Mechanical Regulation of the Magnetic Properties of Uniaxial Anisotropic Hexaferrite Thin Films

Flexible oxide thin films with uniaxial magnetocrystalline anisotropy $(K_u)$ not only have many applications in flexible electronics, but also provide an ideal low-crystal-symmetry material for a fundamental understanding of the competitive interplay among magnetocrystalline anisotropy, shape anisotropy, and stress anisotropy. However, an understanding of the mechanical tuning of magnetic parameters in flexible oxide films with $K_u$ has not been realized up to now. In this work, epitaxial flexible hexaferrite ${\mathrm{Ba}\mathrm{Fe}}_{12}{\mathrm{O}}_{19}$ thin films with a room temperature out-of-plane $K_u$ of 1.1 × ${10}^5$ J/m${}^3$ are fabricated. The continuous and controllable tuning of magnetic parameters is found to be realizable by different bending radii of the film. The changes in magnetic parameters are symmetrical under tensile and compressive bending due to the dominance of film geometry and bending-stress directions, which are perpendicular to the easy axis of $K_u$. The micromagnetic simulations further show that the magnitude of $K_u$ plays a critical role in the mechanical tuning performance of the film, where high $K_u$ drastically reduces the role of stress anisotropy and increases the magnetic bending repeatability of the film by suppressing bending-defect-related anisotropy degradation. This work not only provides an understanding of the role of the direction and magnitude of $K_u$ in the flexible thin films, but also demonstrates that the flexible hexaferrite film is one of the best materials for mechanical tunable devices up to the millimeter-wave region.

Figure 1

(a) XRD patterns of BaM films grown on mica and sapphire substrates. (b) XRD mapping of mica (003), BaM (006), and BaM (008) peaks of the film grown on mica substrate. (c) Raman spectra of BaM films on mica and sapphire substrates. (d) TEM cross-section image and selected-area diffraction pattern of the BaM/mica sample.

Figure 2

(a) Schematics of crystal symmetry of BaM film with magnetization, M, deviating by angle θ from the out-of-plane direction. (b) Out-of-plane and in-plane hysteresis loops of flat BaM film (thickness 180 nm) on mica (001) substrate. (c) Angular magnetic torque (T) of flat BaM film under magnetic field of 50 kOe. (d) Thickness- (t) dependent coercivity, $H_c$, and remanence ratios, $M_r/M_s$, of flexible BaM films.

Figure 3

(a) Schematic illustrations of testing methods for bent film; (b)–(d) magnetic hysteresis loops (in-plane, crossover, and out-of-plane) of flexible BaM film (thickness 180 nm) under different bending radii, R, of R = ∞ (flat), 5.5, 3.5, and 1.5 mm. Tensile (+ε) and compressive (−ε) strains are indicated; (e)–(g) bending-curvature-dependent coercivity, $H_c$; remanence ratios, $M_r/M_s$; and $K_{u\mathrm{eff}}$, respectively; K_flat= 1.01 × 10⁵ J/m³.

Figure 4

(a) Schematic of a micromagnetic calculation cell with directions of local magnetization, M; crystalline c axis; and bending strain, ${\epsilon }_b$, indicated. (b) Examples of simulated cross-section remanent magnetic domains of flat and bent BaM films; directions of $K_u$ and $K_{{\epsilon }_b}$ are indicated. (c) Crossover and (d) out-of-plane hysteresis loops of films with different bending radii: R = ∞ (flat), 5.5, 3.5, and 1.5 mm. Tensile (+ε) and compressive (−ε) strains are indicated. (e) Bending-radius-dependent normalized out-of-plane coercivities, $H_c/H_k$, with different saturation magnetostriction constants (${\lambda }_s=0,-2.28,$ and $-7.6\mathrm{ppm}$).

Figure 5

(a) Schematic picture of a bending cycle of BaM film. (b) Picture of bent BaM film on the bending fixture. (c),d) In-plane and out-of-plane hysteresis loops of BaM film in different bending cycles (from 0 to 1000), with a tensile bending radius of 3.5 mm. (e),(f) Summaries of coercivity, $H_c$, and $M_r/M_s$ in different bending cycles and under different bending conditions, respectively.

Figure 6

(a) Simulated cross-section remanent domain images of BaM films with different sizes (40, 120, and 200 nm) and numbers (one, three, and five) of cracks. Magnetic field dependence of total magnetic anisotropy energy, $E_k$, of BaM films with (b) K_u = 3 × 10⁴ J/m³, (c) K_u = 9 × 10⁴ J/m³, and (d) K_u = 15 × 10⁴ J/m³.