Large orbital moment and spin-orbit enabled Mott transition in the Ising Fe honeycomb lattice of ${\mathrm{BaFe}}_{2}{({\mathrm{PO}}_{4})}_{2}$

Large orbital moment and spin-orbit enabled Mott transition in the Ising Fe honeycomb lattice of ${BaFe}_{2} {({PO}_{4})}_{2}$

Young-Joon Song, Kwan-Woo Lee, and Warren E. Pickett

Phys. Rev. B 92, 125109 – Published 4 September 2015

Abstract

${BaFe}_{2} {({PO}_{4})}_{2}$ is an unusual Ising insulating ferromagnet based on the ${Fe}^{2 +}$ spin $S = 2$ ion, the susceptibility of which suggests a large orbital component to the Fe local moment. We apply density functional theory based methods to obtain a microscopic picture of the competing interactions and the critical role of spin-orbit coupling (SOC) in this honeycomb lattice system. The low-temperature ferromagnetic phase displays a half-semimetallic Dirac point pinning the Fermi level and preventing gap opening before consideration of SOC, presenting a case in which correlation effects modeled by a repulsive Hubbard $U$ fail to open a gap. Simultaneous inclusion of both correlation and SOC drives a large orbital moment in excess of 0.7 $μ_{B}$ (essentially $L = 1$ ) for spin aligned along the $\hat{c}$ axis, with a gap comparable with the inferred experimental value. The large orbital moment accounts for the large Ising anisotropy, in spite of the small magnitude of the SOC strength on the $3 d$ (Fe) ion. Ultimately, the Mott-Hubbard gap is enabled by degeneracy lifting by SOC and the large Fe moments, rather than by standard Hubbard interactions alone. We suggest that competing orbital occupations are responsible for the structural transitions involved in the observed reentrant rhombohedral-triclinic-rhombohedral sequence.

Received 3 June 2015

DOI:https://doi.org/10.1103/PhysRevB.92.125109

Authors & Affiliations

Young-Joon Song¹, Kwan-Woo Lee^1,2,*, and Warren E. Pickett^3,†

¹Department of Applied Physics, Graduate School, Korea University, Sejong 339-700, Korea
²Department of Display and Semiconductor Physics, Korea University, Sejong 339-700, Korea
³Department of Physics, University of California, Davis, California 95616, USA

^*mckwan@korea.ac.kr
^†pickett@physics.ucdavis.edu

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Vol. 92, Iss. 12 — 15 September 2015

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Figure 1
(a) The rhombohedral structure, which contains ${PO}_{4}$ tetrahedra and edge-sharing ${FeO}_{6}$ octahedra, of ${BaFe}_{2} {({PO}_{4})}_{2}$ in its low and high $T$ regimes. (b) Top view of the two-dimensional Fe honeycomb lattice in the $\hat{a} - \hat{b}$ plane. The solid line indicates the unit cell, containing two Fe ions (brown circles). The oxygen ions (small red circles) in the upper layer are denoted by a dot.
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Figure 2
Nonmagnetic GGA band structure (left) and orbital projected densities of states (right) of the rhombohedral structure in the energy region containing Fe $d$ orbitals. Note that the O1 contribution is negligible and invisible here. The occupation confirms the $d^{6} {Fe}^{2 +}$ configuration and the density of states just below the gap shows a quasi-one-dimensional character due to the flat band that extends from $M$ to $K$ , hence all around the edge of the Brillouin zone. The bottom of the gap is denoted by the horizontal dashed line. The $k$ -point labels are for the conventional hexagonal lattice, viz. graphene.
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Figure 3
(a) FM band structures and DOSs within GGA in the range of Fe $d$ bands, indicating a half-semimetallic character in the minority bands (red dashed lines). A Dirac point appears almost exactly at $E_{F}$ at the point $K$ . (b) Overlaid FM GGA (red dashed lines) and GGA+SOC (green solid lines) band structures and total DOS enlarged near $E_{F}$ , in a $\pm 0.3$ -eV region containing only some of the minority $t_{2 g}$ manifold. The Dirac point is split by about 30 meV by SOC. Note that a tiny hole pocket compensating a tiny electron pocket at the $K$ point appears in a region that is not visible along the lines shown.
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Figure 4
Band structures near $E_{F}$ (a)–(c) within GGA+ $U$ and (d)–(f) from GGA+ $U$ +SOC, for $U = 1 - 4$ eV and $J = 0.7$ eV. The spin-up and -down bands in (a)–(c) are denoted by black solid and red dashed lines, respectively, while the bands including SOC (d)–(f) are shown by green solid lines. In (d) the scale is enlarged to allow the gap opening at the Dirac point to be seen. (g) Charge density plot of the minority $d$ orbitals, shown at the isovalue of 0.09 $e / Å^{3}$ . The $\hat{c}$ axis is along the vertical direction. This shape is nearly identical for all calculations performed here. (h) Total DOS at $U = 4$ eV in GGA+SOC+ $U$ , showing a 1.2-eV energy gap between the corresponding up and down bands.
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Figure 5
Variation of the Fe orbital $M_{L}$ moment, and energy gap $E_{g}$ , varying $U$ in GGA+ $U$ +SOC from 0 to 6 eV, with the spin directed along the $\hat{c}$ axis. From $U = 4$ eV, the gap is between the filled spin-up and the unfilled spin-down channels. The critical value of $U$ is in the 2.5–3-eV range.
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Physical Review B

covering condensed matter and materials physics

Large orbital moment and spin-orbit enabled Mott transition in the Ising Fe honeycomb lattice of ${BaFe}_{2} {({PO}_{4})}_{2}$

Young-Joon Song, Kwan-Woo Lee, and Warren E. Pickett

Phys. Rev. B 92, 125109 – Published 4 September 2015

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Physical Review B

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Large orbital moment and spin-orbit enabled Mott transition in the Ising Fe honeycomb lattice of BaFe2(PO4)2

Young-Joon Song, Kwan-Woo Lee, and Warren E. Pickett

Phys. Rev. B 92, 125109 – Published 4 September 2015

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Large orbital moment and spin-orbit enabled Mott transition in the Ising Fe honeycomb lattice of ${BaFe}_{2} {({PO}_{4})}_{2}$