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Ferromagnetism and its stability from the one-magnon spectrum in twisted bilayer graphene

TitleFerromagnetism and its stability from the one-magnon spectrum in twisted bilayer graphene
Publication TypeJournal Article
Year of Publication2020
AuthorsY. Alavirad, and J. Sau
JournalPhys. Rev. B
Date Publisheddec

We study ferromagnetism and its stability in twisted bilayer graphene. We work with a Hubbard-like interaction that corresponds to the screened Coulomb interaction in a well-defined limit where the Thomas-Fermi screening length l(TF) is much larger than monolayer graphene's lattice spacing l(g) {\textless}{\textless} l(TF) and much smaller than the moire superlattice's spacing l(TF) {\textless}{\textless} l(moire). We show that in the perfectly flat band “chiral” limit and at filling fractions +/- 3/4, the saturated ferromagnetic (spin- and valley-polarized) states are ideal ground-state candidates in the large band-gap limit. By assuming a large enough substrate (hBN) induced sublattice potential, the same argument can be applied to filling fractions +/- 1/4. We estimate the regime of stability of the ferromagnetic phase around the chiral limit by studying the exactly calculated spectrum of one-magnon excitations. The instability of the ferromagnetic state is signaled by a negative magnon excitation energy. This approach allows us to deform the results of the idealized chiral model (by increasing the bandwidth and/or modified interactions) toward more realistic systems. Furthermore, we use the low-energy part of the exact one-magnon spectrum to calculate the spin-stiffness of the Goldstone modes throughout the ferromagnetic phase. The calculated value of spin-stiffness can determine the excitation energy of charged skyrmions.