Localized magnetic states in a tilted Dirac cone system

Abstract

We investigate the localized magnetic state in the tilted Dirac cone system, wherein a lattice staggered potential (LSP) is introduced to create a gap between the conduction and valence bands. Our findings reveal that the breaking of symmetry between the sublattices results in depletion of the magnetic region of the impurity for positive LSP values, while a sharp strip is formed for negative LSP values with an increase in the tilt of the Dirac cone. Interestingly, within the magnetic region, the magnetic moment of the impurity remains constant at 0.8 Bohr magneton irrespective of the sign of LSP. However, the magnetic susceptibility at the edge of the magnetic region displays inconsistent behavior for positive and negative LSP values. We also analyze in detail the variations in the magnetic region, magnetic moment, and magnetic susceptibility with LSP strength at a fixed tilt.