Effects of stuffing on the atomic and electronic structure of the pyrochlore ${\mathrm{Yb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$

Effects of stuffing on the atomic and electronic structure of the pyrochlore ${Yb}_{2} {Ti}_{2} O_{7}$

Soham S. Ghosh and Efstratios Manousakis

Phys. Rev. B 97, 245117 – Published 11 June 2018

Abstract

There are reasons to believe that the ground state of the magnetic rare-earth pyrochlore ${Yb}_{2} {Ti}_{2} O_{7}$ is on the boundary between competing ground states. We have carried out ab initio density functional calculations to determine the most stable chemical formula as a function of the oxygen chemical potential and the likely location of the oxygen atoms in the unit cell of the “stuffed” system. We find that it is energetically favorable in the stuffed crystal (with an Yb replacement on a Ti site) to contain oxygen vacancies which dope the Yb $4 f$ orbitals and qualitatively change the electronic properties of the system. In addition, with the inclusion of the contribution of spin-orbit coupling (SOC) on top of the GGA + $U$ approach, we investigated the electronic structure and the magnetic moments of the most stable stuffed system. In our determined stuffed structure the valence bands as compared to those of the pure system are pushed down and a change in hybridization between the O $2 p$ orbitals and the metal ion states is found. Our first-principle findings should form a foundation for effective models describing the low-temperature properties of this material whose true ground state remains controversial.

Received 18 March 2018
Revised 4 May 2018

DOI:https://doi.org/10.1103/PhysRevB.97.245117

Physics Subject Headings (PhySH)

Crystal structure Electronic structure Magnetism

Pyrochlores

Density functional calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Soham S. Ghosh^1,2,* and Efstratios Manousakis^1,2,3

¹Department of Physics, Florida State University, Tallahassee, Florida 32306-4350, USA
²National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32306-4350, USA
³Department of Physics, University of Athens, Panepistimioupolis, Zografos, 157 84 Athens, Greece

^*Corresponding author: sohamsgh@gmail.com

Crystal field excitations from ${Yb}^{3 +}$ ions at defective sites in highly stuffed ${Yb}_{2} {Ti}_{2} O_{7}$

G. Sala, D. D. Maharaj, M. B. Stone, H. A. Dabkowska, and B. D. Gaulin

Phys. Rev. B 97, 224409 (2018)

Dilute stuffing in the pyrochlore iridate ${Eu}_{2} {Ir}_{2} O_{7}$

Prachi Telang, Kshiti Mishra, A. K. Sood, and Surjeet Singh

Phys. Rev. B 97, 235118 (2018)

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Vol. 97, Iss. 24 — 15 June 2018

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Figure 1
(a) The pyrochlore crystal structure of ${Yb}_{2} {Ti}_{2} O_{7}$ showing the corner-sharing tetrahedral Yb network in a conventional simple cubic lattice (Ti and O atoms have been omitted for clarity). (b) One Yb hexagon with a Ti atom at its center forming part of a $\{111\}$ Kagome plane. This Ti atom is replaced by an Yb atom in the stuffed system. Also shown are some selected Yb tetrahedra connected to the Kagome plane and perpendicular to it. One of the oxygen atoms the Ti is bonded to (shown in red) is removed to create a Wyckoff $f$ -site oxygen vacancy. The oxygen atom (shown in yellow) at the center of the Yb tetrahedra is removed to create a Wyckoff $b$ -site vacancy.
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Figure 2
Electronic band structure of ${Yb}_{2} {Ti}_{2} O_{7}$ calculated using the spin-GGA + $U$ + SOC method, for various values of $U$ and $J$ in Yb $f$ orbitals, shown along the crystal high-symmetry lines. In panel (a), we use $U = 0$ eV and $J = 0$ eV, which gives us a metallic ground state. In panel (b), we use $U = 3$ eV and $J = 0.7$ eV, which opens a small gap. In panel (c), we use $U = 6$ eV and $J = 1$ eV.
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Figure 3
Free energy of the oxygen-vacancy process in stuffed ${Yb}_{2} {Ti}_{2} O_{7}$ for $25 %$ and $12.5 %$ Yb stuffing. Three different types of unit cells with the chemical formula ${Yb}_{2 + x} {Ti}_{2 - x} O_{7 - δ}$ are shown and their free energies are compared with those of the corresponding stuffed structures with no oxygen vacancy. The vacancies are at Wyckoff $f$ sites. The limits of the oxygen chemical potential are shown by dotted lines. We use $U_{Yb} = 6$ eV, $J_{Yb} = 1$ eV, $U_{Ti} = 2$ eV, and $J_{Ti} = 0.8$ eV.
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Figure 4
(a) Electronic band structure of stoichiometric ${Yb}_{2} {Ti}_{2} O_{7}$ calculated using the spin-GGA + $U$ + SOC method [Fig 2 repeated]. (b) Electronic band structure of ${Yb}_{2 + x} {Ti}_{2 - x} O_{7 - x / 2}$ ( $x = 1 / 2$ ), shown along the crystal high-symmetry lines. The vacancy is in the Wyckoff $f$ site. The ten energy bands around the Fermi level are $4 f$ in character. Results are for $U_{Yb} = 6$ eV, $J_{Yb} = 1$ eV, $U_{Ti} = 2$ eV, and $J_{Ti} = 0.8$ eV.
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Figure 5
(a) Total and atom-projected density of states (DOS) of ${Yb}_{2} {Ti}_{2} O_{7}$ and (b) ${Yb}_{2 + x} {Ti}_{2 - x} O_{7 - x / 2}$ at $x = 1 / 2$ calculated using the spin-GGA + $U$ + SOC method. It can be seen that stuffing and oxygen vacancy modify the states between $- 5$ and 0 eV, which arise from Yb $4 f$ and O $2 p$ . Yb $4 f$ states make up the sharp peaks in the DOS that form the conduction bands, and are narrower in the stoichiometric system. The states between 2.5 and 5 eV are primarily Ti $3 d$ with some O $2 p$ character. The Fermi energies are set to zero. Results are for $U_{Yb} = 6$ eV, $J_{Yb} = 1$ eV, $U_{Ti} = 2$ eV, and $J_{Ti} = 0.8$ eV.
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Physical Review B

covering condensed matter and materials physics

Effects of stuffing on the atomic and electronic structure of the pyrochlore ${Yb}_{2} {Ti}_{2} O_{7}$

Soham S. Ghosh and Efstratios Manousakis

Phys. Rev. B 97, 245117 – Published 11 June 2018

Abstract

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Authors & Affiliations

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Crystal field excitations from ${Yb}^{3 +}$ ions at defective sites in highly stuffed ${Yb}_{2} {Ti}_{2} O_{7}$

G. Sala, D. D. Maharaj, M. B. Stone, H. A. Dabkowska, and B. D. Gaulin

Phys. Rev. B 97, 224409 (2018)

Dilute stuffing in the pyrochlore iridate ${Eu}_{2} {Ir}_{2} O_{7}$

Prachi Telang, Kshiti Mishra, A. K. Sood, and Surjeet Singh

Phys. Rev. B 97, 235118 (2018)

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Physical Review B

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Effects of stuffing on the atomic and electronic structure of the pyrochlore Yb2Ti2O7

Soham S. Ghosh and Efstratios Manousakis

Phys. Rev. B 97, 245117 – Published 11 June 2018

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

See Also

Crystal field excitations from Yb3+ ions at defective sites in highly stuffed Yb2Ti2O7

G. Sala, D. D. Maharaj, M. B. Stone, H. A. Dabkowska, and B. D. Gaulin

Phys. Rev. B 97, 224409 (2018)

Dilute stuffing in the pyrochlore iridate Eu2Ir2O7

Prachi Telang, Kshiti Mishra, A. K. Sood, and Surjeet Singh

Phys. Rev. B 97, 235118 (2018)

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Effects of stuffing on the atomic and electronic structure of the pyrochlore ${Yb}_{2} {Ti}_{2} O_{7}$

Crystal field excitations from ${Yb}^{3 +}$ ions at defective sites in highly stuffed ${Yb}_{2} {Ti}_{2} O_{7}$

Dilute stuffing in the pyrochlore iridate ${Eu}_{2} {Ir}_{2} O_{7}$