Replacing Ir with Rh in a CoIr system possessing negative uniaxial magnetocrystalline anisotropy (K u ) substantially reduces its magnetic damping and coercivity by more than half while retaining its high negative K u . Moreover, a higher saturation magnetization (M s ) and more isotropic coercivity are achieved. Such material development makes it particularly suitable for use as the soft underlayer (SUL) of magnetic recording media for reducing noise, and as the oscillation layer of a spin-torque oscillator (STO) for achieving higher oscillation frequency, larger AC magnetic field and lower driving current, which can be readily integrated with the current recording head for microwave-assisted magnetic recording. Finally, we recommend a composite free layer by coupling CoIr with a spin polarizer (Co or Co/Cu/Co) for the enhancement of the spin-polarization rate and, therefore, the improvement of STO efficiency. These could pave the way for CoIr-based materials to be implemented in devices requiring a negative Ku with low damping and high 'softness', such as oscillators.