Thickness dependence of anomalous magnetic behavior in epitaxial ${\mathrm{Fe}}_3{\mathrm{O}}_4\left(111\right)$ thin films: Effect of density of antiphase boundaries

We study the magnetic behavior of ${\mathrm{Fe}}_3{\mathrm{O}}_4\left(111\right)$ thin films with thicknesses between $5\mathrm{nm}$ and $50\mathrm{nm}$. The films are epitaxially grown on $\alpha \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3\left(0001\right)$ single crystals by atomic-oxygen-assisted molecular beam epitaxy. The ${\mathrm{Fe}}_3{\mathrm{O}}_4\left(111\right)$ thin films exhibit high structural order with sharp interfaces and low roughness and exhibit a Verwey transition for thicknesses above $8\mathrm{nm}$. However, the samples have magnetic properties that deviate from the bulk ones. The magnetic moment varies between $2.4{\mu }_B$ for $5\text{−}\mathrm{nm}$-thick film and $3.2{\mu }_B$ for $50\text{−}\mathrm{nm}$-thick film in a field of $1.2\mathrm{T}$, which is lower than that of bulk samples ($4.1{\mu }_B∕{\mathrm{Fe}}_3{\mathrm{O}}_4$ formula). Still the magnetic saturation is never reached, even in fields as large as $2T$. The thinner the film, the slower the approach to saturation. Structural analysis, performed using high-resolution transmission electron microscopy, reveals the presence of antiphase boundaries (APB’s), the density of which decreases when the thickness increases. Using a model of ferromagnetic domains separated by antiferromagnetically sharp interfaces, we show that the slow approach to saturation observed in the films as a function of thickness is driven by the APB density.

Figure 1

Typical XRD pattern of a $15\text{−}\mathrm{nm}$-thick ${\mathrm{Fe}}_3{\mathrm{O}}_4$ (111) film. The rocking curve of the (333) peak is shown in the right inset. Left inset: RHEED pattern of the ${\mathrm{Fe}}_3{\mathrm{O}}_4$ (111) thin film when the incident electron beam is along the $\left[1\overline{1}00\right]$ direction of the alumina substrate in the real space. The probed rods in the reciprocal space are labeled with respect to the base vectors $a*$ and $b*$.

Figure 2

Polarized neutrons reflectivity measurements of 50-, 25-, 15-, and $8\text{−}\mathrm{nm}$-thick ${\mathrm{Fe}}_3{\mathrm{O}}_4$ (111) thin films in a $1.2\text{−}\mathrm{T}$ in-plane field at $T=300\mathrm{K}$. The circles (squares) represent the up-up (down-down) reflectivity curves. The numerical adjustments are plotted in solid lines.

Figure 3

Magnetic hysteresis loops and virgin curves by VSM measurement of 50-, 25-, 15-, and $8\text{−}\mathrm{nm}$-thick ${\mathrm{Fe}}_3{\mathrm{O}}_4$ (111) thin films at $T=300\mathrm{K}$ after subtraction of the substrate diamagnetic contribution. Inset: temperature dependence of the susceptibility at low field. The decrease of the susceptibility related to the presence of the Verwey transition can be observed for thickness above $8\mathrm{nm}$.

Figure 4

(a) Cross-sectional HRTEM image of a $15\text{−}\mathrm{nm}$-thick ${\mathrm{Fe}}_3{\mathrm{O}}_4$ (111) thin film along the $\left[11\overline{2}\right]$ direction with the presence of an APB. (b) Sketch of the stacking of (111) atomic layers: the oxygen lattice is undisturbed across the APB while the iron lattice is shifted by a ⟨220⟩ translation vector.

Figure 5

(a) Diffraction pattern along the ⟨111⟩ zone axis of a magnetite layer. The 220-type reflections of the magnetite and the $11\overline{2}0$ ones of $\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3$ substrate are reported. (b)–(d) Dark-field TEM images of 8-, 15-, and $50\text{−}\mathrm{nm}$-thick ${\mathrm{Fe}}_3{\mathrm{O}}_4$ (111) thin films taken with the 220-type reflection along the ⟨111⟩ zone axis. The dark lines correspond to the antiphase boundaries (APB’s).

Figure 6

Virgin magnetization curves at $T=300\mathrm{K}$ for a ${\mathrm{Fe}}_3{\mathrm{O}}_4$ bulk crystal and 50-, 25-, 15-, 8-, and $5\text{−}\mathrm{nm}$-thick ${\mathrm{Fe}}_3{\mathrm{O}}_4$ (111) thin films with fits to describe the approach to saturation. Inset: $b$ parameter evolution with film thickness.