Imaging magnetic vortex configurations in ferromagnetic nanotubes

We image the remnant magnetization configurations of CoFeB and permalloy nanotubes (NTs) using x-ray magnetic circular dichroism photoemission electron microscopy. The images provide direct evidence for flux-closure configurations, including a global vortex state, in which magnetization points circumferentially around the NT axis. Furthermore, micromagnetic simulations predict and measurements confirm that vortex states can be programmed as the equilibrium remnant magnetization configurations by reducing the ratio of the NT's length and diameter.

Figure 1

(a) Schematic drawing of a NT cross-section with incident x rays, photoexcited electrons, and expected XMCD-PEEM contrast for the depicted vortex configuration. The brown central region depicts the nonmagnetic GaAs template material, the gray region the magnetic NT, and the red region the native oxide. (b) SEM of an 11.3-$\mu \mathrm{m}$-long CoFeB NT with a Au alignment marker visible on the right of the image. (c) PEEM image with grayscale contrast corresponding to $I_{\text{PEEM}}$ and (d) XMCD-PEEM image with red (blue) contrast representing positive (negative) $I_{\text{XMCD}}$. The dashed line shows the position of the NT.

Figure 2

XMCD-PEEM images of a 6.9-$\mu \mathrm{m}$-long Py NT with (a) $\widehat{k}\perp \widehat{n}$ and (b) $\widehat{k}\parallel \widehat{n}$ and of a 7.2-$\mu \mathrm{m}$-long CoFeB NT with (c) $\widehat{k}\perp \widehat{n}$ and (d) $\widehat{k}\parallel \widehat{n}$. Dashed outlines indicate the positions of the NTs. Panels (e–h) represent 2-$\mu \mathrm{m}$-long $I_{\text{XMCD}}$ linecuts along the corresponding colored dashed lines in (a–d). In the linecuts, the background intensity is indicated by the level of the horizontal dashed lines and vertical dashed lines delineate the boundaries of the NT. Panels (i) and (j) show simulated remnant magnetic states for a NT with $l=2.1\mu \mathrm{m}$ and $d=245$ nm. Both configurations are mixed states with an axial central domain and vortex ends of either (i) opposing circulation—consistent with (a) and (b)—or (j) matching circulation—consistent with (c) and (d). The color scale corresponds to normalized magnetization along $\widehat{y}$. Arrowheads indicate the local magnetization direction.

Figure 3

XMCD-PEEM images with $\widehat{k}\perp \widehat{n}$ and $\widehat{k}\parallel \widehat{n}$ of short NTs. (a) 1.3-$\mu \mathrm{m}$-long Py NT found in a global vortex state. (b) 0.73-$\mu \mathrm{m}$-long Py NT in an opposing vortex state. (c) 1.06-$\mu \mathrm{m}$-long CoFeB NT in a global vortex state. (d) 0.83-$\mu \mathrm{m}$-long CoFeB NT in an opposing vortex state. Simulated equilibrium states of ferromagnetic NTs ($l=610$ nm, $d=245$ nm) in (e) a global vortex state and in (f) an opposing vortex state. The color-scale corresponds to the normalized magnetization along $\widehat{y}$. Arrowheads indicate the local magnetization direction.

Figure 4

Phase diagrams for (a) CoFeB and (b) Py NTs as a function of $l$ and $d$ considering only magnetization configurations with equal circulation sense. The numerically calculated order parameter $M_n/\left|\mathbf{M}\right|$ is plotted in the color scale and defines the boundary between the mixed and global vortex state. Red (white) points show measurements of real NTs in global vortex (mixed) states as measured by XMCD-PEEM [26].