Symmetry of spin excitation spectra in the tetragonal paramagnetic and superconducting phases of 122-ferropnictides

We study the symmetry of spin excitation spectra in 122-ferropnictide superconductors by comparing the results of first-principles calculations with inelastic neutron-scattering (INS) measurements on BaFe1.85Co0.15As2 and BaFe1.91Ni0.09As2 samples that exhibit neither static magnetic phases nor structural phase transitions. In both the normal and superconducting (SC) states, the spectrum lacks the three-dimensional 4(2)/m screw symmetry around the (1/2 1/2 L) axis that is implied by the I4/mmm space group. This is manifest both in the in-plane anisotropy of the normal- and SC-state spin dynamics and in the out-of-plane dispersion of the spin-resonance mode. We show that this effect originates from the higher symmetry of the magnetic Fe sublattice with respect to the crystal itself, hence the INS signal inherits the symmetry of the unfolded Brillouin zone (BZ) of the Fe sublattice. The in-plane anisotropy is temperature independent and can be qualitatively reproduced in normal-state density-functional-theory calculations without invoking a symmetry-broken (nematic) ground state that was previously proposed as an explanation for this effect. Below the SC transition, the energy of the magnetic resonant mode omega(res), as well as its intensity and the SC spin gap inherit the normal-state intensity modulation along the out-of-plane direction L with a period twice larger than expected from the body-centered-tetragonal BZ symmetry. The amplitude of this modulation decreases at higher doping, providing an analogy to the splitting between even and odd resonant modes in bilayer cuprates. Combining our and previous data, we show that at odd L a universal linear relationship (h) over bar omega(res) approximate to 4.3 k(B)T(c) holds for all the studied Fe-based superconductors, independent of their carrier type. Its validity down to the lowest doping levels is consistent with weaker electron correlations in ferropnictides as compared to the underdoped cuprates.