[en] In this manuscript, we have carried out a combined study of density functional theory and Monte Carlo (MC) simulations for a thorough examination of a single-layer (SL) Ti₂B structure. On the basis of first-principles, spin-polarized density functional calculations, we showed that a free standing SL-Ti₂B structure is dynamically and thermally stable. The atomic structure, phonon spectrum, electronic and magnetic properties of the SL-Ti₂B structure are analyzed. In order to determine ground state, the structure of Ti₂B is optimized for four types of spin oriented configurations, namely ferromagnetic (FM), antiferromagnetic Néel, antiferromagnetic Zigzag and antiferromagnetic Stripy and non-magnetic states. We found that the spin configuration FM corresponds to the ground state for SL-Ti₂B. We also found that the Raman-active modes are softening in the antiferromagnetic cases. On the basis of these results, MC simulations show that the magnetic susceptibility, thermal variations of magnetization, and specific heat curves of Ti₂B exhibit a phase transition between paramagnetic and FM phases at the Curie temperature of 39.06 K. While SL-Ti₂B possess a little out-of-plane magnetic anisotropy, it has not any in plane magnetic anisotropy energy. (paper)