Incommensurate Magnetic Order in Hole-Doped Infinite-Layer Nickelate Superconductors due to Competing Magnetic Interactions

The discovery of superconductivity in hole-doped infinite-layer nickelates has fueled intense research to identify the critical factor responsible for high-T_c superconductivity. Magnetism and superconductivity are closely entangled, and elucidating the magnetic interactions in hole-doped nickelates is critical for understanding the pairing mechanism. Here, these calculations based on the generalized Bloch theorem (GBT) and magnetic force theorem (MFT) consistently reveal that hole doping stabilizes an incommensurate (IC) spin state and increases the IC wave vector continuously, in a way strikingly similar to hole-doped cuprates. Going further, a nonlinear Heisenberg model including first-neighbor and third-neighbor in-plane magnetic interactions is developed. The analytical solutions successfully reproduce GBT and MFT results and reveal that the competition between the two magnetic interactions is the decisive factor for the IC magnetic transition. Eventually, by analyzing the doping-controlled spin splitting of $d_{x^2?y^2}$ band and orbital-contributed exchange interactions, direct links between hole doping, magnetization, exchange constants, and magnetic order are established. This discovery of the IC spin state, new understanding of its electronic origin, and establishment of direct connection with the paring $d_{x^2?y^2}$ electrons radically change the current understanding of the magnetic properties in hole-doped NdNiO₂ and open new perspectives for the superconducting mechanism in nickelates superconductors.