Observation of Tunneling-Assisted Highly Forbidden Single-Photon Transitions in a Ni4 Single-Molecule Magnet

Abstract

Forbidden transitions between energy levels typically involve violation of selection rules imposed by symmetry and/or conservation laws. A nanomagnet tunneling between up and down states violates angular momentum conservation because of broken rotational symmetry. Here we report observations of highly forbidden transitions between spin states in a Ni4 single-molecule magnet in which a single photon can induce the spin to change by several timesh, nearly reversing the direction of the spin. These observations are understood as tunnelingassisted transitions that lift the standard ∆m = ±1 selection rule for single-photon transitions. These transitions are observed at low applied fields, where tunneling is dominated by the molecule's intrinsic anisotropy and the field acts as a perturbation. Such transitions can be exploited to create macroscopic superposition states that are not typically accessible through single-photon ∆m = ±1 transitions.There has been much recent attention to using spin systems as potential qubits [1][2][3][4]. Molecular nanomagnets are particularly attractive as spin qubits [4][5][6][7][8][9][10][11][12] because many of their properties can be chemically engineered. Single-molecule magnets (SMMs) are anisotropic molecular magnets, typically with large total spin, for which the spin is impelled to point along a preferred axis, the "easy" axis [13]. They exhibit remarkable quantum dynamics including tunneling between different orientations [14] and quantum-phase interference [15]. Here we present evidence of highly forbidden transitions in the Ni 4 SMM where the transitions are enabled by tunneling, which lifts the requirement of spin angular momentum conservation. We observe transitions in which the absorption of a single photon permits a near reversal of the molecule's macrospin, grossly violating the standard ∆m = ±1 selection rule. The quantum states that can be generated through these forbidden transitions are non-classical, having a substantial "macroscopicity" by a standard measure. Our results imply that the forbidden transitions observed in this system (and similar molecules with strong anisotropy) can be exploited to create highly nonclassical states with single-photon transitions.From a quantum coherence perspective, forbidden transitions have some distinct advantages: Since the matrix elements for these transitions are small, they tend to have long lifetimes. In addition, they can be less susceptible to magnetic-field fluctuations under certain circumstances, potentially leading to longer coherence times [3,12,16]. Forbidden transitions have been seen in SMMs with very strong tunneling produced by strongly broken symmetry [11,12,17]. In contrast, in our experiments the transitions are dominated by a modest intrinsic anisotropy with an applied field acting as a perturbation.We studied the S = 4 complex [Ni(hmp)(dmb)Cl] 4 (hereafter Ni 4 ), shown in the inset of Fig. 1. The molecule's large ligands isolate the magnetic centers within a crystal from each other [18]. In addition, there a...

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

“…The complex [Ni(hmp)(dmb)Cl] 4 (′Ni 4 ′), where dmb is 3,3‐dimethyl‐1‐butanol, and hmp − is the anion of 2‐hydroxymethylpyridine, is a well‐studied single‐molecule magnet that comprises four Ni 2+ ( s =1) ions in a tetragonally distorted tetrahedral arrangement; the S= 4 ground state displays easy‐axis (Ising type) magnetic anisotropy . With the state space of the MSH having a comparatively small dimension of 3 4 =81, which allows for quick matrix diagonalization, and in view of the available particularly sharp EPR data, Ni 4 represents a prototypical system to study the relation between many‐spin and giant‐spin models . MSH and GSH parameterizations were obtained from a number of complementary experiments, and while they perform similarly well in describing HF‐EPR data, major discrepancies were noted at the much smaller energy scale of the tunnel splitting in the ground doublet, affecting also Berry phase interference (BPI) patterns, that is, quenchings of as a function of the orientation and strength of an external magnetic field .…”

“…This observation casts a doubt on an earlier proposal attributing the extremely fast tunneling in the ground doublet to a transverse anisotropy term; connects the states indirectly, that is, in the second order of perturbation theory, via M =0. Notably, recent low‐frequency EPR measurements evidenced forbidden transitions associated with large changes in the projection quantum number, or , and afforded a direct determination of the energy splitting (tunneling gap) . However, the alleged refined determination of (compared to high‐field EPR results) from was subject to the neglect of higher‐order transverse terms, which requires justification from a microscopic viewpoint (i.e.…”

“…After giving instructions for the construction of the GSH through canonical effective Hamiltonian theory, and by the pseudospin approach, in the following section, we present applications to the indicated tetragonal Ni 4 SMM, that continues to be of high interest …”

Adjustable coupling and in situ variable frequency electron paramagnetic resonance probe with loop-gap resonators for spectroscopy up to X-band

“…3(a) highlights the tunnel splitting gap for these states near zero field. The slight difference in the parameters of the two conformational states leads to the doubling of the EPR spectra 22,23 provided that the microwave frequency is larger than tunneling gaps for both conformational states. The green and red arrows in the Fig.…”

On the Use of Classical and Quantum Fisher Information in Molecular Magnetism

“…In fact, linear superpositions generated through dipole-allowed transitions tend to have low values of H r , whereas linear superpositions with large values of H r tend to correspond to forbidden transitions with |M 1 − M 2 | > 1. A good compromise between the amplitude of a transition and the macroscopicity of the quantum state that this allows one to generate can be achieved close to level anticrossings, where the eigenstates exhibit strong fluctuations of the total spin projection [24].…”