Inelastic neutron scattering study of crystal field levels in $\mathrm{Pr}{\mathrm{Os}}_4{\mathrm{As}}_{12}$

We use neutron scattering to study the ${\mathrm{Pr}}^{3+}$ crystalline electric field (CEF) excitations in the filled skutterudite $\mathrm{Pr}{\mathrm{Os}}_4{\mathrm{As}}_{12}$. By comparing the observed levels and their strengths under neutron excitation with the theoretical spectrum and neutron excitation intensities, we identify the ${\mathrm{Pr}}^{3+}$ CEF levels and show that the ground state is a magnetic ${\Gamma }_4^{\left(2\right)}$ triplet, and the excited states ${\Gamma }_1$, ${\Gamma }_4^{\left(1\right)}$, and ${\Gamma }_{23}$ are at 0.4, 13, and $23\mathrm{meV}$, respectively. A comparison of the observed CEF levels in $\mathrm{Pr}{\mathrm{Os}}_4{\mathrm{As}}_{12}$ with the heavy fermion superconductor $\mathrm{Pr}{\mathrm{Os}}_4{\mathrm{Sb}}_{12}$ reveals the microscopic origin of the differences in the ground states of these two filled skutterudites.

Figure 1

(Color online) (a) The cube of eight Os ions surrounding the central ${\mathrm{Pr}}^{3+}$ ion in $\mathrm{Pr}{\mathrm{Os}}_4{\mathrm{As}}_{12}$. These give an $O_h$-symmetric CEF. (b) The corresponding spectrum of $O_h$-symmetry ${\mathrm{Pr}}^{3+}$ CEF levels. (black: singlet; blue (dark gray): doublet; red (light gray): triplet). The relative coupling $x$ that gives singlet-triplet degeneracy is shown by the dashed vertical. (c) The 12 nearest neighbor As ions surrounding the central ${\mathrm{Pr}}^{3+}$ in $\mathrm{Pr}{\mathrm{Os}}_4{\mathrm{As}}_{12}$, giving a reduced symmetry $\left(T_h\right)$ CEF. (d) The corresponding As-only $T_h$-symmetry ${\mathrm{Pr}}^{3+}$ CEF spectrum in $\mathrm{Pr}{\mathrm{Os}}_4{\mathrm{As}}_{12}$. Here, $W$ and $x$ are the same as defined by Ref. 25.

Figure 2

(Color online) (a) Neutron inelastic scattering at $T=1.5\mathrm{K}$ (black circles) and $T=200\mathrm{K}$ (blue/gray circles) with $E_i=32\mathrm{meV}$, integrated over scattering angles from 9° to 30° (low-angle detectors) and from 105° to 140° (high-angle detectors). (b) The same at $E_i=12\mathrm{meV}$; (c) $E_i=50\mathrm{meV}$. The scattering function $S(Q,\omega )$ was normalized by comparison to a vanadium standard.

Figure 3

(Color online) (a) Low energy spectrum of CEF excitations observed at $T=0.32$, 2.5, and $6.0\mathrm{K}$ using the SPINS spectrometer at NCNR. (b) The wave vector dependence of the excitations at $Q=(0.8,0,0)$, $Q=(1.2,0,0)$, and $Q=(1.7,0,0)$. (c) The expected and observed temperature dependences of the intensity of the $0.4\mathrm{meV}$ mode. (d) The temperature difference spectrum between 0.08 and $4\mathrm{K}$, showing clear reduction in magnetic elastic scattering.

Figure 4

(Color online) The temperature dependence of the excitations observed on HET with $E_i=32\mathrm{meV}$ at (a) $T=1.5$, $5\mathrm{K}$, (b) $50\mathrm{K}$, (c) $100\mathrm{K}$, and (d) $200\mathrm{K}$. The lines are theoretical results for neutron excitation intensities, from the combined Os-As CEF model, with an arbitrary overall scale factor.

Figure 5

(Color online) (a) The theoretical neutron transition intensity for As CEF alone with $b=0.4267$. (b) Neutron excitation intensities predicted by the combined Os-As CEF model.

Figure 6

(Color online) (a) The magnetic field dependence of the low-lying CEF excitations at $Q=(1.2,0,0)$ and $T=0.08\mathrm{K}$. The inset shows the field dependence of the first excited state. (b) The difference spectrum between 0 and $11\mathrm{T}$ at $Q=(1.2,0,0)$ and $T=0.08\mathrm{K}$. The effect of an applied field is to suppress intensity at $\hslash \omega =0\mathrm{meV}$ and to split the spin-triplet ground state; the latter results in the field dependence of the $0.4\mathrm{meV}$ peak in (a), which may involve an intratriplet transition. The elastic intensity suppression effect essentially disappears for fields above $4\mathrm{T}$. (c) The field-induced CEF excitation at $\approx 1.1\mathrm{meV}$ is weakly wave vector dependent and shows essentially no temperature dependence between $T=0.08$ and $4\mathrm{K}$.

Figure 7

(Color online) The boundary between singlet and triplet ground states in skutterudites $(E_1=E_4^{\left(2\right)})$ as a function of $r_6$ and $g_4∕g_6$ and the observed $\mathrm{Pr}{\mathrm{Os}}_4{\mathrm{As}}_{12}$ spectrum.