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The role of anharmonic phonons in under-barrier spin relaxation of single molecule magnets.

ABSTRACT: The use of single molecule magnets in mainstream electronics requires their magnetic moment to be stable over long times. One can achieve such a goal by designing compounds with spin-reversal barriers exceeding room temperature, namely with large uniaxial anisotropies. Such strategy, however, has been defeated by several recent experiments demonstrating under-barrier relaxation at high temperature, a behaviour today unexplained. Here we propose spin-phonon coupling to be responsible for such anomaly. With a combination of electronic structure theory and master equations we show that, in the presence of phonon dissipation, the relevant energy scale for the spin relaxation is given by the lower-lying phonon modes interacting with the local spins. These open a channel for spin reversal at energies lower than that set by the magnetic anisotropy, producing fast under-barrier spin relaxation. Our findings rationalize a significant body of experimental work and suggest a possible strategy for engineering room temperature single molecule magnets.

SUBMITTER: Lunghi A

PROVIDER: S-EPMC5343443 | biostudies-literature | 2017 Mar

REPOSITORIES: biostudies-literature

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The role of anharmonic phonons in under-barrier spin relaxation of single molecule magnets.

Lunghi Alessandro A Totti Federico F Sessoli Roberta R Sanvito Stefano S Sanvito Stefano S

Nature communications 20170306

The use of single molecule magnets in mainstream electronics requires their magnetic moment to be stable over long times. One can achieve such a goal by designing compounds with spin-reversal barriers exceeding room temperature, namely with large uniaxial anisotropies. Such strategy, however, has been defeated by several recent experiments demonstrating under-barrier relaxation at high temperature, a behaviour today unexplained. Here we propose spin-phonon coupling to be responsible for such ano ...[more]

PMID: 28262663

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Project description:Dy(III) bis-cyclopentadienyl (Cp) sandwich compounds exhibit extremely strong single-ion magnetic anisotropy which imbues them with magnetic memory effects such as magnetic hysteresis, and has put them at the forefront of high-performance single-molecule magnets (SMMs). Owing to the great success of design principles focused on maximising the anisotropy barrier, ever higher Ueff values have been reported leading to significant slow down of single-phonon Orbach spin relaxation. However, anisotropy-based SMM design has largely ignored two-phonon Raman spin relaxation, which is still limiting the temperatures at which a memory effect can be observed. In this work, we study the suppression of Raman relaxation through covalent bridging of the Cp ligands by alkyl chains, testing the hypothesis that increasing the rigidity of the ligand framework results in a blue shift of low frequency vibrations in the first coordination sphere of the Dy(III) ion. This reshaping of the vibrational low-energy density of states (DOS) results in lower occupation of pseudo-acoustic phonons available to drive Raman relaxation at low temperatures. We simulate Orbach and Raman spin relaxation in a series of zero-, mono-, di- and tri-bridged [Dy(Cpttt)2]+ analogues fully ab initio, using a quantum mechanics (QM)/molecular mechanics (MM) condensed phase embedding protocol in a periodic solvent matrix as a generic and experimentally testable environment model that can include (pseudo-)acoustic phononic degrees of freedom. We show that this approach can simulate magnetic relaxation dynamics in the condensed phase for the existing non-bridged [Dy(Cpttt)2]+ compound with quantitative experimental accuracy. Subsequently, we find a significant slowing down of Raman relaxation can be achieved for the singly-bridged SMM, while the introduction of further bridges leads to faster relaxation. A key result being that we find the two-phonon Raman rates correlate with the purity of the first-excited Kramers doublet in terms of its mJ = ±13/2 content. Even though the bridging design principle is successful at progressively reshaping the low-energy DOS, the introduction of linker atoms in the equatorial plane successively degrades magnetic anisotropy, suggesting the importance of refined design of the linker chemistry. The accuracy of our results emphasises the value of a generic periodic solvent embedding model, such that it permits the modelling of molecular spin dynamics in the condensed phase without knowledge of a crystal structure. This allows the study of hypothetical molecules or aggregates under real-world conditions, which we expect to have utility beyond the field of molecular magnetism.

Project description:We report a dysprosium(iii) bis(methanediide) single molecule magnet (SMM) where stabilisation of the highly magnetic states and suppression of mixing of opposite magnetic projections is imposed by a linear arrangement of negatively-charged donor atoms supported by weak neutral donors. Treatment of [Ln(BIPMTMS)(BIPMTMSH)] [Ln = Dy, 1Dy; Y, 1Y; BIPMTMS = {C(PPh2NSiMe3)2}2-; BIPMTMSH = {HC(PPh2NSiMe3)2}-] with benzyl potassium/18-crown-6 ether (18C6) in THF afforded [Ln(BIPMTMS)2][K(18C6)(THF)2] [Ln = Dy, 2Dy; Y, 2Y]. AC magnetic measurements of 2Dy in zero DC field show temperature- and frequency-dependent SMM behaviour. Orbach relaxation dominates at high temperature, but at lower temperatures a second-order Raman process dominates. Complex 2Dy exhibits two thermally activated energy barriers (U eff) of 721 and 813 K, the largest U eff values for any monometallic dysprosium(iii) complex. Dilution experiments confirm the molecular origin of this phenomenon. Complex 2Dy has rich magnetic dynamics; field-cooled (FC)/zero-field cooled (ZFC) susceptibility measurements show a clear divergence at 16 K, meaning the magnetic observables are out-of-equilibrium below this temperature, however the maximum in ZFC, which conventionally defines the blocking temperature, T B, is found at 10 K. Magnetic hysteresis is also observed in 10% 2Dy@2Y at these temperatures. Ab initio calculations suggest the lowest three Kramers doublets of the ground 6H15/2 multiplet of 2Dy are essentially pure, well-isolated |±15/2, |±13/2 and |±11/2 states quantised along the C[double bond, length as m-dash]Dy[double bond, length as m-dash]C axis. Thermal relaxation occurs via the 4th and 5th doublets, verified experimentally for the first time, and calculated U eff values of 742 and 810 K compare very well to experimental magnetism and luminescence data. This work validates a design strategy towards realising high-temperature SMMs and produces unusual spin relaxation behaviour where the magnetic observables are out-of-equilibrium some 6 K above the formal blocking temperature.

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The role of anharmonic phonons in under-barrier spin relaxation of single molecule magnets.

Publications

The role of anharmonic phonons in under-barrier spin relaxation of single molecule magnets.

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