We show, with the help of polarized neutrons, that the cubic magnets ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x\mathrm{Si}$ with Dzyaloshinskii-Moriya interaction can be switched between left (for $x=0.1$, 0.15) and right (for $x=0.2$, 0.25, 0.3, 0.5) chiral states of the spin helix. The absolute structure was evaluated using x-ray diffraction. The crystals are shown to be enantiopure and the structural chirality changes from right handed for $x<0.2$ to left handed for $x>0.2$. These compounds are compared with the etalon sample of MnSi which is identified as having the left-handed chirality both in the magnetic and crystallographic sense.

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.

The magnetic structure of ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x\mathrm{Si}$ single crystals with $x=0.10,0.15,0.20,0.50$ has been studied by small angle polarized neutron diffraction and superconducting quantum interference device measurements. Experiments have shown that in zero field the compounds with $x=0.1,0.15$ have a well-defined tendency to order in the one-handed spiral along ⟨100⟩ axes due to the anisotropic exchange, that, however, decreases with increasing Co concentration $x$. The magnetic structure of ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x\mathrm{Si}$ with $x=0.2,0.5$ consists of spiral domains with randomly oriented spiral wave vector $\mathbf{k}$. The applied magnetic field produces a single domain helix oriented along the field. The process of the reorientation starts at the field $H_{C1}$. Further increase of the field leads to a magnetic phase transition from a conical to a ferromagnetic state near $H_{C2}$. In the critical range near $T_C$ the integral intensity of the Bragg reflection shows a well-pronounced minimum at $H_{\mathrm{fl}}$ attributed to a $\mathbf{k}$ flop of the helix wave vector. On the basis of our experiments we built the $H\text{−}T$ phase diagram for each compound. It is shown that the same set of the parameters governs the magnetic properties of these compounds $k$, $H_{C1}$, $H_{\mathrm{fl}}$, and $H_{C2}$. Our experimental findings are well interpreted in the framework of a recently developed theory [Phys. Rev. B 73, 174402 (2006)] for cubic magnets with Dzyaloshinskii-Moriya (DM) interaction. In particular, the theory suggests an additional quantum term in the magnetic susceptibility caused by the DM interaction which is in good agreement with the experiment.