Disorder effects near a magnetic instability in ${\mathrm{CePtSi}}_{1-x}{\mathrm{Ge}}_x$ ($x=0$, $0.1$)

The magnetic susceptibility and nuclear magnetic resonance $\left(\mathrm{NMR}\right)$ linewidth have been measured in the heavy-fermion alloys ${\mathrm{CePtSi}}_{1-x}{\mathrm{Ge}}_x$, $x=0$ and $0.1$, to study the role of disorder in the non-Fermi-liquid $\left(\mathrm{NFL}\right)$ behavior of this system. The theoretical $\mathrm{NMR}$ line shape is calculated from disorder-driven $\mathrm{NFL}$ models and shows the same essential features as the observed spectra. Analysis of ${}^{29}\mathrm{Si}$ and ${}^{195}\mathrm{Pt}$ $\mathrm{NMR}$ linewidths strongly suggests the existence of locally inhomogeneous susceptibility in both materials, and agrees with the widths of the local susceptibility distributions estimated from the susceptibility fits to the disorder-driven $\mathrm{NFL}$ models. Disorder-driven mechanisms can also explain the $\mathrm{NFL}$ behavior in ${\mathrm{CePtSi}}_{0.9}{\mathrm{Ge}}_{0.1}$; the $\mathrm{NMR}$ spectra do not, however, distinguish between the Kondo-disorder and Griffiths phase models. We find that stoichiometric $\mathrm{CePtSi}$ and $\mathrm{Ge}$-doped ${\mathrm{CePtSi}}_{0.9}{\mathrm{Ge}}_{0.1}$ show similar degrees of magnetic disorder, although a narrower distribution of local susceptibilities in $\mathrm{CePtSi}$ allows Fermi-liquid behavior to appear below $1\mathrm{K}$. The residual resistivity reported in $\mathrm{CePtSi}$ is relatively large, which indicates a significant level of intrinsic lattice defects and seems to be consistent with the disorder observed in the $\mathrm{NMR}$ spectra.

Figure 1

Tetragonal crystal structure of ${\mathrm{CePtSi}}_{1-x}{\mathrm{Ge}}_x$. Each $\mathrm{Si}$ or $\mathrm{Pt}$ site has four nearest $\mathrm{Ce}$ neighbors (No. 1) and two $\mathrm{Ce}$ next-nearest neighbors (No. 2).

Figure 2

A plot of the inverse $ab$-plane susceptibility versus temperature for $\mathrm{CePtSi}$. The circles denote the experimental data, and the curve is obtained from the crystalline electric field $\left(\mathrm{CEF}\right)$ calculation.

Figure 3

Temperature dependence of the bulk susceptibilities in $\mathrm{CePtSi}$ (filled symbols) and ${\mathrm{CePtSi}}_{0.9}{\mathrm{Ge}}_{0.1}$ (open symbols). Triangles: the $c$-axis susceptibilities. Circles: the $ab$-plane susceptibilities.

Figure 4

(a) $ab$-plane susceptibilities in $\mathrm{CePtSi}$ (filled symbols) and ${\mathrm{CePtSi}}_{0.9}{\mathrm{Ge}}_{0.1}$ (open symbols). Triangles: low temperatures $(T=0.4–8\mathrm{K})$, applied fields $0.05\mathrm{T}$ and $0.01\mathrm{T}$ for $\mathrm{CePtSi}$ and ${\mathrm{CePtSi}}_{0.9}{\mathrm{Ge}}_{0.1}$, respectively. Squares: low temperatures, $0.1\mathrm{T}$ and $0.05\mathrm{T}$ for $\mathrm{CePtSi}$ and ${\mathrm{CePtSi}}_{0.9}{\mathrm{Ge}}_{0.1}$, respectively. Diamonds: low temperatures, $0.5\mathrm{T}$. Circles: $T>2\mathrm{K}$, $0.5\mathrm{T}$. Stars: estimated susceptibility from extrapolated Wilson ratio (see text). (b) Inverse susceptibilities of $\mathrm{CePtSi}$ and ${\mathrm{CePtSi}}_{0.9}{\mathrm{Ge}}_{0.1}$.

Figure 5

Wilson ratios at low temperatures in $\mathrm{CePtSi}$ (filled circles) and ${\mathrm{CePtSi}}_{0.9}{\mathrm{Ge}}_{0.1}$ (open circles). The straight lines denote the linear extrapolations.

Figure 6

The temperature dependence of $\mathrm{NMR}$ Knight shifts in $\mathrm{CePtSi}$ (filled circles) and ${\mathrm{CePtSi}}_{0.9}{\mathrm{Ge}}_{0.1}$ (open circles).

Figure 7

Susceptibility fits to the Kondo-disorder model in (a) $\mathrm{CePtSi}$ and (b) ${\mathrm{CePtSi}}_{0.9}{\mathrm{Ge}}_{0.1}$. Circles: experimental data. Triangles: estimated data. Dashed curves: fits for only the experimental data from 2 to $300\mathrm{K}$. Solid curves: fits for the entire susceptibilities including the estimated data below $2\mathrm{K}$.

Figure 8

Susceptibility fits to the Griffiths phase model in (a) $\mathrm{CePtSi}$ and (b) ${\mathrm{CePtSi}}_{0.9}{\mathrm{Ge}}_{0.1}$. Circles: experimental data. Triangles: estimated data. Dashed curves: fits for only the experimental data from 2 to $300\mathrm{K}$. Solid curves: fits for the entire susceptibilities including the estimated data below $2\mathrm{K}$.

Figure 9

${}^{29}\mathrm{Si}$ $\mathrm{NMR}$ spectra for the unaligned (solid curve) and aligned (dotted and dashed-dotted curves) $\mathrm{CePtSi}$ powder samples at $4.2\mathrm{K}$ and at a frequency of $25.5\mathrm{MHz}$. Dotted and dashed-dotted curves are for spectra with the $\mathrm{NMR}$ field ${\mathbf{H}}_0$ directed parallel and perpendicular to the crystal $c$ axis, respectively. The reference field is the unshifted resonance field at $30.145\mathrm{kOe}=25.5\mathrm{MHz}∕(\gamma ∕2\pi )$, where $\gamma ∕2\pi =0.8458\mathrm{MHz}∕\mathrm{kOe}$ is the ${}^{29}\mathrm{Si}$ nuclear gyromagnetic ratio.

Figure 10

Plots of ${}^{29}\mathrm{Si}$ $\mathrm{NMR}$ Knight shift $\overline{K}$ and the distribution width of the Knight shifts $\delta K$ as functions of susceptibility in $\mathrm{CePtSi}$ and ${\mathrm{CePtSi}}_{0.9}{\mathrm{Ge}}_{0.1}$.

Figure 11

A plot of the relative spread $\delta \chi ∕\overline{\chi }$ of susceptibility from disorder model fits over the entire temperature range and relative spread $\delta K∕\overline{K}$ of frequency shift from $\mathrm{NMR}$ measurements plotted versus $ab$-plane bulk susceptibility $\chi$ for $\mathrm{CePtSi}$ and ${\mathrm{CePtSi}}_{0.9}{\mathrm{Ge}}_{0.1}$. Solid and dashed curves: predicted $\delta \chi ∕\overline{\chi }$ from Kondo-disorder and Griffiths phase models, respectively. Filled and open circles: $\delta K∕\overline{K}$ from ${}^{29}\mathrm{Si}$ $\mathrm{NMR}$ experiments in $\mathrm{CePtSi}$ and ${\mathrm{CePtSi}}_{0.9}{\mathrm{Ge}}_{0.1}$, respectively. Triangles: $\delta K∕\overline{K}$ from ${}^{195}\mathrm{Pt}$ $\mathrm{NMR}$ experiments in ${\mathrm{CePtSi}}_{0.9}{\mathrm{Ge}}_{0.1}$.

Figure 12

Distributions $P\left(\chi \right)$ of the local susceptibilities estimated in $\mathrm{CePtSi}$ by (a) Kondo-disorder and (b) Griffiths phase models at various temperatures. The asymmetry and broadening in $P\left(\chi \right)$ are enhanced at low temperatures. The singularities at high-$\chi$ ends of $P\left(\chi \right)$ in (b) come from a Griffiths phase singularity $(\lambda <1)$ in Eq. (5) as the local energy $E\to 0$.

Figure 13

Comparisons of normalized experimental ${}^{29}\mathrm{Si}$ $\mathrm{NMR}$ spectra (circles) at $4.2\mathrm{K}$ in ${\mathrm{CePtSi}}_{0.9}{\mathrm{Ge}}_{0.1}$ with calculated spectra at various numbers $n_{\mathrm{eff}}$ of effective near neighbors. (a) Kondo-disorder model. (b) Griffiths phase model.

Figure 14

Comparisons of $\delta K∕\overline{K}$ obtained from (a) Kondo-disorder and (b) Griffiths phase models for various numbers $n_{\mathrm{eff}}$ of effective near neighbors in ${\mathrm{CePtSi}}_{0.9}{\mathrm{Ge}}_{0.1}$. Circles: experimental data.

Figure 15

Distributions of Kondo temperatures from Kondo-disorder model fits in $\mathrm{CePtSi}$ (solid curve) and ${\mathrm{CePtSi}}_{0.9}{\mathrm{Ge}}_{0.1}$ (dashed curve). The shaded area indicates the low-$T_K$ spins which are not quenched at low temperatures and give rise to $\mathrm{NFL}$ behavior.