Manipulating charge ordering in $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ by field cooling

The conductivity of $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ drops two orders of magnitude below the Verwey temperature $T_v$, known as the Verwey transition, due to the formation of charge ordering (CO). Here, we report the discovery of a large birefringence effect correlated with the CO in $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ controlled by ultrafast-laser-assisted magnetic field cooling. The polarization rotation (PR) of the light reflected from a single crystalline $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ film below $T_v$ shows a twofold symmetry as the cooling field (CF) rotates through ${360}^{\circ }$ within the film plane. The maximum PR occurs for the CF parallel to the cubic $\langle 110\rangle$ axes, and its amplitude depends on the sample orientation. These results are well interpreted by taking into account two CO patterns with orthogonal CO orientations, with their fractional areas determined by the ratio of the field components along the [110] and $\left[1\overline{1}0\right]$ axes. Our results indicate that application of the CF along $\langle 110\rangle$ axes may result in the single orientation CO state, which is highly desirable for unraveling the subtle CO structure to better understand the driving mechanism of the Verwey transition. In addition, ultrafast pump-probe measurements reveal a diminishment of the twofold PR at 0.8 ps due to fast melting of the CO state by the ultrafast laser pulse.

Figure 1

(a), (b) The RHEED patterns of 30-nm-thick $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ film on MgO(001). (c) Temperature dependence of the resistivity of $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ films with different thicknesses. (d) Cross-section high-resolution TEM image of a 30-nm-thick $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ film on MgO(001). Interfaces between the 30 nm $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ layer, the 10 nm MgO seed layer, and the MgO substrate are indicated by arrows. The inset shows the good epitaxial growth of the film with sharp interface and (e) dark-field plane-view TEM image of the same sample showing the antiphase boundaries.

Figure 2

Schematic drawing of the experiment setup, where ${\theta }_i$ represents the incident angle of the probe beam. ${\theta }_H, {\theta }_{\mathrm{CF}}$, and ${\theta }_s$ denote the angle of the external field, the cooling field, and the [100] axis of the sample with respect to the horizontal $x$ axis, respectively.

Figure 3

The PR angle δ for (a) $H_E$ sweeping along the [100] direction (${\theta }_H=0^{\circ }$), and (b) $H_E=1000\mathrm{Oe}$ rotated ${360}^{\circ }$ at $T=80\mathrm{K}, {\theta }_s=0^{\circ }$, and varying ${\theta }_{\mathrm{CF}}$.

Figure 4

(a) The twofold ${\delta }_c$ vs ${\theta }_{\mathrm{CF}}$ at various temperatures with ${\theta }_s=0^{\circ }$, and the solid curves are fits with the function $A_{2}sin\left(2{\theta }_{\mathrm{CF}}\right)$. (b) Temperature dependence of the amplitude of the twofold ${\delta }_c$. (c) Amplitude of the twofold PR signal at different temperatures as a function of the pump laser power and (d) temperature dependence of the critical laser power to induce the twofold PR signal. The sample orientation was set at ${\theta }_s=0^{\circ }$. The solid line in (d) is a visual guide.

Figure 5

(a) The twofold signal as a function of the CF direction ${\theta }_{\mathrm{CF}}$ at ${\theta }_s=0^{\circ }$ and $T=80\mathrm{K}$ for different ${\theta }_a$. (b) Comparison of the polarization rotation angle ${\delta }_c$ and ellipticity ${\varepsilon }_c$ with the twofold symmetry at ${\theta }_s=0^{\circ }$. (c) The PR signal as a function of the field orientation for different pump polarizations at $T=80\mathrm{K}$. The measurements in (c) were performed with the pump pulse always on at ${\theta }_s=0^{\circ }$.

Figure 6

Schematic drawings of CO patterns of $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ with the separated $\mathrm{F}{\mathrm{e}}^{2+}$ ($\mathrm{F}{\mathrm{e}}^{3+}$) chains (parallel to the monoclinic $a$ axis) along the [110] (left) and $\left[1\overline{1}0\right]$ (right) axes in (a) monoclinic $P2/c$ structure and (b) $Cc$ structure, where the blue (brown) balls represent the $\mathrm{F}{\mathrm{e}}^{2+}$ ($\mathrm{F}{\mathrm{e}}^{3+}$) ions at octahedral sites and the ball size is used to distinguish their positions along the $c$ axis of the crystal with its primitive unit cell length along the $c$ axis being $z=1$ (top view along the $c$ axis).

Figure 7

Rectified twofold ${\delta }_c^{\prime }$ for (a) ${\theta }_s=0^{\circ }$ and (b) ${\theta }_s={45}^{\circ }$ at $T=80\mathrm{K}$ and ${\theta }_s$ dependence of the amplitude (c) and phase (d) of the twofold ${\delta }_c^{\prime }$. The solid curves in (a) and (b) are fits by the sinusoidal function. The red curves in (c) and (d) are the fitted curve with Eq. (2). The blue curves in (c) and (d) denote the fits with Eq. (4).

Figure 8

(a) ${\theta }_H$-dependent PR angle δ for various time delays after the pump pulse interaction and (b) the time dependent transient δ changes for ${\theta }_H={45}^{\circ }$ and ${135}^{\circ }$.