Avoided ferromagnetic quantum critical point in CeRuPO

CeRuPO is a rare example of a ferromagnetic (FM) Kondo-lattice system. External pressure suppresses the ordering temperature to zero at about $p_c\approx 3$ GPa. Our ac-susceptibility and electrical-resistivity investigations evidence that the type of magnetic ordering changes from FM to antiferromagnetic (AFM) at about $p^{*}\approx 0.87\text{GPa}$. Studies in applied magnetic fields suggest that ferromagnetic and antiferromagnetic correlations compete for the ground state at $p>p^{*}$, but finally the AFM correlations win. The change in the magnetic ground-state properties is closely related to the pressure evolution of the crystalline-electric-field level scheme and the magnetic Ruderman-Kittel-Kasuya-Yosida exchange interaction. The Néel temperature disappears abruptly in a first-order-like fashion at $p_c$, hinting at the absence of a quantum critical point. This is consistent with the low-temperature transport properties exhibiting Landau–Fermi-liquid behavior in the whole investigated pressure range up to 7.5 GPa.

Figure 1

Temperature dependence of the ac susceptibility $\chi {{}^{\prime }}_{ac}$ of CeRuPO at various pressures. The transition temperatures, $T_C$ and $T_N$, are indicated by arrows. The origin of the anomaly at $T_X$ is not clear (see text for details). For clarity, the $\chi {{}^{\prime }}_{ac}\left(T\right)$ curves for $1.31\le p\le 2.04\mathrm{GPa}$ are enlarged in the inset.

Figure 2

Temperature dependence of the (a) real and (b) imaginary parts of the ac susceptibility of CeRuPO at $p=0.71\mathrm{GPa}$ at different modulation fields $B_{ac}$. The evolution of the position of the peak in $\chi {{}^{\prime \prime }}_{ac}\left(T\right)$ with $B_{ac}$ is displayed in the inset of (b) for various pressures.

Figure 3

Temperature dependence of the real component of the ac susceptibility of CeRuPO at $p=1.01\mathrm{GPa}$ as a function of the ac field. The arrows mark the AFM ordering temperature $T_N$ and the anomaly at $T_X$.

Figure 4

Temperature-pressure phase diagram of CeRuPO. In addition to the results from our ac-susceptibility measurements, data from resistivity experiments in a piston-cylinder-type cell (open symbols, Ref. [13]) and a Bridgman-type pressure cell (closed symbols, this work) have been included. The magnetic-ordering temperatures, $T_C$ and $T_N$, are indicated by circles and squares, respectively. The anomaly observed in ${\chi }_{ac}$ measurements at $T_X$ is indicated by $+$. The dashed lines at $p^{*}$ and $p_c$ mark a change in the ground state of the system from FM to AFM and AFM to PM, respectively. The lines are guides to the eye.

Figure 5

Temperature dependence of the real component of the susceptibility $\chi {{}^{\prime }}_{ac}$ of CeRuPO at $p=0.71\mathrm{GPa}$ at different applied magnetic fields $\left(B\parallel c\right)$. At $B=0$, the ordering temperature $T_C$ is marked by an arrow. For $B>0,\chi {{}^{\prime }}_{ac}\left(T\right)$ passes through a maximum which is denoted by $T_m$. Inset: $T_m$ vs magnetic field.

Figure 6

Temperature dependence of the real part of the magnetic susceptibility of CeRuPO at $p=1.77\mathrm{GPa}$ at different magnetic fields $\left(B\parallel c\right)$ in the antiferromagnetic region of the $T-p$ phase diagram. The arrows mark the AFM phase transition at $T_N$, and the crossover temperatures $T_m$ and $T_X$. Inset: The $T-B$ phase diagram for different pressures, all (except 0.87 GPa) in the antiferromagnetic regime.

Figure 7

Temperature dependence of the real part of the magnetic susceptibility of CeRuPO at $p=2.54\mathrm{GPa}$ at different magnetic fields, $B\parallel c$. Due to the low accuracy of the data, we only trace the magnetic field dependencies of the anomalies at $T_N$ and $T_m$ by the dash-dotted lines.

Figure 8

Temperature dependence of the (a) real and (b) imaginary parts of ${\chi }_{ac}\left(T\right)$ of CeRuPO in $B=1\text{T}$ $\left(B\parallel c\right)$ at different $p$. The arrows mark the ordering/crossover temperatures as indicated. For clarity, in both figures the data are shifted on the vertical axis.

Figure 9

Magnetic $T-p$ phase diagram of CeRuPO compiled from ac-susceptibility data at different magnetic fields. The FM and AFM ground states at $B=0$ are indicated. $p^{*}$ marks the pressure where the type of magnetic ordering changes.

Figure 10

(a) Temperature dependence of the electrical resistivity of CeRuPO at various pressures. The dashed and solid lines are the fits to the data according to FM and AFM models corresponding to Eqs. (A2) and (A5), respectively. Pressure dependencies of the parameters extracted from these fits, the magnon excitation gap $\Delta$ [(b), left axis], and for the AFM regime of the phase diagram the parameter $d$ [(b), right axis]. The closed and open symbols indicate the results obtained by employing a piston-cylinder-type and a Bridgman-type pressure cell, respectively. (c) Temperature dependence of the electrical resistivity, $\rho \left(T^2\right)$, of CeRuPO in the PM regime at two selected pressures as indicated. The solid lines are fits to the data according to the LFL theory. The arrows mark $T_{\mathrm{LFL}}$, the upper temperature limit of the $T^2$ dependence of the resistivity.

Figure 11

Pressure dependencies of the parameters ${\rho }_0,A$, and $T_{\mathrm{LFL}}$. The data in the FM and AFM states are obtained from fits of the $\rho \left(T\right)$ data by Eqs. (A2) and (A5), respectively. The results in the PM regime correspond to fits of the low-temperature resistivity by $\rho \left(T\right)={\rho }_0+A{T}^2$. The vertical dotted lines mark the estimated pressure for the change from the FM to the AFM ground state and the critical pressure where the magnetic order is suppressed to zero temperature $p^{*}$ and $p_c$, respectively. The dashed lines are guides to the eye.

Figure 12

(a) Low-temperature electrical resistivity of CeRuPO at $p=4.6\mathrm{GPa}$ plotted against $T^2$ for different magnetic fields. For clarity, the data taken in 4 T have been shifted by 0.2 $\mu \Omega \mathrm{cm}$. The dashed lines describe $\Delta \rho \left(T\right)\propto T^2$. The magnetic field dependence of the parameters (b) ${\rho }_0$ and (c) $A$ obtained from fitting $\rho \left(T\right)$ with $\rho \left(T\right)={\rho }_0+A{T}^2$. (d) Evolution of the upper temperature limit, $T_{\mathrm{LFL}}$, of the $T^2$ dependence of $\rho \left(T\right)$ with magnetic field. The dashed lines are guides to the eye.