Methods and Models of Theoretical Calculation for Single-Molecule Magnets

Abstract

Theoretical calculation plays an important role in the emerging field of single-molecule magnets (SMMs). It can not only explain experimental phenomena but also provide synthetic guidance. This review focuses on discussing the computational methods that have been used in this field in recent years. The most common and effective method is the complete active space self-consistent field (CASSCF) approach, which predicts mononuclear SMM property very well. For bi- and multi-nuclear SMMs, magnetic exchange needs to be considered, and the exchange coupling constants can be obtained by Monte Carlo (MC) simulation, ab initio calculation via the POLY_ANISO program and density functional theory combined with a broken-symmetry (DFT-BS) approach. Further application for these calculation methods to design high performance SMMs is also discussed.

Single-Ion Magnets with Giant Magnetic Anisotropy and Zero-Field Splitting

“…Some of the most elusive representations that may mislead research, for example, arise from the phenomenological superposition of incompatible with respect to their physical background microscopic effective spin models, with the aim to generate a single multispin Hamiltonian or introduce a giant spin one. , One multispin Hamiltonian that inconsistently combines microscopic effective spin models reads Ĥ = ∑ i , j J i j boldŝ i · boldŝ j + ∑ i ŝ i · boldD i i · boldŝ i + ∑ i , j d i j · ( ŝ i × ŝ j ) where i ≠ j run over all effective spin centers in the molecular nanomagnet, J ij are the corresponding exchange couplings, D ii are the one-site traceless symmetric tensors and d ij are the vectors associated with the Dzyaloshinskii Moriya interactions, i.e. the antisymmetric exchange ones.…”

“…The ambiguity occurring from the improper combination of different complete effective spin models, especially the bilinear exchange Hamiltonian 19 with the conventional ZFS one, 20,22 is beyond the scope of this review and will be discussed in a separate paper. 14 On the other hand, the direct definition 5,17,23 of a relation between molecular nanomagnets' FS parameters and the classical magnetocrystalline anisotropy parameters from the phenomenological theory of MA in solids 24−26 strongly misshapes our understanding about the underlying quantum magnetization-reversal processes. If not properly applied, this definition yields an inconsistent theoretical approach for calculating MA and, hence, an unjustified relation between the phenomenological anisotropy constant "K" and FS parameters such as the axial D and rhombic E ones used to characterize ZFS in transition metal complexes.…”

Multi-Technique Experimental Benchmarking of the Local Magnetic Anisotropy of a Cobalt(II) Single-Ion Magnet

“…The rapid growth of the digital ecosystem in recent decades has made the need for powerful processors and high-density data storage systems more apparent, and single-molecule magnets (SMMs) are considered as having great potential in this regard. − The last three decades have seen tremendous progress in this field, both on the synthetic side as well as in the development of computational methods and new advanced spectroscopic techniques that provide a direct correlation between experimental findings and theoretical models. − In recent years, some excellent high-performance 3d- and 4f-ion-based SMMs have been reported that possess a very high effective energy barrier for magnetization reversal ( U eff ) and blocking temperature ( T B ). − In the case of SMMs based on 3d metal ions, magnetic bistability originates from an energy barrier ( U eff ) that in turn results from the zero-field splitting (ZFS) of the ground spin multiplet. Current synthetic strategies thus target systems that minimize quenching of the angular momentum L , usually via ligand field design that preserves degeneracy of the ( d x 2 – y 2 , d xy ) and/or ( d xz , d yz ) orbital pairs.…”

Interplay of Anisotropic Exchange Interactions and Single-Ion Anisotropy in Single-Chain Magnets Built from Ru/Os Cyanidometallates(III) and Mn(III) Complex

“…Depending on the dimensionality of the compounds, the magnetic systems are categorized into single-molecule magnets (SMMs, 0D compounds) [ 15 , 16 , 17 , 18 , 19 , 20 , 21 ] and single-chain magnets (SCMs, 1D compounds) [ 21 , 22 , 23 , 24 , 25 , 26 , 27 ]. Temperature-dependent magnetic dynamics of SMMs and SCMs is defined by the energy barrier for magnetization reversal, U eff , and blocking temperature T b , below which the magnetization is blocked and retained for a long period of time [ 16 , 23 , 26 , 28 , 29 , 30 ]. However, the mechanism underlying the slow relaxation and the origin of the energy barrier in 0D and 1D magnetic systems is different.…”

“…However, the mechanism underlying the slow relaxation and the origin of the energy barrier in 0D and 1D magnetic systems is different. In SMMs, negative uniaxial magnetic anisotropy ( D < 0), together with high-spin ground state ( S ), is responsible for a double-well potential with the energy barrier U eff = Δ = | D | S 2 for integer S and | D |( S 2 −1/4) for half-integer S [ 1 , 3 , 28 ]. In SCMs, the barrier contains an additional energy term, Δ ξ , resulting from exchange coupling ( J ) between the magnetic ions, U eff = k Δ ξ + Δ, where k = 1 for finite or 2 for infinite chain [ 24 , 26 , 27 , 31 , 32 ].…”