Simultaneous tuning of magnetocrystalline anisotropy and spin reorientation transition via Cu substitution in Mn-Ni-Ga magnets for nanoscale biskyrmion formation

Skyrmions with multiple helicity or topology in centrosymmetric crystals are intriguing magnetic-domain objects due to their diverse dynamics under external stimuli. Here we illustrate how the two key gradients of magnetocrystalline anisotropy (MCA) and spin reorientation transition (SRT) affect the skyrmion formation and topology by Cu substitution in the biskyrmion-host MnNiGa alloy. The MCA and SRT are simultaneously tuned in a large scope, while the original high Curie temperature ($T_C$) is retained. Detailed neutron-scattering studies revealed the construction of a noncollinear canted magnetic structure below the SRT temperature ($T_{\mathrm{SR}}$), which effectively correlates the SRT with the evolution of the MCA, as well as the exchange interaction. The Cu substitution raises the $T_{\mathrm{SR}}$ to merge with the $T_{\mathrm{C}}$, and meanwhile, reduces the $c$-axis anisotropy. Lorentz transmission electron microscopy revealed the formation of stacked biskyrmions from above room temperature to lower temperatures in $\mathrm{MnN}{\mathrm{i}}_{1-x}\mathrm{C}{\mathrm{u}}_x\mathrm{Ga}\left(x=0–0.3\right)$ in the presence of proper MCA. Micromagnetic simulations further confirmed the great effect of uniaxial anisotropy on the stabilization of biskyrmions. Our work has helped clarify the evolution of magnetic structures and their correlation to the SRT, providing an account of the effect of MCA and exchange interaction on the biskyrmion formation.

Figure 1

(a) Hexagonal crystal structure of $\mathrm{MnN}{\mathrm{i}}_{1-x}\mathrm{C}{\mathrm{u}}_x\mathrm{Ga}$, where Cu occupies the Ni site. The exact atomic position is determined by neutron diffraction. (b) RT synchrotron XRD patterns for $x=0,0.05,0.15,0.3,0.4$. (c) Variation of the lattice constant with Cu content and indication of the single-phase region. (d) Temperature dependence of the $c/a$ ratios for various compositions.

Figure 2

(a) The real part of the ac susceptibility vs temperature and (b) the extracted Curie temperature $T_{\mathrm{C}}$ and spin reorientation temperature $T_{\mathrm{SR}}$ of the same compositions. (c) RT $M-H$ curve along the easy and hard axis of the magnetically aligned samples of $x=0$ and 0.4. Inset in (c) is the $d^{2}M/\phantom{d^{2}Md{H}^2}d{H}^2$ vs $H$ curve for magnetization in the hard axis, and the abscissa of the peaks are determined as $H_{\mathrm{A}}$ according to the principle of SPD. (d) RT saturated magnetic moment and the derived uniaxial anisotropy constant for the above compositions.

Figure 3

(a), (b) Temperature-dependent evolutions of the (001) peak for $x=0.05$ (a) and 0.3 (b). (c) Observed (black) and fitted neutron diffraction patterns (red) and their difference profiles (gray) for $\mathrm{Cu}\left(x=0.15\right)$ at 300 and 100 K. Vertical lines indicate the peak positions for the nuclear (top) and magnetic (bottom) reflection of the hexagonal MnNiGa phase. The emergence of (001) and (111) diffractions is related to the AFM component in the basal plane.

Figure 4

(a)–(d) Temperature dependence of the refined magnetic moments of the Mn atom for $x=0,0.05,0.15$, and 0.3 alloys. (e) Schematic of the refined magnetic structure at high and low temperatures. (f), (g) Temperature dependence of the tilt angle θ and the total magnetic moment, respectively.

Figure 5

Lorentz TEM images for MnNiGa (adapted from Ref. [12]) and doping content of $x=0.05,0.3$, and 0.4 at RT, at zero field (lower panel), and external fields (upper panel indicated in the figure). Magnified picture is the transport-of-intensity equation of the spin texture of the magnetic domain. Insets of the stripe domains show the Lorentz contrast along the path marked by the dotted green line.

Figure 6

Micromagnetic simulation of the stability of a single biskyrmion. Model size is $400\times 400\times 200\mathrm{n}{\mathrm{m}}^3$. The external field is 200 mT along the $z$ axis. (a) The initial state of an ideal biskyrmion structure. (b) Variation of the domain structures by changing $A$ and $K_{\mathrm{u}}$. (c), (d) A trivial bubble and biskyrmion after relaxation and their evolution under a tilt of $K_{\mathrm{u}}\left({10}^{\circ }\right)$ from the perpendicular direction.