Probing Vibrational Symmetry Effects and Nuclear Spin Economy Principles in Molecular Spin Qubits

Abstract

The selection of molecular spin qubits with a long coherence time, T m , is a central task for implementing molecule-based quantum technologies. Even if a sufficiently long T m can be achieved through an efficient synthetic strategy and ad hoc experimental measurement procedures, many factors contributing to the loss of coherence still need to be thoroughly investigated and understood. Vibrational properties and nuclear spins of hydrogens are two of them. The former plays a paramount role, but a detailed theoretical investigation aimed at studying their effects on the spin dynamics of molecular complexes such as the benchmark phthalocyanine (Pc) is still missing, whereas the effect of the latter deserves to be examined in detail for such a class of compounds. In this work, we adopted a combined theoretical and experimental approach to investigate the relaxation properties of classical [Cu(Pc)] and a Cu II complex based on the ligand tetrakis(thiadiazole)porphyrazine (H 2 TTDPz), characterized by a hydrogen-free molecular structure. Systematic calculations of molecular vibrations exemplify the effect of normal modes on the spin–lattice relaxation process, unveiling a different contribution to T 1 depending on the symmetry of normal modes. Moreover, we observed that an appreciable T m enhancement could be achieved by removing hydrogens from the ligand.

The Impact of Ligand Field Symmetry on Molecular Qubit Coherence

“…6,25 The tensor, , describing the Zeeman effect has been implicated as a major source of spin-phonon coupling in molecular qubits. 15,24 Therefore, to understand the impact of symmetry on spin-phonon coupling, we first turn to the molecular origins of the values in a transition metal complex.…”

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

“…Second, the magnitude of the vibrational derivatives can be directly decreased by employing ligand frameworks with few vibrational modes that can undergo spin‐phonon coupling [48,82] . This can be accomplished by either (1) reducing the vibrational density of states at low energies, [62] as thermal phonon occupation is required for the Raman relaxation process, or (2) tailoring the coordination geometry to reduce spin‐phonon coupling by symmetry [48] . Dynamic ligand field analysis of a [CuCl 4 ] 2− model compound has illuminated how vibrational symmetry can engender an optimal coordination geometry for S= Cu(II) qubits [82] .…”

“…[47] Direct and indirect spin-spin interactions contributing to TM are represented in Figure 4A. Spin-spin decoherence arises primarily through hyperfine coupling with nuclear spins in the solvent, [26,28] hyperfine coupling with nuclear spins on the ligands, [48] and direct spin flip-flops between electronic spin centers. [45,46] To minimize the latter contribution, dilution of the paramagnetic qubit in a matrix of a diamagnetic analog is a commonly employed strategy.…”

“…[48,82] This can be accomplished by either (1) reducing the vibrational density of states at low energies, [62] as thermal phonon occupation is required for the Raman relaxation process, or (2) tailoring the coordination geometry to reduce spin-phonon coupling by symmetry. [48] Dynamic ligand field analysis of a [CuCl4] 2model compound has illuminated how vibrational symmetry can engender an optimal coordination geometry for S = ½ Cu(II) qubits. [82] Depending on the counterion, [CuCl4] 2can adopt a square planar (D4h) or distorted tetrahedral (D2d) crystal geometry.…”

“…times. [79] While vibrational symmetry effects have so far been investigated in the context of discrete molecular qubits, [48] such strategies will likely also prove important in designing arrays of qubits in MOFs, where a large density of low-energy phonons leads to enhanced spin-phonon coupling. [45,46] Notably, the gas phase equilibrium geometries of four-coordinate Cu(II) complexes are D2d.…”