Positive antiphase boundary domain wall magnetoresistance in Fe${}_3$${\mathrm{O}}_4$ (110) heteroepitaxial films

We observe a strong crystallographic direction dependence on the low-field magnetoresistance (MR) behavior of the epitaxial Fe${}_3$${\mathrm{O}}_4$ (110) films grown on MgO (110) substrates. The sign of MR is positive when the current and field are parallel to [001], whereas along the $[\stackrel{̲}{1}10]$ direction its sign is negative, similarly to that commonly observed for (100) oriented Fe${}_3$${\mathrm{O}}_4$ films. We relate this effect to the presence of antiphase boundaries (APB) and subsequent reduction in the width of canted spin structure in its vicinity, due to the hard axis behavior of Fe${}_3$${\mathrm{O}}_4$ (110) films along this crystallographic direction. At fields greater than the anisotropy field, usual negative MR behavior related to a reduction in spin scattering at the APBs is observed. An analytical model based on the half-infinite spin chains across the APBs is provided to show that the positive MR is due to the domain walls along APBs. The temperature and film thickness dependency of the APB domain wall magnetoresistance is discussed.

Figure 1

The ω-2θ scans for Fe${}_3$${\mathrm{O}}_4$ films with different thickness on MgO (110) substrates, measured for symmetric (220) Bragg reflection common to substrate and thin film. Curves are shifted along the vertical axis for clarity.

Figure 2

The ω-$n$θ scans for Fe${}_3$${\mathrm{O}}_4$ films with different thickness on MgO (110) substrates, measured for asymmetric {222} Bragg reflection in (a) grazing exit and (b) grazing incidence common to substrate and thin film. Curves are shifted along the vertical axis for clarity.

Figure 3

Resistivity of films with thicknesses 30, 60, and 90 nm as a function of temperature.

Figure 4

Hysteresis loops obtained for 90-nm Fe${}_3$${\mathrm{O}}_4$ (110) film measured at 300 K with an in-plane field directed along either the $[\stackrel{̲}{1}10]$ or [001] direction.

Figure 5

Magnetoresistance measured at different temperatures for a 90 nm film with an in-plane field and current directed along the [001] direction. Magnetoresistance measured in the $[\stackrel{̲}{1}10]$ direction at 300 K is also shown.

Figure 6

Magnetoresistance as a function of temperature for films having different thickness at 0.9-T field. Magnetic field and current directed along the [001] direction. Different temperature domain areas are marked as I, II, and III.

Figure 7

DWMR${}_{\mathrm{APB}}$ of epitaxial Fe${}_3$${\mathrm{O}}_4$ films measured along the [001] direction as a function of temperature for films having different thicknesses.

Figure 8

Various spin configurations with applied field (a) field along [-110] direction (b) field along [001] below anisotropy field (c) field along [001] above anisotropy field.

Figure 9

$\beta$ as a function of temperature.

Figure 10

Schematic illustration of APB formation with (a) a $\sqrt{3/2}$ a$\langle \stackrel{̲}{1}11\rangle$ shift vector and (b) by a 1/2 a $\langle 001\rangle$ shift vector in (110)-oriented Fe${}_3$${\mathrm{O}}_4$ films grown on MgO (110) substrates. Large square indicates unit cell of Fe${}_3$${\mathrm{O}}_4$ (110) and small square indicates MgO (110) unit cell. (c) Formation of APB with shift vector 1/4 a $\langle 110\rangle$ on MgO (110) surface. [(b) and (c)] The possible antiferromangnetic and ferromagnetic super exchanges (SE) across APBs.