Orbital and spin ordering physics of the Mn3O4 spinel

Abstract

Motivated by recent experiments, we present a comprehensive theoretical study of the geometrically frustrated strongly correlated magnetic insulator Mn3O4 spinel oxide based on a microscopic Hamiltonian involving lattice, spin and orbital degrees of freedom. Possessing the physics of degenerate eg 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 eg 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 lowtemperatures. Finally, we develop a model for a magnetoelastic coupling in Mn3O4, 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.

Orbital competition of Mn3+ and V3+ ions in Mn1+x V2-x O4

“…Therefore, the exchange interaction of Mn 3+ -Mn 3+ exhibites strongly antiferromagnetic in ab-plane, and J c BB is weak along the c-axis due to elongation of BO6 octahedra. With the mechanism such as interplay of JAB and JBB, a collinear Néel phase can not appear in Mn3O4, while a noncollinear ferrimagnetic YK phase presents instead [21,41]. However, JBB is not strong compared with JAB in MnV2O4 and spins of V 3+ ions can be aligned parallel to each other to produce collinear long-range ordering, so the spins of Mn 3+ remain disordered but V 3+ ordered at T1 in Mn1+xV2-xO4.…”

“…Since the antiferromagnetic exchange energy of Mn 3+ -Mn 3+ ( J ab BB ) is much stronger than the Mn 3+ -Mn 2+ coupling (JAB), a collinear magnetic structure can't form under frustration. There are two paths to achieve magnetic interactions between nearestneighbor Mn 3+ ions [40,41]: i) the direct exchange interactions between the neighboring t2g orbitals which are strongly antiferromagnetic; ii) the superexchange interaction involving neighboring eg electrons and middle oxygen's 2p orbital, which is weakly ferromagnetic. Therefore, the exchange interaction of Mn 3+ -Mn 3+ exhibites strongly antiferromagnetic in ab-plane, and J c BB is weak along the c-axis due to elongation of BO6 octahedra.…”

Magnetisation plateaux of the quantum pyrochlore Heisenberg antiferromagnet

“…It will be interesting to test these predictions numerically by looking for signatures in, for instance, exact diagonalization (ED) studies of small clusters. Extending our work to the case of spinel systems (in which both A and B sites are magnetic) should be interesting, as magnetisation plateaux 52 and spin liquid ground states 53,54 in such systems are under investigation. Finally, it will be challenging to adapt either the functional RG method 55 or the renormalisation group method used recently in studying the m/m s = 1/3 plateau of the kagome system 15 to the plateaux we have predicted here for the pyrochlore.…”

Importance of anisotropic Coulomb interactions in the electronic and magnetic properties of Mn$_3$O$_4$

“…The exchange couplings of Mn 3 O 4 have been quantitatively estimated from the spin wave excitations measured by neutron scattering experiments, and have demonstrated that the exchange interactions are determined by the direct orbital overlap and the 90 • superexchange coupling between two Mn 3+ ions via an oxygen bridge. 10,12 Meanwhile, Mn 3 O 4 always exhibits insulating behavior with a band gap of about 2.0 eV. [13][14][15] Mn 3 O 4 is a challenging system to tackle by first- principles calculations, because strong electron correlations are combined with multiple degrees of freedom such as spin, orbital, charge, and lattice.…”