Gradual destruction of magnetism in the superconducting family NaFe${}_{1-x}$Co${}_x$As

The interplay and coexistence of superconducting, magnetic, and structural order parameters in NaFe${}_{1-x}$Co${}_x$As have been studied using superconducting quantum interference device magnetometry, muon spin rotation, and synchrotron x-ray powder diffraction. Substituting Fe by Co weakens the ordered magnetic state through both a suppression of $T_{\mathrm{N}}$ and a reduction in the size of the ordered moment. Upon further substitution of Fe by Co the high sensitivity of the muon as a local magnetic probe reveals a magnetically disordered phase, in which the size of the moment continues to decrease and falls to zero around the same point at which the magnetically driven structural distortion is no longer resolvable. Both magnetism and the structural distortion are weakened as the robust superconducting state is established.

Figure 1

Phase diagram for NaFe${}_{1-x}$Co${}_x$As compiled using data from XRPD ($T_{\mathrm{s}}$), zero-field $\mu$SR ($T_{\mathrm{N}}$), and SQUID magnetometry ($T_{\mathrm{c}}$) and showing regions of antiferromagnetism (AF), superconductivity (SC), and inhomogeneous magnetism (IM), as well as their regions of coexistence. The shading of the SC region corresponds to the volume fraction estimated from susceptibility data.

Figure 2

Susceptibility data for various NaFe${}_{1-x}$Co${}_x$As samples. Inset: estimated volume fractions for all samples with $0\le x\le 0.02$. A full superconducting volume fraction is established around $x\approx 0.0125$.

Figure 3

Comparison of the ZF μSR asymmetry spectra for NaFe${}_{1-x}$Co${}_x$As, measured around 1.5 K.

Figure 4

(a) Muon precession frequency (proportional to the ordered moment) as a function of Néel temperature shown by filled circles. In the IM state, the effective ${\nu }_1\left(0\right)$ is estimated from the magnetic contribution to the rms field width and $T_{\mathrm{N}}$ is taken to be the temperature at which this contribution sets in (see Fig. 7). Inset: the probability distribution for the ordered moment for stoichiometric NaFeAs given the observed precession frequency. (b) The estimated ordered moment as a function of $x$ in the AF state (filled circles) and IM state (open circles).

Figure 5

A Pawley refinement for NaFe${}_{0.98}$Co${}_{0.02}$As at 5 K. Inset: a comparison of the fits to the 022 and 202 peaks in $Cmma$ at 5 and 10 K. These peaks converge into the 112 peak in $P4/nmm$. Note that $\Delta$, the splitting in the $2\theta$ values of the two peaks, is smaller at 5 than at 10 K, suggesting a suppression of the structural distortion at low temperatures. This is in agreement with the behavior of $\delta \left(T\right)$ as obtained from fitting the full pattern.

Figure 6

The evolution of (a) structural and (b) magnetic order parameters with $T$ and $x$. $\delta$ is defined as the difference between the $a$ and $b$ lattice parameters in the low-temperature $Cmma$ phase, and ${\nu }_1$ is the largest observed muon precession frequency in the zero field. The blue line sections show where the sample superconducts, and the shade of blue indicates the volume fraction obtained from SQUID magnetometry. The arrows indicate the suppression of $\delta$ and ${\nu }_1$ in the more highly substituted samples.

Figure 7

The width $B_{\mathrm{rms}}$ vs $T$ for samples close to the magnetic LRO region. For $x=0.0150$ (a) the unusual peak in $B_{\mathrm{rms}}$ matches one observed in the zero-field fast relaxation amplitude $A_{\mathrm{fast}}$. The gray line indicates $T_{\mathrm{c}}$ from SQUID magnetometry (see Fig. 1). The black line in (d) is a fit to a conventional SC order-parameter temperature dependence.