Magnetic bubbles in FePt nanodots with perpendicular anisotropy

We present experimental evidence, by magnetic force microscopy, for the existence of magnetic bubbles in suitably designed high-quality circular FePt nanodots. We specifically study dots of sizes where this fundamental magnetic state is a ground state and it is spontaneously created. We also observe triple-domain states consisting of concentric rings with alternating magnetization. A numerical study confirms the range of stability of the observed magnetic states and predicts the phase diagram in parameter space. Differences in the topology of these states imply distinct dynamical behavior, providing the basis for fundamental dynamical studies.

Figure 1

(Color online) MFM images of $D=0.5\mu \mathrm{m}$ and $D=1\mu \mathrm{m}$ diameter dots. (a) The majority of the $D=0.5\mu \mathrm{m}$ dots are in a single-domain state; approximately 15% of them are in a bidomain state (most of the latter are in a monobubble). (b) The majority of the $D=1\mu \mathrm{m}$ dots are in a bidomain or tridomain state and a few are single domain.

Figure 2

(Color online) (a) The topography (AFM image) of a $D=0.5\mu \mathrm{m}$ FePt dot. (b) The magnetic contrast image (MFM) of the same dot shows the signature of an almost axially symmetric monobubble in the center of the dot.

Figure 3

(Color online) AFM and MFM images of $D=1\mu \mathrm{m}$ dots. (a) Topography (AFM) of a dot. (b) A MFM signal which reveals a ringlike structure indicating three almost concentric magnetic domains of alternating magnetization. (c) In contrast to the concentric structure in (b) and to the usual behavior observed, an irregularly shaped domain is localized in the center and has not branched out.

Figure 4

(Color online) Energy per unit volume (in units of $2\pi M_0^2$) as a function of the particle radius $R$ (in units of ${\ell }_{\mathrm{ex}}$) for the single domain (SD, dotted line), the monobubble (MB, solid line), and the three-ring (TR, dashed line) state. The dot thickness is $t=12.5{\ell }_{\mathrm{ex}}$ and the quality factor $Q=4.7$. The intersection between the dotted and solid lines corresponds to $R_{c1}$, while the one between the solid and dashed lines corresponds to $R_{c2}$ (see text). The insets represent calculated profiles of the perpendicular magnetization for the three states. The color contrast indicates domains of antiparallel magnetization.

Figure 5

(Color online) Magnetization vector at the top surface of a dot in the monobubble state. The inner “down” and the outer “up” domains as well as the Néel-like domain wall in between are illustrated.

Figure 6

(Color online) Phase diagram for varying dot thickness $t$ and radius $R$ (both in units of ${\ell }_{\mathrm{ex}}$). The regimes where the single domain, the monobubble, and the three-ring states are energetically favorable are indicated. We vary the thickness in the range $5{\ell }_{\mathrm{ex}}<t<12.5{\ell }_{\mathrm{ex}}$ (or $20\mathrm{nm}<t<50\mathrm{nm}$). The lines correspond to $R_{c1}$ and $R_{c2}$ as a function of $t$ (see Fig. 4). The numerically calculated points are indicated by circles.