The search for molecular spin qubits with suitable physical properties is one of the main targets on the way to the implementation of quantum spin technologies and quantum computing [1
]. Among other candidates for molecular spin qubits, vanadium-based complexes attracted special attention during the past decade due to their long decoherence times, both at cryogenic and room temperatures [3
]. The vanadium(IV) ion has an electron spin S
= 1/2 and a nuclear spin I
= 7/2 for stable isotope 51
V of nearly 100% natural abundance. These properties determine the intrinsically longer electron spin relaxation times compared to high-spin (S
> 1/2) ions, and, at the same time, provide a set of nuclear spin states for manipulation of multiple coherences. Some previous works were concerned with the frozen solutions of vanadium(IV) complexes [3
], while the others considered solid-state compounds and their relaxation properties. The longest decoherence time (also called dephasing, phase memory, sometimes transverse relaxation time) at room temperature Tm
~1 μs was obtained for vanadyl phthalocyanine complexes with nuclear spin-free ligands in the solid-state [6
Seeking for the molecular systems with the longest decoherence times available, one should also consider some of the stable organic radicals (S
= 1/2), which could have longer Tm
than vanadium ions at room temperatures. For example, triarylmethyl (trityl) radicals are actively used nowadays in biological applications of EPR at ambient conditions [16
]. For instance, it was demonstrated that even in aqueous solution at 310 K the dephasing time of the (immobilized) trityl label attached to DNA can reach Tm
= 1.4 μs, whereas in glassy trehalose powder at 300 K it is Tm
= 2.2 μs, both being longer than the record value for vanadium-based qubit being ~1 μs at 300 K [5
]. Therefore, in terms of the relaxation properties, vanadium-based qubits need further development to outperform the existing molecular competitors such as trityls.
Most of the studies on vanadium-based qubit candidates were dealing with specially designed molecular complexes, even if they were later assembled into the dedicated architectures such as MOFs [11
]. In this work, we approach the same task from the opposite side. In fact, we selected vanadium-containing complexes of lanthanides (initially designed for another research) and attempted to investigate what would be the intrinsic electron spin relaxation of vanadium moieties in such more complicated compounds. As we show below, such ad-hoc testing yielded unexpectedly promising results, and in this way, it outlines possible future strategies for designing complex structures incorporating vanadium-based qubits.
More specifically, it is often attractive to design compounds with multiple functionalities. For instance, developing complexes, which include lanthanide ions along with vanadium building blocks, would potentially pave the way for combining luminescent characteristics and even single-molecule magnetism with qubit-friendly properties of vanadium ions. Although at the moment, this is feasible only in the long run, investigation of representative compounds of this type might be insightful. With this purpose, we have studied the spectroscopic and relaxation properties in a series of vanadium complexes with lanthanides using EPR spectroscopy. All these complexes include VO6
octahedral units, which to the best of our knowledge, have not yet been considered as potential qubits at room temperatures (only low-temperature relaxation studies were performed for some complexes [13
]). At the first step of this research, diamagnetic lanthanides in the complexes with paramagnetic vanadium ions were addressed. Below we describe the developed approaches, the obtained results, and compare them with those of other previously studied vanadium-based molecular spin qubits.
3. Materials and Methods
New compounds (III and IV) were synthesized in air using deionized water as a solvent. Starting reagents were VOSO4·3H2O (>99%), cyclobutane-1,1-dicarboxylic acid (H2cbdc, 99%, “Acros Organics”), NaOH (>99%), Ba(NO3)2 (>98%), Y(NO3)3·5H2O (99.9%), Lu(NO3)3·6H2O (99.9%).
Synthesis of [NaLn(VO)2(cbdc)4(H2O)10]n (III: Ln = Y, IV: Ln = Lu): VOSO4·3H2O (0.100 g, 0.46 mmol) was dissolved in H2O (15 mL), then Ba(NO3)2 (0.120 g, 0.46 mmol) was added, and the reaction mixture was stirred for 20 min at 40 °C. The solution of Na2cbdc obtained by neutralization of H2cbdc (0.133 g, 0.92 mmol) and NaOH (0.074 g, 1.84 mmol) in H2O (10 mL) was added to the reaction mixture and the stirring was continued. After 10 min Y(NO3)3·5H2O (0.112 g, 0.31 mmol) or Lu(NO3)3·6H2O (0.144 g, 0.31 mmol) was added. The reaction mixture was stirred for 10 min more and left to stand for 1 h, then BaSO4 precipitate was removed by filtration. Blue solution (25 mL) was left to evaporate slowly in air at 22 °C. Blue crystals suitable for X-ray diffraction precipitated in 2 months. The crystals were separated from the mother liquor by filtration, washed with H2O (t = 22 °C) and air-dried at 22 °C.
The yield of III was 0.104 g (45.5% based on VOSO4·3H2O). Anal. Calc for C24H44NaO28V2Y (%): C, 28.99; H, 4.46. Found (%): C, 28.83; H, 4.48. IR (ATR), ν/cm–1: 3642 v.w, 3357 br.m, 3243 m, 3000 m, 2957 m, 1633 m, 1582 s, 1556 s, 1443 m, 1431 m, 1391 s, 1349 s, 1254 m, 1242 m, 1230 m, 1196 w, 1123 m, 1061 w, 1012 w, 1000 w, 968 s, 952 s, 924 m, 876 w, 843 w, 807 w, 773 m, 762 m, 725 s, 650 s, 611 s, 561 s, 532 s, 471 s, 451 s, 442 s, 420 s.
The yield of IV was 0.083 (33.5% based on VOSO4·3H2O). Anal. Calc for C24H44NaLuO28V2 (%): C, 26.68; H, 4.10. Found (%): C, 26.56; H, 4.12. IR (ATR), ν/cm–1: 3640 v.w, 3360 br. m, 3230 m, 3000 w, 2956 w, 1632 m, 1582 s, 1555 s, 1443 m, 1431 m, 1391 s, 1349 s, 1254 m, 1242 m, 1230 m, 1195 w, 1162 w, 1123 m, 1063 w, 1012 w, 1000 w, 968 s, 953 s, 924 m, 876 w, 844 w, 807 w, 773 m, 762 m, 725 s, 654 s, 562 s, 533 s, s, 469 s, 445 s, 439 s, 421 s, 407 s.
Infrared spectra of the complexes III and IV were recorded in the frequency range from 4000 to 400 cm−1 on a Perkin-Elmer Spectrum 65 Fourier transform infrared spectrometer equipped with Quest ATR Accessory (Specac) accessory. Elemental analysis of the synthesized compounds was carried out on a EuroEA 3000 CHNS analyzer (EuroVector, S.p.A.). The purity of compound samples was approved by PXRD. The powder patterns were measured on a Bruker D8 Advance diffractometer with LynxEye detector in Bragg-Brentano geometry, with the sample dispersed thinly on a zero-background Si sample holder, λ(CuKα) = 1.54060 Å, θ/θ scan with variable slits (irradiated length 20 mm) from 5° to 41° 2θ, stepsize 0.02°.
EPR measurements were done using a Bruker Elexsys E580 pulse/CW EPR spectrometer (Bruker Biospin, Rheinstetten, Germany) at X-band (9.7 GHz). The spectrometer possessed a cryostat and Oxford Instruments temperature control system allowing measurements within a range of 4 to 300 K. For CW measurements, polycrystalline powder samples were prepared, placed into quartz capillary tubes, and measured as they were. Further simulations we performed using EasySpin software for MatLab [24
Pulse EPR measurements were performed for 2 representative compounds (I
) in a frozen solution of water/glycerol or in glassy trehalose. In the first case, the compounds were dissolved in a water-glycerol mixture, shock-frozen and measured vs. temperature starting from the lowest limit (10 K). In the second case, the compounds were dissolved in a water-trehalose mixture, then shock-frozen in liquid nitrogen and lyophilized at low pressure (~10−2
Torr) to gain a powdered sample (of glassy trehalose), and then placed into a sample tube. This procedure followed our previous work [17
]. Note that in both of these cases, we aimed at diamagnetic dilution of the original solids containing vanadium-based building blocks, but still, we used rather concentrated samples from the point of view of common relaxation measurements in frozen solutions. The approximate concentrations in both water/glycerol and trehalose varied between 10 and 50 mM. Such concentrations corresponded to a roughly ~3 nm average distance between paramagnetic centers in frozen solution. In one of the previous work [3
] in solution, much lower concentrations were used (~1 mM), resulting in a separation between spin centers of about 11 nm. At the same time, some other experiments in diamagnetically diluted solids used a noticeably higher density of spins with a spin-spin separation of about 1 nm [6
]. From general considerations, it is clear that any applications of qubits would require their spatial density to be rather high. Therefore, for the diagnostics of the relaxation properties of vanadium centers in the present work, we did not aim at extreme degrees of dilution. Moreover, the room-temperature decoherence times should not be strongly dependent on the spin concentration within the above-mentioned limits. For verification, we also prepared and investigated the sample of I
in water/glycerol in a concentration ≈0.3 mM.
For transverse relaxation measurement, we employed a 2-pulse Hahn echo sequence (π/2 - τ - π - τ - echo), where interpulse delay τ was incremented, and pulse lengths used were 10–14 ns for π/2 and 20–28 ns for π pulses. For longitudinal relaxation time measurements, we used saturation-recovery sequence with pulse-train (PT) instead of the low-power saturating pulse: PT – T0 - π/2 - τ - π - τ - echo, where T0 was incremented and τ was fixed, and PT = [π - τ0 -]n with n~4–5 and τ0 being approximately the time where inverted echo crosses zero level. The pulse lengths were the same as those used for transverse relaxation measurements.
The X-ray diffraction data set for compound III
was collected on a Bruker SMART APEX II diffractometer equipped with a CCD detector (Mo-Kα
, λ = 0.71073 Å, graphite monochromator) [25
]. For both compounds, semiempirical absorption corrections were applied [26
]. The structure was solved by direct methods and refined by the full-matrix least-squares with anisotropic displacement parameters using the SHELX-2014 [27
] and Olex2 [28
] program packages. The hydrogen atoms were positioned geometrically and refined using the riding model. The crystallographic parameters and the structure refinement statistics for complex III
= 120 K were as follows: C24
w = 994.37 g·mol−1
, blue prismatic crystals, space group C
= 9.077(3), b
= 24.606(8), c
= 17.017(5) Å, β
= 104.752(7)°, V
= 3676(2) Å3
= 4, ρcalc
= 1.797 g cm–3
= 2.18 mm–1
, 2.46 ≤ θ
≤ 30.17°, 17577 measured reflections, 2815 reflections with I
= 0.0936, GooF
= 1.088, R1
)) = 0.0682, wR2
)) = 0.1767, R1
(all data) = 0.0876, wR2
(all data) = 0.1931, Tmin
= 0.4194/0.7461. The structural data for compound III
were deposited with the Cambridge Crystallographic Data Centre (CCDC 1964259; http://www.ccdc.cam.ac.uk/products/csd/request/