Effects of pressure and magnetic field on the reentrant superconductor Eu(${\mathrm{Fe}}_{0.93}{\mathrm{Rh}}_{0.07}{)}_2{\mathrm{As}}_2$

Electron-doped $\mathrm{Eu}{\left({\mathrm{Fe}}_{0.93}{\mathrm{Rh}}_{0.07}\right)}_2{\mathrm{As}}_2$ has been systematically studied by high-pressure investigations of the magnetic and electrical transport properties in order to unravel the complex interplay of superconductivity and magnetism. The compound reveals an exceedingly broad reentrant transition to the superconducting state between $T_{\mathrm{c},\mathrm{on}}=19.8$ K and $T_{\mathrm{c},0}=5.2$ K due to a canted A-type antiferromagnetic ordering of the ${\mathrm{Eu}}^{2+}$ moments at $T_{\mathrm{N}}=16.6$ K and a reentrant spin glass transition at $T_{\mathrm{SG}}=14.1$ K. At ambient pressure evidences for the coexistence of superconductivity and ferromagnetism could be observed, as well as a magnetic-field-induced enhancement of the zero-resistance temperature $T_{\mathrm{c},0}$ up to 7.2 K with small magnetic fields applied parallel to the $ab$ plane of the crystal. We attribute the field-induced-enhancement of superconductivity to the suppression of the ferromagnetic component of the ${\mathrm{Eu}}^{2+}$ moments along the $c$ axis, which leads to a reduction of the orbital-pair-breaking effect. Application of hydrostatic pressure suppresses the superconducting state around 14 kbar along with a linear temperature dependence of the resistivity, implying that a non-Fermi liquid region is located at the boundary of the superconducting phase. At intermediate pressure, an additional feature in the resistivity curves is identified, which can be suppressed by external magnetic fields and competes with the superconducting phase. We suggest that the effect of negative pressure by the chemical Rh substitution in $\mathrm{Eu}{\left({\mathrm{Fe}}_{0.93}{\mathrm{Rh}}_{0.07}\right)}_2{\mathrm{As}}_2$ is partially reversed, leading to a reactivation of the spin density wave.

Figure 1

(a) Technical drawing of the clamp piston pressure cell utilized for this study. The feed-through is equipped with six pairs of twisted wire pairs for the electrical measurements. (b) Microscope picture of the $\mathrm{Eu}{\left({\mathrm{Fe}}_{0.93}{\mathrm{Rh}}_{0.07}\right)}_2{\mathrm{As}}_2$ sample mounted on the kapton sample stage of the pressure cell feed-through. The magnetic field direction as well as the rotation axis for the angle dependent magneto transport measurements are marked in red, while the Manganin wire coil for the in situ pressure determination is indicated in white.

Figure 2

Temperature-dependent dc resistivity data of $\mathrm{Eu}{\left({\mathrm{Fe}}_{0.93}{\mathrm{Rh}}_{0.07}\right)}_2{\mathrm{As}}_2$ at ambient pressure. In the high-temperature regime (gray shaded area) above 100 K, the resistivity shows a linear behavior in $T$ (green dashed line), while the low-temperature region, above the superconducting transition, can be fitted by the power-law term $\rho \left(T\right)={\rho }_0+c·T^n$ (red dashed curve) with an exponent $n=2$.

Figure 3

Comparison between the low-temperature dc resistivity and magnetization data of $\mathrm{Eu}{\left({\mathrm{Fe}}_{0.93}{\mathrm{Rh}}_{0.07}\right)}_2{\mathrm{As}}_2$ recorded at ambient pressure. In (a) the dc resistivity with its clear reentrant superconducting behavior is shown, while (b) displays the thermal hysteresis of the resistivity occurring during the cooling-heating cycle. (c)–(f) illustrate the dc and ac magnetic susceptibility. The dashed lines are guides to the eye and mark the different transitions namely the onset of superconductivity ($T_{\mathrm{c},\mathrm{on}}=19.8$ K, dashed black line), the antiferromagnetic ordering of the ${\mathrm{Eu}}^{2+}$ moments ($T_{\mathrm{N}}=16,6$ K, dashed red line), the reentrant spin glass ($T_{\mathrm{SG}}=14,1$ K, dashed green line), and the approach of zero resistance ($T_{\mathrm{c},0}=5.4$ K, dashed blue line).

Figure 4

(a) In-plane dc magnetization data indicate that the spin glass state of $\mathrm{Eu}{\left({\mathrm{Fe}}_{0.93}{\mathrm{Rh}}_{0.07}\right)}_2{\mathrm{As}}_2$ (indicated by the green arrows) vanishes already in the presence of minor magnetic fields of around 250 G. Comparison of the magnetization (b) data with the evolution of the thermal hysteresis in $\rho$(T) (c) for different magnetic fields applied parallel to the $ab$ plane of the $\mathrm{Eu}{\left({\mathrm{Fe}}_{0.93}{\mathrm{Rh}}_{0.07}\right)}_2{\mathrm{As}}_2$ single crystal. The red dashed arrows are guides to the eye, which indicate the antiferromagnetic transition temperatures. The opening of the big hysteresis feature (labeled with “2” in Fig. 3) turns out to be connected with the antiferromagnetic ordering of the ${\mathrm{Eu}}^{2+}$ moments at $T_{\mathrm{N}}$ and can therefore identify a fast suppression of the antiferromagnetic state. The black and blue arrows indicate—exemplary for two different magnetic fields—$T_{\mathrm{c},\mathrm{on}}$ and $T_{\mathrm{c},0}$ as the opening and closing of the overall hysteresis.

Figure 5

Temperature-dependent out-of-plane ($H\parallel c$) magnetization of $\mathrm{Eu}{\left({\mathrm{Fe}}_{0.93}{\mathrm{Rh}}_{0.07}\right)}_2{\mathrm{As}}_2$ measured in ZFC-FCC-FCH cycles from 2–25 K at applied magnetic fields up to 20 kG. The missing kink from the magnetic ordering transition and the absence of a splitting in the ZFC-FCH data reveals a suppression of $T_{\mathrm{N}}$ between 7.5 kG and 10 kG down to the lowest measured temperature of 2 K.

Figure 6

Magnetic field dependence of the low-temperature phases of $\mathrm{Eu}{\left({\mathrm{Fe}}_{0.93}{\mathrm{Rh}}_{0.07}\right)}_2{\mathrm{As}}_2$. In-plane resistivity data from $T=2$ K to 30 K; when measured with applied magnetic field in- and out-of plane show a clear anisotropic behavior. The in-plane magnetic field (a) leads to a suppression of the magnetic phases (red arrow) and additionally to an enhanced superconductivity at low fields (blue arrow, inset). An applied out-of-plane field (b) directly suppresses the superconductivity (blue arrow) while the magnetic transition temperatures at low fields stays nearly constant below 4 kG (red arrow).

Figure 7

Isothermal magnetization measurements on $\mathrm{Eu}{\left({\mathrm{Fe}}_{0.93}{\mathrm{Rh}}_{0.07}\right)}_2{\mathrm{As}}_2$ at $T=1.8$ K for in- and out-of-plane applied external magnetic fields. (a) Hysteresis loop of the magnetization for $H\parallel c$ were $M_{\mathrm{init}}$ was measured after zero-field cooling. The green dashed line indicates the ideal initial magnetization $M_{\mathrm{SC}}$ in absence of internal magnetic fields. (b) Magnetization hysteresis loop after subtraction of $M_{\mathrm{SC}}$, indicating a ferromagnetic behavior of $\mathrm{Eu}{\left({\mathrm{Fe}}_{0.93}{\mathrm{Rh}}_{0.07}\right)}_2{\mathrm{As}}_2$ along the $c$ axis inside the superconducting phase. (c) Isothermal magnetization at high fields point out a saturation field of approximately 10 kG for $H\parallel c$ and 4 kG for $H\parallel ab$.

Figure 8

Magnetic-field-dependent phase diagrams of $\mathrm{Eu}{\left({\mathrm{Fe}}_{0.93}{\mathrm{Rh}}_{0.07}\right)}_2{\mathrm{As}}_2$ generated by the resistivity and magnetization measurements for the external magnetic field (a) $H\parallel ab$ and $H\parallel c$. The anisotropy becomes clearly visible especially in the low field region, where in-plane fields (top panel) lead to an enhancement of $T_{\mathrm{c},0}$ in combination with a fast suppression of the magnetic ordering phenomena of the ${\mathrm{Eu}}^{2+}$ moments.

Figure 9

Pressure-dependent resistivity measurements of $\mathrm{Eu}{\left({\mathrm{Fe}}_{0.93}{\mathrm{Rh}}_{0.07}\right)}_2{\mathrm{As}}_2$ up to 18 kbar. (a) shows the resistivity data at all measured pressures in a temperature range from 2 K up to 140 K, normalized to their 140 K value. An additional feature is appearing in the $\rho \left(T\right)$ curve (black arrows) at low pressures, leading to an enhancement of $T_{\mathrm{c},0}$ in an intermediate pressure range. At pressures above 16 kbar, the superconducting transition gets completely suppressed and a linear $T$ dependency can be seen (black dashed line). (b) depicts the result of the power-law fitting $\rho \left(T\right)={\rho }_0+c{T}^n$, indicating non-Fermi-liquid-like behavior at the edge of the superconducting dome. (c) Zoom-in to the temperature range of the ${\mathrm{Eu}}^{2+}$ ordering, revealing a clear increase of the antiferromagnetic transition temperature with increasing pressure. (For clarity the curves are shifted with respect to each other.)

Figure 10

Pressure-dependent resistivity measurements of $\mathrm{Eu}{\left({\mathrm{Fe}}_{0.93}{\mathrm{Rh}}_{0.07}\right)}_2{\mathrm{As}}_2$ in the intermediate pressure range. (a) Normalized resistivity plotted in comparison to the ambient pressure resistivity (black curves) to illustrate the appearance of the additional feature above the superconducting phase. (b) Differences of the pressurized resistivity to the ambient pressure data. The orange arrows indicate the temperatures $T_{\mathrm{F}}$ where the system shows the strongest deviation from the 0 kbar data. (c) Low-temperature data before, during, and after the appearance of the resistivity feature; showing a clear broadening in the presence of the feature whereas a sharp transition recovers at higher pressures restoring $T_{c,0}$.

Figure 11

Pressure-dependent phase diagram of $\mathrm{Eu}{\left({\mathrm{Fe}}_{0.93}{\mathrm{Rh}}_{0.07}\right)}_2{\mathrm{As}}_2$ generated from the resistivity measurements depicted in Fig. 9 (pressures are corrected to the pressure loss during the cooling process). The magnetic transition $T_{\mathrm{N}}$ (red squares) increases linearly with increasing pressure, while the superconducting phase (black triangles) gets completely suppressed with pressures around 14 kbar. The local maximum of the reentrant transition, which is probably caused by the SG state, is depicted in green and shows a bit faster increase with pressure than $T_{\mathrm{N}}$. The zero resistance point $T_{\mathrm{c},0}$ as well as $T_{0,1},T_1$, and $T_{10}$ (representing the temperatures were the resistivity drops below $0.1\mu \mathrm{\Omega }\mathrm{cm}, 1\mu \mathrm{\Omega }\mathrm{cm}$, and $10\mu \mathrm{\Omega }\mathrm{cm}$ respectively) are labeled with blue triangles, exhibit an anomaly in the intermediate-pressure range connected to the appearance of the feature at higher temperatures $T_{\mathrm{F}}$ (orange hexagons). Additionally the temperature range were a local minimum of $\rho \left(T\right)$ appears above the superconducting transition is marked in yellow.

Figure 12

Isothermal resistivity measurements under magnetic fields applied perpendicular (left panel) and parallel (right panel) to the $ab$ plane of $\mathrm{Eu}{\left({\mathrm{Fe}}_{0.93}{\mathrm{Rh}}_{0.07}\right)}_2{\mathrm{As}}_2$ at different hydrostatic pressures up to 18 kbar (room temperature pressure values). While for the out-of-plane configuration a purely positive slope can be observed, the in-plane measurements exhibit a negative slope at low fields, connected with the field-induced enhancement of $T_{\mathrm{c},0}$. Two critical fields manifest themselves in the data (a) as a minimum in the in-plane configuration at $H_{\mathrm{AFM}}\approx 4$ kG and (b) as a kink in the out-of-plane measurement at $H_{\mathrm{sat}}\approx 8$ kG (see the black arrows).

Figure 13

Temperature-dependent magnetoresistance measurements at 4.5 kbar show the evolution of the pressure-induced cusp in $\rho \left(T\right)$ at around 25 K with in-plane magnetic fields. The local maximum gets broadened and shifts to higher temperatures till at fields of 40 kG the upturn is no longer present in the resistivity curve.