Figure 1

Magnetic microstructure of ilm70 containing several APDs. The sample edge is indicated by the gray line. Prior to each measurement, the sample was exposed to a saturating field with an in-plane/out-of-plane component of $+1000/+1732\mathrm{mT}$, followed by a smaller field with an in-plane/out-of-plane component of (a) $-1.9/+3.3\mathrm{mT}$, (b) $-10.6/+18.4\mathrm{mT}$, (c) $-12.8/+22.2\mathrm{mT}$. White arrows indicate the direction of the in-plane component of the applied field. The hue and intensity of the color indicates the direction and magnitude of the in-plane component of the magnetic flux in the sample in field-free conditions, as defined by the color wheel on the right. The blue-purple and green-yellow colors correspond to equal and opposite in-plane magnetizations in the direction indicated by the black double arrow. The dark bands indicate regions with weak in-plane magnetization (magnetic domain walls). Dark bands that separate regions of blue and green color correspond to 180° magnetic and chemical walls (e.g., at regions labeled “1” and “2,” respectively). Dark bands that are surrounded by regions of the same color correspond to 0° magnetic walls (e.g., at regions labeled “3”).Reuse & Permissions

Figure 2

Profiles of the holographic phase shift, $\varphi$, across three distinct types of magnetic domain wall. The gradient of each profile is proportional to the in-plane component of the magnetic flux [Eq. (1)]. (a) A freestanding 180° Bloch wall. The solid line is a least-squares fit to the observed profile, obtained by using Eqs. (1, 2) and yielding a wall width of 19 nm. (b) A 180° chemical wall that is coincident with an APB. The dashed line is a fit to the central portion of the wall, obtained by using Eqs. (1, 2) and yielding a wall width of 7 nm. (c) A 0° magnetic wall that is coincident with the same APB as in (b). The slope of the phase profile has the same sign on either side of the wall, indicating that the direction of magnetization is the same. The solid line is a fit to the profile, obtained using Eqs. (1, 3) and yielding a wall width of 30 nm.Reuse & Permissions

Figure 3

Simulated cation and magnetic structure of APBs. Plots show the average values of the order parameter, $Q$, the mole fraction of ilmenite, and the spin on each of the 48 layers of an $8\times 8\times 8$ supercell for ilm70 annealed at (a)–(c) 850 K and (d)–(f) 1100 K. (a) The order parameter profile for a system with short-range cation order shows fully ordered and antiordered APDs ($Q=1$ and $Q=-1$, respectively) separated by disordered APBs $(Q=0)$. (b) The composition profile indicates that the APBs are enriched in hematite relative to the bulk composition (dashed line). (c) The magnetic structure obtained at 25 K consists of an alternating sequence of up ($+\mathrm{ve}$) and down ($-\mathrm{ve}$) spins throughout the supercell. The magnitude of the spins is modulated by the local composition and the degree of cation order. The APD centered on layer 14 is ferrimagnetic with a net negative spin; the APD centered on layer 40 is ferrimagnetic with a net positive spin (indicated by the arrows). (d) The order parameter profile for a system with partial long-range order shows a fully ordered APD ($Q\sim 1$) and a less well (anti)ordered APD ($Q\sim -0.75$). (e) The composition profile shows that the well-ordered APD has $>70\%$ ilmenite, whereas the less-well-ordered APD has $<70\%$ ilmenite. Evidence for Fe enrichment at the APBs is also seen. (f) The spin profile at 25 K shows that the well-ordered APD is strongly ferrimagnetic, whereas the ferrimagnetic spin of the less-well-ordered APD is decreased by the influence of the boundary regions.Reuse & Permissions

Figure 4

Net ferrimagnetic spin, simulated as a function of temperature for systems with short-range cation order (supercell annealed at 850 K, closed circles) and partial long-range cation order (supercell annealed at 1100 K, open circles). The system with partial long-range order displays a self-reversal of net ferrimagnetic spin at $\sim 250\mathrm{K}$.Reuse & Permissions