Competing superconducting and magnetic order parameters and field-induced magnetism in electron-doped $\mathrm{Ba}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x\right)}_2{\mathrm{As}}_2$

We have studied the magnetic and superconducting properties of $\mathrm{Ba}{\left({\mathrm{Fe}}_{0.95}{\mathrm{Co}}_{0.05}\right)}_2{\mathrm{As}}_2$ as a function of temperature and external magnetic field using neutron scattering and muon spin rotation. Below the superconducting transition temperature the magnetic and superconducting order parameters coexist and compete. A magnetic field can significantly enhance the magnetic scattering in the superconducting state, roughly doubling the Bragg intensity at 13.5 T. We perform a microscopic modeling of the data by use of a five-band Hamiltonian relevant to iron pnictides. In the superconducting state, vortices can slow down and freeze spin fluctuations locally. When such regions couple they result in a long-range ordered antiferromagnetic phase producing the enhanced magnetic elastic scattering in agreement with experiments.

Figure 1

(a) Elastic $\mathbf{Q}$ scans of the magnetic $\mathbf{Q}=(\frac{1}{2},\frac{1}{2},3)$ Bragg peak, performed in the longitudinal orientation, i.e., along the $(h,h,3)$ direction in reciprocal space which is equivalent to $(h,0,3)$ in the orthorhombic notation. The figure shows scans at ${\mu }_0{H}_{}=0$ T, $7.5$ T, and $13.5$ T. The solid lines represents fits to a single Gaussian peak. (b) Elastic $\mathbf{Q}$ scans of the magnetic $\mathbf{Q}=(\frac{1}{2},\frac{1}{2},3)$ Bragg peak, made in the transverse orientation, i.e., along the $(h,\overline{h},3)$ direction in reciprocal space, which is equivalent to $(0,k,3)$ in the orthorhombic notation. The figure shows scans made at ${\mu }_0{H}_{}=0$ T and $13.5$ T. (c) The Gaussian FWHM obtained in both orientations as a function of field.

Figure 2

(a) Intensity of the $\mathbf{Q}=(\frac{1}{2},\frac{1}{2},3)$ Bragg peak measured by elastic neutron scattering in the longitudinal orientation (L) and the transverse orientation (T). The SDW intensity is seen to increase at low temperature upon applying a magnetic field. The solid lines are guides to the eyes. (b) Elastic $\mathbf{Q}$ scans of the $\mathbf{Q}=(\frac{1}{2},\frac{1}{2},3)$ Bragg peak at temperatures 2 K, 20 K, 35 K, and 50 K in zero field. No changes in the peak position are observed. The solid lines are fits of a single Gaussian peak on a flat background. The background is determined from the 50 K scan. (c) The Gaussian FWHM as a function of temperature below $T_N$ at ${\mu }_0{H}_{}=0$ T and $13.5$ T.

Figure 3

(a) Transverse field $\mu \mathrm{SR}$ time spectra. Below $T_c$ we observe a magnetic component from the sample and a nonmagnetic component which we believe to be from muons stopping outside the sample. (b) $\mu \mathrm{SR}$ line shapes from the pinning experiment, showing one narrow peak corresponding to the external field in the otherwise nonmagnetic region, and one broad peak corresponding to magnetic flux trapped as pinned vortices coexisting with antiferromagnetism. (c) Temperature dependence of the magnetic volume fraction at ${\mu }_0{H}_{}=300$ mT below 30 K.

Figure 4

Real-space plot of the amplitude of the superconducting order parameter $\left|\Delta \right({\mathbf{r}}_{\mathbf{i}}\left)\right|$ for different temperatures $T/T_N$ and constant field $B=43.5$ T. The cores exhibit the usual suppression of $\left|\Delta \right({\mathbf{r}}_{\mathbf{i}}\left)\right|$.

Figure 5

Real-space plot of the total magnetization $M\left({\mathbf{r}}_{\mathbf{i}}\right)\left[{\mu }_B\right]$ for different temperatures $T/T_N$ and constant field $B=43.5$ T. The vortices are clearly seen to nucleate magnetic order.

Figure 6

Amplitude of the $(\pi ,0)$ peak of the Fourier transform of the magnetization $M\left(\mathbf{r}\right)\left[{\mu }_B\right]$ versus temperature $T/T_N$ for different values of the magnetic field $B$.