Phase-transition kinetics of magnetic skyrmions investigated by stroboscopic small-angle neutron scattering

We investigated the phase-transition kinetics of magnetic skyrmion lattice (SkL) in MnSi by means of stroboscopic small-angle neutron scattering (SANS). Temporal evolutions of SANS patterns were measured with time resolution of 13 ms while sweeping temperature as fast as $50{\mathrm{Ks}}^{-1}$. It turned out that the paramagnetic-to-SkL transition immediately occurs upon traversing the equilibrium phase boundary on the rapid cooling, whereas the SkL-to-conical transition can be kinetically avoided to realize the low-temperature metastable SkL with a long-range magnetic order. The formation of the metastable SkL was found to be strongly dependent not only on cooling rate, but also on magnetic field and trajectory in the $H\text{−}T$ phase diagram.

Figure 1

(a) $H\text{−}T$ magnetic phase diagram of MnSi for magnetic fields along the [001] axis (redrawn from the data presented in Ref. [19]). Time profiles of the (b) electric current pulse, (c) nominal temperature $T_{\mathrm{nom}}$, and (d) integrated intensity of the magnetic Bragg reflections from the SkL order, $I_{\mathrm{SkL}}$. Inset schematically shows the integrated area. (e) Typical SANS patterns at selected time frames during the current pulse applications.

Figure 2

$T_{\mathrm{nom}}$ and $T$ variations of (a) $I_{\mathrm{SkL}}$, (b) length of the magnetic modulation wave vector $\left|Q\right|$, and half-widths of the half maximum of the Bragg reflections along the (c) radial and (d) azimuthal directions. Solid and dashed lines in (a) are guides to the eyes. Insets in (c) and (d) schematically show the relationships between the crystallographic and magnetic field directions and the radial and azimuthal directions in the reciprocal lattice space, respectively.

Figure 3

(a) Temporal profiles of $T_{\mathrm{nom}},I_{\mathrm{SkL}}$, and $I_C$ measured at a number of magnetic fields. (b) $I_{\mathrm{SkL}}$ and $I_C$ replotted as functions of $T_{\mathrm{nom}}$. Solid lines are guides to the eyes. (c) Integrated area for magnetic reflections of the conical phase. (d) Magnetic field dependence of $I_{\mathrm{SkL}}$ measured in two different paths shown in (b). The lines are guides to the eyes. (e) Metastable state and equilibrium phase diagram of MnSi. The phase boundaries are redrawn from the data presented in Ref. [19]. The light-blue area shows where the metastable SkL state (labeled “m-SkL”) has a life time longer than about ${10}^2$ s, once it is created. The green area qualitatively shows the $H$ and $T$ range where the metastable SkL state can temporarily exist upon quenching with the cooling rate of $50{\mathrm{K}\mathrm{s}}^{-1}$.