Origin of Ferromagnetism and Magnetic Anisotropy in a Family of Copper(II) Triangles

Abstract

Previously reported ferromagnetic triangles (NnBu 4) 2 [Cu 3 (m 3-Cl) 2 (m-4-NO 2-pz) 3 Cl 3 ] (1), (PPN) 2 [Cu 3 (m 3-Cl) 2 (mpz) 3 Cl 3 ] (2), (bmim) 2 [Cu 3 (m 3-Cl) 2 (m-pz) 3 Cl 3 ] (3) and newly reported (PPh 4) 2 [Cu 3 (m 3-Cl) 2 (m-4-Ph-pz) 3 Cl 3 ] (4) were studied by magnetic susceptometry, electron paramagnetic resonance (EPR) spectroscopy and ab initio calculations to assess the origins of their ferromagnetism and of the magnetic anisotropy of their ground S = 3/2 state (PPN + = bis(triphenylphosphine)iminium, bmim + = 1-butyl-3-methylbenzimidazolium, pz À = pyrazolate). Ab initio studies revealed the d z 2 character of the magnetic orbitals of the compressed trigonal bipyramidal copper(II) ions. Ferromagnetic interactions were attributed to weak orbital overlap via the pyrazolate bridges. From the wavefunctions expansions, the ratios of the magnetic couplings were determined, which were indeterminate by magnetic susceptometry. Single-crystal EPR studies of 1 were carried out to extend the spin Hamiltonian with terms which induce zero-field splitting (zfs), namely dipolar interactions, anisotropic exchange and Dzyaloshinskii-Moriya interactions (DMI). The data were treated through both a giant-spin model and through a multispin exchangecoupled model. The latter indicated that % 62 % of the zfs is due to anisotropic and % 38 % due to dipolar interactions. The powder EPR data of all complexes were fitted to a simplified form of the multispin model and the anisotropic and dipolar contributions to the ground state zfs were estimated.

Half‐Integer Spin Triangles: Old Dogs, New Tricks

“…[126,135,154] Recently,w eu ndertook detailed EPR studies on as eries of FM spin triangles, including single-crystal studies (Figure 5). [53] With the help of ab initio calculations, these were analyzed through the full multispin Hamiltonian, explicitly accounting for isotropic, anisotropic, and dipolar interactions. The result was the deconvolution of dipolar from anisotropic interactions, af irst in complexes of nuclearity higher than two.…”

“…The former term refers to an exchangei nteraction, transmitted through the orbitals of diamagneticb ridges, whereas the latter refers to through-space interactions notr equiring as uperexchange pathway.D espite their mathematical similarities, the two may be deconvoluted by appropriate experimental and theoretical procedures. [53] An otable absence from the above list is that of single-ion anisotropy (zero-field splitting, zfs) terms. Althought his may well be operative in spin triangles, their geometry is usually such that the single-ion contributions cancel each other out owing to the symmetric tensoro rientations.…”

“…Interactions within spin triangles are described by a spin Hamiltonian that includes the Heisenberg–Dirac–van Vleck (isotropic), Dzyaloshinskii–Moriya (antisymmetric), anisotropic and dipolar terms [Eq. ]: [53] …”

“…The former term refers to an exchange interaction, transmitted through the orbitals of diamagnetic bridges, whereas the latter refers to through‐space interactions not requiring a superexchange pathway. Despite their mathematical similarities, the two may be deconvoluted by appropriate experimental and theoretical procedures [53] …”

Observation and deconvolution of a unique EPR signal from two cocrystallized spin triangles

“…The theory that describes the magnetism of spin triangles has been developed over the past seven decades, starting from the first use of the isotropic Heisenberg-Dirac-van Vleck Hamiltonian Hamiltonian for polynuclear complexes by Kambe. 10 Since then, the theoretical framework has been enhanced with the inclusion of isosceles distortions of the isotropic exchange, 11 DMI, 12 hyperfine interactions 13,14 and dipolar inter- 15,16 and intramolecular 17 interactions. These have been recently reviewed by one of us.…”