# Review of Magnetoelectric Effects on Coaxial Fibers of Ferrites and Ferroelectrics
## 6 Discussion
In fibers with a ferrite core, one anticipates an increase in the dipole-dipole interaction when the thickness of the ferroelectric shell decreases, leading to a further reduction in DEVC [41; 47]. Another source of reduction in HEVC in films is the fiber discontinuity (porosity). This can be taken into account by assuming an air inclusion along the fiber axis that will result in a demagnetizing effect and a reduction in the internal magnetic field and a decrease in ME coupling strength. Assuming an air gap of length L\({}_{\text{a}}\) in a fiber of length L, one can estimate the resulting reduction in HEVC. Figure 15 shows the estimated effective fractional HEVC vs. L\({}_{\text{a}}\)/L for fibers of the NFO core-BTO shell [41]. A very large reduction in HEVC due to fiber discontinuity is evident from Figure 15. An air gap of 17%, for example, will result in three orders of magnitude reduction in HEVC. Thus, the weakening of the ME coupling strength observed in 2D- and 3D-assembled films of fibers could be primarily due to an air gap (or porosity) in the film. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Material** & **Connectivity** & \multicolumn{2}{c}{**MEVC**} & \\  & & **(mVcm\({}^{-1}\)Oe\({}^{-1}\))** & **Reference** \\ \hline Bulk Composites & & & \\
0.3 CoFe\({}_{2}\)O\({}_{4}\).0.7 BiFeO\({}_{3}\) & 0-3 & 285 & [83] \\ CuFe\({}_{2}\)O\({}_{4}\)-PbZr\({}_{0.53}\)Ti\({}_{0.47}\)O\({}_{3}\) & 0-3 & 425 & [84] \\ PZT-CFO & 0-3 & 549 & [85] \\ BTO-CFO & 0-3 & 2540 & [86] \\ PZT-Ni\({}_{0.85}\)Co\({}_{0.15}\)Cu\({}_{0.02}\)Fe\({}_{1.9}\)O\({}_{4}\) & 0-3 & 3150 & [87] \\ PZT-NFO & 0-3 & \(6700\) & [88] \\ PZT-NEFO & 0-3 & \(1.3\times 10^{4}\) & [89] \\ PZT-NFO & 0-3 & \(2.9\times 10^{4}\) & [90] \\ BaM-PZT & 0-3 & 95 & [91] \\ Layered Composites & & & \\ PZT-NFO & 2-2 & 1500 & [92] \\ BTO-CFO & 2-2 & 944,000 & [93] \\ BaM-PZT & 2-2 & 5 & [94] \\ Fiber films & & & \\ SrM-PZT & 1-1 & 22 & [76] \\ SrM-BTO & 1-1 & 14.7 & [76] \\ Ni\({}_{2}\)Y-PZT/BTO & 1-1 & 11.5 & [79] \\ Zn\({}_{2}\)Y-PZT/BTO & 1-1 & 16.5 & [79] \\ Co\({}_{2}\)W-PZT/BTO & 1-1 & 12.3 & [79] \\ Zn\({}_{2}\)W-PZT/BTO & 1-1 & 10.4 & [79] \\ NFO-BTO & 1-1 & 0.45 & [41] \\ NZero-PZT & 1-1 & 20 & [59] \\ Single fiber & & & \\ CFO-BTO & 1-1 & \(3.5\times 10^{4}\) & [67] \\ CFO-PZT & 1-1 & \(2.95\times 10^{4}\) & [57] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: MEVC for ferrite/ferroelectric composites with various mechanical connectivities [83; 84; 85; 86; 87; 88; 89; 90; 91; 92; 93; 94; 95]. Figure 15: Effective fractional HEVC as a function of \(L_{a}\)/L for an assembled film of fibers of sample A. \(L_{a}\) is the air gap in a fiber of length \(L\)[41]. Although DEVC measurements in the assembled film indicated a weak coupling, a strong or even a \"giant ME effect\" was evident from H-induced polarization measurements on the discs of the fibers of NFO and NZFO and PZT or BTO, with a fractional change in P\({}_{\rm r}\) in NZFO-PZT as high as \(-80\%\)[59; 68; 69]. A similar strong DME was evident from ferroelectric polarization under H in discs of fibers of M-, Y-, or W-type hexagonal ferrites and PZT or BTO. Results of similar studies on bulk or layered composites are lacking regarding any meaningful comparison with results for coaxial fiber samples. Finally, in addition to coaxial ferrite/ferroelectric fibers, there have been several reports in recent years on ME effects on ferrite/ferroelectric core-shell wires, Janus-type fibers, and ferrite fibers embedded in ferroelectric thin films. A template-assisted synthesis of CFO-BTO nanowires was utilized to control the magnetic parameters, in particular the anisotropy of CFO, and the ME coupling strength was probed by measuring the variations in the magnetic properties before and after thermal depolarization of the composite [96]. In the Janus nanofiber, in which half the fiber contains CFO and the remaining half BTO, the ME coupling was studied by second harmonic generation polarimetry under an applied magnetic field [97].