Variation of skyrmion forms and their stability in MnSi thin plates

By systematic real-space observations using Lorentz transmission electron microscopy, we report here various forms of skyrmions (and related spin textures) for a prototype of cubic helimagnet MnSi as well as their stability that depends on crystalline-orientation and crystal-plate thickness. Below a crossover thickness $(t_{\mathrm{c}}\sim 75\mathrm{nm})$ of a sample, the robust two-dimensional hexagonal skyrmion crystal (SkX) appears over a wide window of temperature and magnetic field, regardless of crystal orientation, while the SkX phase region shrinks to a small pocket near the helical transition temperature $T_{\mathrm{N}}$ in a (111) plate with the thickness above $t_{\mathrm{c}}$, in contrast to the stable SkX in (110) and (001) plates. This observation indicates the importance of the magnetic anisotropy and thermal fluctuation effects for the skyrmion stability. Furthermore, the forms of skyrmions have been found to change from multidomain state of SkX to skyrmion glass structure via single domain state of SkX with increasing magnetic field.

Figure 1

(a)–(f) LTEM images (defocus distance $\sim -30\mu \mathrm{m}$) at 6 K [(a)–(c) in zero field and (d)–(f) in a magnetic field] and (g)–(i) magnetization maps for one unit cell of SkX as derived from TIE analysis of the data shown within dashed squares in (d)–(f). (a), (d), (g); (b), (e), (h); and (c), (f), (i) are for (111), (110), and (001) thin plates, respectively. The thickness of these thin plates is around 30 nm. Insets at the lower left corners of (a)–(f) are SAED patterns (upper) and FFT (lower) of LTEM images. Colors and white arrows in (g)–(i) indicate the magnitude and direction of in-plane magnetizations, while the black area shows zero in-plane magnetization or out-of-plane magnetization. (a)–(c) Helimagnetic stripe domain structures at zero magnetic field; (d)–(f) magnetic SkX with hexagonal symmetry under normal magnetic fields of 220 mT, 300 mT, and 250 mT, respectively. All LTEM images were taken at the underfocused Lorentz mode.

Figure 2

(a)–(f) Changes in magnetic textures in a (111) thin plate with the thickness of $\sim 30\mathrm{nm}$ with varying magnetic fields at 18 K. LTEM images (underfocus, defocus distance $\sim -36\mu \mathrm{m}$) and corresponding FFTs (insets) obtained under various magnetic fields demonstrate (a) the helical structure with an in-plane propagation vector in zero magnetic field, (b) random/rotating-$q$ stripes under a weak field of $25\mathrm{mT}$, (c) two domains of SkX, (d) single-domain state of SkX, (e) SkG structure with an obscured FFT pattern, and (f) single-domain state of field-induced ferromagnetic structure. (g)–(i) Temperature evolution of skyrmion form observed at the overfocused Lorentz mode (defocus distance $\sim 36\mu \mathrm{m}$) for a (110) plate with the thickness of $45\mathrm{nm}<t<75\mathrm{nm}$ at a constant field of $B=300\mathrm{mT}$ from (g) single SkX to (i) paramagnetic structure via (h) SkG. Insets show the corresponding FFT of LTEM images.

Figure 3

Thickness dependence of magnetic structures in a wedge-shaped (111) MnSi plate. (a), (b) 2D thickness map obtained by EELS and the averaged line profile [over the surrounded area with red dashed lines shown in (a)] of the sample thickness, respectively. (c) LTEM image taken under zero field at 6 K. The defocus distance is approximately $-30\mu \mathrm{m}$. Dashed line indicates the boundary between areas 3 and 4. (d)–(g) FFT of each local LTEM image for areas 1–4 taken at 6 K under zero magnetic field and (h)–(k) under 290 mT field. (l), (m) LTEM images for the same area as presented in (c), obtained under 200 mT field at (l) 15 K and (m) 20 K, respectively.

Figure 4

Magnetic phase diagrams obtained for wedge-shaped (111), (110), and (001) MnSi thin plates with thickness gradient. (a)–(c) 2D thickness maps of the (a) (111), (b) (110), and (c) (001) plates, respectively. The phase diagrams in the $T\text{−}B$ plane obtained in (A) thick regions with thickness of $75\mathrm{nm}<t<120\mathrm{nm}$ [(d)–(f)], (B) intermediate-thickness regions between 45 nm and 75 nm [(g)–(i)], and (C) thin regions with thickness below 45 nm [(j)–(l)]. These diagrams are obtained from LTEM images taken at the regions designated as A, B, and C, respectively, in (a)–(c). H, $\mathrm{R}q\text{−}\mathrm{H}$, SkX, V-H/C, and FM are the in-plane helical structure, random/rotating-$q$ helical structure, skyrmion crystal state, (possibly) vertical helical or conical structure, and field-induced ferromagnetic state, respectively. The open circles show the data points where LTEM snapshots were taken.