Paramagnetic rare-earth oxide $\mathrm{Nd}{}_2\mathrm{O}{}_3$ investigated by muon spin spectroscopy

In the context of a systematic study of oxide materials with the muon spin spectroscopy ($\mu \mathrm{SR}$) technique, we report here on an investigation of paramagnetic ${\mathrm{Nd}}_2{\mathrm{O}}_3$. The question was whether the magnetism of ${\mathrm{Nd}}^{3+}$ has an influence on the observed signals. In ${\mathrm{Nd}}_2{\mathrm{O}}_3$, as in the other oxides, a weakly paramagnetic component is observed besides the pure diamagnetic fraction. The paramagnetic part is assigned to a transient state formed between the initial atomic and the final bound muonium configuration. In addition, a fast relaxing signal ($\lambda \sim 7\mu {\mathrm{s}}^{-1}$) with 10% to 20% fraction is seen in longitudinal field. Contrary to this general behavior of the oxide materials, in the present magnetic compound, a resonancelike structure is seen in the temperature range around 40 K. We assign it tentatively to a dynamical process related to the population of the first excited Kramers doublet of the ${\mathrm{Nd}}^{3+}$ ion at 2.6 meV.

Figure 1

Temperature dependence of the inverse magnetic volume susceptibility (in the SI system) of ${\mathrm{Nd}}_2{\mathrm{O}}_3$, for an external applied magnetic field $B_{\mathrm{ap}}=10$ mT. The inset shows the well-known lifting of the degeneracy of the tenfold ${}^4{I}_{9/2}$ ground state of the ${\mathrm{Nd}}^{3+}$ paramagnetic ion due to the effect of the crystal field.

Figure 2

Transverse field time spectrum at $T=100$ K and $B=10$ mT. Two relaxations can be distinguished: Slow $\left[0.05\left(1\right)\mu {\mathrm{s}}^{-1}\right]$ and moderate $\left[0.38\left(3\right)\mu {\mathrm{s}}^{-1}\right]$. The total asymmetry is shown in the upper panel, together with the fitted slow relaxing component (red line). The lower panel displays the data after subtracting the slow component (red line in the upper panel), together with the fitted moderately relaxing component (red line in the lower panel).

Figure 3

Longitudinal field time spectrum at $T=300$ K and $B=0.5$ mT. The long-time behavior is fitted with a weakly relaxing function (red solid line) to allow an extrapolation to early times. The inset shows the first 2 $\mu \mathrm{s}$ of the spectrum.

Figure 4

Diamagneticlike component at a transverse magnetic field of $B=10$ mT: Fraction, relaxation ($\lambda$), frequency, and phase from one-component analysis. The red lines mark the overall behavior of the parameters without the resonancelike feature at about 40 K.

Figure 5

Temperature dependence of the fractions $f_{\text{dia}}$, $f_{\text{para}}$, and $f_{\text{tot}}=f_{\text{dia}}+f_{\text{para}}$, highlighting the conversion of the paramagnetic to diamagnetic fraction in the temperature region around 150 to 250 K. The fractions are shown in the upper frame and the relaxation rate of the moderately relaxing signal is shown in the lower frame. The relaxation of this component is caused by a distribution of internal fields $\left({\lambda }_0={\lambda }_{\mathrm{e}}+{\lambda }_{\mathrm{n}}\right)$ and the contribution $1/\tau$ from lifetime broadening. The fit curves correspond to an activation energy of 0.14(2) eV.