Pr magnetism and its interplay with the Fe spin-density wave in PrFeAsO${}_{1-x}$F${}_x$ ($x=0$,0.15)

We have studied the magnetism of the Pr${}^{3+}$ ions in PrFeAsO${}_{1-x}$F${}_x$ ($x=0,0.15$) and its interaction with the Fe magnetic order (for $x=0$). Specific-heat data confirm the presence of a first excited crystal electric-field (CEF) level around 3.5 meV in the undoped compound PrFeAsO. This finding is in agreement with recent neutron-scattering experiments. The doped compound is found to have a much lower first CEF splitting of about 2.0 meV. The Pr ordering in PrFeAsO gives rise to large anomalies in the specific heat and the thermal-expansion coefficient. In addition, a field-induced transition is found at low temperatures that is most pronounced for the magnetostriction coefficient. This transition, which is absent in the doped compound, is attributed to a reversal of the Fe spin canting as the antiferromagnetic Pr order is destroyed by the external magnetic field.

Figure 1

(a) Specific heat $c_p$ divided by temperature $T$ for PrFeAsO${}_{1-x}$F${}_x$ ($x=0,0.15$) in zero magnetic field and 9 T. For $x=0$ a clear anomaly with a maximum at 11.3 K is observed in zero field originating from the magnetic ordering of the Pr${}^{3+}$ ions at $T_{\mathrm{N}}^{\mathrm{Pr}}$. The specific heat of LaFeAsO${}_{0.9}$F${}_{0.1}$ used as a phonon background is also shown for comparison. (b) Behavior of the anomaly at $T_{\mathrm{N}}^{\mathrm{Pr}}$ of PrFeAsO in magnetic field. (c) The superconducting transition of the sample with $x=0.15$ gives rise to a small anomaly seen in $\Delta c_p/T=c_p\left(0\right)/T-c_p\left(9\mathrm{T}\right)/T$.

Figure 2

Estimate of the magnetic contribution to the specific heat of PrFeAsO${}_{1-x}$F${}_x$ ($x=0,0.15$) calculated by subtracting the data of LaFeAsO${}_{0.9}$F${}_{0.1}$. The solid lines are the results of a fit to a Schottky contribution from CEF splitting for $x=0.15$. Above $T_{\mathrm{c}}$ an additional charge carrier contribution $\Delta \gamma =25.2$ mJ/mol K${}^2$ is taken into account, which leads to a shift of the line. The dotted line is the calculated Schottky contribution for a ground-state singlet and an excited doublet at 41 K. The agreement with the data for $x=0$ is much improved by adding a second doublet at 160 K (dashed line). Inset: estimated contribution to $c_{\mathrm{mag}}$ of $x=0.15$ from sites with one or more fluorine neighbors in a model with different CEF schemes for differing environments[16] as explained in the text. The dotted line is the calculated contribution expected for two singlet states at 0 and 23 K for 37$\%$ of the Pr sites.

Figure 3

Temperature dependence of the linear thermal-expansion coefficient $\alpha \left(T\right)$ of PrFeAsO${}_{1-x}$F${}_x$ ($x=0,0.15$) in magnetic fields of 0 and 9 T. Clear anomalies are seen in the zero-field thermal-expansion curve for $x=0$ at the structural and SDW transitions and at the magnetic ordering temperature of the Pr${}^{3+}$ ions. These are absent for the doped compound. Application of a magnetic field leads to a strong change of $\alpha \left(T\right)$ for PrFeAsO below 70 K. By contrast, there is almost no effect on $\alpha \left(T\right)$ for the doped compound. Inset: low-$T$ part on a larger scale.

Figure 4

Magnetostriction coefficient $\beta$ vs magnetic field $B$ of PrFeAsO at different temperatures up to 100 K (full symbols). For $T=5$, 7.5, and 10 K kinks marked by arrows are observed at 5.8, 5.4, and 3.7 T, respectively. At higher $T$ the transition disappears. For comparison, data for PrFeAsO${}_{0.85}$F${}_{0.15}$ measured at 5 K are shown (open symbols). At higher temperature, $\beta$ is even smaller for this compound.

Figure 5

Inset: example for the field dependence of the magnetization $M\left(B\right)$ of PrFeAsO at 10 K. $M\left(B\right)$ exhibits an almost linear behavior with small deviations above approximately 4 T, as illustrated by the dashed line. They are better seen as a step in $dM/dB$ shown in the main plot for different temperatures. The solid lines for 1.8, 7.5, and 10 K are fits to an empiric formula as explained in the text. The lines for 12.5 and 15 K are guides to the eye. For clarity, not all investigated temperatures are shown.

Figure 6

The magnetic phase diagram of PrFeAsO, which was obtained from the magnetostriction (green triangles) and the magnetization (black squares) data. The error bars for the magnetization results have been determined from the width of the transition in $dM/dB$ as explained in the text. The red crosses indicate the positions of the maxima in $c_p/T$, while the blue triangle corresponds to the maximum in the thermal expansion coefficient. The adjacent dotted lines mark the potential range for the phase transitions. The zero-field ranges for $c_p/T$ and $\alpha$ are almost identical and therefore hard to distinguish in the plot. The dashed line is a guide to the eye, whereas the shaded area marks the region of Pr AFM order at low $T$ and $B$.