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Magnetism and superconductivity are closely entangled, elucidating themagnetic interactions in nickelate superconductors is at the heart ofunderstanding the pairing mechanism. Our first-principles and spin-wave theorycalculations highlight that NdNiO$_2$ is in the vicinity of a transitionbetween a quasi-two-dimensional (2D) antiferromagnetic (AFM) state and athree-dimensional (3D) C-AFM state. Both states could accurately reproduce theexperimentally measured magnetic excitation spectra, which was previouslyexplained in terms of a 2D model. We further reveal that hole doping stabilizesan incommensurate (IC) spin state and the IC wave vector increasescontinuously. Direct links between hole doping, magnetization, exchangeconstants, and magnetic order are established, revealing that the competitionbetween first-neighbor and third-neighbor in-plane magnetic interactions is thekey for the IC magnetic order.

Incommensurate Magnetic Order in Hole-Doped Infinite-layer Nickelate Superconductors