Coexistence of superconductivity and ferromagnetism in P-doped ${\text{EuFe}}_2{\mathrm{As}}_2$

The magnetic structure of the Eu${}^{2+}$ moments in the superconducting EuFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$ sample with $x=0.15$ has been determined using element-specific x-ray resonant magnetic scattering. Combining magnetic, thermodynamic, and scattering measurements, we conclude that the long-range ferromagnetic order of the Eu${}^{2+}$ moments aligned primarily along the c axis coexists with the bulk superconductivity at zero field. At an applied magnetic field $\ge$0.6 T, superconductivity still coexists with the ferromagnetic Eu${}^{2+}$ moments, which are polarized along the field direction. We propose a spontaneous vortex state for the coexistence of superconductivity and ferromagnetism in EuFe${}_2$(As${}_{0.85}$P${}_{0.15}$)${}_2$.

Figure 1

(a) and (b) Temperature dependencies of the magnetic susceptibility measured on heating of the zero-field cooled (ZFC) and field cooled (FC) sample at an applied magnetic field of 1 mT along the crystallographic ${\left[110\right]}_T$ and ${\left[001\right]}_T$ directions, respectively. (c) and (d) $M$-$H$ curves for magnetic fields parallel and perpendicular to the c axis at $T$ = 5 K (below magnetic and superconducting transitions) and 30 K (above superconducting and magnetic transitions). Horizontal dashed lines in both figures denote a fully saturated moment of Eu${}^{2+}$. Lower insets for both figures show the hysteresis curves after subtraction of the ferromagnetic contribution as described in the text. The upper inset of Fig. 1 shows details of the M-H dependence in the low-field region. (e) Temperature dependence of the specific heat. Upper and lower insets show details near the magnetic ordering of the Eu${}^{2+}$ and the superconducting transition, respectively. The solid curve represents the fit using Debye and Einstein contributions for the lattice part of the specific heat. The lattice part was subtracted from the total heat capacity to calculate the entropy release at $T_{\mathrm{C}}$.

Figure 2

(a) Temperature dependence of the orthorhombic distortion for the $x=0.15$ sample. The inset shows ($\xi$ $\xi$ 0)${}_T$ scans through the (2 2 8)${}_T$ position above and below the structural phase transition. The lines represent fits to the data using either one (red) or two (blue) Lorentzian squared peaks. (b) Temperature dependence of the (2 1 7) reflection in both the $\pi \to {\sigma }^{\prime }$ and $\pi \to {\pi }^{\prime }$ scattering geometries at zero filed. The schematic shows the used scattering geometry. (c) Same as (b) but in an applied magnetic field of 0.5 T. The temperature dependencies were measured at the peak energy ($\sim$6.973 keV) of the resonance enhancement observed in the energy scans.

Figure 3

(a) Energy scan of the fluorescence yield. The dashed line depicts the Eu $L_3$ absorption edge as determined from the inflection point of the fluorescence yield. (b) and (c) Energy scans for the (2 1 7) reflection after subtraction of the nonmagnetic background at high temperature for (b) and at zero magnetic field for (c). (d) and (e) Energy scans through the antiferromagnetic (0 0 3) and (0 0 9) positions for the 15% and 5% samples, respectively. Lines serve as guides to the eye.

Figure 4

(a) Magnetic structures of the Eu${}^{2+}$ moments in zero and applied magnetic fields. Only the Eu${}^{2+}$ magnetic moments are shown. (b) Field dependence of the intensities of the (2 1 7) reflection measured in the $\pi \to {\pi }^{\prime }$ scattering geometry after zero field cooling of the sample from 80 K. (c) Temperature dependence of the bulk magnetization at different applied magnetic fields along the $\left[1\overline{2}0\right]$ direction measured using an MPMS. (d) Magnetic phase diagram for the 15% doped sample constructed using magnetization and scattering measurements. Filled symbols are derived from the scattering measurement and the open symbols from $M$-$T$ (square) and $M$-$H$ (circles) measurements at different fields and temperatures, respectively. The transition temperatures, $T_{\mathrm{SC}}$ and $T_{\mathrm{C}}$, at zero field are consistent with the published results of Ref. [33].