Doping dependence of spin excitations and its correlations with high-temperature superconductivity in iron pnictides

Abstract

High-temperature superconductivity in iron pnictides occurs when electrons and holes are doped into their antiferromagnetic parent compounds. Since spin excitations may be responsible for electron pairing and superconductivity, it is important to determine their electron/hole-doping evolution and connection with superconductivity. Here we use inelastic neutron scattering to show that while electron doping to the antiferromagnetic BaFe₂As₂ parent compound modifies the low-energy spin excitations and their correlation with superconductivity (<50 meV) without affecting the high-energy spin excitations (>100 meV), hole-doping suppresses the high-energy spin excitations and shifts the magnetic spectral weight to low-energies. In addition, our absolute spin susceptibility measurements for the optimally hole-doped iron pnictide reveal that the change in magnetic exchange energy below and above T(c) can account for the superconducting condensation energy. These results suggest that high-T(c) superconductivity in iron pnictides is associated with both the presence of high-energy spin excitations and a coupling between low-energy spin excitations and itinerant electrons.

Figure 1. Summary of transport and neutron scattering results.

(a) The electronic phase diagram of electron and hole-doped BaFe₂As₂ (ref. 9). The right inset shows crystal and AF spin structures of BaFe₂As₂ with marked the nearest (J_1a, J_1b) and next nearest neighbor (J₂) magnetic exchange couplings. The left insets show the evolution of low-energy spin excitations in Ba_1−xK_xFe₂As₂. (b,c) Temperature dependence of magnetic susceptibility for our KFe₂As₂ and Ba_0.67K_0.33Fe₂As₂. (d) Temperature dependence of the resistivity for BaFe_1.7Ni_0.3As₂. (e–g) The filled circles are spin excitation dispersions of KFe₂As₂ at 5 K, Ba_0.67K_0.33Fe₂As₂ at 9 K, and BaFe_1.7Ni_0.3As₂ at 5 K, respectively. The shaded areas indicate vanishing spin excitations and the solid lines show spin wave dispersions of BaFe₂As₂ (ref. 13). (h) Energy dependence of χ^″(ω) for BaFe_1.9Ni_0.1As₂ (dashed line), BaFe_1.7Ni_0.3As₂ (green solid circles), Ba_0.67K_0.33Fe₂As₂ below (solid red circles and solid red line) and above (open purple circles and solid lines) T_c. The inset shows Energy dependence of χ^″(ω) for KFe₂As₂. The vertical error bars indicate the statistical errors of one standard deviation. The horizontal error bars in (h) indicate the energy integration range.

Figure 2. Schematics of Fermi surface evolution as a function of Ni-doping for BaFe_2−xNi_xAs₂ and for Ba_0.67K_0.33Fe₂As₂.

(a–c) Evolution of Fermi surfaces with Ni-dopings of x_e=0,0.1,0.3. The d_xz, d_yz, and d_xy orbitals for different Fermi surfaces are coloured as red, green and blue, respectively. (d) Fermi surfaces for Ba_0.67K_0.33Fe₂As₂.

Figure 3. Constant-energy slices through magnetic excitations of iron pnictides at different energies.

The colour bars represent the vanadium normalized absolute spin excitation intensity in the units of mbarn sr⁻¹ meV⁻¹ f.u.⁻¹. 2D images of spin excitations at 5 K for KFe₂As₂ (a) E=8±3 meV obtained with E_i=20 meV. The right side incommensurate peak is obscured by background scattering. (b) 13±3 meV with E_i=35 meV, (c) 53±10 meV with E_i=80 meV. For Ba_0.67K_0.33Fe₂As₂ at T=45 K, images of spin excitations at (d) E=5±1 meV obtained with E_i=20 meV, (e) 15±1 meV with E_i=35 meV, and (f) 50±2 meV obtained with E_i=80 meV. The dashed box in (d) indicates the AF zone boundaries for a single FeAs layer and the black dashed lines mark the orientations of spin excitations at different energies. Images of spin excitations for BaFe_1.7Ni_0.3As₂ at T=5 K and (g) E=9±3 meV obtained with E_i=80 meV, (h) 30±10 meV with E_i=450 meV, and (i) 59±10 meV with E_i=250 meV. The white crosses indicate the position of Q_AF.

Figure 4. The dispersion of spin excitations for BaFe_2−xNi_xAs₂ along the [1,K] direction.

(a,b) The dispersion cuts of BaFe₂As₂ with E_i=250 meV and E_i=450 meV along [1,K] direction. The data are from MAPS. (c,d) Identical dispersion cuts of BaFe_1.7Ni_0.3As₂ (x_e=0.3) at MAPS.

Figure 5. Constant-energy images of spin excitations of iron pnictides and its comparison with RPA/DMFT calculations.

Spin excitations of BaFe_1.7Ni_0.3As₂ in the 2D [H,K] plane at energy transfers of (a) E=70±10 meV obtained with E_i=250 meV; (b) 112±10 meV E_i=250 meV; (c) 157±10 meV and (d) 214±10 meV with E_i=450 meV. All obtained at 5 K. A flat backgrounds have been subtracted from the images. Spin excitations of Ba_0.67K_0.33Fe₂As₂ at energy transfers of (e) E=70±10 meV obtained with E_i=170 meV; (f) 115±10 meV; (g) 155±10 meV; (h) 195±10 meV obtained with E_i=450 meV, all at 9 K. Wave vector dependent backgrounds have been subtracted from the images. RPA calculations of spin excitations for Ba_0.67K_0.33Fe₂As₂ at (i) E=70 meV and (j) E=155 meV. DMFT calculations for Ba_0.67K_0.33Fe₂As₂ at (k) E=70 meV and (l) E=155 meV.

Figure 6. The effect of magnetic exchange couplings J (J_1a, J_1b and J₂) on the band top of spin excitations.

The black line is energy cut at (0.8<H<1.2, 0.8<K<1.2) r.l.u for BaFe₂As₂ in the Heisenberg spin wave model. The red line is for Ba_0.67K_0.33Fe₂As₂ with 10 % soften band top. The blue line is a similar estimation for KFe₂As₂ assuming zone boundary is around E=25 meV.

Figure 7. RPA and LDA+DMFT calculated local susceptibility for different iron pnictides.

RPA and LDA+DMFT calculations of χ^″(ω) in absolute units for KFe₂As₂ and Ba_0.67K_0.33Fe₂As₂ comparing with earlier results for BaFe₂As₂ and BaFe_1.9Ni_0.1As₂.

Figure 8. Properties of the resonance across T_c=38.5 K for Ba_0.67K_0.33Fe₂As₂.

Constant-energy (E=15±1 meV) images of spin excitations at (a) T=25, (b) 38, (c) 40, and (d) 45 K obtained with E_i=35 meV. In order to make fair comparison of the scattering line shape at different temperatures, the peak intensity at each temperature is normalized to 1. The pink and green arrows in (a) mark wave vector cut directions across the resonance. The integration ranges are −0.2≤K≤0.2 along the [H,0] direction and 0.8≤H≤1.2 along the [1,K] direction. The full-width-at-half-maximum (FWHM) of spin excitations are marked as dashed lines. (e) The FWHM of the resonance along the [H,0] and [1,K] directions as a function of temperature across T_c. (f) Energy dependence of the resonance obtained by subtracting the low-temperature data from the 45 K data, and correcting for the Bose population factor. (g) The black diamonds show temperature dependence of the sum of hole and electron pocket electronic gaps obtained from Angle Resolved Photoemission experiments for Ba_0.67K_0.33Fe₂As₂ (ref. 40). The red solid circles show temperature dependence of the resonance. (h) Temperature dependence of the superconducting condensation energy from heat capacity measurements and the intensity of the resonance integrated from 14–16 meV. The error bars indicate the statistical errors of one s.d.