Zero-Field Quantum Tunnelling of the Magnetisation in a Series of High Energy-Barrier Dysprosium(III) Single-Molecule Magnets Fabrizio Ortu,1,§ Daniel Reta,1,§ You-Song Ding,2 Conrad A. P. Goodwin,1 Matthew P. Gregson,1 Eric J. L. McInnes,1 Richard E. P. Winpenny,1 Yan-Zhen Zheng,2,* Stephen T. Liddle,1,* David P. Mills1,* and Nicholas F. Chilton1,* 1School of Chemistry, The University of Manchester, Oxford Road, Manchester, M13 9PL, U.K. 2Frontier Institute of Science and Technology, and State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, 99 Yanxiang Road ， Xi’an, Shaanxi 710054, China. *For correspondence: [email protected]; [email protected]; [email protected]; [email protected] §These authors contributed equally. Abstract Energy barriers to magnetisation reversal (Ueff) in single-molecule magnets (SMMs) ttt have vastly increased recently, but only for the dysprosocenium SMM [Dy(Cp )2] ttt t [B(C6F5)4] (Cp = C5H2 Bu3-1,2,4) has this translated into a considerable increase in magnetic hysteresis temperatures. The lack of concomitant increases in hysteresis temperatures with Ueff values is due to efficient magnetic relaxation at zero-field, referred to as quantum tunnelling of the magnetisation (QTM); however, the exact nature of this phenomenon is unknown. Recent hypotheses suggest that both transverse dipolar magnetic fields and hyperfine coupling play a significant role in t this process for Dy(III) SMMs. Here, by studying the compounds [Dy( BuO)Cl(THF)5] [BPh4] (1), [K(18-crown-6-ether)(THF)2][Dy(BIPM)2] (2, BIPM = C{PPh2NSiMe3}2), ttt and [Dy(Cp )2][B(C6F5)4] (3), we show conclusively that neither of these processes are the main contributor to zero-field QTM for Dy(III) SMMs, and suggest that its origin instead owes to molecular flexibility. By analysing the vibrational modes of the three molecules, we show that the modes that most impact the magnetic ion occur at the lowest energies for 1, at intermediate energies for 2 and at higher energies for 3, in correlation with their ability to retain magnetisation. Therefore, we conclude that SMM performance could be improved by employing more rigid ligands with higher- energy metal-ligand vibrational modes. Introduction Single-molecule magnets (SMMs) are molecules that show slow relaxation of their magnetisation and thus can exhibit magnetic memory effects at the molecular level. This in principle permits the possibility of using individual molecules as bits in high- density data storage devices1, however current generation SMMs require very low temperatures to retain their magnetic memory effect; typically, this is the liquid helium regime rather than that of liquid nitrogen which is cheap and plentiful. This has remained the key roadblock, frustrating technological viability and exploitation. Therefore, one of the most important aims in this area is to raise the temperature at which the memory effect persists. SMMs display slow magnetic relaxation because of an internal energy barrier to the inversion of their magnetic moment (Ueff), and increasing the size of this barrier was postulated to be crucial for developing SMMs with higher operating temperatures. However, the magnetisation dynamics of monometallic lanthanide SMMs are multifaceted, and such compounds often display magnetic relaxation via pathways 2 that circumvent the Ueff barrier. For example, the current record holder for the largest 3 Ueff barrier does not show magnetic hysteresis at a temperature higher than the first 4 SMM reported nearly a quarter of a century ago , and so maximising Ueff is clearly not the sole consideration for overcoming low operating temperatures. Excluding the recent dysprosocenium SMM that shows magnetic hysteresis up to 60 K (ref. 5), the magnetic hysteresis loops of most high-barrier SMMs have a characteristic fingerprint, exhibiting a “waist-restricted” or “butterfly” shape, exemplified in Figure 2a. This directly highlights the key problem: there are significant magnetic memory effects (i.e. open hysteresis) at non-zero magnetic fields, but the hysteresis abruptly collapses at zero magnetic field. This efficient magnetic relaxation is often referred to as quantum tunnelling of the magnetisation (QTM), an effect that has been extensively studied in manganese-based SMMs6–10, and also for some of the more recent lanthanide-based SMMs11–13. However, QTM should not occur for monometallic Dy(III) compounds, which are the most common high-barrier SMMs3,5,14–17. This is because the ground electronic state is, by design, a pure mJ = ±15/2 Kramers doublet. According to Kramers’ theorem for half-integer total angular momentum there can be no mixing between the mJ = +15/2 and mJ = -15/2 states (which is required for efficient relaxation) in zero magnetic field. However, this idealised picture is clearly inconsistent with experimental data. One suggestion to explain the experimental observations has been that the presence of small transverse magnetic fields (dipolar or stray fields perpendicular to the main magnetic axis of the molecule) break the Kramers degeneracy in “zero” applied magnetic field, thus allowing QTM18,19. Indeed, numerous experiments have shown that diluting Dy(III) SMMs in a diamagnetic matrix to reduce the dipolar fields can reduce zero-field QTM17,20–23, however, this approach has not completely prevented efficient zero-field relaxation to yield SMMs with significantly higher operating temperatures. Another proposed source of QTM is hyperfine coupling of the electronic angular momentum J = 15/2 to the non-zero nuclear spin of the metal nucleus ( 161Dy and 163Dy have I = 5/2, comprising approximately 44% of the naturally abundant Dy isotopes), which can also break the Kramers degeneracy. Indeed, experiments at mK temperatures have shown that QTM occurs at avoided crossings that arise from hyperfine coupling12,13, and experiments with isotopically pure 161Dy (I = 5/2) vs. 164Dy (I = 0) have shown that the former has enhanced magnetic relaxation in the QTM regime24,25. However, these experiments have also not been able to completely remove the zero-field QTM step, and, importantly, have thus far only been performed on SMMs with moderate Ueff values, for which thermally activated relaxation may be important even at low temperatures. Therefore, whether nuclear hyperfine coupling or transverse dipolar fields are the dominant causes of QTM in Dy(III) SMMs with very large Ueff barriers has remained an open question. Herein we have synthesised dilute paramagnetic samples of three Dy(III) SMMs with 164 large Ueff barriers, employing natural abundance Dy and enriched Dy, and compared their magnetic hysteresis profiles to the undiluted natural abundance Dy analogues in order to directly probe the contribution of dipolar fields and nuclear hyperfine coupling to the zero-field QTM step at low temperatures. We focus on magnetic hysteresis as this is the crucial experiment that demonstrates the utility of a memory effect for an SMM. We find only a small effect on the zero-field step in the hysteresis loop upon both paramagnetic dilution and isotopic enrichment with nuclear-spin-free 164Dy, and conclude that the nature of the ligand environment encapsulating the Dy(III) ion is much more important than transverse dipolar fields or hyperfine coupling in determining zero-field magnetic relaxation. Results In order to address the question of the origin of QTM in high-performance SMMs, we t 26 selected the compounds [Dy( BuO)Cl(THF)5][BPh4] (1) , [K(18-crown-6-ether)(THF)2] 16 ttt ttt [Dy(BIPM)2] (2, BIPM = C{PPh2NSiMe3}2) , and [Dy(Cp )2][B(C6F5)4] (3, Cp = t 5 -1 C5H2 Bu3-1,2,4) , Figure 1, with Ueff barriers of 665, 565, and 1223 cm , respectively. Magnetic relaxation via the Orbach mechanism involves sequential direct single- phonon transitions between excited crystal field states27, and therefore there must be phonon modes of the same energy as the difference between subsequent crystal field states. Because the energies of the first excited crystal field states in the three compounds (397, 168 and 485 cm-1, respectively5,16,26) are at least two orders of magnitude larger than kT at 2 K (ca. 1.4 cm-1), the Orbach mechanism should have no contribution to magnetic relaxation at this temperature. Furthermore, all three compounds show a clear step in their magnetisation hysteresis curves at zero magnetic field and 2 K, blue traces in Figure 2, which directly indicates an efficient relaxation process with a strong field dependence. As there should only be a minor field dependence for the Raman and Orbach mechanisms28,29, this clearly indicates a QTM regime at zero field and 2 K. However, the three compounds display markedly different QTM efficiencies at zero field, leading to coercive fields of ca. 0, 11 and 28 kOe, respectively, despite all having well-isolated mJ = ±15/2 ground states. Figure 1. Molecular structures of complex ions in compounds 1 (a), 2 (b) and 3 (c). Counter-ions omitted for clarity. In order to examine the contribution of transverse dipolar fields to zero-field QTM, all three compounds were prepared with naturally abundant Dy at a ~5% dilution level in a matrix of the isostructural diamagnetic yttrium congener. The diluted samples (black traces in Figure 2) show slightly slower zero-field relaxation compared to their concentrated samples (blue traces in Figure 2). It is clear from these data that a significant zero-field step remains for compounds 1 and 2, and therefore that transverse dipolar fields cannot be the sole cause of QTM. This is a significant outcome towards the applicability of SMMs in high-density data storage, where the molecules would have to be tightly packed to realise high-density storage devices. To examine the contribution of the Dy nuclear spin to zero-field QTM, we prepared a third set of compounds with 96.80% isotopic purity 164Dy, again at a ~5% dilution level in the isostructural yttrium analogues.