Insights on the coupling between vibronically active molecular vibrations and lattice phonons in molecular nanomagnets

Spin–lattice relaxation is a key open problem to understand the spin dynamics of single-molecule magnets and molecular spin qubits. While modelling the coupling between spin states and local vibrations allows to determine the more relevant molecular vibrations for spin relaxation, this is not sufficient to explain how energy is dissipated towards the thermal bath. Herein, we employ a simple and efficient model to examine the coupling of local vibrational modes with long-wavelength longitudinal and transverse phonons in the clock-like spin qubit [Ho(W₅O₁₈)₂]⁹⁻. We find that in crystals of this polyoxometalate the vibrational mode previously found to be vibronically active at low temperature does not couple significantly to lattice phonons. This means that further intramolecular energy transfer <em>via</em> anharmonic vibrations is necessary for spin relaxation in this system. Finally, we discuss implications for the spin–phonon coupling of [Ho(W₅O₁₈)₂]⁹⁻ deposited on a MgO (001) substrate, offering a simple methodology that can be extrapolated to estimate the effects on spin relaxation of different surfaces, including 2D materials.自旋-晶格弛豫（Spin–lattice relaxation）是理解单分子磁体（single-molecule magnets）与分子自旋量子比特（molecular spin qubits）自旋动力学的核心开放性问题。尽管对自旋态（spin states）与局域振动（local vibrations）间的耦合进行建模，可确定与自旋弛豫相关性更高的分子振动模式，但这仍不足以解释能量向热浴（thermal bath）耗散的具体机制。本文采用一种简洁高效的模型，研究了类时钟自旋量子比特（clock-like spin qubit）[Ho(W₅O₁₈)₂]⁹⁻中局域振动模式（local vibrational modes）与长波长纵声子、横声子（long-wavelength longitudinal and transverse phonons）的耦合作用。研究发现，在该多金属氧酸盐（polyoxometalate）的晶体中，此前被报道于低温下表现出振子活性（vibronically active）的振动模式，并未与晶格声子发生显著耦合。这意味着，该体系的自旋弛豫需经由非简谐振动（anharmonic vibrations）完成进一步的分子内能量转移。最后，本文探讨了沉积于氧化镁(MgO)(001)衬底上的[Ho(W₅O₁₈)₂]⁹⁻的自旋-声子耦合相关研究启示，并提出了一种可推广的简便方法，用以估算包括二维材料（2D materials）在内的各类表面对自旋弛豫的影响。