Understanding Covalent versus Spin–Orbit Coupling Contributions to Temperature-Dependent Electron Spin Relaxation in Cupric and Vanadyl Phthalocyanines

Abstract

Recent interest in transition-metal complexes as potential quantum bits (qubits) has reinvigorated the investigation of fundamental contributions to electron spin relaxation in various ligand scaffolds. From quantum computers to chemical and biological sensors, interest in leveraging the quantum properties of these molecules has opened a discussion of the requirements to maintain coherence over a large temperature range, including near room temperature. Here we compare temperature-, magnetic field position-, and concentration-dependent electron spin relaxation in copper­(II) phthalocyanine (CuPc) and vanadyl phthalocyanine (VOPc) doped into diamagnetic hosts. While VOPc demonstrates coherence up to room temperature, CuPc coherence times become rapidly T 1-limited with increasing temperature, despite featuring a more covalent ground-state wave function than VOPc. As rationalized by a ligand field model, this difference is ascribed to different spin–orbit coupling (SOC) constants for Cu­(II) versus V­(IV). The manifestation of SOC contributions to spin–phonon coupling and electron spin relaxation in different ligand fields is discussed, allowing for a further understanding of the competing roles of SOC and covalency in electron spin relaxation.

The Impact of Ligand Field Symmetry on Molecular Qubit Coherence

“…29 To illustrate the power of this approach in understanding spin-phonon coupling contributions to decoherence in molecular qubits, we turn to a comparison between vanadyl phthalocyanine (VOPc) and copper phthalocyanine (CuPc) (Figure 1A). 19 with D2d CuCl4 2possessing more spin-phonon coupling than D4h CuCl4 2owing to a greater number of totally symmetric modes. 22 Though totally symmetric vibrational modes dominate 0 coupling for both VOPc and CuPc, the change in point group between C4v and D4h nonetheless has important consequences for spin-phonon coupling.…”

Deconvolving Contributions to Decoherence in Molecular Electron Spin Qubits: A Dynamic Ligand Field Approach

“…The well‐studied class of V(IV) qubits contain experimental examples in each of the three decoherence regimes, providing an instructive conceptual comparison. The electron spin relaxation of vanadyl phthalocyanine (VOPc) has been studied in a glassy frozen solution, [59] a pure crystalline solid, [38] and diamagnetically diluted crystalline dispersions in titanyl phthalocyanine (TiOPc) host at 1 : 10, 1 : 100, and 1 : 1000 concentrations [38,49] . At 300 K in 1 : 10 dilution, VOPc exists in the spin‐spin regime, where T M is significantly smaller than T 1 owing to electronic dipolar contributions to decoherence.…”

“…The interplay between factors in the dynamic ligand field model can be illustrated by recent studies comparing Cu(II) and V(IV) S= qubit candidates [49,62] . It was experimentally shown that the T 1 of vanadyl phthalocyanine (VOPc) is longer than that of copper phthalocyanine (CuPc) at higher temperatures (>25 K) where the spin‐phonon regime dominates, [49] with VOPc exhibiting coherence up to room temperature [38] . These results can be rationalized and quantitatively understood using the spin‐phonon coupling factors found in Equation 5: (1) the energy of the ligand field excited state that spin‐orbit couples with the ground state, (2) the covalencies of the ligand‐metal bonds, and (3) the spin‐orbit coupling constant.…”

“…[45,46] To minimize the latter contribution, dilution of the paramagnetic qubit in a matrix of a diamagnetic analog is a commonly employed strategy. [49] The suppression of hyperfine coupling is attained through nuclear-spin-free ligand scaffolds and spin-free solvents, such as carbon disulfide, which have shown great success. [28] An additional key consideration is the spin-diffusion barrier, [50,51] in which nuclear spins that are within a 4-8 Å radius of the electron spin contribute only a small degree to decoherence.…”

“…The electron spin relaxation of vanadyl phthalocyanine (VOPc) has been studied in a glassy frozen solution, [59] a pure crystalline solid, [38] and diamagnetically diluted crystalline dispersions in titanyl phthalocyanine (TiOPc) host at 1:10, 1:100, and 1:1000 concentrations. [38,49] At 300 K in 1:10 dilution, VOPc exists in the spin-spin regime, where TM is significantly smaller than T1 owing to electronic dipolar contributions to decoherence. However, the 1:1000 dilution displays TM ~ T1 at 300 K, indicating TM is T1 limited.…”