Relationship between Torsion and Anisotropic Exchange Coupling in a TbIII-Radical-Based Single-Molecule Magnet

Ab initio-based determination of lanthanoid-radical exchange as visualised by inelastic neutron scattering

Magnetic exchange coupling can modulate the slow magnetic relaxation in single-molecule magnets. Despite this, elucidation of exchange coupling remains a significant challenge for the lanthanoid(iii) ions, both experimentally and computationally. In this work, the crystal field splitting and 4f-π exchange coupling in the erbium-semiquinonate complex [ErTp2dbsq] (Er-dbsq; Tp- = hydro-tris(1-pyrazolyl)borate, dbsqH2 = 3,5-di-tert-butyl-1,2-semiquinone) have been determined by inelastic neutron scattering (INS), magnetometry, and CASSCF-SO ab initio calculations. A related complex with a diamagnetic ligand, [ErTp2trop] (Er-trop; tropH = tropolone), has been used as a model for the crystal field splitting in the absence of coupling. Magnetic and INS data indicate antiferromagnetic exchange for Er-dbsq with a coupling constant of Jex = -0.23 meV (-1.8 cm-1) (-2Jex formalism) and good agreement is found between theory and experiment, with the low energy magnetic and spectroscopic properties well modelled. Most notable is the ability of the ab initio modelling to reproduce the signature of interference between localised 4f states and delocalised π-radical states that is evident in the Q-dependence of the exchange excitation. This work highlights the power of combining INS with EPR and magnetometry for determination of ground state properties, as well as the enhanced capability of CASSCF-SO ab initio calculations and purposely developed ab initio-based theoretical models. We deliver an unprecedentedly detailed representation of the entangled character of 4f-π exchange states, which is obtained via an accurate image of the spin-orbital transition density between the 4f-π exchange coupled wavefunctions.

Spatially Resolving Electron Spin Resonance of π-Radical in Single-molecule Magnet

The spintronic properties of magnetic molecules have attracted significant scientific attention. Special emphasis has been placed on the qubit for quantum information processing. The single-molecule magnet bis(phthalocyaninato (Pc)) Tb(III) (TbPc2) is one of the best examined cases in which the delocalized π-radical electron spin of the Pc ligand plays the key role in reading and intermediating the localized Tb spin qubits. We utilized the electron spin resonance (ESR) technique implemented on a scanning tunneling microscope (STM) and use it to measure local the ESR of a single TbPc2 molecule decoupled from the Cu(100) substrate by a two-monolayer NaCl film to identify the π-radical spin. We detected the ESR signal at the ligand positions under the resonance condition expected for an S = 1/2 spin. The results reveal that the π-radical electron is delocalized within the ligands and exhibits intramolecular coupling susceptible to the chemical environment.

Observation of Yu-Shiba-Rusinov States and Inelastic Tunneling Spectroscopy for Intramolecule Magnetic Exchange Interaction Energy of Terbium Phthalocyanine (TbPc) Species Adsorbed on Superconductor NbSe2

We investigated the spin properties of the terbium phthalocyanine (TbPc) species adsorbed on the superconductor NbSe2 surface using scanning tunneling microscopy and spectroscopy. TbPc2 is a molecule in a class of single-molecule magnets (SMMs), and the use of superconductor electrodes attracts attention for the application to the devices using the spin degree of freedom. TbPc is a building block of TbPc2 and can reveal the spin component's behavior. In the experiment, TbPc species were placed on the surface of the superconductor NbSe2. We measured Yu-Shiba-Rusinov (YSR) states caused by the interaction between the superconducting state and magnetic impurity and inelastic tunneling spectroscopy (IETS) for the spin excitation, below 1 K. We also measured the Kondo state formed by the magnetic singlet formation. We detected the radical spin at the ligand position of the TbPc by the presence of the Kondo peak and demonstrated that the radical spin forms the YSR feature. In addition, the exchange interaction energy (Eex) between the spins of the radical ligand (Pc) and the center 4f metal atom (Tb3+) is determined by using the IETS technique. Eex is a critical parameter that determines the blocking temperature, below which the sample behaves as an SMM. IETS results show that the statistical distribution of Eex has peaked at 1.3, 1.6, and 1.9 meV. The energy range is comparable to the recent theoretical calculation result. In addition, we show that the energy variation is correlated with the bonding configuration of TbPc.

Molecular S = 2 High-Spin, S = 0 Low-Spin and S = 0 ⇄ 2 Spin-Transition/-Crossover Nickel(II)-Bis(nitroxide) Coordination Compounds

Heterospin systems have a great advantage in frontier orbital engineering since they utilize a wide diversity of paramagnetic chromophores and almost infinite combinations and mutual geometries. Strong exchange couplings are expected in 3d–2p heterospin compounds, where the nitroxide (aminoxyl) oxygen atom has a direct coordination bond with a nickel(II) ion. Complex formation of nickel(II) salts and tert-butyl 2-pyridyl nitroxides afforded a discrete 2p–3d–2p triad. Ferromagnetic coupling is favored when the magnetic orbitals, nickel(II) dσ and radical π*, are arranged in a strictly orthogonal fashion, namely, a planar coordination structure is characterized. In contrast, a severe twist around the coordination bond gives an orbital overlap, resulting in antiferromagnetic coupling. Non-chelatable nitroxide ligands are available for highly twisted and practically diamagnetic complexes. Here, the Ni–O–N–Csp2 torsion (dihedral) angle is supposed to be a useful metric to describe the nickel ion dislocated out of the radical π* nodal plane. Spin-transition complexes exhibited a planar coordination structure in a high-temperature phase and a nonplanar structure in a low-temperature phase. The gradual spin transition is described as a spin equilibrium obeying the van’t Hoff law. Density functional theory calculation indicates that the energy level crossing of the high- and low-spin states. The optimized structures of diamagnetic and high-spin states well agreed with the experimental large and small torsions, respectively. The novel mechanism of the present spin transition lies in the ferro-/antiferromagnetic coupling switch. The entropy-driven mechanism is plausible after combining the results of the related copper(II)-nitroxide compounds. Attention must be paid to the coupling parameter J as a variable of temperature in the magnetic analysis of such spin-transition materials. For future work, the exchange coupling may be tuned by chemical modification and external stimulus, because it has been clarified that the parameter is sensitive to the coordination structure and actually varies from 2J/kB = +400 K to −1400 K.

A Hidden Coordination-Bond Torsional Deformation as a Sign of Possible Spin Transition in Nickel(II)-Bis(nitroxide) Compounds

Complex formation of nickel(II) tetrafluoroborate and tert-butyl 5-phenyl-2-pyridyl nitroxide (phpyNO) in the presence of sodium cyanate gave a discrete molecule [Ni(phpyNO)2(X)2] (X = NCO). The Ni-O-N-Csp2 torsion angles were reduced on heating; 33.5(5)° and 36.2(4)° at 100 K vs. 25.7(10)° and 32.3(11)° at 400 K. The magnetic behavior was almost diamagnetic below ca. 100 K, and the χmT value reached 1.04 cm3 K mol-1 at 400 K. An analysis using the van't Hoff equation indicates a possible spin transition at T1/2 >> 400 K. Density functional theory calculation shows that the singlet-quintet energy gap decreases as the structural change from 100 to 400 K. The geometry optimization results suggest that the diamagnetic state has the Ni-O-N-Csp2 torsion angles of 32.7° while the Stotal = 2 state has those of 11.9°. The latter could not be experimentally observed even at 400 K. After overviewing the results on the known X = Br, Cl, and NCS derivatives, the magnetic behavior is described in a common phase diagram. The Br and Cl compounds undergo the energy level crossing of the high-/low-spin states, but the NCS and NCO compounds do not in a conventional experimental temperature range. The spin transition mechanism in this series involves the exchange coupling switch between ferro- and antiferromagnetic interactions, corresponding to the high- and low-spin phases, respectively.

Inter-Kramers Transitions and Spin-Phonon Couplings in a Lanthanide-Based Single-Molecule Magnet

Spin-phonon coupling plays a critical role in magnetic relaxation in single-molecule magnets (SMMs) and molecular qubits. Yet, few studies of its nature have been conducted. Phonons here refer to both intermolecular and intramolecular vibrations. In the current work, we show spin-phonon couplings between IR-active phonons in a lanthanide molecular complex and Kramers doublets (from the crystal field). For the SMM Er[N(SiMe3)2]3 (1, Me = methyl), the couplings are observed in the far-IR magnetospectroscopy (FIRMS) of crystals with coupling constants ≈ 2-3 cm-1. In particular, one of the magnetic excitations couples to at least two phonon excitations. The FIRMS reveals at least three magnetic excitations (within the 4I15/2 ground state/manifold; hereafter, manifold) at 0 T at 104, ∼180, and 245 cm-1, corresponding to transitions from the ground state, MJ = ±15/2, to the first three excited states, MJ = ±13/2, ±11/2, and ±9/2, respectively. The transition between the ground and first excited Kramers doublet in 1 is also observed in inelastic neutron scattering (INS) spectroscopy, moving to a higher energy with an increasing magnetic field. INS also gives complete phonon spectra of 1. Periodic DFT computations provide the energies of all phonon excitations, which compare well with the spectra from INS, supporting the assignment of the inter-Kramers doublet (magnetic) transitions in the spectra. The current studies unveil and measure the spin-phonon couplings in a typical lanthanide complex and throw light on the origin of the spin-phonon entanglement.

High-Spin and Incomplete Spin-Crossover Polymorphs in Doubly Chelated [Ni(L)2Br2] (L = tert-Butyl 5-Phenyl-2-pyridyl Nitroxide)

Complexation of nickel(II) bromide with tert-butyl 5-phenyl-2-pyridyl nitroxide (phpyNO) gave two morphs of doubly chelated [Ni(phpyNO)₂Br₂] as a 2p-3d-2p heterospin triad. The α phase crystallizes in the orthorhombic space group Pbcn. An asymmetric unit involves a half-molecule. The torsion angle around Ni-O-N-C_2py is as small as 6.5(3)° at 100 K and 7.0(6)° at 400 K, guaranteeing an orthogonal arrangement between the magnetic radical π* and metal 3d_x²-y² and 3d_z² orbitals. Magnetic study revealed the high-spin ground state with the exchange coupling constant 2J/k_B = +288(5) K, on the basis of a symmetrical spin Hamiltonian. The β phase crystallizes in the monoclinic space group P2₁/n. The whole molecule is an independent unit. The Ni-O-N-C_2py torsion angles are 24.2(6) and 37.2(5)° at 100 K and 10.4(7) and 25.9(6)° at 400 K. A magnetic study revealed a very gradual and nonhysteretic spin transition. An analysis based on the van't Hoff equation gave a successful fit with the spin-crossover temperature of 134(1) K, although the susceptibility did not reach the theoretical high-spin value at 400 K. Density functional theory calculation on the β phase showed ground S_total = 0 in the low-temperature structure while S_total = 2 in the high-temperature structure, supporting the synchronized exchange coupling switch on both sides. Consequently, the β phase can be recognized as an "incomplete spin crossover" material, as a result of conflicting thermal depopulation effects in a high-temperature region.

Ferromagnetic coupling between 4f- and delocalized π-radical spins in mixed (phthalocyaninato)(porphyrinato) rare earth double-decker SMMs

Ferromagnetic π–f exchange couplings were revealed in [RE^III(Pc)(Por)]⁰ SMMs (RE = Tb and Dy) by HF-EPR measurements.

A series of CuII–LnIII complexes of an N2O3 donor asymmetric ligand and a possible CuII–TbIII SMM candidate in no bias field

Among four isostructural heterometallic Cu^II–Ln^III complexes (Ln = Tb, Dy, Ho or Er) of an N₂O₃ donor asymmetric ligand, only the Cu^II–Tb^III complex shows SMM behavior at zero bias field but at applied bias field both the Cu^II–Tb^III and Cu^II–Dy^III complexes show SMM behavior.

Giant coercivity and high magnetic blocking temperatures for N23- radical-bridged dilanthanide complexes upon ligand dissociation

Increasing the operating temperatures of single-molecule magnets—molecules that can retain magnetic polarization in the absence of an applied field—has potential implications toward information storage and computing, and may also inform the development of new bulk magnets. Progress toward these goals relies upon the development of synthetic chemistry enabling enhancement of the thermal barrier to reversal of the magnetic moment, while suppressing alternative relaxation processes. Herein, we show that pairing the axial magnetic anisotropy enforced by tetramethylcyclopentadienyl (Cp^Me4H) capping ligands with strong magnetic exchange coupling provided by an N₂³⁻ radical bridging ligand results in a series of dilanthanide complexes exhibiting exceptionally large magnetic hysteresis loops that persist to high temperatures. Significantly, reducing the coordination number of the metal centers appears to increase axial magnetic anisotropy, giving rise to larger magnetic relaxation barriers and 100-s magnetic blocking temperatures of up to 20 K, as observed for the complex [K(crypt-222)][(Cp^Me4H₂Tb)₂(μ−\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm{N}}_2^ \cdot$$\end{document}N2⋅)].

Single-molecule magnets typically only retain information in the presence of an applied magnetic field and at very low temperatures. Here, Demir, Long and co-workers design N₂^3– radical-bridged dilanthanide complexes that exhibit giant coercivities and 100-s magnetic blocking temperatures of up to 20 K.

Single-molecule magnet involving strong exchange coupling in terbium(iii) complex with 2,2′-bipyridin-6-yl tert-butyl nitroxide

Intramolecular antiferromagnetic interaction in Tb-6bpyNO was confirmed by comparison with the magnetic properties of Tb-6bpyCO and Y-6bpyNO. Tb-6bpyNO showed a hysteresis loop below 1.6 K, but Tb-6bpyCO did not behave as a single-molecule magnet.