  The long-standing issue of the competition between the magnetic field and the
Kondo effect, favoring, respectively, triplet and singlet ground states is
addressed using a cluster slave-rotor mean field theory for the Hubbard model
and its spin-correlated, spin-frustrated extensions in 2 dimension. The
metamagnetic jump is established and compared with earlier results of dynamical
mean-field theory. The present approach also reproduces the emergent
super-exchange energy scale in the insulating side. A scaling is found for the
critical Zeeman field in terms of the intrinsic coherence scale just below the
metal-insulator transition where the critical spin fluctuations are soft. The
conditions for metamagnetism to appear at a reasonable field are also
underlined. The Gutzwiller analysis on the 2D Hubbard model and a quantum Monte
Carlo calculation on the Heisenberg spin system are performed to check the
limiting cases of the cluster slave-rotor results for the Hubbard model.
Low-field scaling features for magnetization are discussed.
