High-temperature Magnetodielectric Bi ( Fe 0.5 Mn 0.5 ) O 3 Thin Films with Checkerboard-Ordered Oxygen Vacancies and Low Magnetic Damping

The possibility of aﬀecting the magnetic properties of a material by dielectric means, and vice versa, remains an attractive perspective for modern electronics and spintronics. Here, we report on epitaxial Bi ( Fe 0.5 Mn 0.5 ) O 3 thin ﬁlms with exceptionally low Gilbert damping and magnetoelectric coupling above room temperature ( < 400 K). The ferromagnetic order, not observed in bulk, has been detected with a total magnetization of 0.44 μ B / formula units with low Gilbert damping parameter (0.0034), both at room temperature. Additionally, a previously overlooked check-board ordering of oxygen vacancies is observed, providing insights on the magnetic and dielectric origin of the multifunctional properties of the ﬁlms. Finally, intrinsic magnetodielectric behavior is observed as revealed by the variation of dielectric permittivity well above room temperature. These ﬁndings show the possibility of electric-ﬁeld-controlled magnetic properties, in low Gilbert-damping-based spintronic devices, using single-phase multiferroic materials.

Bi 2 FeMnO 6 (BFMO) lies between two of the most well-studied multiferroic materials in the field, BiFeO 3 (BFO) [38,39] and BiMnO 3 (BMO) [40,41], the characteristics of which are well described in the literature and still gain considerable attention among researchers. The interest in BiFeO 3 originates due to the stable ferroelectric and antiferromagnetic ordering at room temperature [42] (Néel temperature T N ≈ 643 K). However, BiFeO 3 has a low magnetic moment in bulk and thin-film form (approximately equal to 0.02 μ B /Fe) [43][44][45][46], hindering desired applications. On the other hand, BiMnO 3 is the only material where the coexistence of ferromagnetic and ferroelectric order is well established [41,47]. Although FE order is present above room temperature (Curie temperature T C ≈ 450 K), the FM ordering appears at a rather low temperature T C ≈ 105 K [48], thus efforts on the study of highly doped BiMnO 3 to increase FM Curie temperature have been carried out in the literature [6,47]. These studies include the B-site partial substitution, such as in the case on Bi 2 CoMnO 6 and Bi 2 NiMnO 6 [4,25,27,28,49,50]. Nevertheless, recent experimental results on Bi(Mn x Fe 1−x )O 3 , with x = 0.5 have driven new attention to this compound [30,51].
Considerable attention has been focused on understanding the magnetic properties of Bi(Mn x Fe 1−x )O 3 with x = 0.0-0.2 in bulk [31,42] and x = 0.5 in rather thick films [31] by neutron diffraction. A G-type antiferromagnetic spin structure with a Néel temperature of T N = 120 K has been reported [35]. In bulk however, these compounds are very difficult to stabilize unless high pressures are employed [25]. The common approach is to dope the structure with considerable quantities of lanthanum, however, such an approach complicates the distinction between intrinsic effect and dopant effects in both magnetic and crystalline properties [49,52]. Polycrystalline solid solutions show a distinctive magnetic response, with a very low magnetic moment 0.02μ B /formula units (f.u.), x = 0.2%. Thin-film studies, however, have shown a small increment of magnetization with 0 ≤ x ≤ 0.5 of Mn substitution, while highly strained films, with partial substitution of x = 0.5 exhibited strong room-temperature magnetism. The work reported by Choi et al. [34], showed an increment on the magnetization to rather competitive levels, approximately 0.58 μ B /B-site ion at room temperature. The important enhancement of the magnetic properties was attributed to the high level of strain induced by the epitaxial growth. However, no ferroelectric response was reported, or the ferroelectric cycle.
Additionally, electrical measurements performed on the mixed B-site Bi(Mn 0.5 Fe 0.5 )O 3 thin films, have already been performed in the literature [37], showing a typical relaxor behavior in a film of 180 nm thickness. The lack of "strong" magnetism in those results seems to suggest that such a behavior is closely related to the bulk behavior rather than to the highly strained film one [53], due to the role of epitaxial strain in the stabilization of the trigonal phase and its strong magnetism. Therefore, such measurements are not compatible with the highly strained thin-film scenario, and thus the dielectric behavior of highly strained BFMO thin films is still unknown. Later reports by Choi et al. [54] have addressed the magnetic response of thin films with different epitaxial strain. Additionally, from the dielectric point of view, the switchable (180 • ) response of the films is unequivocally shown by piezoelectric force microscopy. Nevertheless, conclusive magnetodielectric response or any correlation between ferroic orders have yet to be investigated.
Furthermore, although the magnetic nature of the highly strained material is quite well established to date, the magnetic damping of the BFMO is not. Magnetic relaxation processes play an important role in the magnetization switching speed and switching power of spin-transfertorque-(STT-)based devices, especially for materials where the total magnetization is relatively low, since it directly translates into low switching currents [55,56]. Possibly more exciting are the important and intrinsic applications that a ferromagnetic material with strong magnetodielectric coupling could provide in the spin-wave propagation field. As shown in recent studies conducted on BiFeO 3 -based spin-wave devices [57,58], there is an interesting applicability of multiferroic materials as generators, guides, and controllers for magnonic devices.
Having shown the current scenario of BFMO thin films, it is clear that experimental confirmation of magnetodielectric response, in a multiferroic (ferroelectric and ferromagnetic) materials, with low magnetic damping, is an appealing perspective for both the multiferroic and spinwave community. Therefore, here we focus on the magnetic and magnetodielectric properties of highly strained thin films deposited by pulsed-laser deposition (PLD). First, we show the structural quality of the films, in particular, the existence of coordinated oxygen vacancies, contributing to the relaxor behavior of the perovskite. Then, we explore the magnetic response of the samples confirming the presence of low-magnetization damping, which along with the low magnetization make this material appealing for STT devices. Finally, we will show that the dielectric response of the films can be externally affected by a magnetic field well above room temperature, clearly showing evidence of strong magnetodielectric coupling in this material.

A. Film deposition
Films (approximately equal to 43 nm) are deposited by a KrF excimer laser (248 nm) by Lambda Physik LPC205i, focused on a stoichiometric ceramic target with a bismuth excess of 10%. Samples are grown on two substrates SrTiO 3 (001) (STO), used for magnetic measurements, and Nb(0.5%):SrTiO 3 (001), used for dielectric measurements. Substrate temperature is set to 650 • C according to optimization studies performed on this material and similar compounds in order to avoid losses of bismuth during deposition [25,59]. Depositing conditions are set as follows: oxygen pressure at 0.6 mbar, ablation rate at 5 Hz, and laser fluency at approximately 1.7 J cm −2 .

B. Structural characterization
X-ray diffractograms (XRD) and reciprocal space maps (RPMs) are obtained using a PANalytical X'Pert3 (MRD) system, working with a Cu source (K α 0.15406 nm). Microstructure is investigated by high-resolution (HR) TEM using a JEOL ARM200F working in the scanning mode. An accelerating voltage of 200 kV is used to perform structural characterization. Cross sections are prepared by FIB milling using a JEOL JIB-4000. A gold film is sputtered on top of the selected area to protect it from ion damage during the FIB milling. A Ga + beam with different acceleration voltages (5-30 kV) is used to prepare the cross sections. Stoichiometry and valence of the films 054072-2 (Bi, Fe, and Mn ions) are studied by x-ray photoelectron spectroscopy (XPS) using a SAGE HR100 (SPECS) system with a nonmonochromatic source (Al K α 1486.6 eV). Calibration of the spectra is performed by placing the C-C carbon peak at 284.8 eV. Crystallographic structures are build using the CaRine 4.0 software.

C. Functional characterization
Magnetic measurements are performed by a SQUID magnetometer using a Quantum Design MPMS XL-7 system. Magnetization dynamics is investigated using vector network analyzer ferromagnetic resonance (VNA FMR) in the range of 3-30 GHz under a maximum external field of 10 kOe. The applied frequencies are kept constant while the magnetic field is swept. To enhance the FMR signal, the Au-coating is applied to the back side of the substrates [60]. The samples are placed with the film facing towards the coplanar waveguide (CPW), where the impedance changes at resonance causing a change in the S21 transmission signal detected by VNA. The obtained resonance lines are fitted with a Lorentz function giving the resonance field and the resonance linewidth, and allowing for the determination of magnetization and Gilbert damping constants.
Impedance spectroscopy (IS) measurements are performed by means of an impedance analyzer (HP4129 LF, Agilent Co.) with an excitation voltage of 50 mV at frequencies ranging from 10 Hz to 10 MHz. Samples are placed on a Lakeshore 4 tip probe station with nitrogen gas flow working from 90 to 400 K. Samples are measured in the so-called top-top configuration [61], using sputtered Pt electrodes (60 μm in diameter). Magnetic impedance measurements are performed by placing a neodymium solid-state magnet providing a total effective field approximately equal to 4 kOe, underneath the sample holder after full range sweeps. The magnitude of the magnetic field at the sample position is tested by Gaussmeter measurement. Impedance data is analyzed in order to extract the intrinsic dielectric permittivity of the film, as described below, following analyzes described elsewhere [16,49,52].
According to the interplanar distance of d[00l] and both the Bragg equation and the Nelson-Riley correction, the out-of-plane parameter of the BFMO unit cell is calculated as being approximately equal to 3.99 Å. Asymmetrical measurements (φ scans) performed along the STO(110) direction, are shown in Fig. 1(c). Results clearly show the cube-on-cube orientation of the BFMO film with respect to the STO substrate. Moreover, the reciprocal space maps, Fig. 1(d), show that in fact the BFMO layer is fully epitaxial and strained. This observation is congruent with other reports in the literature regarding BFMO [34,39,54]. Additionally, the in-plane parameter of the BFMO is also extracted by using the a = 2/λ × h/q x formula, where λ is the K α value of Cu, q x represents the horizontal value in reciprocal coordinates, and q x is defined by q x = sin sin( − ω). The lattice parameters extracted from the x-ray experiments are similar to those reported by Choi et al. [34] with a = b = 3.93 ± 0.02 Å and c = 3.99 ± 0.02 Å, corresponding to a compressive stress of −0.64% of in-plane stress and a total deformation of −2.81% from the bulk-simulated lattice, as shown in Table I. It is important to remark that although the relaxation thickness, in which the highly strained lattice returns to the relaxed state is unknown, studies in other perovskites congruently indicate the critical thicknesses above 70 nm [68]. Thus, it is important to keep the films in their highly strained thickness approximately equal to 40 nm, in order to conclusively show the interplay between ferromagnetic ordering (observed in the highly strained samples) and ferroelectric response.
Microstructure of the films is investigated by HR TEM, general results are shown in Fig. 2(a). Insets show the lowmagnification view of the film allowing the total thickness of the film 43.5 ± 1.2 nm to be extracted in agreement with XRR. Also, the inverse fast Fourier transformation (IFFT), performed using the in-plane (100) and (100) diffraction peaks, for both the substrate and the films, show the perfect matching of the lattices [inset in Fig. 2(a)]. Additionally, the high-resolution images show the highordered STO(001) and BFMO(001) structures pointing to the B sites of the BFMO perovskite. Selected 100 nm width area of electron diffraction (SAED) is collected, which includes reflections from the substrate and the film, and is presented in Fig. 2(b). The high-intensity peaks of the STO structure (red dashed line) overlap with those of the BFMO structure (blue dashed lines). Nevertheless, due to the difference in the out-of-plane parameter between the film and substrate, the peaks at higher-order reflections (002) and (002) are well separated, as shown by the top or the bottom of the image [circled areas in Fig. 2(b)]. Additionally, the SAED pattern shows the presence of small, well-distributed peaks (marked in yellow). The presence of those peaks is a signature of superior organization of the perovskites, which clearly follows the film reflection, as seen in the yellow squared segment of Fig. 2 Table I the center of the small peaks is centered on the BFMO peaks. In order to understand the observed reflections, a unit cell of four times the nominal size of the BFMO unit cell is built. The atomic positions of the elements are calculated accordingly to a 4 × 4 BFMO unit cell. It is important to remark that two cases are considered, Bsite ordered and B-site mixed, and both of the scenarios proved not to be compatible with the observed diffraction peaks. Nevertheless, the periodicity and locations of the supercell patterns can be extracted, as shown in Figs. 2(c) and 2(d), the periodicity follows a cell that is approximately equal to 1.28 nm. The nature of this cell is then evidenced by the location and geometry of the simulated lattice, corresponding to ordered oxygen vacancies on the BFMO lattice, which is further confirmed by the SAED pattern and the angular bright-field (ABF) images. Those vacancies have been observed in other perovskite systems, and the ordering is considered to affect the magnetic properties of the perovskites [69,70]. Equally important, the clear ordering of the O-site vacancies, Fig. 2(b), might contribute to the already relaxor and nanopolar ferroelectric ordering in BFMO films [29,31,33,53,71]. The film stoichiometry is investigated by XPS. The survey spectrum of the film surface [ Fig. S1(a) in Ref. [72] ] shows the nominal composition of the Bi 2 FeMnO 6 perovskite. High-resolution Bi 4f spectra shows the single Bi 3+ [73] valence of the A-site cation [ Fig. S1(b) in Ref. [72] ]. Regarding the B site, although the iron Fe 2p region is quite complex to analyze [74,75], the peak position and its shape is congruent with Fe 3+ and traces of Fe 2+ [Fig. S1(c) in Ref. [72] ], while the Mn 2p shows a slight mixture of Mn 3+ and Mn 4+ [75], which confirm the observations of Ahmed et al. [76] [ Fig. S1d in Ref. [72] ]. Attempts of cleaning the surface and performing depth-profiling studies by Ar + plasma etching, results in the expected valence shifts of the iron ions moving towards metallic Fe 0 , [74,75] The stress as 100% × (n film − n bulk )/n bulk , where n bulk is the in-plane lattice of Bi 2 FeMnO 6 / √ 2. b The lattice mismatch as 100% × (a substrate − a film )/a film , where a substrate and a film are the substrate and films lattice constants. Bulk material is assigned to the P4/mbc space group. Notice that calculations performed with Fe 3+ and Mn 3+ give differences of less than 0.5% to the one presented.
Ref. [72] ]. Although the Fe profiling cannot be fully reliable due to the large reducing effects, the Mn peaks are less susceptible to the Ar + damage and allow a scenario of single Bi 3+ and Mn 4+ valence to be suggested, while leaving the Fe valence uncertain. Nevertheless, profiling is needed in order to avoid the mixed states, or recombination of valences, that tend to appear at the outer surface of these materials [78]. Nonetheless, these results show an interesting scenario, in which both nanopolar ordering and valence compensation could coexist in this perovskite. To sum up this section, our results follow the high mixture of valences in this perovskite and complex polar orderings [39,79,80].

B. Magnetic properties
The results of magnetic studies are shown in Fig. 3.  [72] ], temperature is swept from room temperature down to 5 K and allowed for the determination of transition temperature T C as explained below. The M (H ) plots confirmed the ferromagnetic ordering of the film in the whole range of available temperatures, as shown by the hysteresis loops at room temperature, Fig. 3(a) and at 10 K [ Fig. S2 in Ref. [72] ]. The total magnetization of the film is calculated according to the Bsite (Fe-Mn) ordering as 0.48 μ B /f.u. (Fe-Mn), which is congruent with the data reported in the literature for these films [34,39].
To determine suitability of BFMO for spintronic and magnonic applications, the magnetization dynamics is investigated. Using Kittel's dispersion relation without an anisotropy term, where H r is the resonance magnetic field, γ = 1.76 × 10 7 G −1 s −1 is the gyromagnetic ratio, the saturation magnetization M s equal to 68.8 emu/cm 3 (0.44 μ B /f.u.) is derived in agreement with the value from SQUID magnetometry and previous literature studies [34,39] [see the inset of Fig. 3(b)]. From resonance linewidth H vs frequency f dependence, the Gilbert damping parameter α is determined according to the equation H = (4πα/γ )f + H 0 , where H 0 is related to extrinsic contributions such as sample inhomogeneities and two-magnon scattering [ Fig. 3(b)]. The fitting is performed for the frequencies above 9 GHz corresponding to the field of 2.8 kOe. At lower frequencies, depicted by the shaded area, the data significantly deviates from linear dependence. For the fields in the range 0-2 kOe the magnetization is not saturated magnetically [see Fig. 3(a)], which consequently leads to substantial line broadening [81], as shown in Fig.  S3 in Ref. [72]. The α constant is equal to 0.0034, which settles the BFMO among the so-called low-damping materials [Table S-I in Ref. [72] ]. The H 0 is equal to 5.34 Oe pointing to the flat film surfaces (as proved with x-ray reflectometry), homogeneity of the sample, and negligible two-magnon scattering contribution for the in-plane applied magnetic field.

C. Magnetodielectric characterization
Dielectric studies are carried out using a temperaturedependent impedance spectroscopy method in the toptop configuration. The typical behavior of a ferroelectric relaxor is evidenced by a shift in both the imaginary part of the dielectric permittivity (ε ) and the real part (ε ) vs temperature, with variations of frequency [ Fig. 3(c)]. Although the origin of this behavior is not clearly understood, it is a common feature characterizing this kind of ferroelectrics. A similar behavior has already been reported 054072-5 in the literature for BFMO [82] and for other materials with nanopolar regions [83][84][85][86].
Using the impedance spectra (Z /Z ) and by representing the temperature-dependent curves as Nyquist plots [ Fig. 3(d)], the presence of two dielectric contributions can be observed. This representation is vital in order to avoid the confusion of intrinsic and extrinsic effects [87]. These two contributions, one at high frequencies and the other at low, have been explored before in single-perovskite thin films (BMO and BFO [88]) as well as for double perovskites [49,89]. It is clear by now that each contribution is related to a different mechanism, with the high-frequency contribution, containing the intrinsic properties of the perovskite, while the low frequencies represent the extrinsic effects in the compound and experimental setup. These two mechanisms respond differently in the impedance spectra and can be modeled independently. The low-frequency contribution can be expressed as one resistive element R, accounting for the leakage of the material, and one capacitive C, accounting for the dielectric character. Conversely, the high-frequency regime can be modeled in similar fashion, but the capacitive element is replaced by a constant phase element (CPE), which models the nonideal behavior of the capacitor. The impedance of this R CPE circuit is given by where Q denotes the amplitude and α deals with the phase of the CPE. The typical values range from α ≤ 0.6 − 1, being α = 1 the value for an ideal capacitor, and in this case C = Q. Capacitance C and dielectric permittivity ε values can be obtained according to the relationship C = (Q × R) (1/α ) /R [90], and C = εA/2t, where A accounts for the area of the electrode and t for the thickness of the sample. It is important to remark, as mentioned before, that the nonideality of the capacitive response of the material can be qualitatively observed by the values of the α variable in the CPE element. Therefore, the general behavior of the sample at any given temperature can be fitted by the following formula: where the first term corresponds to the intrinsic (I ) contribution of BFMO film and the second term deals with the extrinsic contributions (E). The two RC contributions of the equivalent circuit are sketched in the insets of Fig. 3(d), where the line through data points corresponds to the performed fitting showing the goodness of the fit, with values below χ 2 ≤ 3 × 10 −4 . The extracted dielectric permittivity for each mechanism, allows the intrinsic contribution of the film to be further identified by its extracted value of the ε = 175, and resistivity = 10 5 close to that previously reported in similar studies for the same compound [91]. The dielectric response remains constant in the whole range of temperature explored of 90-390 K.
However, when the spectroscopy measurements are repeated under external magnetic field (4 kOe) small changes on the spectroscopic response can be observed.
After extracting the associated dielectric value, a peak starting around 375 K can be observed  [92][93][94]. It is important to remark, that in both of the cases, with and without magnetic field, the exponent α of the CPE element, remains relatively constant [see the inset of Fig. 3(f)], confirming the stable capacitive response of the film in the entire range examined.

D. Discussion
It is worthwhile to note the important differences and similarities between our samples and those previously reported in the literature. Sun et al. [51] have reported long-range B-site ordering on Bi 2 FeMnO 6 films, however, the thickness of the films investigated is well above the relaxation point for the highly strained phase (190 nm).

054072-7
Additionally, their magnetic studies showed unusually low magnetization, when compared with other works on highly strained BFMO thin films. The stoichiometry found in the aforementioned studies was the so-called vibronic ordering of Fe 3+ -O-Mn 3+ [80], which nominally would provide AFM to FM interactions, giving a total magnetization well below 0.02 μ B /f.u.(Fe-Mn) at room temperature. The weak magnetism and strong ferroelectric response, suggest that the observed ordering is related to the previously observed bulk properties of BFMO [76]. Nevertheless, close inspection of previously reported, highly strained BFMO/STO films in the literature, shows the presence of similar features as the one described in this paper by HR TEM, but not addressed in their corresponding articles. Chen et al. [39] showed a complete study of the strain of BFMO films grown on several substrates and upon closer inspection, their SAED pattern, described in Ref. [39], shows faint, but clear peaks, similar to the ones reported in this article. Additionally, the same figure shows clear features as the ones shown here in Fig. 2(c) for the darkfield images. Li et al. [95], report on the interface effects of BFMO films, once again with a similar SAED pattern, shown in Ref. [95]. This seems to suggest that this feature is not in fact a casuistic or uncommon behavior of our film, but a generally overlooked feature in thin films of BFMO.
Regarding the origin of magnetic response in BFMO films, the Goodenough-Kanamori rules for 180 • superexchange couplings can be evaluated. In principle, there are two possibilities for superexchange magnetism. First, the so-called vibronic FM to AFM ordering of Mn 3+ -O-Mn 3+ with a theoretical μ eff = 4 μ B /B-site ion for ferromagnetic ordering and the second one, so-called vibronic AFM to FM ordering of Fe 3+ -O-Mn 3+ , with a total magnetization of the 1 μ B /B-site ion, none of which are in agreement with the data presented here or reported in the literature [34,39]. However, as shown previously in our XPS studies, the apparition of consistent Mn 4+ across the sample, allows for the Mn 4+ -O-Fe 3+ FM to AFM [76]. Although it is still considerably higher than the theoretical 4.42 μ B /f.u. for this ordered configuration, it is clear at this point that it is very complex to determine the true origin of the observed magnetization in BFMO. Nevertheless, recent studies have demonstrated the intrinsic role of the epitaxial strain on the origin of observed magnetization, suggesting the cooperative nature of both ferrimagnetic ordering and the Goodenough-Kanamori spin-canted effect at room temperature [34,39]. The role of oxygen vacancies in this matter is still unclear.
One of the most interesting aspect of this material, is relatively high magnetic transition temperature and its room-temperature ferroelectric response. Previous studies by Choi et al. [34], have shown a magnetic transition temperature around 600 K for the strained BFMO films. In our case, temperatures above 300 K are inaccessible, therefore, a rough estimation of the transition temperature is obtained from the Weiss model, which provides a critical temperature T C in the range 620 ± 80 K [ Fig. S2 in Ref. [72] ]. Nevertheless, the M (H ) plots confirm the ferromagnetic ordering of the film in the whole range of available temperatures, as shown by the hysteresis loops at room temperature, Fig. 3(a) and 10 K [ Fig. S2 in Ref. [72] ]. On the other hand, the dielectric studies clearly show an anomaly that seems not to follow the estimated magnetic transition temperature of the strained films (620 ± 80 K). Impedance spectroscopy measurements, tend to show erratic behavior when close to the magnetic transition giving unclear results about magnetodielectric coupling effects. However, in this case, such phenomena can be ruled out, due to no evident variation of the dielectric permittivity with the absence of external magnetic field. Nonetheless, the clear correlation between the applied external magnetic field and the anomalous dielectric response at high-temperature points to a strong magnetodielectric coupling [87] well above room temperature Fig. 3(f), which, in addition to the roomtemperature ferroelectric [54] and ferromagnetic character of BFMO, makes BFMO interesting for applications.

IV. CONCLUSION
In conclusion, we investigate the dielectric and magnetic properties of highly strained Bi(Fe 0.5 Mn 0.5 )O 3 (001)/SrTiO 3 (001) thin films. Films show strong roomtemperature magnetic response, attributed to the ferromagnetic ordering and spin-canting effect of the STO(001) interface. Magnetic transition temperature is estimated to be around 620 ± 80 K with a room-temperature magnetic saturation of 68.8 emu/cm 3 (0.44 μ B /f.u.). Furthermore, our dielectric studies show an anomalous response of the dielectric permittivity under external magnetic field that clearly suggest above room-temperature magnetodielectric coupling. Additionally to the room-temperature magnetization, the low Gilbert damping (α = 0.0034) observed in BFMO, not only places them among the low Gilbert damping materials, but also positions it as one of a kind (ferroelectric and ferromagnetic) multiferroic perovskite with low damping. These facts offer a new perspective in the field of spin-transfer-torque devices as the Gilbert constant appears to be lower than in commonly employed permalloy [96] or (Co, Fe)B [55,97] films. Moreover, large relaxation times combined with magnetodielectric coupling can potentially be used for voltage-driven excitation and control of spin waves [57,98,99]. The phenomena observed is attributed to strain induced on the epitaxial growth and its quantum-mechanical origin should be further investigated.