Coexistence and competition of ferromagnetism and p-wave superconductivity in holographic model

By combining a holographic p-wave superconductor model and a holographic ferromagnetism model, we study the coexistence and competition of ferromagnetism and p-wave superconductivity. It is found that the results depend on the self-interaction of magnetic moment of the complex vector field and which phase appears first. In the case where the ferromagnetic phase appears first, if the interaction is attractive, the system shows the ferromagnetism and superconductivity can coexist at low temperatures. If the interaction is repulsive, the system will only be in a pure ferromagnetic state. In the case where the superconducting phase appears first, the attractive interaction will lead to a magnetic p-wave superconducting phase at low temperatures. If the interaction is repulsive, the system will be in a pure p-wave superconducting phase or a ferromagnetic phase when the temperature is lowered.