How to create giant Dzyaloshinskii-Moriya interactions? Analytical derivation and ab initio calculations on model dicopper(II) complexes.

This paper is a theoretical "proof of concept" on how the on-site first-order spin-orbit coupling (SOC) can generate giant Dzyaloshinskii-Moriya interactions in binuclear transition metal complexes. This effective interaction plays a key role in strongly correlated materials, skyrmions, multiferroics, and molecular magnets of promising use in quantum information science and computing. Despite this, its determination from both theory and experiment is still in its infancy and existing systems usually exhibit very tiny magnitudes. We derive analytical formulas that perfectly reproduce both the nature and the magnitude of the Dzyaloshinskii-Moriya interaction calculated using state-of-the-art ab initio calculations performed on model bicopper(II) complexes. We also study which geometrical structures/ligand-field forces would enable one to control the magnitude and the orientation of the Dzyaloshinskii-Moriya vector in order to guide future synthesis of molecules or materials. This article provides an understanding of its microscopic origin and proposes recipes to increase its magnitude. We show that (i) the on-site mixings of 3d orbitals rule the orientation and magnitude of this interaction, (ii) increased values can be obtained by choosing more covalent complexes, and (iii) huge values (∼1000 cm-1) and controlled orientations could be reached by approaching structures exhibiting on-site first-order SOC, i.e., displaying an "unquenched orbital momentum."

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.

From Positive to Negative Zero-Field Splitting in a Series of Strongly Magnetically Anisotropic Mononuclear Metal Complexes.

A series of mononuclear [M(hfa)2(pic)2] (Hhfa = 1,1,1,5,5,5-hexafluoro-2,4-pentanedione; pic = 4-methylpyridine; M = FeII, CoII, NiII, ZnII) compounds were obtained and characterized. The structures of the complexes have been resolved by single-crystal X-ray diffraction, indicating that, apart from the zinc derivative, the complexes are in a trans configuration. Moreover, a dramatic lenghthening of the Fe-N distances was observed, whereas the nickel(II) complex is almost perfectly octahedral. The magnetic anisotropy of these complexes was thoroughly studied by direct-current (dc) magnetic measurements, high-field electron paramagnetic resonance, and infrared (IR) magnetospectroscopy: the iron(II) derivative exhibits an out-of-plane anisotropy (DFe = -7.28 cm-1) with a high rhombicity, whereas the cobalt(II) and nickel(II) complexes show in-plane anisotropy (DCo ∼ 92-95 cm-1; DNi = 4.920 cm-1). Ab initio calculations were performed to rationalize the evolution of the structure and identify the excited states governing the magnetic anisotropy along the series. For the iron(II) complex, an out-of-phase alternating-current (ac) magnetic susceptibility signal was observed using a 0.1 T dc field. For the cobalt(II) derivative, the ac magnetic susceptibility shows the presence of two field-dependent relaxation phenomena: at low field (500 Oe), the relaxation process is beyond single-ion behavior, whereas at high field (2000 Oe), the relaxation of magnetization implies several mechanisms including an Orbach process with Ueff = 25 K and quantum tunneling of magnetization. The observation by µ-SQUID magnetization measurements of hysteresis loops of up to 1 K confirmed the single-ion-magnet behavior of the cobalt(II) derivative.

Ising-type Magnetic Anisotropy and Slow Relaxation of the Magnetization in Four-Coordinate Amido-Pyridine FeII Complexes.

A family of four-coordinate FeII complexes formed with N,N'-chelating amido-pyridine ligands was synthesized, and their magnetic properties were investigated. These distorted tetrahedral complexes exhibit significant magnetic anisotropy with zero-field splitting parameter D ranging between -17 and -12 cm-1. Ab initio calculations enabled identification of the structural factors that control the nature of the magnetic anisotropy and the rationalization of the variation of D in these complexes. It is shown that a reduced N-Fe-N angle involving the chelating nitrogen atoms of the ligands is at the origin of the negative D value and that the torsion between the two N-Fe-N planes imposed by steric hindrances further increases the |D| value. Field-induced slow relaxation of magnetization was observed for the three compounds, and a single-molecule magnet behavior with an energy barrier for magnetization flipping (Ueff) of 27 cm-1 could be evidenced for one of them.

Magnetism, Spin Texture, and In-Gap States: Atomic Specialization at the Surface of Oxygen-Deficient SrTiO_{3}.

Motivated by recent spin- and angular-resolved photoemission (SARPES) measurements of the two-dimensional electronic states confined near the (001) surface of oxygen-deficient SrTiO_{3}, we explore their spin structure by means of ab initio density functional theory (DFT) calculations of slabs. Relativistic nonmagnetic DFT calculations display Rashba-like spin winding with a splitting of a few meV and when surface magnetism on the Ti ions is included, bands become spin-split with an energy difference ∼100 meV at the Γ point, consistent with SARPES findings. While magnetism tends to suppress the effects of the relativistic Rashba interaction, signatures of it are still clearly visible in terms of complex spin textures. Furthermore, we observe an atomic specialization phenomenon, namely, two types of electronic contributions: one is from Ti atoms neighboring the oxygen vacancies that acquire rather large magnetic moments and mostly create in-gap states; another comes from the partly polarized t_{2g} itinerant electrons of Ti atoms lying further away from the oxygen vacancy, which form the two-dimensional electron system and are responsible for the Rashba spin winding and the spin splitting at the Fermi surface.

Reduced effective spin-orbital degeneracy and spin-orbital ordering in paramagnetic transition-metal oxides: Sr2IrO4 versus Sr2RhO4.

We discuss the notions of spin-orbital polarization and ordering in paramagnetic materials, and address their consequences in transition-metal oxides. Extending the combined density functional and dynamical mean field theory scheme to the case of materials with large spin-orbit interactions, we investigate the electronic excitations of the paramagnetic phases of Sr(2)IrO(4) and Sr(2)RhO(4). We show that the interplay of spin-orbit interactions, structural distortions and Coulomb interactions suppresses spin-orbital fluctuations. As a result, the room temperature phase of Sr(2)IrO(4) is a paramagnetic spin-orbitally ordered Mott insulator. In Sr(2)RhO(4), the effective spin-orbital degeneracy is reduced, but the material remains metallic, due to both, smaller spin-orbit and smaller Coulomb interactions. The corresponding spectra are in excellent agreement with photoemission data. Finally, we make predictions for the spectra of paramagnetic Sr(2)IrO(4).