Three-Leaf Quantum Interference Clovers in a Trigonal Single-Molecule Magnet

Atkinson, James H.; Inglis, Ross; Barco, Enrique del; Brechin, Euan K.

doi:10.1103/physrevlett.113.087201

Cited by 13 publications

(20 citation statements)

References 19 publications

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“…It turned out that both sets of GSH parameters differ appreciably for

λ > 1.5

, but for all practical intents they are the same for smaller

λ

, including

λ

=1, that is, effective Hamiltonian theory and the recently developed pseudospin strategy are in nice agreement for the ′actual′ MSH parameterization. We have further checked that this is also true for some other weakly‐coupled spin clusters, including an Fe 2 system, and two different trigonal Mn 3 SMMs, (results shall be presented elsewhere). Although the pseudospin technique is not limited to parameter regimes where perturbation theory converges, its relation to existing schemes of degenerate perturbation theory should be strictly investigated by future theoretical work .…”

Section: Resultsmentioning

confidence: 69%

“…However, in the growing number of weakly‐coupled spin clusters reported in the literature, the strong‐exchange limit fails qualitatively; one striking shortcoming is the strict absence of transverse anisotropy (anisotropy with respect to rotations about the molecular axis, the easy axis of SMMs) in systems with rotational symmetry of order n ≥3 . GSH terms of rank k ≥4 (i.e.…”

Section: Introductionmentioning

confidence: 99%

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Exact Mapping from Many‐Spin Hamiltonians to Giant‐Spin Hamiltonians

Tabrizi

Arbuznikov

Kaupp

2018

Chemistry A European J

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Thermodynamic and spectroscopic data of exchange-coupled molecular spin clusters (e.g. single-molecule magnets) are routinely interpreted in terms of two different models: the many-spin Hamiltonian (MSH) explicitly considers couplings between individual spin centers, while the giant-spin Hamiltonian (GSH) treats the system as a single collective spin. When isotropic exchange coupling is weak, the physical compatibility between both spin Hamiltonian models becomes a serious concern, due to mixing of spin multiplets by local zero-field splitting (ZFS) interactions ('S-mixing'). Until now, this effect, which makes the mapping MSH→GSH ('spin projection') non-trivial, had only been treated perturbationally (up to third order), with obvious limitations. Here, based on exact diagonalization of the MSH, canonical effective Hamiltonian theory is applied to construct a GSH that exactly matches the energies of the relevant (2S+1) states comprising an effective spin multiplet. For comparison, a recently developed strategy for the unique derivation of effective ('pseudospin') Hamiltonians, now routinely employed in ab initio calculations of mononuclear systems, is adapted to the problem of spin projection. Expansion of the zero-field Hamiltonian and the magnetic moment in terms of irreducible tensor operators (or Stevens operators) yields terms of all ranks k (up to k=2S) in the effective spin. Calculations employing published MSH parameters illustrate exact spin projection for the well-investigated [Ni(hmp)(dmb)Cl] ('Ni ') single-molecule magnet, which displays weak isotropic exchange (dmb=3,3-dimethyl-1-butanol, hmp is the anion of 2-hydroxymethylpyridine). The performance of the resulting GSH in finite field is assessed in terms of EPR resonances and diabolical points. The large tunnel splitting in the M=± 4 ground doublet of the S=4 multiplet, responsible for fast tunneling in Ni , is attributed to a Stevens operator with eightfold rotational symmetry, marking the first quantification of a k=8 term in a spin cluster. The unique and exact mapping MSH→GSH should be of general importance for weakly-coupled systems; it represents a mandatory ultimate step for comparing theoretical predictions (e.g. from quantum-chemical calculations) to ZFS, hyperfine or g-tensors from spectral fittings.

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“…It turned out that both sets of GSH parameters differ appreciably for

λ > 1.5

, but for all practical intents they are the same for smaller

λ

, including

λ

Section: Resultsmentioning

confidence: 69%

Section: Introductionmentioning

confidence: 99%

Exact Mapping from Many‐Spin Hamiltonians to Giant‐Spin Hamiltonians

Tabrizi

Arbuznikov

Kaupp

2018

Chemistry A European J

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“…Magnetometry measurements on two closely related Mn 3 species, [NEt 3 Mn 3 Zn 2 (sao) 3 O(N 3 ) 6 X 2 ] (saoH 2 =salicylaldoxime; X=Cl, Br), for the first time revealed theoretically expected symmetry‐enforced selection rules for quantum tunneling . A subsequent QTM spectroscopic investigation on a different Mn 3 complex, [Mn 3 O(Et‐sao) 3 (Et‐py) 3 ClO 4 ] (py=pyridine) evidenced threefold Berry phase interference (BPI) patterns (tunnel quenchings) as a function of the orientation of the transverse magnetic field, most clearly reflecting the trigonal molecular symmetry. Additionally, high‐field (HF) EPR experiments revealed the ramifications of unbroken trigonal and tetragonal molecular symmetry of Fe 3 Cr and Mn 12 t BuAc ([Mn 12 O 12 ( t BuCH 2 CO 2 ) 16 (CH 3 OH) 4 ] ⋅ CH 3 OH), respectively, in the modulation of the resonance fields as a function of the orientation of the field in the hard plane of magnetization.…”

Section: Introductionmentioning

confidence: 97%

“…Tunnel splittings between otherwise degenerate spin sublevels are caused by transverse anisotropy terms in the Hamiltonian describing the cluster. Recent progress in the understanding of the influence of transverse anisotropy on spectroscopic properties and the magnetization dynamics was achieved by experiments on small molecules, notably different Mn 3 species, and a star‐shaped Fe 3 Cr complex, all with trigonal symmetry. Magnetometry measurements on two closely related Mn 3 species, [NEt 3 Mn 3 Zn 2 (sao) 3 O(N 3 ) 6 X 2 ] (saoH 2 =salicylaldoxime; X=Cl, Br), for the first time revealed theoretically expected symmetry‐enforced selection rules for quantum tunneling .…”

Section: Introductionmentioning

confidence: 99%

“…In these systems, axial ZFS terms (commuting with

{\hat{S}}_{z}

) influence the resonance locations for an applied longitudinal field (along the easy axis), and transverse terms cause periodic modulations of the HF‐EPR resonances with respect to the orientation of the magnetic field in the hard plane of magnetization. Operators with ranks up to

k = 6

are also needed to account for experimentally detected BPI patterns in terms of giant‐spin models …”

Section: Introductionmentioning

confidence: 99%

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Construction of Giant‐Spin Hamiltonians from Many‐Spin Hamiltonians by Third‐Order Perturbation Theory and Application to an Fe₃Cr Single‐Molecule Magnet

Tabrizi

Arbuznikov

Kaupp

2016

Chemistry A European J

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A general giant-spin Hamiltonian (GSH) describing an effective spin multiplet of an exchange-coupled metal cluster with dominant Heisenberg interactions was derived from a many-spin Hamiltonian (MSH) by treating anisotropic interactions at the third order of perturbation theory. Going beyond the existing second-order perturbation treatment allows irreducible tensor operators of rank six (or corresponding Stevens operator equivalents) in the GSH to be obtained. Such terms were found to be of crucial importance for the fitting of high-field EPR spectra of a number of single-molecule magnets (SMMs). Also, recent magnetization measurements on trigonal and tetragonal SMMs have found the inclusion of such high-rank axial and transverse terms to be necessary to account for experimental data in terms of giant-spin models. While mixing of spin multiplets by local zero-field splitting interactions was identified as the major origin of these contributions to the GSH, a direct and efficient microscopic explanation had been lacking. The third-order approach developed in this work is used to illustrate the mapping of an MSH onto a GSH for an S=6 trigonal Fe3 Cr complex that was recently investigated by high-field EPR spectroscopy. Comparisons between MSH and GSH consider the simulation of EPR data with both Hamiltonians, as well as locations of diabolical points (conical intersections) in magnetic-field space. The results question the ability of present high-field EPR techniques to determine high-rank zero-field splitting terms uniquely, and lead to a revision of the experimental GSH parameters of the Fe3 Cr SMM. Indeed, a bidirectional mapping between MSH and GSH effectively constrains the number of free parameters in the GSH. This notion may in the future facilitate spectral fitting for highly symmetric SMMs.

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