Spin-glass ground state in ${\text{Mn}}_{1-x}{\text{Co}}_x\text{Si}$

We report the discovery of a spin-glass ground state in the transition-metal monosilicides with the B20 crystallographic structure. Magnetic, transport, neutron, and muon investigations of the solid solution ${\text{Mn}}_{1-x}{\text{Co}}_x\text{Si}$ have revealed a new dome in the phase diagram with evidence of antiferromagnetic interactions. For Mn-rich compounds, a sharp decrease in the Curie temperature is observed upon Co doping and neutron elastic scattering shows that helimagnetic order of MnSi persists up to $x=0.05$ with a shortening of the helix period. For higher Co $\left(0.05<x<0.90\right)$ concentrations, the Curie-Weiss temperature changes sign and the system enters a spin-glass state upon cooling ($T_g=9\text{K}$ for $x_{\text{Co}}=0.50$), due to chemical disorder. In this doping range, a minimum appears in the resistivity, attributed to scattering of conduction electron by localized magnetic moments.

Figure 1

(Color online) (a) Magnetic ordering temperatures of monosilicides. (b) Expended scale of the region around $x=0.05$ of the magnetic phase diagram. The dashed vertical line indicates the concentration of the helimagnetic-spin-glass transition found in ${\text{Mn}}_{1-x}{\text{Co}}_x\text{Si}$ in this work.

Figure 2

(Color online) (a) Evolution of the length of the helix as a function of the relative lattice parameter in the case of hydrostatic pressure on MnSi (Ref. 19) and chemical substitution of Mn with Co (Ref. 14). (b) Neutron intensity color map taken at 1.8 K in the vicinity of the (110) nuclear Bragg peak showing the magnetic satellites of the helimagnetic structure along the [111] direction.

Figure 3

(Color online) (a) Comparison of the temperature dependence of the resistivity of MnSi ( Ref. 21) (red dashed curve), ${\text{Mn}}_{0.944}{\text{Co}}_{0.056}\text{Si}$ (blue solid curve), and MnSi at $P=12.9\text{kbar}$ (Ref. 22) (green dotted curve). [(b) and (c)] Relative magnetoresistance $\Delta \rho /{\rho }_0$ and resistivity $\rho \left(T\right)$ for ${\text{Mn}}_{0.944}{\text{Co}}_{0.056}\text{Si}$. Magnetic field values are given in the figure.

Figure 4

(Color online) (a) Temperature dependence of the zero-field-cooled (ZFC) (full symbols) and FC (open symbols) dc magnetic susceptibility for three different compositions of ${\text{Mn}}_{1-x}{\text{Co}}_x\text{Si}$ ($x=0.1$, $x=0.5$, and $x=0.8$). The temperature of the magnetic transition is indicated as a vertical dashed-dotted line as the FC and ZFC curves start to overlap. (b) Hysteresis loop for the sample ${\text{Mn}}_{0.5}{\text{Co}}_{0.5}\text{Si}$ at 5 K. The field sequence is numbered.

Figure 5

(Color online) In-phase component of the ac magnetic susceptibility for (a) ${\text{Mn}}_{0.77}{\text{Co}}_{0.23}\text{Si}$ and (b) ${\text{Mn}}_{0.5}{\text{Co}}_{0.5}\text{Si}$ at four different frequencies. (c) Frequency dependence of the inverse of the freezing temperature $1/T_g$ versus $\text{log}\left(F\right)$. The parameters of linear fits (dashed lines) are reported in the figure for each composition.

Figure 6

(Color online) Temperature dependence of the power $\beta$ in Eq. (1) for ${\text{Mn}}_{1-x}{\text{Co}}_x\text{Si}$ samples with $x=0.06$, $x=0.23$, and $x=0.50$ on a reduced temperature scale. The value goes from $\beta =1$ above $T_g$ (paramagnetism) to $\beta =\frac{1}{2}$ at $T_g$ upon cooling.

Figure 7

(Color online) (Left axis) Temperature dependence of the static field $\left(a_s\right)$ below the spin-glass transition $T_g$ from the fit of muon-spin-relaxation signal with Eq. (2) for cobalt concentrations $x=0.06$ (green symbols), $x=0.23$ (blue symbols), and $x=0.50$ (red symbols). $T_g$ is indicated as vertical dashed-dotted lines. (Right axis) Temperature evolution above $T_g$ of the depolarization rate $\left({\lambda }_d\right)$ from Eq. (1).

Figure 8

(Color online) Temperature dependence of (a) the resistivity $\rho$ and (b) the relative magnetoresistance $\Delta \rho /{\rho }_0$ for ${\text{Mn}}_{0.5}{\text{Co}}_{0.5}\text{Si}$. Magnetic fields are given in the figure. (c) Temperature dependence of $T_g$ and the temperature of the upturn of resistivity. The dashed line corresponds to the formula of magnetic disorder resistivity defined in the text (Ref. 34).

Figure 9

(Color online) (a) Temperature dependence of the resistivity of ${\text{Mn}}_{0.5}{\text{Co}}_{0.5}\text{Si}$. The dotted lines represent the three regions, parabolic (fast LSF), linear, and logarithmic regimes (slow LSF) (Ref. 35). The contribution of phonons is removed by subtraction of the scaled (s) resistivity of CoSi (b). The scaled resistivity curve of ${\text{Mn}}_{0.95}{\text{Co}}_{0.05}\text{Si}$ is shown as a dashed-dotted line. (c) Resistivity versus the square of the magnetic moment per transition-metal atomic site at $T=5\text{K}$.