[Paper Review] Electronic structure of spin frustrated magnets: Mn$_3$O$_4$ spinel and postspinel

Shuichiro Hirai, Yoshihiro Gotō+4 more|arXiv (Cornell University)|Jun 12, 2014

Multiferroics and related materialsMaterials Science4 citations

TL;DR

This study combines optical absorption measurements and ab initio calculations to investigate the electronic band structures of Mn₃O₄ in its spinel and postspinel phases under ambient and high-pressure conditions. It reveals that both phases exhibit characteristic conduction band splitting and are charge-transfer insulators, with band gaps of 1.91(6) eV (spinel) and 0.94(2) eV (postspinel), respectively, and identifies Mn³⁺ d-t₂g and O 2p orbitals as forming antibonding states in the conduction band.

ABSTRACT

Mn$_3$O$_4$ is a spin frustrated magnet that adopts a tetragonally distorted spinel structure at ambient conditions and a CaMn$_2$O$_4$-type postspinel structure at high pressure. We conducted both optical measurements and \emph{ab} \emph{initio} calculations, and systematically studied the electronic band structures of both the spinel and postspinel Mn$_3$O$_4$ phases. For both phases, theoretical electronic structures are consistent with the optical absorption spectra, and display characteristic band-splitting of the conduction band. The band gap obtained from the absorption spectra is 1.91(6) eV for the spinel phase, and 0.94(2) eV for the postspinel phase. Both phases are charge-transfer type insulators. The Mn 3\emph{d} $t_2$$_g$ and O 2\emph{p} form antibonding orbitals situated at the conduction band with higher energy.

Motivation & Objective

• To systematically investigate the electronic band structures of Mn₃O₄ in its spinel and postspinel phases using combined optical and theoretical methods.
• To resolve discrepancies in prior theoretical studies of Mn₃O₄ band structure by validating results with experimental optical absorption spectra.
• To clarify the nature of the electronic gap and the role of d-orbital hybridization in Mn₃O₄ phases under structural and magnetic frustration.
• To examine the magnetic ground state and spin frustration in the postspinel phase using ab initio calculations.
• To establish the electronic origin of the observed insulating behavior in both phases, particularly the role of charge-transfer mechanisms.

Proposed method

• Performed optical diffuse reflectance measurements on bulk polycrystalline Mn₃O₄ spinel and postspinel samples, converting them to absorption spectra using the Kubelka-Munk equation.
• Conducted ab initio density functional theory (DFT) calculations with a Hubbard U parameter (U-J = 5 eV) to model electronic structures and density of states (DOS).
• Used X-ray diffraction to confirm phase purity and structural characteristics of both Mn₃O₄ phases.
• Analyzed local charge density maps and orbital projections to identify the nature of conduction band states (t₂g vs eg).
• Compared theoretical DOS with experimental absorption spectra to validate band gap and electronic transitions.
• Evaluated multiple magnetic configurations (AFM 3 and AFM 7) to assess stability and consistency with experimental magnetic behavior.

Experimental results

Research questions

• RQ1 What is the electronic band structure of Mn₃O₄ in its spinel and postspinel phases, and how do they differ under structural distortion?
• RQ2 How do the experimental optical absorption spectra compare with ab initio calculations in determining the band gap and electronic transitions?
• RQ3 What is the nature of the conduction band splitting in Mn₃O₄, and which orbitals (Mn 3d or O 2p) dominate the conduction band states?
• RQ4 Is Mn₃O₄ in the postspinel phase a charge-transfer insulator, and how does this relate to the observed band gap and electronic structure?
• RQ5 How does the small energy difference between competing antiferromagnetic states in the postspinel phase relate to its short-range magnetic order below 55 K?

Key findings

• The optical band gap of Mn₃O₄ spinel is 1.91(6) eV, while that of the postspinel phase is 0.94(2) eV, indicating a significant reduction under high pressure.
• Ab initio calculations confirm that both phases are charge-transfer type insulators, with the conduction band dominated by antibonding Mn 3d t₂g and O 2p hybridized states.
• Theoretical density of states (DOS) shows clear band splitting in the conduction band for both phases, consistent with experimental absorption spectra.
• In both phases, the higher-energy conduction band is primarily composed of Mn 3d e_g orbitals, while the lower-energy conduction band arises from Mn 3d t₂g and O 2p hybridization.
• The calculated energy difference between the two most stable antiferromagnetic states in the postspinel phase is only 3.1 meV/f.u., consistent with the observed short-range magnetic order below 55 K.
• Local charge density maps confirm that Mn³⁺ 3d t₂g orbitals hybridize strongly with O 2p orbitals in both phases, forming bonding and antibonding states that define the electronic band structure.