Crystalline electric field effects in ${\text{PrNi}}_2{\text{B}}_2\text{C}$: Inelastic neutron scattering

${\text{PrNi}}_2{\text{B}}_2\text{C}$ as a member of the borocarbide series is characterized by antiferromagnetic order below $T_N=4\text{K}$ and the absence of superconductivity (at least down to 100 mK). There are two effects responsible for the absence of superconductivity in ${\text{PrNi}}_2{\text{B}}_2\text{C}$. These are the strong conduction electron–Pr moment interaction and a comparatively lower density of states. We studied the crystalline electric field (CEF) excitations and excitons in this compound by inelastic neutron scattering. The CEF level scheme obtained from these data comprises a singlet ground state, a doublet at 1 meV, and further higher levels at 5.2, 24.3 (doublet), 25.1, 29.4, and 31.5 meV. Large dispersion was found for the 1 meV excitation and explained theoretically taking into account magnetic exchange interactions. The calculated crystal-field parameters explain satisfactorily the neutron spectra as well as the heat-capacity and magnetic-susceptibility data. This leads to the conclusion that ${\text{PrNi}}_2{\text{B}}_2\text{C}$ can be described by the standard model of rare-earth magnetism. Thus the heavy-fermion concept, suggested by some groups earlier in literature, is not the cause of the suppression of superconductivity. Excitation spectra of the diluted series ${\text{Pr}}_{1-x}{\text{Y}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$ were also investigated. No drastic changes in the CEF level scheme have been observed in these compounds. Hence the CEF level scheme of the full compound, i.e., ${\text{PrNi}}_2{\text{B}}_2\text{C}$, is reasonably valid for these samples too. The superconducting-transition temperature $T_C\sim 15.5\text{K}$ for ${\text{YNi}}_2{\text{B}}_2\text{C}$ decreases linearly with decreasing Y concentration $x$. Samples with $x\le 0.65$ do not exhibit superconductivity down to 2 K.

Figure 1

(Color online) Variation in the lattice parameters of ${\text{Pr}}_{1-x}{\text{Y}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$. The lines are guides for the eyes.

Figure 2

(Color online) ac-susceptibility measurements on ${\text{Pr}}_{1-x}{\text{Y}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$. Samples with $x\le 0.65$ do not show superconductivity down to 2 K. The inset shows $T_C$ as a function of the concentration $x$.

Figure 3

(Color online) Inelastic-neutron-scattering spectra of ${\text{PrNi}}_2{\text{B}}_2\text{C}$ measured at SV29 with $E_i=56\text{eV}$ for different temperatures. Each spectrum has been shifted vertically for clarity. $⟨Q⟩$ represents averaging for $Q=\left(2.70\pm 0.49\right){\text{Å}}^{-1}$. The thick lines indicate the results of CEF calculations for 2, 10, and 50 K with an added elastic line (linewidth from vanadium measurement) and a straight-line background on the positive-energy-transfer side.

Figure 4

(Color online) Inelastic-neutron-scattering spectra of ${\text{PrNi}}_2{\text{B}}_2\text{C}$ measured at SV29 with $E_i=25\text{meV}$ for different temperatures. Each spectrum has been shifted vertically for clarity. $⟨Q⟩$ represents averaging for $Q=\left(1.73\pm 0.31\right){\text{Å}}^{-1}$. The thick lines indicate the results of CEF calculations for 2, 10, and 50 K with an added elastic line (linewidth from vanadium measurement) and a small exponentially increasing background on the positive-energy-transfer side to model the intensity observed at $T=2\text{K}$.

Figure 5

(Color online) Inelastic-neutron-scattering spectra of ${\text{PrNi}}_2{\text{B}}_2\text{C}$ measured at IN6 with $E_i=3.15\text{meV}$ for different temperatures. The neutron-energy-gain spectra have been modified according to the detailed-balance condition. Each spectrum has been shifted vertically for clarity. $⟨Q⟩$ represents averaging for $Q=\left(1.5\pm 0.1\right){\text{Å}}^{-1}$. The thick lines indicate the results of CEF calculations for 10, 50, and 150 K. The inset shows the presence of the magnetic (001) Bragg peak indicating the antiferromagnetic ordering at 2 K $\left(T_N\sim 4\text{K}\right)$.

Figure 6

(Color online) Inelastic-neutron-scattering spectra of ${\text{PrNi}}_2{\text{B}}_2\text{C}$ measured at IN6 at 2 K (top left) and 10 K (top right): a color-coded map of the neutron intensity vs energy and momentum transfer. For comparison, the figures at bottom left and bottom right show the results of the model calculation (for details see text).

Figure 7

(Color online) Inelastic-neutron-scattering spectra of ${\text{Pr}}_{0.9}{\text{Y}}_{0.1}{\text{Ni}}_2{\text{B}}_2\text{C}$ measured at IN6 with $E_i=3.15\text{meV}$ for different temperatures. The neutron-energy-gain spectra have been modified according to the detailed-balance condition. Each spectrum has been shifted vertically for clarity. $⟨Q⟩$ represents averaging for $Q=\left(1.5\pm 0.1\right){\text{Å}}^{-1}$. The inset shows the presence of the magnetic (001) Bragg peak indicating antiferromagnetic ordering at 2 K.

Figure 8

(Color online) Inelastic-neutron-scattering spectra of ${\text{Pr}}_{1-x}{\text{Y}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$ for $x=0$, 0.1, 0.8, 0.95, and 1 measured at IN6 with $E_i=3.15\text{meV}$ at 150 K. The neutron-energy-gain spectra have been modified according to the detailed-balance condition. Each spectrum has been shifted vertically for clarity. $⟨Q⟩$ represents averaging for $Q=\left(1.5\pm 0.1\right){\text{Å}}^{-1}$. All spectra were scaled to Pr concentration, except that of ${\text{YNi}}_2{\text{B}}_2\text{C}$, where the scaling factor is the same $\left(100/5=20\right)$ as that of ${\text{Pr}}_{0.05}{\text{Y}}_{0.95}{\text{Ni}}_2{\text{B}}_2\text{C}$.

Figure 9

(Color online) The magnetic contribution $\left(4f\right)$ to heat capacity ($\Delta C_p$ vs $T$) in ${\text{PrNi}}_2{\text{B}}_2\text{C}$ deduced by subtracting the heat-capacity data of ${\text{LaNi}}_2{\text{B}}_2\text{C}$ (Ref. 25). Corresponding magnetic-entropy gain for ${\text{PrNi}}_2{\text{B}}_2\text{C}$ has been plotted in the same figure (right-hand-side axis). The dotted line represents the calculated magnetic heat capacity as derived from the CEF level scheme in the paramagnetic range. The thin solid line indicates the results of a model with a modified crystal-field level scheme in order to take into account qualitatively the effect of exchange interaction (see text).

Figure 10

(Color online) Temperature dependence of the (scaled) intensity of the inelastic peak at 1 meV in ${\text{PrNi}}_2{\text{B}}_2\text{C}$ and ${\text{Pr}}_{0.9}{\text{Y}}_{0.1}{\text{Ni}}_2{\text{B}}_2\text{C}$ measured at IN6 (see Figs. 5, 7) and compared to the inverse of the partition function as deduced from heat-capacity data of ${\text{PrNi}}_2{\text{B}}_2\text{C}$ (solid line) and as calculated from the proposed CEF scheme (dotted line).

Figure 11

(Color online) CEF splitting and charge density at $T=10\text{K}$ for ${\text{Pr}}^{3+}$ in ${\text{PrNi}}_2{\text{B}}_2\text{C}$ as calculated from our CEF model (see text). For comparison the magnetic and crystal structure are shown.

Figure 12

(Color online) Inverse magnetic susceptibility of ${\text{PrNi}}_2{\text{B}}_2\text{C}$ along and perpendicular to the (110) plane (from Ref. 30). The solid lines represent susceptibility calculated from our proposed CEF model (see text).