${}^{31}$P NMR investigations on the ferromagnetic quantum critical system YbNi${}_4$P${}_2$

We studied the heavy-fermion system YbNi${}_4$P${}_2$, which presents strong ferromagnetic correlations, using the local ${}^{31}$P NMR probe over a wide field (0.2–8.6 T) and temperature (1.8–200 K) range. The ${}^{31}$P NMR Knight shift provides the static spin susceptibility which tracks the bulk susceptibility whereas the spin-lattice relaxation rate ${}^{31}(1/T_1$) provides information about the fluctuations of the Yb $4f$ moment. The Korringa law is valid over a wide range of temperature and field. The Korringa product ${}^{31}(1/T_{1}T{K}^2{S}_0)\ll 1$ gives evidence for the presence of strong ferromagnetic correlations. A ${}^{31}(1/T_{1}T)\sim T^{-3/4}$ behavior was found over two decades in temperature.

Figure 1

(a) ${}^{31}$P field-sweep NMR spectra at 147 MHz at different temperatures (* marks the maximum position used for the shift calculation whereas $\#$ marks the nonmagnetic impurity Ni${}_3$P). (b) Comparison of the ${}^{31}$P field-sweep NMR and FT-NMR spectra taken at 4.2 K and 6 MHz. (c) ${}^{31}$P FT-NMR spectra at different temperatures at 6 MHz corresponding to the field 0.351 T.

Figure 2

${}^{31}K(\%)$ as a function of temperature for YbNi${}_4$P${}_2$ at different frequencies (fields), as indicated. The field values are calculated from a NMR resonance frequency using ${}^{31}\gamma /2\pi =17.10$ MHz/T. The inset shows the temperature vs susceptibility plot at different fields, as indicated. The fields are chosen similar to the NMR fields.

Figure 3

${}^{31}$($1/\sqrt{T_{1}T}$) as a function of ${}^{31}K(\%)$ at different fields, as indicated. The dotted line indicates the linear ${}^{31}K\left(T\right)$ dependence. At high ${}^{31}$K values (low temperatures) the experimental data show an upward turn for low fields due to critical fluctuations, and a downward turn for high fields due to a field polarized state. The inset shows the $T$ dependence of the Korringa product $\alpha ={}^{31}(1/T_{1}T{K}^2{S}_0)$ (see text).

Figure 4

${}^{31}$($1/T{T}_1$) vs $T$ plot at different fields, as indicated. The blue circles represent the ${}^{29}$Si NMR data for YbRh${}_2$Si${}_2$ at 2.42 T (Ref. 18) after multiplying by ${\left(A_{\mathrm{hf}}^2{\gamma }^2\right)}_{\mathrm{P}}/{\left(A_{\mathrm{hf}}^2{\gamma }^2\right)}_{\mathrm{Si}}$. The inset shows the ${}^{31}$($1/T_1$) as a function of temperature at different fields, as indicated.