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We study the ground state of the Hubbard model on a square lattice with two degenerate orbitals per site and at integer fillings as a function of onsite Hubbard repulsion $U$ and Hund's intra-atomic exchange coupling $J$. We use a variational slave-spin mean field (VSSMF) method which allows symmetry broken states to be studied within the computationally less intensive slave-spin mean field formalism, thus making the method more powerful to study strongly correlated electron physics. The results show that at half-filling, the ground state at smaller $U$ is a Slater antiferromagnet (AF) with substantial local charge fluctuations. As $U$ is increased, the AF state develops a Heisenberg behavior, finally undergoing a first order transition to a Mott insulating AF state at a critical interaction $U_c$ which is of the order of the bandwidth. Introducing the Hund's coupling $J$ correlates the system more and reduces $U_c$ drastically. At quarter-filling with one electron per site, the ground state at smaller $U$ is paramagnetic metallic. At finite Hund's coupling $J$, as interaction is increased above a lower critical value $U_{c1}$, it goes to a fully spin polarized ferromagnetic state coexisting with an antiferro-orbital order. The system eventually becomes Mott insulating at a higher critical value $U_{c2}$. The results as a function of $U$ and $J$ are thoroughly discussed., Comment: 7 pages, 9 figures