${\mathrm{Y}\mathrm{b}\mathrm{R}\mathrm{h}}_2{\mathrm{S}\mathrm{i}}_2$: Spin Fluctuations in the Vicinity of a Quantum Critical Point at Low Magnetic Field

We report a ${}^{\mathrm{29}}\mathrm{S}\mathrm{i}$ NMR study on aligned single crystals of ${\mathrm{Y}\mathrm{b}\mathrm{R}\mathrm{h}}_2{\mathrm{S}\mathrm{i}}_2$ which shows behavior characteristic of a quantum critical point (QCP: $T_{\mathrm{N}}\to 0$). The Knight shift $K$ and the nuclear spin-lattice relaxation rate $1/T_1$ of Si show a strong dependence on the external field $H$, especially below 5 kOe. At the lowest $H$ used in this measurement ($H\sim 1.5\mathrm{k}\mathrm{O}\mathrm{e}$), it was found that $1/T_{1}T$ continues to increase down to 50 mK, whereas $K$ stays constant with a large magnitude below 200 mK. This result strongly suggests the development of antiferromagnetic fluctuations with finite $\mathit{q}$ vectors that compete with $\mathit{q}=0$ spin fluctuations in the vicinity of the QCP near $H=0.5\mathrm{k}\mathrm{O}\mathrm{e}$.

Figure 1

$T$ dependence of ${}^{\mathrm{29}}\mathrm{S}\mathrm{i}$ Knight shift (${}^{29}K$) under 24.2 kOe above 10 K, under 10.0 kOe below 20 K. The inset shows the dependence of ${}^{29}K$ on the susceptibility along the $a$ axis at 10 kOe.

Figure 2

$T$ dependence of the ${}^{\mathrm{29}}\mathrm{S}\mathrm{i}$ Knight shift (${}^{29}K$) at various $H$. Arrows indicate the temperature $T_{\mathrm{F}\mathrm{L}}$ below which ${}^{29}K$ saturates. The inset shows the $-{}^{29}K$ (%) vs $T$ in a log-log plot. Below 20 K, the $T$ dependence of ${}^{29}K$ obeys approximately the $T^{-1/2}$ relation.

Figure 3

$T$ dependence of $1/T_{1}T$ of ${}^{\mathrm{29}}\mathrm{S}\mathrm{i}$ $\mathbf{(}{}^{29}(1/T_{1}T)\mathbf{)}$ due to the ${\mathrm{Y}\mathrm{b}}^{3+}$ fluctutions at various $H$ in a log-log plot. $1/T_{1}T$ is plotted in a linear scale in the inset. Arrows show $T_{\mathrm{F}\mathrm{L}}$ in ${}^{29}(1/T_{1}T)$, below which ${}^{29}(1/T_{1}T)$ saturates.

Figure 4

(a) Field dependence of $-{}^{29}K$, ${}^{29}(1/T_{1}T{)}^{1/2}$, and of the $\gamma$ coeffecient in the specific heat at 100 mK, where the respective vertical scales are normalized arbitrarily. The dashed line is an eye guide for the increase of $K$ on $H$. The inset shows the plot of $-{}^{29}K$ vs ${}^{29}(1/T_{1}T{)}^{1/2}$. (b) Field dependence of $T_{\mathrm{F}\mathrm{L}}$ in $K$, $1/T_{1}T$, and $\gamma$. $T_{\mathrm{F}\mathrm{L}}$ is the characteristic $T$ of the LFL state, below which the respective quantities become $T$ independent. The region denoted by slanted lines is that where AFM fluctuations with finite wave vectors $\mathit{q}\mathbf{(}\chi (\mathit{q})\mathbf{)}$ continue to grow although $K\mathbf{[}\chi (0)\mathbf{]}$ remains constant. The $H$ dependence of the AFM ordering $T$ as determined from $ac$ susceptibility measurements is also presented (closed squares).