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 CoII 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 dxy 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.

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.

Spin-resolved atomic orbital model refinement for combined charge and spin density analysis: application to the YTiO3 perovskite.

A new crystallographic method is proposed in order to refine a spin-resolved atomic orbital model against X-ray and polarized neutron diffraction data. This atomic orbital model is applied to the YTiO3 perovskite crystal, where orbital ordering has previously been observed by several techniques: X-ray diffraction, polarized neutron diffraction and nuclear magnetic resonance. This method gives the radial extension, orientation and population of outer atomic orbitals for each atom. The interaction term between Ti3+, Y3+ cations and O2- ligands has been estimated. The refinement statistics obtained by means of the orbital method are compared with those obtained by the multipole model previously published.

Magnetization Density Distribution of Sr_{2}IrO_{4}: Deviation from a Local j_{eff}=1/2 Picture.

5d iridium oxides are of huge interest due to the potential for new quantum states driven by strong spin-orbit coupling. The strontium iridate Sr_{2}IrO_{4} is particularly in the spotlight because of the so-called j_{eff}=1/2 state consisting of a quantum superposition of the three local t_{2g} orbitals with, in its simplest version, nearly equal populations, which stabilizes an unconventional Mott insulating state. Here, we report an anisotropic and aspherical magnetization density distribution measured by polarized neutron diffraction in a magnetic field up to 5 T at 4 K, which strongly deviates from a local j_{eff}=1/2 picture even when distortion-induced deviations from the equal weights of the orbital populations are taken into account. Once reconstructed by the maximum entropy method and multipole expansion model refinement, the magnetization density shows four cross-shaped positive lobes along the crystallographic tetragonal axes with a large spatial extent, showing that the xy orbital contribution is dominant. The analogy to the superconducting copper oxide systems might then be weaker than commonly thought.

Spin resolved electron density study of YTiO3 in its ferromagnetic phase: signature of orbital ordering.

The present work reports on the charge and spin density modelling of YTiO3 in its ferromagnetic state (T C = 27 K). Accurate polarized neutron diffraction and high-resolution X-ray diffraction (XRD) experiments were carried out on a single crystal at the ORPHÉE reactor (LLB) and SPRING8 synchrotron source. The experimental data are modelled by the spin resolved pseudo-atomic multipolar model (Deutsch et al., 2012 ▸). The refinement strategy is discussed and the result of this electron density modelling is compared with that from XRD measured at 100 K and with density functional theory calculations. The results show that the spin and charge densities around the Ti atom have lobes directed away from the O atoms, confirming the filling of the t 2g orbitals of the Ti atom. The d xy orbital is less populated than d xz and d yz , which is a sign of a partial lift of degeneracy of the t 2g orbitals. This study confirms the orbital ordering at low temperature (20 K), which is already present in the paramagnetic state above the ferromagnetic transition (100 K).

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

The anisotropy of the magnetic properties of molecular magnets is a key descriptor in the search for improved magnets. Herein, it is shown how an analytical approach using single-crystal polarized neutron diffraction (PND) provides direct access to atomic magnetic susceptibility tensors. The technique was applied for the first time to two Dy-based single-molecule magnets and showed clear axial atomic susceptibility for both DyIII ions. For the triclinic system, bulk magnetization methods are not symmetry-restricted, and the experimental magnetic easy axes from both PND, angular-resolved magnetometry (ARM), and theoretical approaches all match reasonably well. ARM curves simulated from the molecular susceptibility tensor determined with PND show strong resemblance with the experimental ones. For the monoclinic compound, comparison can only be made with the theoretically calculated magnetic anisotropy, and in this case PND yields an easy-axis direction that matches that predicted by electrostatic methods. Importantly, this technique allows the determination of all elements of the magnetic susceptibility tensor and not just the easy-axis direction, as is available from electrostatic predictions. Furthermore, it has the capacity to provide each of the anisotropic magnetic susceptibility tensors for all independent magnetic ions in a molecule and thus allows studies on polynuclear complexes and compounds of higher crystalline symmetry than triclinic.

Structural and magnetic phase transitions in Cs2[FeCl5(H2O)].

The compound [Formula: see text] is magnetoelectric but not multiferroic with an erythrosiderite-related structure. We present a comprehensive investigation of its structural and antiferromagnetic phase transitions by polarization microscopy, pyroelectric measurements, x-ray diffraction and neutron diffraction. At about [Formula: see text] K, the compound changes its symmetry from Cmcm to I2/c, with a doubling of the original c-axis. This transformation is associated with rotations of the [Formula: see text] octahedra and corresponds to an ordering of the [Formula: see text] molecules and of the related [Formula: see text] bonds. A significant ferroelectric polarization can be excluded for this transition by precise pyrocurrent measurements. The antiferromagnetic phase transition occurring at [Formula: see text] results in the magnetic space group [Formula: see text], which perfectly agrees with previous measurements of the linear magnetoelectric effect and magnetization.

Polarized Neutron Diffraction as a Tool for Mapping Molecular Magnetic Anisotropy: Local Susceptibility Tensors in Co(II) Complexes.

Polarized neutron diffraction (PND) experiments were carried out at low temperature to characterize with high precision the local magnetic anisotropy in two paramagnetic high-spin cobalt(II) complexes, namely [Co(II) (dmf)6 ](BPh4 )2 (1) and [Co(II) 2 (sym-hmp)2 ](BPh4 )2 (2), in which dmf=N,N-dimethylformamide; sym-hmp=2,6-bis[(2-hydroxyethyl)methylaminomethyl]-4-methylphenolate, and BPh4 (-) =tetraphenylborate. This allowed a unique and direct determination of the local magnetic susceptibility tensor on each individual Co(II) site. In compound 1, this approach reveals the correlation between the single-ion easy magnetization direction and a trigonal elongation axis of the Co(II) coordination octahedron. In exchange-coupled dimer 2, the determination of the individual Co(II) magnetic susceptibility tensors provides a clear outlook of how the local magnetic properties on both Co(II) sites deviate from the single-ion behavior because of antiferromagnetic exchange coupling.

Antiferromagnetism and superconductivity in the half-Heusler semimetal HoPdBi.

We observed the coexistence of superconductivity and antiferromagnetic order in the single-crystalline ternary pnictide HoPdBi, a plausible topological semimetal. The compound orders antiferromagnetically at TN = 1.9 K and exhibits superconductivity below Tc = 0.7 K, which was confirmed by magnetic, electrical transport and specific heat measurements. The specific heat shows anomalies corresponding to antiferromagnetic ordering transition and crystalline field effect, but not to superconducting transition. Single-crystal neutron diffraction indicates that the antiferromagnetic structure is characterized by the propagation vector. Temperature variation of the electrical resistivity reveals two parallel conducting channels of semiconducting and metallic character. In weak magnetic fields, the magnetoresistance exhibits weak antilocalization effect, while in strong fields and temperatures below 50 K it is large and negative. At temperatures below 7 K Shubnikov-de Haas oscillations with two frequencies appear in the resistivity. These oscillations have non-trivial Berry phase, which is a distinguished feature of Dirac fermions.

Origin of the large dispersion of magnetic properties in nanostructured oxides: Fe(x)O/Fe3O4 nanoparticles as a case study.

The intimate relationship between stoichiometry and physicochemical properties in transition-metal oxides makes them appealing as tunable materials. These features become exacerbated when dealing with nanostructures. However, due to the complexity of nanoscale materials, establishing a distinct relationship between structure-morphology and functionalities is often complicated. In this regard, in the FexO/Fe3O4 system a largely unexplained broad dispersion of magnetic properties has been observed. Here we show, thanks to a comprehensive multi-technique approach, a clear correlation between the magneto-structural properties in large (45 nm) and small (9 nm) FexO/Fe3O4 core/shell nanoparticles that can explain the spread of magnetic behaviors. The results reveal that while the FexO core in the large nanoparticles is antiferromagnetic and has bulk-like stoichiometry and unit-cell parameters, the FexO core in the small particles is highly non-stoichiometric and strained, displaying no significant antiferromagnetism. These results highlight the importance of ample characterization to fully understand the properties of nanostructured metal oxides.

Magnetic behaviour of synthetic Co(2)SiO(4).

Synthetic Co(2)SiO(4) crystallizes in the olivine structure (space group Pnma) with two crystallographically non-equivalent Co positions and shows antiferromagnetic ordering below 50 K. We have investigated the temperature variation of the Co(2)SiO(4) magnetic structure by means of non-polarized and polarized neutron diffraction for single crystals. Measurements with non-polarized neutrons were made at 2.5 K (below T(N)), whereas polarized neutron diffraction experiments were carried out at 70 and 150 K (above T(N)) in an external magnetic field of 7 T parallel to the b axis. Additional accurate non-polarized powder diffraction studies were performed in a broad temperature range from 5 to 500 K with small temperature increments. Detailed symmetry analysis of the Co(2)SiO(4) magnetic structure shows that it corresponds to the magnetic (Shubnikov) group Pnma, which allows the antiferromagnetic configuration (G(x), C(y), A(z)) for the 4a site with inversion symmetry 1 (Co1 position) and (0,C(y),0) for the 4c site with mirror symmetry m (Co2 position). The temperature dependence of the Co1 and Co2 magnetic moments obtained from neutron diffraction experiments was fitted in a modified molecular-field model. The polarized neutron study of the magnetization induced by an applied field shows a non-negligible amount of magnetic moment on the oxygen positions, indicating a delocalization of the magnetic moment from Co towards neighbouring O owing to superexchange coupling. The relative strength of the exchange interactions is discussed based on the non-polarized and polarized neutron data.