Chiral Properties of Structure and Magnetism in ${\mathrm{Mn}}_{1\mathrm{\text{−}}x}{\mathrm{Fe}}_x\mathrm{Ge}$ Compounds: When the Left and the Right are Fighting, Who Wins?

Magnetic susceptibility measurements have shown that the compounds ${\mathrm{Mn}}_{1\mathrm{\text{−}}x}{\mathrm{Fe}}_x\mathrm{Ge}$ are magnetically ordered through the whole range of concentrations $x=[0.0,1.0]$. Small-angle neutron scattering reveals the helical nature of the spin structure with a wave vector, which changes from its maximum ($|\mathbf{k}|=2.3{\mathrm{nm}}^{-1}$) for pure MnGe, through its minimum ($|\mathbf{k}|\to 0$) at $x_c\approx 0.75$, to the value of $|\mathbf{k}|=0.09{\mathrm{nm}}^{-1}$ for pure FeGe. The macroscopic magnetic measurements confirm the ferromagnetic nature of the compound with $x=x_c$. The observed transformation of the helix structure to the ferromagnet at $x=x_c$ is explained by different signs of chirality for the compounds with $x>x_c$ and $x<x_c$. We used x-ray diffraction and polarized neutron scattering to evaluate the crystallographic chirality ${\Gamma }_c$ and the magnetic chirality ${\gamma }_m$ of the FeGe single crystals. Similar to previous observations for FeSi-based compounds, FeGe demonstrates left- (right-)handed crystalline chirality acompained by right (left) handedness of the magnetic helix (${\Gamma }_c{\gamma }_m=-1$). At variance, MnSi related compounds show the opposite behavior (${\Gamma }_c{\gamma }_m=1$). Since the magnetic chirality ${\gamma }_m$ relates to the sign of the Dzyaloshinskii-Moriya interaction (DMI), for the same geometrical arrangement (${\Gamma }_c$) the sign of DMI can be set by the proper choice of the transition metal.