Introduction of spin centers in single crystals of $\mathrm{B}{\mathrm{a}}_{2}\mathrm{CaW}{\mathrm{O}}_{6\ensuremath{-}\ensuremath{\delta}}$

Introduction of spin centers in single crystals of $B a_{2} CaW O_{6 - δ}$

Mekhola Sinha, Tyler J. Pearson, Tim R. Reeder, Hector K. Vivanco, Danna E. Freedman, W. Adam Phelan, and Tyrel M. McQueen

Phys. Rev. Materials 3, 125002 – Published 18 December 2019

Abstract

Developing the field of quantum information science (QIS) hinges upon designing viable qubits, the smallest unit in quantum computing. One approach to creating qubits is introducing paramagnetic defects into semiconductors or insulators. This class of qubits has seen success in the form of nitrogen-vacancy centers in diamond, divacancy defects in SiC, and P doped into Si. These materials feature paramagnetic defects in a low-nuclear-spin environment to reduce the impact of nuclear spin on electronic spin coherence. In this work, we report single-crystal growth of $B a_{2} CaW O_{6 - δ}$ and the coherence properties of introduced $W^{5 +}$ spin centers generated by oxygen vacancies. $B a_{2} CaW O_{6 - δ}$ ( $δ = 0$ ) is a B-site ordered double perovskite with a temperature-dependent octahedral tilting wherein oxygen vacancies generate $W^{5 +}$ ( $d^{1}$ ), $S = 1 / 2$ , $I = 0$ , centers. We characterized these defects by measuring the spin-lattice ( $T_{1}$ ) and spin-spin relaxation ( $T_{2}$ ) times from $T = 5 - 150 K$ . At $T = 5 K$ , $T_{1} = 310 ms$ and $T_{2} = 4 μ s$ , establishing the viability of these qubit candidates. With increasing temperature, $T_{2}$ remains constant up to $T = 60 K$ and then decreases to $T_{2} \sim 1 μ s$ at $T = 90 K$ , and remains roughly constant until $T = 150 K$ , demonstrating the remarkable stability of $T_{2}$ with increasing temperature. Together, these results demonstrate that systematic defect generation in double-perovskite structures can generate viable paramagnetic point centers for quantum applications and expand the field of potential materials for QIS.

Received 9 May 2019
Revised 29 August 2019

DOI:https://doi.org/10.1103/PhysRevMaterials.3.125002

Physics Subject Headings (PhySH)

Crystal defects Crystal growth Crystal structure Defects Electronic structure Point defects Structural properties

Single crystal materials

Crystal structures Electron paramagnetic resonance X-ray diffraction

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Mekhola Sinha ¹, Tyler J. Pearson², Tim R. Reeder³, Hector K. Vivanco¹, Danna E. Freedman², W. Adam Phelan¹, and Tyrel M. McQueen^1,3,4,*

¹Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
²Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA
³Department of Physics and Astronomy and the Institute for Quantum Matter, The Johns Hopkins University, Baltimore, Maryland 21218, USA
⁴Department of Materials Science and Engineering, The Johns Hopkins University, Baltimore, Maryland 21218, USA

^*Corresponding author: mcqueen@jhu.edu

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Vol. 3, Iss. 12 — December 2019

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Figure 1
(a) Double-perovskite structure of $B a_{2} CaW O_{6}$ ( $δ = 0$ ) containing alternate octahedra of $W O_{6}$ (orange) and $Ca O_{6}$ (gray) and 12 coordinate Ba atoms in the A site. The isolated $W O_{6}$ octahedra are primed to become spin centers upon introduction of electrons by removal of oxygen (red spheres). (b) A typical $B a_{2} CaW O_{6}$ single crystal. (c) Representative Laue diffraction along the (101) direction, perpendicular to the growth axis. (d) Oxygen vacancy concentration can be tuned by sintering under controlled oxygen partial pressure.
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Figure 2
Standard deviations from the pseudocubic lattice parameters (distortion index) for a single crystal of $B a_{2} CaW O_{6 - δ}$ with increasing temperature where β is the angle between the a and c axes. A line to guide the eye (red) shows the distortion index starts decreasing at around $T = 140 K$ and reaches closest to the pseudocubic structure at $T = 230 K$ (black line) before going up again. Crystal structure of $B a_{2} CaW O_{6 - δ}$ obtained from refined synchrotron XRPD data collected at $T = 295 K$ and $T = 100 K$ shows the double-perovskite structure containing alternate octahedra of $Ca O_{6}$ (gray) and $W O_{6}$ (orange). The structure shows an octahedral tilt pattern of ( $a^{-} b^{-} c^{0}$ ) at each temperature. This octahedral distortion is expected to activate low-lying phonon modes in the structure, resulting in faster relaxation of the spin.
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Figure 3
Heat capacity ( $C_{p}$ ) divided by temperature cubed ( $T^{3}$ ) vs log of temperature (T) for a single-crystal piece of $B a_{2} CaW O_{6 - δ}$ . The red line shows a fit to the experimental data, including the Einstein and Debye terms. Contributions of individual components are plotted below: pink – Debye 1 phonon mode heat capacity, green – Debye 2 phonon mode heat capacity, and blue – low-energy Einstein phonon mode. The low-lying Einstein peak describes the distortion in the local modes, while the high-temperature Debye mode is associated with higher energy vibrations due to atoms having lower masses, and the lower temperature Debye mode is associated with lower energy vibrations of atoms having higher atomic masses.
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Figure 4
Comparison between the resonance peak obtained from experimental cw spectra and the simulated fit to the experimental data to a spin doublet with $g = 1.96$ using easyspin.
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Figure 5
Pulse electron paramagnetic resonance spectroscopic data. (a) Inversion recovery curve used for calculating the spin-lattice relaxation time $T_{1}$ at $T = 40 K$ . (b) Temperature dependence plot of the rate of longitudinal relaxation ${T_{1}}^{- 1}$ with a quantitative fit to a combination of a direct, two “Raman” (Debye-phonon), and one “local” (Einstein-phonon) contributions. Parameters obtained from the fit (red line) are $A_{dir} = 0.49 (09) K^{- 1} s^{- 1}$ , $A_{ram 1} = 4.4 (8) \times 10^{6} s^{- 1}$ , ${A_{ram}}_{2} = 3.2 (8) \times 10^{8} s^{- 1}$ , and $A_{loc} = 8 (2) \times 10^{3} s^{- 1}$ . The associated Debye and Einstein temperatures were fixed at the values obtained from heat-capacity measurements. (c) Hahn-echo decay curve used to calculate spin-spin relaxation time $T_{2}$ . (d) Temperature dependence plot of $T_{2}$ and $T_{1}$ . (Lines to guide the eye show the trend followed by $T_{1}$ and $T_{2}$ with temperature.)
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Introduction of spin centers in single crystals of Ba2CaWO6−δ

Mekhola Sinha, Tyler J. Pearson, Tim R. Reeder, Hector K. Vivanco, Danna E. Freedman, W. Adam Phelan, and Tyrel M. McQueen

Phys. Rev. Materials 3, 125002 – Published 18 December 2019

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Introduction of spin centers in single crystals of $B a_{2} CaW O_{6 - δ}$