Controlling Dzyaloshinskii-Moriya interactions in the skyrmion host candidates ${\mathrm{FePd}}_{1-x}{\mathrm{Pt}}_x{\mathrm{Mo}}_3\mathrm{N}$

Ferromagnets crystallizing in structures described by chiral cubic space groups, including compounds with the B20 or $\beta$-Mn structures, are known to host long-period chiral spin textures such as skyrmion lattices. These spin textures are stabilized by a competition between ferromagnetic exchange and antisymmetric Dzyaloshinskii-Moriya (DM) exchange, which is enhanced by the spin-orbit coupling associated with high-atomic-number elements. For real-world application, it is desirable to find materials that can host compact skyrmion lattices at readily accessible temperatures. Here, we report on the crystal chemistry and magnetic phase diagrams of a family of compounds with the filled $\beta$-Mn structure, ${\mathrm{FePd}}_{1-x}{\mathrm{Pt}}_x{\mathrm{Mo}}_3\mathrm{N}$, with $T_C$ ranging from 175 to 240 K. DC and AC magnetization measurements reveal magnetic phase diagrams consistent with the formation of a skyrmion pocket just below $T_C$. The magnitudes of ferromagnetic and DM exchanges are determined from the phase diagrams, demonstrating that the introduction of increasing amounts of Pt can be used to increase spin-orbit coupling in order to control the expected skyrmion lattice parameter between 140 and 65 nm while simultaneously increasing $T_C$.

Figure 1

(a) Crystal structure of the cubic series ${\mathrm{FePd}}_{1-x}{\mathrm{Pt}}_x{\mathrm{Mo}}_3\mathrm{N}$ (space group $P{4}_{1}32$), shown projected down one of the cubic axes. The origin of the cell has been translated by 0.25 of a unit cell such that the chiral fourfold screw axis ($4_1$) is centered in the cell. (b) Evolution of the lattice parameter $a$ as a function of $x$ (error bars are smaller than the points). (c) Synchrotron diffraction pattern shown with Rietveld fits to the $P{4}_{1}32\beta$-Mn structure.

Figure 2

(a) Magnetization as a function of temperature collected under an applied magnetic field of $H$ = 0.02 T, collected while warming after either cooling under zero field (dotted line) or cooling under a field (solid line). (b) Magnetization as a function of the applied magnetic field at $T$ = 2 K. (c) $T_C$ and ${\mu }_{\mathrm{sat}}$ as a function of $x$.

Figure 3

Magnetic characterization of ${\mathrm{FePtMo}}_3\mathrm{N}$. (a) Magnetization vs magnetic field. For visual clarity, the curves are each offset by 0.2 ${\mathrm{Am}}^2{\mathrm{kg}}^{-1}$. (b) $dM/dH$ with an offset between the curves of 0.02 ${\mathrm{Am}}^2{\mathrm{kg}}^{-1}{\mathrm{mT}}^{-1}$. (c) $d^{2}M/d{H}^2$ shifted by 2 ${\mathrm{kAm}}^2{\mathrm{kg}}^{-1}{\mathrm{mT}}^{-2}$. (d) ${\chi }^{\prime }$ with an offset of 0.01 ${\mathrm{Am}}^2{\mathrm{kg}}^{-1}{\mathrm{mT}}^{-1}$ and (e) $d{\chi }^{\prime }/dH$ shifted by 4 ${\mathrm{kAm}}^2{\mathrm{kg}}^{-1}{\mathrm{mT}}^{-2}$. The (c) $d^{2}M/d{H}^2$ curves and (e) $d{\chi }^{\prime }/dH$ below the magnetic transition temperature show features corresponding to magnetic phase transitions, which can be used to draw a phase diagram in (f). The proposed skyrmionic pocket (A) is shown in red. Solid lines represent first-order phase transitions. The dashed lines represent continuous transitions. FD: fluctuation disordered.

Figure 4

Magnetic characterization of (a) ${\mathrm{FePd}}_{0.5}{\mathrm{Pt}}_{0.5}{\mathrm{Mo}}_3\mathrm{N}$ and (b) ${\mathrm{FePdMo}}_3\mathrm{N}$. $d{\chi }^{\prime }/dH$ has been used to construct the phase diagrams. The proposed skyrmionic pocket (A) is shown in red. Solid lines represent first-order phase transitions. The dashed lines represent continuous transitions. FD: fluctuation disordered.

Figure 5

Magnetoentropic characterization of ${\mathrm{FePtMo}}_3\mathrm{N}$. (a) Magnetization vs temperature shows precursor anomalies characteristic for skyrmion host materials, which are seen as features in (b) $dM/dT$ = $dS/dH$. In (b), the orange triangles indicate the anomaly corresponding to the Brazovskii transition, and the teal to the transition from the conical to A state. The curves are offset from each other by 0.1 J ${\mathrm{kg}}^{-1}$ ${\mathrm{K}}^{-1}$ ${\mathrm{T}}^{-1}$ for clarity. (c) Map of the magnetocaloric effect ($\mathrm{\Delta }{S}_M$) with the features from $dM/dT$ indicated as orange and teal lines. The phase transition lines from AC magnetic measurements are shown as black dotted lines.

Figure 6

(a) Values of $H_{\mathrm{C}2}$ for ${\mathrm{FePtMo}}_3\mathrm{N}$ below the Brazovskii transition and the fit used to obtain the parameter $D$ using Eq. (5) and the values for $S\left(T\right)$. (b) Exchange stiffness $A$ and DM interaction density $D$ vs the composition of the series $x$. (c) Helical wavelengths $\lambda$ against $x$.