Structural and Magnetic Phase Transitions near Optimal Superconductivity in ${{\mathrm{BaFe}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x)}_2$

We use nuclear magnetic resonance (NMR), high-resolution x-ray, and neutron scattering studies to study structural and magnetic phase transitions in phosphorus-doped ${{\mathrm{BaFe}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x)}_2$. Previous transport, NMR, specific heat, and magnetic penetration depth measurements have provided compelling evidence for the presence of a quantum critical point (QCP) near optimal superconductivity at $x=0.3$. However, we show that the tetragonal-to-orthorhombic structural ($T_s$) and paramagnetic to antiferromagnetic (AF, $T_N$) transitions in ${{\mathrm{BaFe}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x)}_2$ are always coupled and approach $T_N\approx T_s\ge T_c$ ($\approx 29\mathrm{K}$) for $x=0.29$ before vanishing abruptly for $x\ge 0.3$. These results suggest that AF order in ${{\mathrm{BaFe}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x)}_2$ disappears in a weakly first-order fashion near optimal superconductivity, much like the electron-doped iron pnictides with an avoided QCP.

Figure 1

(a) The AF-ordered phase of ${{\mathrm{BaFe}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x)}_2$, where the magnetic Bragg peaks occur at ${\mathbf{Q}}_{\text{AF}}=(1,0,L)$ ($L=1,3,\dots$) positions. (b) Temperature dependence of the resistance for the $x=0.31$ sample, where $RRR=R(300\mathrm{K})/R(0\mathrm{K})\sim 17$. In previous work on similar P-doped samples, $RRR\sim 13$ [28]. (c) The phase diagram of ${{\mathrm{BaFe}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x)}_2$, where the Ort, Tet, and SC are orthorhombic, tetragonal, and superconductivity phases, respectively. The inset shows the expanded view of the P-concentration dependence of $T_s$, $T_N$, and, $T_c$ near optimal superconductivity. The color bar represents the temperature and doping dependence of the normalized magnetic Bragg peak intensity. The dashed region indicates the mesoscopic coexisting AF and SC phases.

Figure 2

[(a),(c),(e)] Wave vector scans along the $[H,0,3]$ direction at different temperatures for $x=0.19,0.28$, 0.29, and 0.31, respectively. Horizontal bars indicate instrumental resolution. [(b),(d),(f)] Temperature dependence of the magnetic scattering at ${\mathbf{Q}}_{\text{AF}}=(1,0,3)$ for $x=0.19,0.28$, and 0.29, respectively. (g) NRSE measurement of temperature dependence of the energy width ($\mathrm{\Gamma }$ is the full-width-at-half-maximum (FHWM) of scattering function and 0 indicates instrumental resolution limited) at ${\mathbf{Q}}_{\text{AF}}=(1,0,3)$ for $x=0.29$. (h) The magnetic order parameters from the normal triple-axis measurement on the same sample.

Figure 3

Temperature evolution of $\delta$ for (a) $x=0.19$ and (b) $x=0.28$ samples. The solid circles indicate x-ray data where clear orthorhombic lattice distortions are seen. The open circles are data where one can only see peak broadening due to orthorhombic lattice distortion. Temperature dependence of the $[H,0,0]$ scans for (c) $x=0.29$ and (d) $x=0.31$. The vertical color bar indicates x-ray scattering intensity. The data were collected while warming the system from base temperature to a temperature well above $T_s$.

Figure 4

(a) Temperature dependence of the paramagnetic spectral weight for $x=0.25$ and 0.29 samples from NMR measurements. For $x=0.25$, there are no paramagnetic phases below 40 K, suggesting a fully magnetic-ordered phase. At $T_c$ of the $x=0.29$ sample, there are still 50% paramagnetic phases suggesting the presence of magnetic signal outside of the radio frequency window of the NMR measurement. The spectral weight loss below $T_c$ is due to superconductivity. The vertical dashed lines mark $T_N$ determined from neutron scattering. (b) The P-doping dependence of $M^2$ estimated from normalizing the magnetic Bragg intensity to weak nuclear peaks assuming 100% magnetically ordered phase. The blue solid circles are from Ref. [34]. The P-doping levels for different experiments are normalized by their $T_N$ values. The inset shows the expanded view of $M^2$ around optimal doping above (solid squares) and below (open squares) $T_c$. (c) The P-doping dependence of $\delta$, where the blue diamonds and green squares are from Refs. [34] and [28], respectively. For samples near optimal superconductivity, the filled and open red circles are $\delta$ above and below $T_c$, respectively.