Helical spin structure of ${\text{Mn}}_{1-y}{\text{Fe}}_y\text{Si}$ under a magnetic field: Small angle neutron diffraction study

The magnetic structure of the noncentrosymmetric cubic magnets with Dzyaloshinskii-Moriya interaction ${\text{Mn}}_{1-y}{\text{Fe}}_y\text{Si}$ with $y=0.0,0.06,0.08,0.10$ has been studied by means of the small angle neutron diffraction and magnetization measurements. The compounds order in the spin helix structure below $T_c$ that decreases linearly with the Fe doping and approaches zero at $y>0.13$. We build the $\left(H\text{−}T\right)$ phase diagrams for each compound and interpret them on the basis of the Bak-Jensen hierarchical model of the principal interactions. Among these interactions are the spin-wave stiffness that decreases linearly with $y$, obviously duplicating the change of $T_c$, and the Dzyaloshinskii interaction showing the moderate evolution with $y$. It is shown that these compounds undergo the transition from the paramagnetic to helimagnetic phase through the intermediate chiral fluctuating phase. The discussion is given on the comparison of the $\left(T\text{−}P\right)$ phase diagram in pure MnSi and $\left(T\text{−}y\right)$ phase diagram of the ${\text{Mn}}_{1-y}{\text{Fe}}_y\text{Si}$ compounds showing the role of the principal interactions on the critical temperature $T_c$ of these systems.

Figure 1

(Color online) Maps of the polarized SANS intensities of the sample ${\text{Mn}}_{0.92}{\text{Fe}}_{0.08}\text{Si}$ $\left(T_c=10.55\pm 0.05\text{K}\right)$ for the polarization ${\mathbf{P}}_0$ along the guide field (left) and opposite to it (right) at $T=14\text{K}$ (a), $T=10.75\text{K}$ (b), $T=8.75\text{K}$ (c).

Figure 2

(Color online) The schematic distribution of the scattered intensity on the sphere of radius $\left|\mathbf{k}\right|$ in the reciprocal space for the sample ${\text{Mn}}_{0.92}{\text{Fe}}_{0.08}\text{Si}$ (a). The SANS map taken for nonpolarized neutrons represents the cross section of the sphere by the plane $\left(1\overline{1}0\right)$ (b).

Figure 3

Magnetic-field dependence of the magnetization $M$ and susceptibility $\chi$ taken at $T=2\text{K}$ (a) and $T=10\text{K}$ (b) for ${\text{Mn}}_{0.92}{\text{Fe}}_{0.08}\text{Si}$ compound.

Figure 4

(Color online) Maps of the polarized SANS intensities of the ${\text{Mn}}_{0.92}{\text{Fe}}_{0.08}\text{Si}$ compound under applied magnetic field $H=20\text{mT}$ (a), 50 mT (b), and 120 mT (c) at $T=8\text{K}$.

Figure 5

(Color online) Map of the polarized SANS intensity of the ${\text{Mn}}_{0.92}{\text{Fe}}_{0.08}\text{Si}$ compound under applied magnetic field $H=200\text{mT}$ at $T=10\text{K}$.

Figure 6

The field dependence of the integral SANS intensity at $\mathbf{k}\parallel \mathbf{H}$ for the ${\text{Mn}}_{0.92}{\text{Fe}}_{0.08}\text{Si}$ compound at $T=10\text{K}$. The inset gives the field dependence of the integral SANS intensity at $\mathbf{k}\perp \mathbf{H}$.

Figure 7

$\left(H\text{−}T\right)$ phase diagrams for ${\text{Mn}}_{0.94}{\text{Fe}}_{0.06}\text{Si}$ (a), ${\text{Mn}}_{0.92}{\text{Fe}}_{0.08}\text{Si}$ (b), and ${\text{Mn}}_{0.9}{\text{Fe}}_{0.1}\text{Si}$ (c) compounds.

Figure 8

Dependence of the helix wave vector $k$ (a), the critical field $H_{C2}$ (b), the critical field $H_{C1}$ (c), and the field $H_{\text{gap}}$ (d) on the Fe concentration $y$ for ${\text{Mn}}_{1-y}{\text{Fe}}_y\text{Si}$ compounds.

Figure 9

Dependence of the estimated values of the exchange energy of the order $A/a^2$ (a), DM energy $SD/a$ (b), the anisotropy constant $F/a^2$ (c) and the spin-wave gap $\Delta$ (d) on the Fe concentration $y$ for ${\text{Mn}}_{1-y}{\text{Fe}}_y\text{Si}$ compounds.

Figure 10

(Color online) Critical temperatures ($T_c$ and $T^{\ast }$), and spin-wave stiffness $A/\left(a^2{k}_B\right)$ along with the Dzyaloshinskii constant $SD/\left(a{k}_B\right)$ as functions of the Fe concentration $y$.

Figure 11

Dependence of the temperature $\Delta T^{\ast }$ on the squared the wave vector. The line is the fit $\Delta T^{\ast }=C{\left(ka\right)}^2$ with $C=3.5\pm 0.3\text{K}$.

Figure 12

Dependence of the DM constant $D/a$ on the Fe concentration $y$ for ${\text{Mn}}_{1-y}{\text{Fe}}_y\text{Si}$ compounds and Co concentration $x$ for ${\text{Fe}}_{1-x}{\text{Co}}_x\text{Si}$ compounds.