Muon-spin-relaxation studies of magnetic order and superfluid density in antiferromagnetic NdFeAsO, ${\text{BaFe}}_2{\text{As}}_2$, and superconducting ${\text{Ba}}_{1-x}{\text{K}}_x{\text{Fe}}_2{\text{As}}_2$

Zero-field (ZF) muon-spin-relaxation $\left(\mu \text{SR}\right)$ measurements have revealed static commensurate magnetic order of Fe moments in NdFeAsO below $T_N\sim 135\text{K}$, with the ordered moment size nearly equal to that in LaFeAsO, and confirmed similar behavior in ${\text{BaFe}}_2{\text{As}}_2$. In single crystals of superconducting ${\text{Ba}}_{0.55}{\text{K}}_{0.45}{\text{Fe}}_2{\text{As}}_2$, $\mu \text{SR}$ spectra indicate static magnetism with incommensurate or short-ranged spin structure in $\sim 70\%$ of volume below $T_N\sim 80\text{K}$, coexisting with the remaining volume which exhibits a superfluid response below $T_c\sim 30\text{K}$.

Figure 1

(Color online) (a) Time spectra of $\text{ZF-}\mu \text{SR}$ in NdFeAsO. (b) Temperature dependence of the precession frequency of $\text{ZF-}\mu \text{SR}$ in NdFeAsO (present study) and LaFeAsO (Ref. 13). (c) Fraction of muons in a paramagnetic environment estimated from the precession amplitude in a WTF of 100 G, as well as from the amplitude of the nonoscillating signals in the $\text{ZF-}\mu \text{SR}$ spectra.

Figure 2

(Color online) Time spectra of $\text{ZF-}\mu \text{SR}$ in (a) a ceramic specimen of ${\text{BaFe}}_2{\text{As}}_2$ and in (b) a single-crystal mosaic of ${\text{Ba}}_{0.55}{\text{K}}_{0.45}{\text{Fe}}_2{\text{As}}_2$. The inset of (b) compares the observed spectra with a Bessel function multiplied by a small exponential damping (solid line). The long-lived oscillation signal in (a) indicates commensurate magnetic order, while the Bessel function shape in (b) suggests the possibility of an incommensurate or stripe spin structure.

Figure 3

(Color online) (a) Muon-spin precession frequency in zero field as determined by fitting to the sum of two damped cosine signals for polycrystalline ${\text{BaFe}}_2{\text{As}}_2$ and a single Bessel function for single-crystal ${\text{Ba}}_{0.55}{\text{K}}_{0.45}{\text{Fe}}_2{\text{As}}_2$. Note that our transition temperature for ${\text{BaFe}}_2{\text{As}}_2$ indeed corresponds to that expected for polycrystalline specimens rather than single crystals. (b) The fraction of the signal from muons in a paramagnetic/nonmagnetic environment measured in both a ceramic ${\text{BaFe}}_2{\text{As}}_2$ specimen and single crystals of ${\text{Ba}}_{0.55}{\text{K}}_{0.45}{\text{Fe}}_2{\text{As}}_2$. The paramagnetic fraction was derived as described in the caption of Fig. 1c.

Figure 4

(Color online) The relaxation rate ${\sigma }_{\text{sc}}$ due to superconductivity in single crystals of ${\text{Ba}}_{0.55}{\text{K}}_{0.45}{\text{Fe}}_2{\text{As}}_2$, in transverse fields of 100 and 500 G parallel to the $c$ axis, obtained after quadratically subtracting the background relaxation due to nuclear dipolar fields from the observed Gaussian relaxation rate $\sigma$ shown in the inset. The temperature dependence is compared to BCS theory for isotropic $s$-wave pairing (broken line) and scaled results from the YBCO cuprate superconductor (Ref. 27) (small open diamond symbols).