelectric coupling in synthetic multiferroic structure can be used for electric-field-controlled parametric amplifier 25 , VCMA has some additional advantages over them in terms of localization area which can be as small as few tens of nanometer. The VCMA can also amplify the SWs in metallic FM by reducing Gilbert damping parameter 44 . As the use of ultrathin FM films is essential for reducing dimension of magnonic devices and controlling interfacial magnetic properties, it is important to study the SW properties in ultrathin FM films. Electrical detection of SWs is required for practical applications. SW detection by microwave antenna through inductive coupling becomes very inefficient method, especially, for ultrathin films possessing iPMA. MTJs which have proven to be a very sensitive method for reading data in modern magnetic recording media and detecting FMR, could be an alternative way to detect SWs in ultrathin films.

Future perspectives
Recently, magnetic Skyrmions which are non-trivial nanoscale topological chiral spin structures, promise to have huge potential for the application as a high-density data storage and as an information carrier. Skyrmion size, nucleation field, and dynamic modes can be controlled by VCMA 104 . Moreover, SWs can drive Skyrmions by STT at ultralow power consumption 105 through a virtual channel created by VCMA 106 . These results show the possibility of combining Skyrmions into VCMA-controlled magnonics devices.

Data availability
The related data are available from the corresponding authors on request.