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Vibronic Relaxation Pathways in Molecular Spin Qubit Na 9 [Ho(W 5 O 18 ) 2 ]·35H 2 O under Pressure

In order to explore how spectral sparsity and vibronic decoherence pathways can be controlled in a model qubit system with atomic clock transitions, we combined diamond anvil cell techniques with synchrotron-based far infrared spectroscopy and first-principles calculations to reveal the vibrational response of Na 9 [Ho(W 5 O 18 ) 2 ]·35H 2 O under compression. Because the hole in the phonon density of states acts to reduce the overlap between the phonons and f manifold excitations in this system, we postulated that pressure might move the HoO 4 rocking, bending, and asymmetric stretching modes that couple with the M J = ±5, ±2, and ±7 levels out of resonance, reducing their interactions and minimizing decoherence processes, while a potentially beneficial strategy for some molecular qubits, pressure slightly hardens the phonons in Na 9 [Ho(W 5 O 18 ) 2 ]·35H 2 O and systematically fills in the transparency window in the phonon response. The net result is that the vibrational spectrum becomes less sparse and the overlap with the various M J levels of the Ho 3+ ion actually increases. These findings suggest that negative pressure, achieved using chemical means or elongational strain, could further open the transparency window in this rare earth-containing spin qubit system, thus paving the way for the use of device surfaces and interface elongational/compressive strains to better manage decoherence pathways.

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Materials Data on Ho(SiNi)2 by Materials Project

Ho(NiSi)2 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Ho3+ is bonded in a distorted body-centered cubic geometry to eight equivalent Si4- atoms. All Ho–Si bond lengths are 3.04 Å. Ni+2.50+ is bonded to four equivalent Si4- atoms to form a mixture of edge and corner-sharing NiSi4 tetrahedra. All Ni–Si bond lengths are 2.30 Å. Si4- is bonded in a 9-coordinate geometry to four equivalent Ho3+, four equivalent Ni+2.50+, and one Si4- atom. The Si–Si bond length is 2.40 Å.

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Materials Data on Ho(NiB)2 by Materials Project

Ho(NiB)2 crystallizes in the monoclinic C2/c space group. The structure is three-dimensional. Ho3+ is bonded in a 6-coordinate geometry to six equivalent B3- atoms. There are a spread of Ho–B bond distances ranging from 2.69–2.88 Å. Ni+1.50+ is bonded in a 4-coordinate geometry to four equivalent B3- atoms. There are a spread of Ni–B bond distances ranging from 2.02–2.07 Å. B3- is bonded in a 8-coordinate geometry to three equivalent Ho3+, four equivalent Ni+1.50+, and one B3- atom. The B–B bond length is 1.74 Å.

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Materials Data on Ho(SiAu)2 by Materials Project

Ho(AuSi)2 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Ho3+ is bonded to eight equivalent Si4- atoms to form HoSi8 hexagonal bipyramids that share corners with sixteen equivalent AuSi4 tetrahedra, edges with four equivalent HoSi8 hexagonal bipyramids, edges with eight equivalent AuSi4 tetrahedra, and faces with four equivalent HoSi8 hexagonal bipyramids. All Ho–Si bond lengths are 3.22 Å. Au+2.50+ is bonded to four equivalent Si4- atoms to form AuSi4 tetrahedra that share corners with eight equivalent HoSi8 hexagonal bipyramids, corners with four equivalent AuSi4 tetrahedra, edges with four equivalent HoSi8 hexagonal bipyramids, and edges with four equivalent AuSi4 tetrahedra. All Au–Si bond lengths are 2.56 Å. Si4- is bonded in a 9-coordinate geometry to four equivalent Ho3+, four equivalent Au+2.50+, and one Si4- atom. The Si–Si bond length is 2.29 Å.

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Materials Data on Ho(IO3)3 by Materials Project

Ho(O3I)3 crystallizes in the monoclinic P2_1/c space group. The structure is three-dimensional. Ho3+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Ho–O bond distances ranging from 2.29–2.77 Å. There are nine inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted single-bond geometry to two I5+ atoms. There are one shorter (1.84 Å) and one longer (2.67 Å) O–I bond lengths. In the second O2- site, O2- is bonded in a 2-coordinate geometry to one Ho3+ and one I5+ atom. The O–I bond length is 1.86 Å. In the third O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one Ho3+ and one I5+ atom. The O–I bond length is 1.84 Å. In the fourth O2- site, O2- is bonded in a bent 150 degrees geometry to one Ho3+ and one I5+ atom. The O–I bond length is 1.83 Å. In the fifth O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two equivalent Ho3+ and one I5+ atom. The O–I bond length is 1.86 Å. In the sixth O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one Ho3+ and two I5+ atoms. There are one shorter (1.85 Å) and one longer (2.85 Å) O–I bond lengths. In the seventh O2- site, O2- is bonded in a distorted water-like geometry to one Ho3+ and one I5+ atom. The O–I bond length is 1.85 Å. In the eighth O2- site, O2- is bonded in a 1-coordinate geometry to three I5+ atoms. There are a spread of O–I bond distances ranging from 1.87–2.67 Å. In the ninth O2- site, O2- is bonded in a bent 120 degrees geometry to one Ho3+ and one I5+ atom. The O–I bond length is 1.85 Å. There are three inequivalent I5+ sites. In the first I5+ site, I5+ is bonded in a 6-coordinate geometry to six O2- atoms. In the second I5+ site, I5+ is bonded in a 3-coordinate geometry to four O2- atoms. In the third I5+ site, I5+ is bonded in a 3-coordinate geometry to three O2- atoms.

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Materials Data on Ho(Bi3O5)4 by Materials Project

Ho(Bi3O5)4 crystallizes in the cubic I23 space group. The structure is three-dimensional. Ho3+ is bonded to four equivalent O2- atoms to form HoO4 tetrahedra that share corners with twelve equivalent BiO5 square pyramids. All Ho–O bond lengths are 2.17 Å. Bi+3.08+ is bonded to five O2- atoms to form distorted BiO5 square pyramids that share corners with eight equivalent BiO5 square pyramids, a cornercorner with one HoO4 tetrahedra, and an edgeedge with one BiO5 square pyramid. There are a spread of Bi–O bond distances ranging from 2.10–2.55 Å. There are three inequivalent O2- sites. In the first O2- site, O2- is bonded in a trigonal planar geometry to three equivalent Bi+3.08+ atoms. In the second O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to three equivalent Bi+3.08+ atoms. In the third O2- site, O2- is bonded to one Ho3+ and three equivalent Bi+3.08+ atoms to form corner-sharing OHoBi3 tetrahedra.

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Materials Data on Ho(CuO2)2 by Materials Project

Ho(CuO2)2 crystallizes in the tetragonal I4_1/a space group. The structure is three-dimensional. Ho3+ is bonded in a 8-coordinate geometry to eight equivalent O2- atoms. There are four shorter (2.37 Å) and four longer (2.38 Å) Ho–O bond lengths. Cu+2.50+ is bonded in a square co-planar geometry to four equivalent O2- atoms. There is two shorter (1.90 Å) and two longer (1.92 Å) Cu–O bond length. O2- is bonded to two equivalent Ho3+ and two equivalent Cu+2.50+ atoms to form a mixture of distorted corner and edge-sharing OHo2Cu2 tetrahedra.

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Materials Data on Ho(AlC)3 by Materials Project

Ho(AlC)3 crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. Ho3+ is bonded to six equivalent C4- atoms to form HoC6 octahedra that share corners with six equivalent AlC4 tetrahedra, edges with six equivalent HoC6 octahedra, and edges with six equivalent AlC4 tetrahedra. All Ho–C bond lengths are 2.54 Å. There are two inequivalent Al3+ sites. In the first Al3+ site, Al3+ is bonded to four C4- atoms to form AlC4 tetrahedra that share corners with three equivalent HoC6 octahedra, corners with seven equivalent AlC4 tetrahedra, and edges with three equivalent HoC6 octahedra. The corner-sharing octahedral tilt angles are 19°. There are one shorter (2.02 Å) and three longer (2.10 Å) Al–C bond lengths. In the second Al3+ site, Al3+ is bonded in a trigonal planar geometry to three equivalent C4- atoms. All Al–C bond lengths are 1.98 Å. There are two inequivalent C4- sites. In the first C4- site, C4- is bonded in a 6-coordinate geometry to three equivalent Ho3+ and three equivalent Al3+ atoms. In the second C4- site, C4- is bonded to five Al3+ atoms to form corner-sharing CAl5 trigonal bipyramids.

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Materials Data on Ho(IO3)3 by Materials Project

Ho(O3I)3 crystallizes in the orthorhombic Pmmn space group. The structure is three-dimensional. Ho3+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Ho–O bond distances ranging from 2.19–2.74 Å. There are four inequivalent O2- sites. In the first O2- site, O2- is bonded in a 2-coordinate geometry to one Ho3+ and two I5+ atoms. There are one shorter (1.93 Å) and one longer (2.45 Å) O–I bond lengths. In the second O2- site, O2- is bonded in a distorted single-bond geometry to one Ho3+ and two equivalent I5+ atoms. Both O–I bond lengths are 2.80 Å. In the third O2- site, O2- is bonded in a distorted trigonal non-coplanar geometry to one Ho3+ and two equivalent I5+ atoms. Both O–I bond lengths are 2.12 Å. In the fourth O2- site, O2- is bonded in a 2-coordinate geometry to one Ho3+ and one I5+ atom. The O–I bond length is 1.90 Å. There are two inequivalent I5+ sites. In the first I5+ site, I5+ is bonded in a 6-coordinate geometry to six O2- atoms. In the second I5+ site, I5+ is bonded in a 4-coordinate geometry to four equivalent O2- atoms.

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Materials Data on Ho(BRu)4 by Materials Project

Ho(RuB)4 crystallizes in the tetragonal I4_1/acd space group. The structure is three-dimensional. Ho3+ is bonded in a 12-coordinate geometry to twelve equivalent B3- atoms. There are a spread of Ho–B bond distances ranging from 2.95–3.22 Å. Ru+2.25+ is bonded to five equivalent B3- atoms to form a mixture of distorted corner and edge-sharing RuB5 trigonal bipyramids. There are a spread of Ru–B bond distances ranging from 2.15–2.29 Å. B3- is bonded in a 6-coordinate geometry to three equivalent Ho3+, five equivalent Ru+2.25+, and one B3- atom. The B–B bond length is 1.79 Å.

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Materials Data on Ho(Co2B)6 by Materials Project

Ho(Co2B)6 crystallizes in the trigonal R-3m space group. The structure is three-dimensional. Ho3+ is bonded in a hexagonal planar geometry to six equivalent B3- atoms. All Ho–B bond lengths are 3.03 Å. There are two inequivalent Co+1.25+ sites. In the first Co+1.25+ site, Co+1.25+ is bonded in a T-shaped geometry to three equivalent B3- atoms. There are one shorter (2.10 Å) and two longer (2.11 Å) Co–B bond lengths. In the second Co+1.25+ site, Co+1.25+ is bonded to four equivalent B3- atoms to form a mixture of distorted edge and corner-sharing CoB4 trigonal pyramids. There are two shorter (2.02 Å) and two longer (2.04 Å) Co–B bond lengths. B3- is bonded in a 7-coordinate geometry to one Ho3+ and seven Co+1.25+ atoms.

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Materials Data on Ho(Ni2B)6 by Materials Project

Ho(Ni2B)6 crystallizes in the orthorhombic Cmc2_1 space group. The structure is three-dimensional. Ho3+ is bonded in a distorted hexagonal planar geometry to six B3- atoms. There are a spread of Ho–B bond distances ranging from 2.96–3.29 Å. There are seven inequivalent Ni+1.25+ sites. In the first Ni+1.25+ site, Ni+1.25+ is bonded to four B3- atoms to form a mixture of edge and corner-sharing NiB4 tetrahedra. There are a spread of Ni–B bond distances ranging from 1.98–2.09 Å. In the second Ni+1.25+ site, Ni+1.25+ is bonded in a 3-coordinate geometry to four B3- atoms. There are a spread of Ni–B bond distances ranging from 2.10–2.57 Å. In the third Ni+1.25+ site, Ni+1.25+ is bonded to four B3- atoms to form a mixture of distorted edge and corner-sharing NiB4 tetrahedra. There are a spread of Ni–B bond distances ranging from 2.02–2.10 Å. In the fourth Ni+1.25+ site, Ni+1.25+ is bonded in a T-shaped geometry to three B3- atoms. There are two shorter (2.00 Å) and one longer (2.09 Å) Ni–B bond lengths. In the fifth Ni+1.25+ site, Ni+1.25+ is bonded in a distorted T-shaped geometry to three B3- atoms. There are one shorter (2.05 Å) and two longer (2.13 Å) Ni–B bond lengths. In the sixth Ni+1.25+ site, Ni+1.25+ is bonded in a T-shaped geometry to three B3- atoms. There are a spread of Ni–B bond distances ranging from 2.03–2.10 Å. In the seventh Ni+1.25+ site, Ni+1.25+ is bonded to four B3- atoms to form a mixture of edge and corner-sharing NiB4 tetrahedra. There are a spread of Ni–B bond distances ranging from 2.01–2.08 Å. There are four inequivalent B3- sites. In the first B3- site, B3- is bonded in a 7-coordinate geometry to one Ho3+ and seven Ni+1.25+ atoms. In the second B3- site, B3- is bonded in a 7-coordinate geometry to one Ho3+ and seven Ni+1.25+ atoms. In the third B3- site, B3- is bonded in a 7-coordinate geometry to one Ho3+ and seven Ni+1.25+ atoms. In the fourth B3- site, B3- is bonded in a 9-coordinate geometry to one Ho3+ and eight Ni+1.25+ atoms.

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Materials Data on Ho(ZnP)3 by Materials Project

Ho(ZnP)3 crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. Ho3+ is bonded to six equivalent P3- atoms to form HoP6 octahedra that share corners with six equivalent ZnP4 tetrahedra, edges with six equivalent HoP6 octahedra, and edges with six equivalent ZnP4 tetrahedra. All Ho–P bond lengths are 2.83 Å. There are two inequivalent Zn2+ sites. In the first Zn2+ site, Zn2+ is bonded in a trigonal planar geometry to three equivalent P3- atoms. All Zn–P bond lengths are 2.30 Å. In the second Zn2+ site, Zn2+ is bonded to four P3- atoms to form ZnP4 tetrahedra that share corners with three equivalent HoP6 octahedra, corners with seven equivalent ZnP4 tetrahedra, and edges with three equivalent HoP6 octahedra. The corner-sharing octahedral tilt angles are 14°. There are one shorter (2.40 Å) and three longer (2.47 Å) Zn–P bond lengths. There are two inequivalent P3- sites. In the first P3- site, P3- is bonded to three equivalent Ho3+ and three equivalent Zn2+ atoms to form PHo3Zn3 octahedra that share corners with three equivalent PHo3Zn3 octahedra, corners with three equivalent PZn5 trigonal bipyramids, and edges with nine equivalent PHo3Zn3 octahedra. The corner-sharing octahedral tilt angles are 0°. In the second P3- site, P3- is bonded to five Zn2+ atoms to form PZn5 trigonal bipyramids that share corners with six equivalent PHo3Zn3 octahedra and corners with six equivalent PZn5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 69°.

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Materials Data on Ho(CuS)3 by Materials Project

Ho(CuS)3 crystallizes in the trigonal R-3 space group. The structure is three-dimensional. Ho3+ is bonded to six equivalent S2- atoms to form HoS6 octahedra that share corners with twelve equivalent CuS4 tetrahedra, edges with three equivalent HoS6 octahedra, and edges with six equivalent CuS4 tetrahedra. All Ho–S bond lengths are 2.74 Å. Cu1+ is bonded to four equivalent S2- atoms to form CuS4 tetrahedra that share corners with four equivalent HoS6 octahedra, corners with six equivalent CuS4 tetrahedra, edges with two equivalent HoS6 octahedra, and edges with three equivalent CuS4 tetrahedra. The corner-sharing octahedra tilt angles range from 17–55°. There are a spread of Cu–S bond distances ranging from 2.35–2.43 Å. S2- is bonded in a 6-coordinate geometry to two equivalent Ho3+ and four equivalent Cu1+ atoms.

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Materials Data on Ho(CuTe)3 by Materials Project

Ho(CuTe)3 crystallizes in the trigonal R-3 space group. The structure is three-dimensional. Ho3+ is bonded to six equivalent Te2- atoms to form HoTe6 octahedra that share corners with twelve equivalent CuTe4 tetrahedra, edges with three equivalent HoTe6 octahedra, and edges with six equivalent CuTe4 tetrahedra. There are three shorter (3.04 Å) and three longer (3.05 Å) Ho–Te bond lengths. Cu1+ is bonded to four equivalent Te2- atoms to form CuTe4 tetrahedra that share corners with four equivalent HoTe6 octahedra, corners with six equivalent CuTe4 tetrahedra, edges with two equivalent HoTe6 octahedra, and edges with three equivalent CuTe4 tetrahedra. The corner-sharing octahedra tilt angles range from 15–57°. There are a spread of Cu–Te bond distances ranging from 2.61–2.65 Å. Te2- is bonded to two equivalent Ho3+ and four equivalent Cu1+ atoms to form a mixture of distorted edge and corner-sharing TeHo2Cu4 octahedra. The corner-sharing octahedra tilt angles range from 1–91°.

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Materials Data on CuP2(HO)4 by Materials Project

CuP2(HO)4 crystallizes in the orthorhombic Pbca space group. The structure is two-dimensional and consists of two CuP2(HO)4 sheets oriented in the (0, 0, 1) direction. Cu2+ is bonded in a square co-planar geometry to four O2- atoms. All Cu–O bond lengths are 1.97 Å. P1+ is bonded in a distorted tetrahedral geometry to two H1+ and two O2- atoms. There is one shorter (1.41 Å) and one longer (1.42 Å) P–H bond length. There is one shorter (1.53 Å) and one longer (1.54 Å) P–O bond length. There are two inequivalent H1+ sites. In the first H1+ site, H1+ is bonded in a single-bond geometry to one P1+ atom. In the second H1+ site, H1+ is bonded in a single-bond geometry to one P1+ atom. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted bent 120 degrees geometry to one Cu2+ and one P1+ atom. In the second O2- site, O2- is bonded in a bent 120 degrees geometry to one Cu2+ and one P1+ atom.

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Materials Data on SrP2(HO)4 by Materials Project

SrP2(HO)4 crystallizes in the monoclinic C2/c space group. The structure is two-dimensional and consists of two SrP2(HO)4 sheets oriented in the (1, 0, 0) direction. Sr2+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Sr–O bond distances ranging from 2.65–2.67 Å. P1+ is bonded in a distorted tetrahedral geometry to two H1+ and two O2- atoms. Both P–H bond lengths are 1.42 Å. Both P–O bond lengths are 1.53 Å. There are two inequivalent H1+ sites. In the first H1+ site, H1+ is bonded in a single-bond geometry to one P1+ atom. In the second H1+ site, H1+ is bonded in a single-bond geometry to one P1+ atom. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted single-bond geometry to two equivalent Sr2+ and one P1+ atom. In the second O2- site, O2- is bonded in a distorted single-bond geometry to two equivalent Sr2+ and one P1+ atom.

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Materials Data on CdP2(HO)4 by Materials Project

CdP2(HO)4 crystallizes in the monoclinic C2/c space group. The structure is two-dimensional and consists of two CdP2(HO)4 sheets oriented in the (1, 0, 0) direction. Cd2+ is bonded to six O2- atoms to form distorted CdO6 octahedra that share corners with six equivalent PH2O2 tetrahedra and edges with two equivalent CdO6 octahedra. There are a spread of Cd–O bond distances ranging from 2.27–2.38 Å. P1+ is bonded to two H1+ and two O2- atoms to form distorted PH2O2 tetrahedra that share corners with three equivalent CdO6 octahedra. The corner-sharing octahedra tilt angles range from 36–56°. Both P–H bond lengths are 1.42 Å. There is one shorter (1.52 Å) and one longer (1.54 Å) P–O bond length. There are two inequivalent H1+ sites. In the first H1+ site, H1+ is bonded in a single-bond geometry to one P1+ atom. In the second H1+ site, H1+ is bonded in a single-bond geometry to one P1+ atom. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded in a bent 150 degrees geometry to one Cd2+ and one P1+ atom. In the second O2- site, O2- is bonded in a distorted trigonal planar geometry to two equivalent Cd2+ and one P1+ atom.

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