Coexistence of antiferromagnetic ordering and superconductivity in the Ba(Fe${}_{0.961}$Rh${}_{0.039}$)${}_2$As${}_2$ compound studied by Mössbauer spectroscopy

The results of a ${}^{57}\mathrm{Fe}$ Mössbauer spectroscopy study between 2.0 and 294 K of superconducting Ba(Fe${}_{0.961}$Rh${}_{0.039}$)${}_2$As${}_2$ are reported. The main component of the electric field gradient tensor at 294 K is shown to be positive and its increase with decreasing temperature is well described by a $T^{3/2}$ power-law relation. The shape of the Mössbauer spectra below the Néel temperature $T_N=55.5(1)$ K is shown to result from the presence of doping-induced disorder rather than of incommensurate spin-density-wave order. The measured hyperfine magnetic field reaches its maximum value at the critical temperature $T_c=14$ K and then decreases by 4.2% upon further cooling to 2.0 K. This constitutes direct evidence of the coexistence of and competition between superconductivity and magnetic order. The extrapolated value of the Fe magnetic moment at 0 K is determined to be 0.35(1) ${\mu }_B$. The Debye temperature of Ba(Fe${}_{0.961}$Rh${}_{0.039}$)${}_2$As${}_2$ is found to be 357(3) K.

Figure 1

${}^{57}\mathrm{Fe}$ Mössbauer spectrum of Ba(Fe${}_{0.961}$Rh${}_{0.039}$)${}_2$As${}_2$ at 294.3 K fitted (solid line) with an asymmetric quadrupole doublet, as described in the text. The zero-velocity origin is relative to $\alpha$-Fe at room temperature.

Figure 2

Temperature dependence of the quadru-pole splitting $\Delta$ of Ba(Fe${}_{0.961}$Rh${}_{0.039}$)${}_2$As${}_2$. The solid line is the fit to Eq. (1).

Figure 3

(a) ${}^{57}\mathrm{Fe}$ Mössbauer spectrum of Ba(Fe${}_{0.961}$Rh${}_{0.039}$)${}_2$As${}_2$ at 2.0 K fitted (solid line) with the disorder-induced hyperfine magnetic field distribution $P(H)$ shown in (b).

Figure 4

${}^{57}\mathrm{Fe}$ Mössbauer spectra of Ba(Fe${}_{0.961}$Rh${}_{0.039}$)${}_2$As${}_2$ at the indicated tem-peratures (left panels) fitted (solid line) with the disorder-induced hyperfine magnetic field distribution $P(H)$ (right panels).

Figure 5

Temperature dependence of $\stackrel{̲}{H}$. Inset: An enlarged region around the superconducting transition $T_c$. The solid line is the power-law fit of the $\stackrel{̲}{H}$ data, as described in the text.

Figure 6

(a) ${}^{57}\mathrm{Fe}$ Mössbauer spectrum of Ba(Fe${}_{0.961}$Rh${}_{0.039}$)${}_2$As${}_2$ at 2.0 K fitted (solid line) with an incommensurate modulation of the hyperfine magnetic field, as described in the text. (b) Resulting shape of the spin density wave. (c) Resulting hyperfine magnetic field distribution.

Figure 7

${}^{57}\mathrm{Fe}$ Mössbauer spectra of Ba(Fe${}_{0.961}$Rh${}_{0.039}$)${}_2$As${}_2$ at the indicated temperatures fitted (solid line) with an incommensurate modulation of the hyperfine magnetic field (left panels), the corresponding shapes of the spin density wave (middle panels), and the resulting hyperfine magnetic field distributions (right panels).

Figure 8

Temperature dependence of the harmonic amplitudes.

Figure 9

Temperature dependence of $H_{\max }$, $\stackrel{̲}{H}$, and $H_{\mathrm{rms}}$. Insets: An enlarged region around the superconducting transition $T_c$. The solid line is the power-law fit of the $H_{\mathrm{rms}}$ data, as described in the text.

Figure 10

Temperature dependence of the center shift $\delta$ of Ba(Fe${}_{0.961}$Rh${}_{0.039}$)${}_2$As${}_2$. The solid line is the fit to Eq. (3), as explained in the text.