Half-Integer Spin Triangles: Old Dogs, New Tricks

Spin triangles, that is, triangular complexes of half-integer spins, are the oldest molecular nanomagnets (MNMs). Their magnetic properties have been studied long before molecular magnetism was delineated as a research field. This Review presents the history of their study, with references to the parallel development of new experimental investigations and new theoretical ideas used for their interpretation. It then presents an indicative list of spin-triangle families to illustrate their chemical diversity. Finally, it makes reference to recent developments in terms of theoretical ideas and new phenomena, as well as to the relevance of spin triangles to spintronic devices and new physics.

Nuclear-spin-pattern control of electron-spin dynamics in a series of V(iv) complexes

Achieving control of phase memory relaxation times (T m) in metal ions is an important goal of molecular spintronics. Herein we provide the first evidence that nuclear-spin patterning in the ligand shell is an important handle to modulate T m in metal ions. We synthesized and studied a series of five V(iv) complexes with brominated catecholate ligands, [V(C6H4-n Br n O2)3]2- (n = 0, 1, 2, and 4), where the 79/81Br and 1H nuclear spins are arranged in different substitutional patterns. High-field, high-frequency (120 GHz) pulsed electron paramagnetic resonance spectroscopic analysis of this series reveals a pattern-dependent variation in T m for the V(iv) ion. Notably, we show that it is possible for two molecules to have starkly different (by 50%) T m values despite the same chemical composition. Nuclear magnetic resonance analyses of the protons on the ligand shell suggest that relative chemical shift (δ), controlled by the patterning of nuclear spins, is an important underlying design principle. Here, having multiple ligand-based protons with nearly identical chemical shift values in the ligand shell will, ultimately, engender a short T m for the bound metal ion.

Exploring Through-Space Spin-Spin Couplings for Quantum Information Processing: Facing the Challenge of Coherence Time and Control Quantum States

Nuclear magnetic resonance (NMR) is a powerful tool for studying quantum information processing (QIP). Recently quantum technologies have been proposed to overcome the challenges in large-scale NMR QIP. Furthermore, computational chemistry can promote its improvement. Nuclear spins-¹/₂ are natural qubits and have been used in most NMR quantum computation experiments. However, molecules that enable many qubits NMR QIP implementations should meet some requirements regarding their spectroscopic properties. Exceptionally large through-space (TS) P-P spin-spin coupling constants (SSCC or J) observed in 1,8-diphosphanaphthalenes (PPN) and in naphtho[1,8- cd]-1,2-dithiole phenylphosphines (NTP) were proposed and investigated to provide more accurate control within large-scale NMR QIP. Spectroscopic properties of PPN and NTP derivatives were explored by theoretical strategies using locally dense basis sets (LDBS). ³¹P chemical shifts (δ) calculated at the B3LYP/aug-cc-pVTZ-J level and TS P-P SSCCs at the PBE1PBE/pcJ-2 (LDBS-1) level are very close to the experimental data for the PPN molecule. Differently, for the NTP dimer, PBE1PBE/pcJ-2 (LDBS-2) predicts more accurate ³¹P δ, whereas PBE1PBE/Def2-TZVP (LDBS-1) forecasts more accurate TS P-P SSCCs. From our results, PPN_o-F, PPN_o-ethyl, and PPN_o-NH₂ were the best candidates for NMR QIP, in which the large TS SSCCS could face the need of long-time quantum gates implementations. Therefore, it could overcome natural limitations concerning the development of large-scale NMR.

Relevance of Dzyaloshinskii–Moriya spectral broadenings in promoting spin decoherence: a comparative pulsed-EPR study of two structurally related iron(iii) and chromium(iii) spin-triangle molecular qubits

Two related iron(iii) and chromium(iii) spin-triangle molecular qubits show coherent driving of their spins, and decoherence that is not significantly affected by Dzyaloshikskii–Moriya spectral broadenings.

Interactions between H-bonded [CuII3(μ3-OH)] triangles; a combined magnetic susceptibility and EPR study

X-band EPR spectroscopy and magnetic susceptibility studies elucidate the magnetic exchange scheme within a triangular CuII3(μ₃-OH) complex and the intermolecular dipolar interactions between two H-bonded CuII3(μ₃-OH) units.

A scalable architecture for quantum computation with molecular nanomagnets

A proposal for a magnetic quantum processor that consists of individual molecular spins coupled to superconducting coplanar resonators and transmission lines is carefully examined. We derive a simple magnetic quantum electrodynamics Hamiltonian to describe the underlying physics. It is shown that these hybrid devices can perform arbitrary operations on each spin qubit and induce tunable interactions between any pair of them. The combination of these two operations ensures that the processor can perform universal quantum computations. The feasibility of this proposal is critically discussed using the results of realistic calculations, based on parameters of existing devices and molecular qubits. These results show that the proposal is feasible, provided that molecules with sufficiently long coherence times can be developed and accurately integrated into specific areas of the device. This architecture has an enormous potential for scaling up quantum computation thanks to the microscopic nature of the individual constituents, the molecules, and the possibility of using their internal spin degrees of freedom.

Electronic Structure of a Mixed-Metal Fluoride-Centered Triangle Complex: A Potential Qubit Component

A novel fluoride-centered triangular-bridged carboxylate complex, [Ni2Cr(μ3-F)(O2C(t)Bu)6(HO2C(t)Bu)3] (1), is reported. Simple postsynthetic substitution of the terminal pivalic acids in 1 with pyridine and 4-methylpyridine led to the isolation of [Ni2Cr(μ3-F)(O2C(t)Bu)6(C5H5N)3] (2) and [Ni2Cr(μ3-F)(O2C(t)Bu)6((4-CH3)C5H4N)3] (3). Structural and magnetic characterizations carried out on the series reveal a dominating antiferromagnetic interaction between the nickel and chromium centers leading to an S = (1)/2 ground state with a very unusual value of geff = 2.48.

Integrated information storage and transfer with a coherent magnetic device

Quantum systems are inherently dissipation-less, making them excellent candidates even for classical information processing. We propose to use an array of large-spin quantum magnets for realizing a device which has two modes of operation: memory and data-bus. While the weakly interacting low-energy levels are used as memory to store classical information (bits), the high-energy levels strongly interact with neighboring magnets and mediate the spatial movement of information through quantum dynamics. Despite the fact that memory and data-bus require different features, which are usually prerogative of different physical systems – well isolation for the memory cells, and strong interactions for the transmission – our proposal avoids the notorious complexity of hybrid structures. The proposed mechanism can be realized with different setups. We specifically show that molecular magnets, as the most promising technology, can implement hundreds of operations within their coherence time, while adatoms on surfaces probed by a scanning tunneling microscope is a future possibility.

Multiple quantum coherences from hyperfine transitions in a vanadium(IV) complex

We report a vanadium complex in a nuclear-spin free ligand field that displays two key properties for an ideal candidate qubit system: long coherence times that persist at high temperature, T2 = 1.2 μs at 80 K, and the observation of quantum coherences from multiple transitions. The electron paramagnetic resonance (EPR) spectrum of the complex [V(C8S8)3](2-) displays multiple transitions arising from a manifold of states produced by the hyperfine coupling of the S = ½ electron spin and I = 7/2 nuclear spin. Transient nutation experiments reveal Rabi oscillations for multiple transitions. These observations suggest that each pair of hyperfine levels hosted within [V(C8S8)3](2-) are candidate qubits. The realization of multiple quantum coherences within a transition metal complex illustrates an emerging method of developing scalability and addressability in electron spin qubits. This study presents a rare molecular demonstration of multiple Rabi oscillations originating from separate transitions. These results extend observations of multiple quantum coherences from prior reports in solid-state compounds to the new realm of highly modifiable coordination compounds.

Coherent manipulation of electron spins in the {Cu3} spin triangle complex impregnated in nanoporous silicon

We report on coherent manipulation of electron spins in an antiferromagnetically coupled spin triangle {Cu3-X} (X=As, Sb) impregnated in freestanding nanoporous silicon (NS) by using 240 GHz microwave pulses. Rabi oscillations are observed and the spin coherence time is found to be T(2)=1066 ns at 1.5 K. This demonstrates that the {Cu3-X}:NS hybrid material provides a promising scheme for implementing spin-based quantum gates. By measuring the spin relaxation times of samples with different symmetries and environments we give evidence that a spin chirality is the main decoherence source of spin triangle molecules.

Direct observation of quantum coherence in single-molecule magnets

Direct evidence of quantum coherence in a single-molecule magnet in a frozen solution is reported with coherence times as long as T{2}=630+/-30 ns. We can strongly increase the coherence time by modifying the matrix in which the single-molecule magnets are embedded. The electron spins are coupled to the proton nuclear spins of both the molecule itself and, interestingly, also to those of the solvent. The clear observation of Rabi oscillations indicates that we can manipulate the spin coherently, an essential prerequisite for performing quantum computations.