Mapping the Magnetic Anisotropy at the Atomic Scale in Dysprosium Single-Molecule Magnets

Elucidating Individual Magnetic Contributions in Bi-Magnetic Fe3 O4 /Mn3 O4 Core/Shell Nanoparticles by Polarized Powder Neutron Diffraction

Heterogeneous bi-magnetic nanostructured systems have had a sustained interest during the last decades owing to their unique magnetic properties and the wide range of derived potential applications. However, elucidating the details of their magnetic properties can be rather complex. Here, a comprehensive study of Fe3 O4 /Mn3 O4 core/shell nanoparticles using polarized neutron powder diffraction, which allows disentangling the magnetic contributions of each of the components, is presented. The results show that while at low fields the Fe3 O4 and Mn3 O4 magnetic moments averaged over the unit cell are antiferromagnetically coupled, at high fields, they orient parallel to each other. This magnetic reorientation of the Mn3 O4 shell moments is associated with a gradual evolution with the applied field of the local magnetic susceptibility from anisotropic to isotropic. Additionally, the magnetic coherence length of the Fe3 O4 cores shows some unusual field dependence due to the competition between the antiferromagnetic interface interaction and the Zeeman energies. The results demonstrate the great potential of the quantitative analysis of polarized neutron powder diffraction for the study of complex multiphase magnetic materials.

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

A comprehensive understanding of the ligand field and its influence on the degeneracy and population of d-orbitals in a specific coordination environment are crucial for the rational design and enhancement of magnetic anisotropy of single-ion magnets (SIMs). Herein, we report the synthesis and comprehensive magnetic characterization of a highly anisotropic Co^II SIM, [L₂Co](TBA)₂ (L is an N,N'-chelating oxanilido ligand), that is stable under ambient conditions. Dynamic magnetization measurements show that this SIM exhibits a large energy barrier to spin reversal U _eff > 300 K and magnetic blocking up to 3.5 K, and the property is retained in a frozen solution. Low-temperature single-crystal synchrotron X-ray diffraction used to determine the experimental electron density gave access to Co d-orbital populations and a derived U _eff, 261 cm^-1, when the coupling between the d _{x ² - y ²} and d_xy orbitals is taken into account, in very good agreement with ab initio calculations and superconducting quantum interference device results. Powder and single-crystal polarized neutron diffraction (PNPD, PND) have been used to quantify the magnetic anisotropy via the atomic susceptibility tensor, revealing that the easy axis of magnetization is pointing along the N-Co-N' bisectors of the N,N'-chelating ligands (3.4° offset), close to the molecular axis, in good agreement with complete active space self-consistent field/N-electron valence perturbation theory to second order ab initio calculations. This study provides benchmarking for two methods, PNPD and single-crystal PND, on the same 3d SIM, and key benchmarking for current theoretical methods to determine local magnetic anisotropy parameters.

Polarized Neutron Diffraction: An Excellent Tool to Evidence the Magnetic Anisotropy—Structural Relationships in Molecules

This publication reviews recent advances in polarized neutron diffraction (PND) studies of magnetic anisotropy in coordination compounds comprising d or f elements and having different nuclearities. All these studies illustrate the extent to which PND can provide precise and direct information on the relationship between molecular structure and the shape and axes of magnetic anisotropy of the individual metal sites. It makes this experimental technique (PND) an excellent tool to help in the design of molecular-based magnets and especially single-molecule magnets for which strong uniaxial magnetic anisotropy is required.

Magnetic anisotropies of Ho(III) and Dy(III) single-molecule magnets experimentally determined via polarized neutron diffraction

We present the magnetic anisotropy of two isostructural pentagonal-bipyramidal complexes, [Ln(H₂O)₅(HMPA)₂]I₃·2HMPA (HMPA = hexamethylphosphoramide, Ln = Dy, Ho). Using ac magnetic susceptibility measurements, we find magnetic relaxation barriers of 600 K and 270 K for the Dy- and Ho-compounds, respectively. This difference is supported by polarized neutron diffraction (PND) measured at 5 K and 1 T which provides the first experimental evidence that the transverse elements in the magnetic anisotropy of the Ho-analogue are significant, whereas the Dy-analogue has a near-axial magnetic anisotropy with vanishing transverse contributions. The coordination geometries of the two complexes are highly similar, and we attribute the loss of strong magnetic axiality as expressed in the atomic susceptibility tensors from PND, as well as the smaller relaxation barrier in the Ho-complex compared to the Dy-complex, to the less favorable interaction of the pentagonal bipyramidal crystal field with the characteristics of the Ho(III) 4f-charge distribution.

Quantifying magnetic anisotropy using X-ray and neutron diffraction

In this work, the magnetic anisotropy in two iso-structural distorted tetrahedral Co(II) complexes, CoX 2tmtu2 [X = Cl(1) and Br(2), tmtu = tetra-methyl-thio-urea] is investigated, using a combination of polarized neutron diffraction (PND), very low-temperature high-resolution synchrotron X-ray diffraction and CASSCF/NEVPT2 ab initio calculations. Here, it was found consistently among all methods that the compounds have an easy axis of magnetization pointing nearly along the bis-ector of the compression angle, with minute deviations between PND and theory. Importantly, this work represents the first derivation of the atomic susceptibility tensor based on powder PND for a single-molecule magnet and the comparison thereof with ab initio calculations and high-resolution X-ray diffraction. Theoretical ab initio ligand field theory (AILFT) analysis finds the d xy orbital to be stabilized relative to the d xz and d yz orbitals, thus providing the intuitive explanation for the presence of a negative zero-field splitting parameter, D, from coupling and thus mixing of d xy and . Experimental d-orbital populations support this interpretation, showing in addition that the metal-ligand covalency is larger for Br-ligated 2 than for Cl-ligated 1.

Experimental Determination of Magnetic Anisotropy in Exchange-Bias Dysprosium Metallocene Single-Molecule Magnets

We investigate a family of dinuclear dysprosium metallocene single-molecule magnets (SMMs) bridged by methyl and halogen groups [Cp'₂ Dy(μ-X)]₂ (Cp'=cyclopentadienyltrimethylsilane anion; 1: X=CH₃ ^- ; 2: X=Cl^- ; 3: X=Br^- ; 4: X=I^- ). For the first time, the magnetic easy axes of dysprosium metallocene SMMs are experimentally determined, confirming that the orientation of them are perpendicular to the equatorial plane which is made up of dysprosium and bridging atoms. The orientation of the magnetic easy axis for 1 deviates from the normal direction (by 10.3°) due to the stronger equatorial interactions between Dy^III and methyl groups. Moreover, its magnetic axes show a temperature-dependent shifting, which is caused by the competition between exchange interactions and Zeeman interactions. Studies of fluorescence and specific heat as well as ab initio calculations reveal the significant influences of the bridging ligands on their low-lying exchange-based energy levels and, consequently, low-temperature magnetic properties.

Observation of the asphericity of 4f-electron density and its relation to the magnetic anisotropy axis in single-molecule magnets

The distribution of electrons in the 4f orbitals of lanthanide ions is often assigned a crucial role in the design of single-molecule magnets, which maintain magnetization in zero external field. Optimal spatial complementarity between the 4f-electron density and the ligand field is key to maximizing magnetic anisotropy, which is an important factor in the ability of lanthanide complexes to display single-molecule magnet behaviour. Here we have experimentally determined the electron density distribution in two dysprosium molecular complexes by interpreting high-resolution synchrotron X-ray diffraction with a multipole model. The ground-state 4f-electron density is found to be an oblate ellipsoid, as is often deduced from a simplified Sievers model that assumes a pure |±15/2> ground-state doublet for the lanthanide ion. The large equatorial asymmetry-determined by a model wavefunction-was found to contain considerable M_J mixing of |±11/2> and only 81% of |±15/2>. The experimental molecular magnetic easy axes were recovered, and found to deviate by 13.1° and 8.7° from those obtained by ab initio calculations.

Insights into Single-Molecule-Magnet Behavior from the Experimental Electron Density of Linear Two-Coordinate Iron Complexes

A breakthrough in the study of single-molecule magnets occurred with the discovery of zero-field slow magnetic relaxation and hysteresis for the linear iron(I) complex [Fe(C(SiMe₃)₃)₂]^- (1), which has one of the largest spin-reversal barriers among mononuclear transition-metal single-molecule magnets. Theoretical studies have suggested that the magnetic anisotropy in 1 is made possible by pronounced stabilization of the iron d _z² orbital due to 3d _z²-4s mixing, an effect which is predicted to be less pronounced in the neutral iron(II) complex Fe(C(SiMe₃)₃)₂ (2). However, experimental support for this interpretation has remained lacking. Here, we use high-resolution single-crystal X-ray diffraction data to generate multipole models of the electron density in these two complexes, which clearly show that the iron d _z² orbital is more populated in 1 than in 2. This result can be interpreted as arising from greater stabilization of the d _z² orbital in 1, thus offering an unprecedented experimental rationale for the origin of magnetic anisotropy in 1.

Evidencing under-barrier phenomena in a Yb(iii) SMM: a joint luminescence/neutron diffraction/SQUID study

The synthesis, spectroscopic and magnetic characterisation and ab initio investigation of a new Yb based complex, [YbTp₂NO₃], are reported and exploited to rationalise its field-induced SMM behaviour.

From zero-dimensional to one-dimensional chain N-oxide bridged compounds with enhanced single-molecule magnetic performance

A series of zero-dimensional dinuclear dysprosium complexes bridged by pyridine-NO ligands were extended by double N-oxide bridged ligand to series of one-dimensional chain complexes with repeated Dy2 unit, they were structurally and magnetically characterized in this work.