Orbital and spin ordering physics of the Mn${}_3$O${}_4$ spinel

Abstract

Motivated by recent experiments, we present a comprehensive theoretical study of the geometrically frustrated strongly correlated magnetic insulator Mn${}_3$O${}_4$ spinel oxide based on a microscopic Hamiltonian involving lattice, spin and orbital degrees of freedom. Possessing the physics of degenerate e${}_g$ orbitals, this system shows a strong Jahn-Teller effect at high temperatures. Further, careful attention is paid to the special nature of the superexchange physics arising from the 90${}^o$ Mn-O-Mn bonding angle. The Jahn-Teller and superexchange-based orbital-spin Hamiltonians are then analysed in order to track the dynamics of orbital and spin ordering. We find that a high-temperature structural transition results in orbital ordering whose nature is mixed with respect to the two originally degenerate $e_g$ orbitals. This ordering of orbitals is shown to relieve the intrinsic geometric frustration of the spins on the spinel lattice, leading to ferrimagnetic Yafet-Kittel ordering at low-temperatures. Finally, we develop a model for a magnetoelastic coupling in Mn${}_3$O${}_4$, enabling a systematic understanding of the experimentally observed complexity in the low-temperature structural and magnetic phenomenology of this spinel. Our analysis predicts that a quantum fluctuation-driven orbital-spin liquid phase may be stabilised at low temperatures upon the application of pressure.

arXiv comment11 pages, 8 figures

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Cited by in corpus (4)

• Correlated spin liquids in the quantum kagome antiferromagnet at finite field: a renormalisation group analysis
• Magnetisation plateaux of the quantum pyrochlore Heisenberg antiferromagnet
• Importance of anisotropic Coulomb interactions in the electronic and magnetic properties of Mn${}_3$O${}_4$
• Tuning the orbital-lattice fluctuations in the mixed spin-dimer system Ba${}_{3-x}$Sr${}_x$Cr${}_2$O${}_8$