Collective excitation of electron spin structure in titanium-based MXenes*

Using the second quantized formalism, magnetism and the behavior of the quantized spin wave, called magnons, are analyzed in the titanium-based MXene.  Magnons are spin-1 bosons carrying energy and lattice momentum in crystals and depict the wave propagation due to a small fluctuation of electron’s moment around the natural direction in magnetic substances. The electronic and magnetic properties of these MXenes are evaluated using density functional calculations. Structural and termination group dependency of electronic and magnetic properties of MXenes make them very interesting. For example, pristine Ti₃N₂ has zero electronic band gap and shows ferromagnetic ordering with a total magnetization of about 0.8 Bohr magneton per formula unit in the hexagonal layered structure. Interestingly, ferromagnetism disappears in Ti₃N₂’s comparatively less symmetric Corundum trigonal structure. We semi-analytically investigate the collective excitation of electron spin structure in Ti₃N₂ and Ti₂N. The exchange energy parameter is evaluated using density functional theory, which is then used to set up the Heisenberg Hamiltonian and magnon dispersion relation. The Department of Energy BES-RENEW award number DE-SC0024611 has supported this research work.