Evolution of helimagnetic correlations in ${\mathrm{Mn}}_{1-x}{\mathrm{Fe}}_x\mathrm{Si}$ with doping: A small-angle neutron scattering study

We present a comprehensive small-angle neutron scattering study of the doping dependence of the helimagnetic correlations in ${\mathrm{Mn}}_{1-x}{\mathrm{Fe}}_x\mathrm{Si}$. The long-range helimagnetic order in ${\mathrm{Mn}}_{1-x}{\mathrm{Fe}}_x\mathrm{Si}$ is suppressed with increasing Fe content and disappears for $x>x^{*}\approx 0.11$, i.e., well before $x_C\approx 0.17$ where the transition temperature vanishes. For $x>x^{*}$, only finite isotropic helimagnetic correlations persist which bear similarities with the magnetic correlations found in the precursor phase of MnSi. Magnetic fields gradually suppress and partly align these short-ranged helimagnetic correlations along their direction through a complex magnetization process.

Figure 1

SANS patterns recorded at zero magnetic field and different temperatures for ${\mathrm{Mn}}_{1-x}{\mathrm{Fe}}_x\mathrm{Si}$ with (a) $x=0$, (b) $x=0.03$, (c) $x=0.09$, (d) $x=0.10$, (e) $x=0.11$, and (f) $x=0.14$.

Figure 2

Scattering function $S\left(Q\right)$, deduced by radially averaging the scattered intensity, at zero field for ${\mathrm{Mn}}_{1-x}{\mathrm{Fe}}_x\mathrm{Si}$. (a) $S\left(Q\right)$ is determined for $T<T_C$ and the Fe concentrations indicated in the legend. $S\left(Q\right)$ was measured at $T=2.5\mathrm{K}$ for $x\le 0.11$ and $T=2.0\mathrm{K}$ for $x=0.14$ and is normalized to its maximum value. (b)–(d) $S\left(Q\right)$ shown for the indicated temperatures and for (b) $x=0.09$, (c) $x=0.11$, and (d) $x=0.14$. The solid lines in (a) indicate the best fits of the data to a Gaussian for $x<0.11$ where the width of the Gaussian is fixed by the instrumental resolution. For $x\ge 0.11$ and in (b)–(d) the solid lines represent the best fits of Eq. (1) (convoluted with the instrumental resolution) to the data.

Figure 3

Temperature dependence of (a) the pitch of the helical modulation $\ell$ and (b) the magnetic correlation length $\xi$ at zero magnetic field and for the ${\mathrm{Mn}}_{1-x}{\mathrm{Fe}}_x\mathrm{Si}$ compositions indicated in the legend. The values of $\xi$ are obtained by fitting $S\left(Q\right)$ to Eq. (1). For $x\le 0.10$ and $T<T_C$, $\ell$ was obtained from fitting $S\left(Q\right)$ to a Gaussian centered at $\tau =2\pi /\ell$. For $T<T_C$ and $x\le 0.10$, the linewidth of $S\left(Q\right)$ is limited by the experimental resolution and $\xi$ cannot be determined.

Figure 4

SANS patterns measured at $T<T_C$ as a function of the magnetic field for ${\mathrm{Mn}}_{1-x}{\mathrm{Fe}}_x\mathrm{Si}$ with (a),(b) $x=0.09$ at $T=2.5\mathrm{K}$, (c),(d) $x=0.11$ at $T=2.5\mathrm{K}$, and (e),(f) $x=0.14$ at $T=2.0\mathrm{K}$. The magnetic field was applied (a),(c),(f) parallel to the incoming neutron beam ($\vec{H}\left|\right|{\vec{k}}_i$) and (b),(d),(e) perpendicular to it ($\vec{H}\perp {\vec{k}}_i$). The two ${30}^{\circ }$ red wedges in (d) and (f) indicate the section of the detector over which the radial integration was performed to obtain $S\left(Q\right)$ for $\vec{H}\perp {\vec{k}}_i$.

Figure 5

SANS results under magnetic field for ${\mathrm{Mn}}_{0.89}{\mathrm{Fe}}_{0.14}\mathrm{Si}$ at $T=2.0\mathrm{K}$. (a) Scattering function $S\left(Q\right)$ in arbitrary units obtained by radial averaging the scattered intensity over the entire detector with the magnetic field applied parallel to the incoming neutron beam ($\vec{H}\left|\right|{\vec{k}}_i$). (b) $S\left(Q\right)$ in arbitrary units with the magnetic field applied perpendicular to the incoming neutron beam ($\vec{H}\perp {\vec{k}}_i$). In (b), $S\left(Q\right)$ is deduced by radial averaging the scattered intensity over the two ${30}^{\circ }$ wedges along the magnetic field direction indicated in Fig. 4. (c) Magnetic field dependence of the total scattered intensity obtained by summing the intensity over the entire detector for $\vec{H}\left|\right|{\vec{k}}_i$ and over the two ${30}^{\circ }$ wedges along the magnetic field for $\vec{H}\perp {\vec{k}}_i$. (d) Magnetic field dependence of the FWHM of $S\left(Q\right)$; inset shows the field dependence of the pitch of the helix $\ell$ as obtained from fitting the data of (a) and (b) to Eq. (1). These fits are indicated by the solid lines in (a) and (b).

Figure 6

Temperature dependence of the total scattered intensity at ${\mu }_{0}H=0.20\mathrm{T}$ for ${\mathrm{Mn}}_{1-x}{\mathrm{Fe}}_x\mathrm{Si}$ with (a) $x=0$, (b) $x=0.09$, (c) $x=0.10$, and (d) $x=0.11$. The field was applied both parallel ($\vec{H}\left|\right|{\vec{k}}_i$) and perpendicular ($\vec{H}\perp {\vec{k}}_i$) to the incoming neutron beam. The insets show characteristics SANS patterns at the indicated temperatures for both field configurations.

Figure 7

Contour plots showing the total scattered SANS intensity in arbitrary units in the configuration where the magnetic field was applied parallel to the incoming neutron beam ($\vec{H}\left|\right|{\vec{k}}_i$) for ${\mathrm{Mn}}_{1-x}{\mathrm{Fe}}_x\mathrm{Si}$ with (a) $x=0$, (b) $x=0.09$, (c) $x=0.10$, and (d) $x=0.11$. The black dots indicate the points at which the SANS measurements were performed.

Figure 8

Same as Fig. 7, but with the magnetic field applied perpendicular to the incoming neutron beam ($\vec{H}\perp {\vec{k}}_i$).

Figure 9

Fe concentration dependence of (a) the critical temperature $T_C$ and $T^{\prime }$ and (b) the pitch of the helix $\ell$. The critical temperature $T_C$ and $T^{\prime }$, which mark the onset of the (short-ranged) helimagnetic correlations in the precursor phase, are adapted from [11]. LO indicates long-range helimagnetic correlations, SO short-range helimagnetic correlations, P the precursor phase, and PM the paramagnetic phase.