Interplay between magnetism and superconductivity in EuFe${}_{2-x}$Co${}_x$As${}_2$ studied by ${}^{57}$Fe and ${}^{151}$Eu M$\ddot{\mathrm{o}}$ssbauer spectroscopy

The compound EuFe${}_{2-x}$Co${}_x$As${}_2$ was investigated by means of ${}^{57}$Fe and ${}^{151}$Eu Mössbauer spectroscopy versus temperature (4.2–300 K) for $x$ = 0 (parent), $x$ = 0.34–0.39 (superconductor), and $x$ = 0.58 (overdoped). It was found that the spin density wave (SDW) is suppressed by Co substitution; however, it survives in the region of superconductivity, but iron spectra exhibit some nonmagnetic components in the superconducting region. Europium orders magnetically, regardless of the cobalt concentration, with the spin reorientation from the $a$-axis in the parent compound toward the $c$-axis with increasing replacement of iron by cobalt. The reorientation takes place close to the $a$-$c$ plane. Some trivalent europium appears in EuFe${}_{2-x}$Co${}_x$As${}_2$ versus substitution due to the chemical pressure induced by Co atoms, and it experiences some transferred hyperfine field from Eu${}^{2+}$. Iron experiences some transferred field due to the europium ordering for substituted samples in the SDW and nonmagnetic state both, while the transferred field is undetectable in the parent compound. Superconductivity coexists with the 4f-europium magnetic order within the same volume. It seems that superconductivity has some filamentary character in EuFe${}_{2-x}$Co${}_x$As${}_2$, and it is confined to the nonmagnetic component seen by the iron Mössbauer spectroscopy.

Figure 1

Relative resistivity (normalized to the resistivity at 300 K for each sample) plotted versus temperature for all samples investigated. The current was applied in the $a$-$b$ plane. Blue arrows indicate change of the slope due to the SDW development. Red arrow shows change of the slope due to the europium magnetic ordering in the parent compound. Note that zero resistance is obtained only for $x$ = 0.39 sample. A significant drop in the resistivity is observed for $x$ = 0.34 and $x$ = 0.37 samples due to development of the superconductivity. $T_s$ denotes transition temperature to the superconducting state. Lattice constants a and c are shown as well.[11] Insets show expanded regions of the low temperatures.

Figure 2

Section (a) shows the real part of the magnetic susceptibility ${{\chi }^{\prime }}_{ac}$ plotted versus temperature $T$ for the crystal with composition $x$ = 0.37. A direct current (dc) field of $H$ = 0, 5, and 10 kOe was applied along the $c$-axis. The alternating current ($ac$) field of $h_{ac}$ = 10 Oe and frequency $f$ = 57 Hz was applied in the same direction. Results were obtained for zero-field-cooled (ZFC) and field-cooled states. The inset shows expanded vertical scale for $H$ = 5 and 10 kOe. Diamagnetic behavior below 5 K is more pronounced for $H$ = 10 kOe, and it was obtained in the ZFC state. Section (b) shows magnetization $M$ loops obtained at 2, 20, and 100 K versus external field $H$ for the sample with composition $x$ = 0.37. The field $H$ was applied along the $c$-axis. For the lowest temperature of 2 K, magnetization $M$ saturates in the field of about 5 kOe at the value of 83 emu/g, corresponding to the magnetic moment in the ordered state of 6.2 Bohr magnetons per chemical formula.

Figure 3

${}^{57}$Fe Mössbauer spectra of EuFe${}_{2-x}$Co${}_x$As${}_2$ for various concentrations $x$ obtained at room temperature (RT), 80 K, and 4.2 K. Contribution due to the nonmagnetic (NM) component is shown in the lower-right corner of each spectrum. Amplitudes $\sqrt{\langle B^2\rangle }$ of the SDW fields are shown in blue. Transferred field on iron for the SDW component is shown in green on the left, together with the angle α${}_t$. For $x$ = 0.39, it is impossible to separate the SDW and transferred fields for the SDW component. Transferred field on iron for the NM component is shown in green on the right, together with the angle θ.

Figure 4

Shape of SDW and corresponding hyperfine field distribution for EuFe${}_{2-x}$Co${}_x$As${}_2$ obtained at 80 K and 4.2 K for various cobalt concentrations $x$. Amplitudes of the first two harmonics $h_1$ and $h_3$ are shown. The maximum amplitude of SDW $B_{\max }$ is shown, too. The symbol $qx$ denotes the phase of SDW. The symbol $\langle \left|B\right|\rangle$ stands for the average field of the distribution.[4]

Figure 5

Geometry of the SDW field ${\mathbf{B}}_{SDW}$, transferred field ${\mathbf{B}}_t$, and the principal component of the axially symmetric EFG tensor $V_{zz}$ in the crystal axes $\mathbf{abc}$ of the orthorhombic unit cell as seen by the iron nucleus. Note that for $\phi =0$, one obtains ${\alpha }_t+\theta ={90}^{\circ }$.

Figure 6

Selected ${}^{57}$Fe Mössbauer spectra obtained versus temperature for $x$ = 0.34. Amplitudes $\sqrt{\langle B^2\rangle }$ of the SDW fields are shown in blue. A contribution due to the nonmagnetic (NM) component is shown. Transferred field $B_t$ on iron is shown on the left for the SDW component and on the right for the NM component of the spectrum.

Figure 7

Plot of the SDW amplitude $\sqrt{\langle B^2\rangle }$ versus temperature for various cobalt concentrations $x$. Solid lines represent total, coherent, and incoherent contributions as described in Ref. 4. For $x$ = 0.37, there is not enough spectral SDW component, and the SDW amplitude is too small to obtain reliable results.

Figure 8

${}^{151}$Eu Mössbauer spectra of EuFe${}_{2-x}$Co${}_x$As${}_2$ for various cobalt concentrations $x$ obtained at RT, 80 K, and 4.2 K. Apparent contribution due to Eu${}^{3+}$ is shown. Hyperfine magnetic field and the angle θ for Eu${}^{2+}$ are shown in blue. Transferred field on Eu${}^{3+}$ is shown in green.