Skyrmion Liquid Phase of the Quantum Ferromagnet in Two Dimensions

The two-dimensional quantum ferromagnet filled with a liquid of skyrmions is studied theoretically in the context of the quantum Hall effect near electronic filling factor $\nu = 1$. A cross-over between the classical ferromagnetic phase at $\nu =1$ and a classical paramagnetic phase at $\nu \neq 1$ is obtained, which is consistent with recent Knight-shift measurements. A new collective mode associated with the skyrmion liquid that is of the cyclotron type is also identified.