Effect of Ge substitution on magnetic properties in the itinerant chiral magnet MnSi

We have investigated the effect of Ge substitution on the magnetic ordering in the B20 itinerant chiral magnet MnSi prepared by melting and annealing under ambient pressure. From a metallurgical survey, the solubility limit of Ge was found to be $x=0.144\left(5\right)$ with annealing temperature $T_{\mathrm{an}}=1073$ K. Magnetization measurements on ${\mathrm{MnSi}}_{1-x}{\mathrm{Ge}}_x$ samples show that the helical ordering temperature $T_{\mathrm{c}}$ increases rapidly in the low-$x$ range, whereas it becomes saturated at higher concentration $x>0.1$. The Ge substitution also increases both the saturation magnetization $M_{\mathrm{s}}$ and the critical field to the fully polarized state $H_{\mathrm{c}2}$. In contrast to the saturation behavior of $T_{\mathrm{c}}$, those parameters increase linearly up to the highest Ge concentration investigated. In the temperature-magnetic field phase diagram, we found enlargement of the skyrmion phase region for large $x$ samples. We, furthermore, observed the nonlinear behavior of helical modulation vector $k$ as a function of Ge concentration, which can be described qualitatively using the mean field approximation.

Figure 1

(a) The composition determined by the EDX analysis of the main phase of ${\mathrm{MnSi}}_{1-x}{\mathrm{Ge}}_x$ alloys annealed at $T_{\mathrm{an}}=1073$, 1173, and 1273 K for 5 days, as a function of nominal composition, (b) lattice constants of all prepared samples at different annealing temperatures, as a function of EDX-determined Ge concentration (the dashed line is a guide for the eye), (c) XRD patterns for MnSi (black line) and ${\mathrm{MnSi}}_{1-x}{\mathrm{Ge}}_x$ (color lines) at different annealing temperatures $T_{\mathrm{an}}$, and (d) magnified XRD patterns around the 210 reflection.

Figure 2

BSE images for $x_0=0.15$ with the annealing temperature (a) $T_{\mathrm{an}}=1273$ K and (b) $T_{\mathrm{an}}=1073$ K.

Figure 3

Comparison of XRD patterns for different nominal Ge concentration and longer annealing time at $T_{\mathrm{an}}=1073$ K.

Figure 4

(a) $M\text{−}T$ (filled circles) and $dM/dT$ (open circles) curves under an external magnetic field $H=100$ Oe for $x=0.105\left(7\right)$ sample (see the Supplemental Material [19] for all Ge-doped MnSi samples), and (b) Ge-concentration dependence of $T_{\mathrm{c}}$ obtained from the temperature dependence of magnetization (M) measured under $H=100$ Oe and neutron experiment (N) under $H=0$ Oe.

Figure 5

(a) $M\text{−}H$ (filled circles) and $dM/dH$ (open circles) curves at $T=5$ K for the $x=0.105\left(7\right)$ sample, and (b) Ge-concentration dependence of saturation moment $M_{\mathrm{s}}$ and critical field $H_{\mathrm{c}2}$.

Figure 6

(a) $M\text{−}T$ (filled circles) and $dM/dT$ (open circles) curves with an external magnetic field $H=2000$ Oe, (b) $M\text{−}H$ (filled circles) and $dM/dH$ (open circles) curves with temperature $T=38$ K, (c) The determined full phase diagram for representing sample $x=0.144\left(5\right)$, and (d) Ge-concentration dependence of the width of the skyrmion-phase region $W$.

Figure 7

(a)–(c) Neutron diffraction patterns in the small $Q$ range for the three ${\mathrm{MnSi}}_{1-x}{\mathrm{Ge}}_x$ samples with (a) $x=0.15$, (b) 0.07, and (c) 0.06. The temperatures were given in the figures. (d) Temperature dependence of the peak intensity for (open circles) $x=0.15$, (filled circles) 0.07, and (open triangles) 0.06. The transition temperatures were estimated as $T_{\mathrm{c}}=42.6$(1), 40.5(3), and 38.6(3) K for $x=0.15$, 0.07, and 0.06, respectively. The background, estimated at high temperature paramagnetic data, is subtracted from the data. The solid lines are the results of the fitting to the power law.

Figure 8

Ge-concentration dependence of the modulation vectors $k$ estimated from the neutron diffraction data at $T=30$ K shown in Fig. 7 (filled circles) for three representative ${\mathrm{MnSi}}_{1-x}{\mathrm{Ge}}_x$ samples. The modulation vectors of MnSi are obtained at $T=29$ K (Ref. [23], filled up triangle) and $T=4.2$ K (Ref. [8], filled down triangle). The calculated modulation vectors $k$ derived from magnetization measurement at $T=5$ K are shown by open diamond as described in the discussion. The dashed lines are a guide for the eye.

Figure 9

Ge-concentration dependence of the spin-wave stiffness $A$. The observed spin-wave stiffness $A_{\mathrm{expt}}$ of MnSi is obtained from Refs. [25, 26].

Figure 10

Ge-concentration dependence of exchange $\left(JS\right)$ and Dzyaloshinskii-Moriya $\left(DS\right)$ parameters.