Electron spin resonance in Eu-based iron pnictides

The phase diagrams of EuFe${}_{2-x}$Co${}_x$As${}_2$ $(0\le x\le 0.4)$ and EuFe${}_2$As${}_{2-y}$P${}_y$ $(0\le y\le 0.43)$ are investigated by Eu${}^{2+}$ electron spin resonance (ESR) in single crystals. From the temperature dependence of the linewidth $\Delta H\left(T\right)$ of the exchange narrowed ESR line, the spin-density wave (SDW) $(T<T_{\mathrm{SDW}})$ and the normal metallic regime $(T>T_{\mathrm{SDW}})$ are clearly distinguished. At $T>T_{\mathrm{SDW}}$ the isotropic linear increase of the linewidth is driven by the Korringa relaxation which measures the conduction-electron density of states at the Fermi level. For $T<T_{\mathrm{SDW}}$ the anisotropy probes the local ligand field, while the coupling to the conduction electrons is strongly weakened. With increasing substitution of $x$ or $y$ the transition temperature $T_{\mathrm{SDW}}$ decreases linearly accompanied by a linear decrease of the Korringa-relaxation rate from 8 Oe/K at $x=y=0$ down to 3 Oe/K at the onset of superconductivity. For $x>0.2$ and $y>0.3$ it remains nearly constant. Comparative ESR measurements on single crystals of the Eu diluted SDW compound Eu${}_{0.2}$Sr${}_{0.8}$Fe${}_2$As${}_2$ and superconducting (SC) Eu${}_{0.22}$Sr${}_{0.78}$Fe${}_{1.72}$Co${}_{0.28}$As${}_2$ corroborate the leading influence of the ligand field on the Eu${}^{2+}$ spin relaxation in the SDW regime as well as the Korringa relaxation in the normal metallic regime. A coherence peak is not detected in the latter compound below $T_{\mathrm{c}}=21$ K, which is in agreement with the expected complex anisotropic SC gap structure. In contrast, indications for phase coexistence and BCS-type superconductivity are found in EuFe${}_2$As${}_{1.57}$P${}_{0.43}$.

Figure 1

ESR spectra obtained on single crystals of EuFe${}_{2-x}$Co${}_x$As${}_2$ with $x=0.069$ (upper), 0.140 (middle), and 0.3 (lower frames) at $T=50$ K for the magnetic field applied parallel (left column) or perpendicular (right column) to the tetragonal $c$ axis. Red solid lines indicate the fit by a Dyson shape.

Figure 2

Dispersion-to-absorption ratio (right ordinate) and inverse ESR intensity (left ordinate) before (closed squares) and after (open squares) skin-depth correction for a single crystal EuFe${}_{1.86}$Co${}_{0.14}$As${}_2$. The red dashed line indicates a Curie-Weiss-like behavior.

Figure 3

Temperature dependence of the ESR linewidth $\Delta H$ in EuFe${}_{2-x}$Co${}_x$As${}_2$ for $0\le x\le 0.4$ for the magnetic field aligned along the principal axes. The concentration dependence of the SDW transition ($T_{\mathrm{SDW}}$) and of the magnetic ordering transition of the Eu spins ($T_{\mathrm{N},\mathrm{Eu}}$) is illustrated by solid lines. The straight solid lines in each graph indicate the linear Korringa law.

Figure 4

Temperature dependence of the resonance field $H_{\mathrm{res}}$ in EuFe${}_{2-x}$Co${}_x$As${}_2$ for $0\le x\le 0.4$ for the magnetic field aligned along the principal axes. The concentration dependence of the SDW transition ($T_{\mathrm{SDW}}$) and of the magnetic ordering transition of the Eu spins ($T_{\mathrm{N},\mathrm{Eu}}$) is illustrated by solid lines. The blue solid lines in each graph are guides for the eye.

Figure 5

Angular dependence of linewidth (left frames) and resonance field (right frames) for EuFe${}_{2-x}$Co${}_x$As${}_2$ single crystals with $x=0.069$ and 0.170 at $T=50$ K.

Figure 6

Concentration dependence of Korringa slope $b$ (main frame) in the normal metallic regime, averaged $g$ value $\langle g\rangle$ at 200 and 240 K (lower inset), and corresponding Korringa ratio $r_{\mathrm{K}}$ (upper inset) in EuFe${}_{2-x}$Co${}_x$As${}_2$. Solid lines are drawn to guide the eye.

Figure 7

Temperature dependence of the linewidth in EuFe${}_{1.7}$Co${}_{0.3}$As${}_2$ for the magnetic field aligned along the principal axes at three different microwave frequencies.

Figure 8

ESR spectra and corresponding fit curves for single crystals of EuFe${}_2$As${}_{2-y}$P${}_y$ with $y=0$ (upper), 0.28 (middle), and 0.43 (lower frames) at $T=50$ K for the magnetic field applied parallel (left column) or perpendicular (right column) to the tetragonal $c$ axis.

Figure 9

Temperature dependence of the ESR linewidth $\Delta H$ in EuFe${}_2$As${}_{2-y}$P${}_y$ for $y=0.28$ and $y=0.43$. The SDW transition ($T_{\mathrm{SDW}}$) and the magnetic ordering transition of the Eu spins ($T_{\mathrm{N}}$) are marked by vertical lines. The blue solid lines indicate the linear Korringa law.

Figure 10

Temperature dependence of the ESR intensity, resonance field, and linewidth $\Delta H$ in EuFe${}_2$As${}_{1.57}$P${}_{0.43}$ obtained from a fit by the sum of two resonance lines. Inset: ESR signal and fit curves at $T=23$ K. Superconducting transition ($T_{\mathrm{c}}$) and the magnetic ordering transition of the Eu spins ($T_{\mathrm{N}}$) are marked by vertical lines.

Figure 11

ESR spectra and corresponding fit curves for a single crystal of Eu${}_{0.2}$Sr${}_{0.8}$Fe${}_2$As${}_2$ at $T=4$ K for the magnetic field applied perpendicular (upper frame, $X$ band) and parallel (middle frame, $X$ and $Q$ bands) to the tetragonal $c$ axis. The lower frame shows the Zeeman splitting of the ground state for the case of a zero-field splitting $D=4.7$ GHz with the corresponding magnetic dipolar transtions at $X$-band and $Q$-band frequencies. Inset: temperature dependence of ESR intensity (solid spheres), resonance field (open triangles), and linewidth (open squares) for $H\perp c$.

Figure 12

ESR spectra and corresponding fit curves of a single crystal of Eu${}_{0.22}$Sr${}_{0.78}$Fe${}_{1.72}$Co${}_{0.28}$As${}_2$ at $T=4$ K for the magnetic field applied parallel to the tetragonal $c$ axis. Upper Inset: lower critical field $H_{\mathrm{c}1}$ as a function of temperature. Lower inset: temperature dependence of ESR intensity (solid spheres), resonance field (open triangles), and linewidth (open squares).