Scaling between Magnetic and Lattice Fluctuations in Iron Pnictide Superconductors

The phase diagram of the iron arsenides is dominated by a magnetic and a structural phase transition, which need to be suppressed in order for superconductivity to appear. The proximity between the two transition temperature lines indicates correlation between these two phases, whose nature remains unsettled. Here, we find a scaling relation between nuclear magnetic resonance and shear modulus data in the tetragonal phase of electron-doped $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ compounds. Because the former probes the strength of magnetic fluctuations while the latter is sensitive to orthorhombic fluctuations, our results provide strong evidence for a magnetically driven structural transition.

Figure 1

Scaling between the shear modulus $C_s$ (open symbols, from Ref. 7, continuous line from Ref. 8) and the NMR spin-lattice relaxation rate $1/T_1$ (closed symbols, from Ref. 3) in the tetragonal phase of the parent compound ${\mathrm{BaFe}}_2{\mathrm{As}}_2$. $C_{s,0}$ denotes the noncritical, high-temperature shear modulus. The fitting parameters are $a=0.65(\mathrm{sK}{)}^{-1}$ and $b=1.3$ in Eq. (2). The inset schematically represents the magnetoelastic coupling, which makes bonds connecting antiparallel (parallel) spins expand (shrink).

Figure 2

Comparison between the relative shear modulus $C_s/C_{s,0}$ (continuous lines, from Ref. 8) and the rescaled NMR $1/T_{1}T$ (closed symbols, from Ref. 3) for different “effective” Co concentrations in $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$. The “effective” Co concentration was determined by comparing the available transition temperatures ($T_s$, $T_N$, $T_c$) of the two sets of samples with a third independent phase diagram (from Ref. 39).

Figure 3

Doping dependence of the fitting parameters $a$ and $b$, and the phase diagram of $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$. Notice that $a$ remains nearly constant, whereas $b$ approaches zero near optimal doping, where the superconducting transition temperature is the highest. The transition temperatures in the phase diagram were obtained from resistivity measurements of Ref. 39. The bare transition temperatures $T_{T_{1}T}$ and $T_{C_s}$ are obtained from Curie-Weiss fittings of the data from Refs. 3, 8, respectively. Lines are a guides to the eye.