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The discovery of time-reversal-invariant topological states has drawn greatattention in recent decades. However, despite the potential of displaying avariety of exotic physics, the study of magnetic topological phases lags behinddue to underlying added complexity of magnetism. In this work, we predict theinterplay of magnetism and topology in the non-centrosymmetric ternarymanganese compound MnIn$_2$Te$_4$, using first-principles calculations. Atambient pressure, the ground state of the system is an antiferromagneticinsulator. With the application of small hydrostatic pressure ($\sim$0.50 GPa),it undergoes a magnetic transition and the ferromagnetic state becomesenergetically favourable. At $\sim$2.92 GPa, the system undergoes a transitioninto a Weyl semimetallic phase, which hosts multiple Weyl points in the bulkand is associated with non-trivial surface Fermi arcs. Remarkably, we discoverthat the number of Weyl points in this system can be controlled by pressure andthat these manifest in an anomalous Hall conductivity (AHC). In addition toproposing a new candidate magnetic topological material, our work demonstratesthat pressure can be an effective way to induce and control topological phases,as well as AHC, in magnetic materials. These properties may allow our proposedmaterial to be used as a novel pressure-controlled Hall switch.

Pressure-induced magnetic and topological transitions in non-centrosymmetric MnIn$_{2}$Te$_{4}$