Coexistence and Competition of the Short-Range Incommensurate Antiferromagnetic Order with the Superconducting State of ${\mathrm{BaFe}}_{2-x}{\mathrm{Ni}}_x{\mathrm{As}}_2$

Superconductivity in the iron pnictides develops near antiferromagnetism, and the antiferromagnetic (AF) phase appears to overlap with the superconducting phase in some materials such as ${\mathrm{BaFe}}_{2-x}{T}_x{\mathrm{As}}_2$ (where $T=\mathrm{Co}$ or Ni). Here we use neutron scattering to demonstrate that genuine long-range AF order and superconductivity do not coexist in ${\mathrm{BaFe}}_{2-x}{\mathrm{Ni}}_x{\mathrm{As}}_2$ near optimal superconductivity. In addition, we find a first-order-like AF-to-superconductivity phase transition with no evidence for a magnetic quantum critical point. Instead, the data reveal that incommensurate short-range AF order coexists and competes with superconductivity, where the AF spin correlation length is comparable to the superconducting coherence length.

Figure 1

(a) Electronic phase diagram of ${\mathrm{BaFe}}_{2-x}{\mathrm{Ni}}_x{\mathrm{As}}_2$ as a function of $x$. The long-range commensurate AF (C-AF) order changes into short-range incommensurate AF (IC-AF) order for $x=0.085–0.096$. The optimal superconductivity occurs at $x=0.10$, where the static AF order is suppressed [22]. The inset shows the C-AF and IC-AF positions in reciprocal space in tetragonal notation, where $\delta =ϵ/\sqrt{2}$. (b) The Ni-doping dependence of the in-plane AF spin-spin correlation length. For $x=0.096$, we have ${\xi }^{\mathrm{AF}}\approx 66\AA$ and the superconducting coherence length ${\xi }_{ab}^{\mathrm{SC}}\approx 27\AA$ [40]. (c) The doping dependence of the ordered magnetic moment $M$ [23]. (d) Temperature dependence of the magnetic order parameter at $Q=(0.5,0.5,1)$ and $(0.5,0.5,3)$ AF Bragg positions for $x=0,0.03,0.065$, and (e) $x=0.085,0.092,0.096$.

Figure 2

Temperature and wave vector dependence of the C-AF and IC-AF scattering for ${\mathrm{BaFe}}_{2-x}{\mathrm{Ni}}_x{\mathrm{As}}_2$ with $x=0.085$, 0.092, and 0.096. Samples are aligned in the $[H,H,6H]$ and $[H,1-H,3]$ scattering plane. The solid red lines are the instrumental resolutions obtained using $\lambda /2$ scattering from the $(1,1,6)$ nuclear Bragg peak above $T_N$ without filter. Data in (a)–(d) are collected on C-5. (a),(b) Longitudinal and transverse scans at different temperatures through the $(0.5,0.5,3)$ AF Bragg peak for $x=0.085$. The scattering is commensurate in both directions but not instrumental resolution limited. The solid lines in transverse scans are Lorentzian fits to the data. (c),(d) Identical scans using the same experimental setup for $x=0.092$, which show clear incommensurate scattering along the transverse direction. (e),(f) Longitudinal and transverse scans for $x=0.096$ at $Q=(0.5,0.5,3)$ collected on Rita-2. The solid horizontal bars are the calculated instrumental resolution, determined by the supermirror guide before the monochromator, the ${80}^{\prime }$ collimation, the radial collimator of the Be filter (about ${150}^{\prime }$), the neutron-absorbing guide after the analyzer (effective collimation of ${40}^{\prime }$), and a sample mosaic spread of $\sim {15}^{\prime }$. Insets show the color images of incommensurate peaks centered around $Q=(0.5,0.5,3)$ and the scan directions at 2 K.

Figure 3

Effect of a 14.8 T magnetic field on the short-range incommensurate AF order in the $x=0.096$ sample. For this experiment on Rita-2, a single crystal of mass about 0.5 gram and mosaic of 0.45° was aligned in a 15-T magnet in the $[H,H,6H]$ and $[H,1-H,3]$ scattering plane as shown in the insets of (b) and (c). Neutrons of $E_i=E_f=4.6\mathrm{meV}$ were selected, with the nine blades of the analyzer set to probe different points in reciprocal space. Two filters were employed to remove higher order neutrons: a pyrolytic graphite placed just before the sample, along with a ${80}^{\prime }$ collimator, and cooled Be placed just after the sample. (a) Transverse scans at zero field and at $T=2\mathrm{K}$ (below $T_c$), 20 K (around $T_c$), 25 K ($T_c<T<T_N$), and 40 K (above $T_N$). The incommensurability $\pm \delta$ remains at 0.018 for all measured temperatures. (b) Comparison between zero and 14.8 T fields at $T=2\mathrm{K}$. The 14.8 T magnetic field clearly enhances the IC-AF order. (c) Identical scans at $T=25\mathrm{K}$ where a 14.8 T field suppresses the incommensurate AF order. (d) The effect of a 14.8 T field on the incommensurate AF order. While the field enhances the IC-AF order at 2 K, it may suppress the IC-AF order in the normal state. (e) Temperature dependence of the magnetic order parameters at the incommensurate position $Q=(0.48,0.52,3)$ for 0 and 14.8 T fields. The superconducting transition temperature $T_c$ is seen to shift from $\sim 19\mathrm{K}$ to $\sim 15\mathrm{K}$. (f) Magnetic field dependence of the AF Bragg peak intensity at $Q=(0.48,0.52,3)$. The data show a linear field dependence, consistent with a field-induced suppression of the superconducting transition temperature $\Delta T_c=[T_c(0)-T_c(B)]/T_c(0)$ as determined from resistivity measurements on the same sample (solid blue circles and lines).

Figure 4

Temperature and doping dependence of in-plane resistivity of ${\mathrm{BaFe}}_{2-x}{\mathrm{Ni}}_x{\mathrm{As}}_2$ in the normal state ($T>T_N$, $T>T_c$) derived from Refs. 21, 33, where ${\rho }_{ab}(T=300\mathrm{K})$ is assumed to decrease linearly with increasing $x$. The gradient color is the first order differential of resistivity in the normal state, $d{\rho }_{ab}/dT$, suggesting the linear term emerges from the overdoped regime. Open symbols are the exponent $n$ deduced from fitting $\rho ={\rho }_0+A{T}^n$ in the normal state, which minimizes to $n\approx 1.5$ near $x=0.15$. An anomalous $n$ is found for the IC-AF sample.