Common origin of the two types of magnetic fluctuations in iron chalcogenides

We use inelastic neutron scattering to study the low energy spin excitations in moderately doped non-superconducting Fe${}_{1.01}$Te${}_{0.72}$Se${}_{0.28}$. The spin excitations in this system contain components near (0.5,0,0) and (0.5,0.5,0) in a-b plane reciprocal lattice units using tetragonal unit cell notation (a=b=3.772 \AA and c=6.061 \AA). At low energies the scattering is centered around (0.5,0,0). With increasing energy, the spectral weight of low energy spin excitations centered around (0.5,0,0) abruptly shifts around 3 meV to the incommensurate spin excitations centered around (0.5,0.5,0). However both types of spin fluctuations exhibit the identical temperature dependence. These results indicate that the (0.5,0,0) type spin excitations and the incommensurate excitations around the (0.5,0.5,0) position have a common origin and both must be taken into account to understand the nature of magnetism and superconducting pairing in the iron chalcogenides.