Quantum Spin Dynamics of Molecular Spintronic Devices Based on Single-molecule Nanomagnets Author Supervisor Kieran HYMAS Assoc. Prof. Alessandro SONCINI ORCID: 0000-0003-1761-4298 Submitted in total fulfilment of the requirements of the degree of Doctor of Philosophy School of Chemistry The University of Melbourne September 19, 2020 This page is intentionally left blank Abstract In recent years, molecular analogues to electronic devices have been sought after to remedy the practical limitations imposed on classical circuits by Moore's law leading to the inception of the multidisciplinary research field of molecular electronics. In addition to the miniaturisation of current electronic technologies, researchers have sought also to exploit the interplay between the spin degree of freedom inherent to magnetic molecules embedded in devices and to the local electronic currents to which they are coupled. Single- molecule magnets (SMMs), metal complexes with large magnetically anisotropic spin moments that exhibit slow relaxation effects, have enjoyed a position in the subfield of molecular spin-electronics (spintronics) as magnetic units that may act as elements in new molecular-scale spintronic technologies. In this thesis, three projects composed of theoretical models of spin transport through single-molecule magnet-based spintronic devices are presented which serve to predict and explain the quantum spin dynamics exhibited by novel device set-ups that are based on current state-of-the-art experimental systems. In the first project, I have contributed to the development of two models of spin-polarised transport through a general molecular nanomagnet device that is perturbed either by some time dependent, resonant perturbation or by a static perturbation. In the former case, a study of the time evolution of the quantum states of the nanomagnet revealed Rabi oscillations between spin states that are resonantly coupled by the perturbation, suggesting that these states could behave as a molecular qubit for quantum computation that is addressed with a spin-polarised current. In the steady-state limit of the time-dependent model the device functions as a spin current pump, amplifier and inverter which could be potentially useful for logic gates in novel circuitry based on the spin degree of freedom of an electronic current rather than on the charge; these effects are preserved in time-averaged current measurements of the device operating under a pulsed radiation regimen. In the second model, the spin inversion property of the device is preserved even when using a static rather than a time-dependent perturbation owing to a mixing between electric current blockaded and non-blockaded states. In the second project, I have contributed to the theoretical description of electron transport through a molecular break junction device housing a single terbium bis-phthalocyaninato (TbPc2) nanomagnet. The i ii model developed in this project is shown to capture all experimental properties measured for the single- molecule device, in particular, its magneto-conductance dependence on the applied magnetic field, gate and bias voltage. Crucially, using the model it was possible to confirm that different states of the molecular magnet give rise to disparate signals in the magneto-conductance which may be used to perform an electrical read-out of the molecular states of the device. At variance with previous interpretations that advocated for a strongly coherent regime of electron transport through the device, the behaviour of the experimentally observed magneto-conductance is shown here to be fully captured within the incoherent sequential tunnelling regime. In the third project, I have contributed to the understanding of an experimentally realised molecular spin valve by providing the first simulations of the hysteresis of the differential magneto-conductance for a hybrid molecular-quantum point contact three-terminal device, triggered by the slow relaxation of the SMMs grafted to the device in a time-dependent sweeping magnetic field. The transport dynamics were modelled here in a completely incoherent transport regime without necessitating the tenuous assumption of spin dependent Fano-resonance interference that were invoked in previous theoretical studies of the devices. The signature of the slow relaxation of two or more TbPc2 single-molecule magnets manifests in magneto-conductance measurements owing to a phonon-mediated direct relaxation process between the Tb electronic states leading to the transient population of non-conducting anti-parallel configurations of the TbPc2 magnetic moments. The model developed here was also able to capture well the temperature dependence of the experimentally measured molecular spin valve magneto-conductance as well as its dependence on bias voltage in the static field regime. Declaration In this declaration, I certify that this Ph.D. Thesis is comprised only of my original work except where otherwise stated. Appropriate credit has been given in this thesis whenever work of others has been ref- erenced. I also declare that this thesis is less than 100,000 words in length, exclusive of tables, maps, bibliographies and appendices. Kieran Hymas Date iii Preface This Ph.D. has been funded by the Australian Government through an Australian Government Research Training Program Scholarship from 2016 to 2019. Participation in international conferences has been fa- cilitated by funding from the University of Melbourne through a Science Abroad Travelling Scholarship (2017). The following papers have been published by the candidate and have been included as chapters in this thesis: K. Hymas and A. Soncini, \Molecular spintronics using single-molecule magnets under irradiation", Phys. Rev. B, 99, 245404, (2019) DOI: https://doi.org/10.1103/PhysRevB.99.245404 K. Hymas and A. Soncini, \Mechanisms of spin-charge conversion for the electrical read-out of 4f- quantum states in a TbPc2 single-molecule magnet spin transistor", Phys. Rev. B, 102, 045313, (2020) DOI: https://doi.org/10.1103/PhysRevB.102.045313 K. Hymas and A. Soncini, \Origin of the hysteresis of magneto-conductance in a supramolecular spin valve based on a TbPc2 single-molecule magnet", Phys. Rev. B, in press (2020) Kieran Hymas Date iv Acknowledgements The title doctor of philosophy (PhD) signifies that its bearer has contributed original research to their particular academic field of interest. More than that though, it represents passion, persistence, skill and integrity; it represents a constitution for creativity and a disposition for diligence. It is an object of prestige purchased only with late nights, many failures, few successes and almost certainly with some degree of caffeine addiction. While my postgraduate pursuit has been an incredible experience overall, I would feel disingenuous if not to say that it has been a true test of my character. Now, as I stride towards the end of this momentous journey and look back at how far I have come, I think back to a particular line pertaining to the philosophy of self-overcoming from Friedrich Nietzsche's magnum opus: Thus Spoke Zarathustra. The quote reads: Ready must thou be to burn thyself in thine own flame; how couldst thou become new if thou have not first become ashes! Friedrich Nietzsche, Thus Spoke Zarathustra Much like The Creating One who is idealised by Zarathustra in the passage above, after this academic trial by fire, I have appeared on the other side anew as a much better version of myself. It goes without saying that the pursuit of a PhD never occurs in a vacuum and therefore I have many people to thank for their support along the way. Among those that have shaped me into a better scientist, thinker and person, I must give special mention to my supervisor Associate Professor Alessandro Soncini. Alessandro's passion for science and his drive remain, to this day, unmatched by anybody that I have met. As well as his tremendous laughter, his bottomless motivation and unabashed passion for science are positively infectious and I would always leave his office cheery, reinvigorated and with a new perspective for the problem at hand. On top of this, Alessandro's academic history represents an intimidating tour de force in this challenging field and, on more than one occasion, I have found great inspiration for my own work while perusing his publications. I regularly half- joked throughout my PhD that I have learned more about science during my time in Alessandro's research v vi group than during my entire undergraduate degree. While this may be somewhat hyperbolic, I believe that the way I have \learned to learn" new skills and information during my PhD will stay with me for a great deal longer than any obscure chemical structure committed to memory during my undergraduate years. So then, I can't thank Alessandro enough for providing me with a position as a PhD student in his group, introducing me to this phenomenal field and offering his guidance and patience over these last four years. Furthermore, I count myself superbly lucky to have been a member of a research group filled with such kind, talented and interesting individuals. I thank Matteo Piccardo for the many coffees, beers and (most importantly) stimulating scientific and philosophical conversations, Shashank Rao for entertaining not only my scientific curiosity but also my interest in classical literature and philosophy, Simone Calvello and Haibei Huang for their many enlightening seminars and Jared Ashtree for his ruthless attention to detail when proof reading my writing or critiquing my practice talks. Throughout my postgraduate studies I have also received support from people outside of our research group. Asim Najibi has been my desk neighbour and closest friend throughout this degree and, in spite of his love for arcane middle-eastern music and his tendency towards dreadful puns, I must thank him extensively for making even the most frustrating days bearable. Furthermore, I would like to thank both Dr Lars Goerigk and Dr Wallace Wong for appearing with Alessandro on my PhD committee. By unhesitatingly assuming the role of committee chair, Lars also took on an extra degree of responsibility for which I am grateful.