Topology of spin meron pairs in coupled Ni/Fe/Co/Cu(001) disks

The meron is a special topological object that carries only one-half of the topological charge unit. In condensed matter physics, a spin meron corresponds to one-half of a spin skyrmion. As compared to the many fascinating topological properties of skyrmion materials, little is known of the properties of spin merons especially about their formation. It was confirmed only recently that hedgehog merons could exist in pairs with opposite helicities via a spin flux closure. However, it is unclear whether a single hedgehog meron could ever exist by pairing with another type of meron. Using element-resolved magnetic imaging measurements on epitaxial trilayer disks, we show that a spin meron with a full range of helicity, including the hedgehog meron, can be stabilized by pairing with another vortex meron with a fine tuning of the magnetic coupling between the two merons. Furthermore, the meron divergence is fully controlled by the polarity of the vortex meron, independent of the vortex helicity.

Figure 1

(a) Schematic drawing of the Ni/Fe/Co/Cu(001) trilayer disks in which the ferromagnetic Ni and Co are magnetically coupled across the antiferromagnetic fcc Fe spacer layer. (b) PEEM image of the Ni/Fe/Co/Cu(001) trilayer disks. (c) LEED patterns from each stage of the Ni(5 ML)/Fe(wedge)/Co(150 ML)/Cu(001) film growth confirm the epitaxial growth of fcc Ni, Fe, and Co single-crystalline films.

Figure 2

Element-resolved hysteresis loops of Ni(5 ML)/Fe/Co(150 ML)/Cu(001). (a) $d_{\mathrm{Fe}}=5\mathrm{ML}$ (b) $d_{\mathrm{Fe}}=5.5\mathrm{ML}$, (c) $d_{\mathrm{Fe}}=5.75\mathrm{ML}$, and (d) $d_{\mathrm{Fe}}=6\mathrm{ML}$. The Ni magnetization saturates in the opposite direction of Co at $d_{\mathrm{Fe}}=5$ ML, indicating a strong antiferromagnetic interlayer coupling between the Ni and Co magnetizations. The Ni and Co have identical shape of hysteresis loops at $d_{\mathrm{Fe}}=6\mathrm{ML}$, indicating a ferromagnetic interlayer coupling between the Ni and Co magnetizations. The linear slopes in Ni hysteresis loops above the coercivity are described by Eq. (1).

Figure 3

Element-resolved magnetic images of Ni and Co in Ni/Fe/Co/Cu(001) single-crystalline disks. (a)–(e) Co always forms a vortex meron with the magnetization curling along four equivalent [110] easy magnetization axes. (f)–(j) Ni domain shapes follow that of Co but the Ni helicities change continuously from ${\gamma }_{\mathrm{Ni}}=-\pi /2$ to ${\gamma }_{\mathrm{Ni}}=+\pi /2$ with increasing fcc AFM Fe thickness, showing a full range of Ni helicity control by the magnetic interlayer coupling.

Figure 4

At any given coupling angle ($\mathrm{\Delta }\theta =\pi /3$ in this figure) between Ni and Co magnetizations, there are $2^4=16$ possible Ni meron configurations resulting from the same Co vortex state, of which only two have the same winding number ($w=+1$) as Co.

Figure 5

Hedgehog/vortex meron pairs in Ni/Fe(5.55 ML)/Co/Cu(001) disks. (a) and (c) Co disk exhibits vortex meron state, and (b) and (d) Ni disk exhibits hedgehog meron state with either divergent structure for $p=+1$ core polarity or convergent structure for $p=-1$ core polarity.

Figure 6

Element-resolved magnetic images of Ni and Co in Ni/Fe/Co/Cu(001) single crystalline disks. (a)–(e) Co disks always form vortex merons. (f)–(j) Ni disks form hedgehog merons that vary from disk to disk. There is no correlation between the circulation of Co vortex merons with the convergence/divergence of the corresponding Ni hedgehog merons.

Figure 7

(a) Sketch of the sample geometry used in the micromagnetic simulation. (b)–(d) shows typical micromagnetic simulation results using object oriented micromagnetic framework (oommf) package [32]. Both divergent and convergent meron states can be stabilized in the Ni disk while the much thicker Co disk retains a vortex meron state The gray-scale color is used here to emulate the measurement results from PEEM, which is sensitive only to magnetization along the x-ray direction.

Figure 8

Micromagnetic simulation of of the stray field from the Co vortex meron with out-of-plane polarity at a position 1.5 nm above the Co disk top surface. The arrows indicate the in-plane component of the stray magnetic field. The red and blue colors indicate the out-of-plane stray magnetic field component. (a) From right-handed circulation disk. (b) From left-handed circulation disk. (c) From a single magnetic moment positioned ∼17 nm below the calculated surface.

Figure 9

Energy difference between convergent and divergent meron states as a function of Ni thickness. The red squares are from oommf simulations. The blue line is from Eq. (3) of the simplified model.