Table of contents

Dielectric measurements of PbMg_1/3Nb_2/3O₃ (PMN) powder and dense ceramics with grain sizes between 15 nm and two microns were carried out in a broad frequency range (20 Hz–1 GHz). Clear grain size dependence of relaxor behavior was evidenced. A progressive transformation from Vogel-Fulcher behavior towards the Arrhenius process in the PMN with reduction of grain size in both ceramics and powder was observed. In the case of ceramics we were able to extract deeper information from the distributions of relaxation times and an analysis using the Vogel-Fulcher law, revealing two main contributions: a fast part of distribution of relaxation times with a maximum close to 10⁻¹¹ s, which is almost grain-size independent and has a non-polar origin; whereas, a process with long relaxation times (in the time range of 10⁻⁸ to 10⁻⁵ s) is associated with the dynamics of the polar nanoregions and is strongly suppressed with reduction of grain size. The results of dielectric investigations are confirmed by Nuclear Magnetic Resonance experiments.

How does magnetism behave when the physical dimension is reduced to the size of nanostructures? The multiplicity of magnetic states in these systems can be very rich, in that their properties depend on the atomic species, the cluster size, shape and symmetry or choice of the substrate. Small variations of the cluster parameters may change the properties dramatically. Research in this field has gained much by the many novel experimental methods and techniques exhibiting atomic resolution. Here we review the ab-initio approach, focusing on recent calculations on magnetic frustration and occurrence of non-collinear magnetism in antiferromagnetic nanostructures deposited on surfaces.

Using the nonlocal coherent-potential approximation we study the effect of intersite spatial correlations on the transition from band insulator to metal as well as from metal to Mott insulator in the 'alloy analogy' approach to the paramagnetic solution of the half-filled ionic Hubbard model. We find that intersite spatial correlations enhance the metallic phase.

On the basis of constrained density functional theory, we present ab initio calculations for the Hubbard U parameter of transition metal impurities in dilute magnetic semiconductors, choosing Mn in GaN as an example. The calculations are performed by two methods: (i) the Korringa–Kohn–Rostoker (KKR) Green function method for a single Mn impurity in GaN and (ii) the full-potential linearized augmented plane-wave (FLAPW) method for a large supercell of GaN with a single Mn impurity in each cell. By changing the occupancy of the majority t₂ gap state of Mn, we determine the U parameter either from the total energy differences E(N + 1) and E(N − 1) of the (N ± 1)-electron excited states with respect to the ground state energy E(N), or by using the single-particle energies for $n_0\pm \frac {1}{2}$ occupancies around the charge-neutral occupancy n₀ (Janak's transition state model). The two methods give nearly identical results. Moreover the values calculated by the supercell method agree quite well with the Green function values. We point out an important difference between the 'global' U parameter calculated using Janak's theorem and the 'local' U of the Hubbard model.

To gain insight into the mechanism of charge ordering transitions, which conventionally are pictured as a disproportionation of an ion M as 2Mⁿ⁺→M⁽ⁿ⁺¹⁾⁺ + M⁽ⁿ⁻¹⁾⁺, we (1) review and reconsider the charge state (or oxidation number) picture itself, (2) introduce new results for the putative charge ordering compound AgNiO₂ and the dual charge state insulator AgO, and (3) analyze the cationic occupations of the actual (not formal) charge, and work to reconcile the conundrums that arise. We establish that several of the clearest cases of charge ordering transitions involve no disproportion (no charge transfer between the cations, and hence no charge ordering), and that the experimental data used to support charge ordering can be accounted for within density functional-based calculations that contain no charge transfer between cations. We propose that the charge state picture retains meaning and importance, at least in many cases, if one focuses on Wannier functions rather than atomic orbitals. The challenge of modeling charge ordering transitions with model Hamiltonians isdiscussed.

We present total energy and force calculations for the (GaN)_1−x(ZnO)_x alloy. Site-occupancy configurations are generated from Monte Carlo (MC) simulations, on the basis of a cluster expansion model proposed in a previous study. Local atomic coordinate relaxations of surprisingly large magnitude are found via density-functional calculations using a 432-atom periodic supercell, for three representative configurations at x = 0.5. These are used to generate bond-length distributions. The configurationally averaged composition- and temperature-dependent short-range order (SRO) parameters of the alloys are discussed. The entropy is approximated in terms of pair distribution statistics and thus related to SRO parameters. This approximate entropy is compared with accurate numerical values from MC simulations. An empirical model for the dependence of the bond length on the local chemical environments is proposed.

We will extend the concept of electron band Berry curvatures to superconducting materials. We show that this can be defined for the Bogoliubov–de Gennes equation describing the superconducting state in a periodic crystal. In addition, the concept is exploited to understand the driving mechanism for the optical Kerr effect in time reversal symmetry breaking superconductors. Finally, we establish a sum rule analogue to the normal state Hall sum rule making quantitative contact between the imaginary part of the optical conductivity and the Berry curvature. The general theory will be applied and tested against the drosophila of the p-wave paired materials Sr₂RuO₄.

The electronic structure and magnetic properties of the disordered alloy system fcc-Fe_xNi_1−x (fcc: face centered cubic) have been investigated by means of the KKR-CPA (Korringa–Kohn–Rostoker coherent potential approximation) band structure method. To investigate the impact of correlation effects, the calculations have been performed on the basis of the LSDA (local spin density approximation), the LSDA + U as well as the LSDA + DMFT (dynamical mean field theory). It turned out that the inclusion of correlation effects hardly changed the spin magnetic moments and the related hyperfine fields. The spin–orbit induced orbital magnetic moments and hyperfine fields, on the other hand, show a pronounced and element-specific enhancement. These findings are in full accordance with the results of a recent experimental study.

Recently, a generalized relativistic phase shift model was proposed (Fedorovet al 2013 Phys. Rev. B 88 085116) for the description of the skew-scattering contribution to the spin Hall effect caused by impurities. Here, we inspect this model by means of a systematic comparison with the results of first-principles calculations performed for several metallic host systems with different substitutional impurities. It is found that for its proper application, the differences between impurity and host phase shifts should be used as input parameters. Generally, the model provides good qualitative agreement with ab initio results for hosts with a free-electron-like Fermi surface and a relatively weak spin–orbit coupling, but fails otherwise.

An important step in electronic structure calculations using multiple-scattering theory is obtaining the density of states for the central site from the Green's function for that site. We have found that the Krein's spectral displacement function for the central site contributes significantly to the understanding of these calculations. We argue that these insights can lead to improvements in the robustness of MST electronic structure codes without negatively impacting their performance.

We develop a cluster typical medium theory to study localization in disordered electronic systems. Our formalism is able to incorporate non-local correlations beyond the local typical medium theory in a systematic way. The cluster typical medium theory utilizes the momentum-resolved typical density of states and hybridization function to characterize the localization transition. We apply the formalism to the Anderson model of localization in one- and two-dimensions. In one-dimension, we find that the critical disorder strength scales inversely with the linear cluster size with a power law, W_c ∼ (1/L_c)^1/ν, whereas in two-dimensions, the critical disorder strength decreases logarithmically with the linear cluster size. Our results are consistent with previous numerical work and are in agreement with the one-parameter scaling theory.

We briefly describe the density functional theory (DFT)-based 'disordered local moment' (DLM) picture for magnetism at finite temperatures. It shows how relatively slowly fluctuating local moments can emerge from the interacting electrons of many materials. Such entities have rigid magnitudes and fluctuate their orientations from atomic site to atomic site on a timescale long compared to other electronic times. We illustrate this theory with calculations of the magnetocaloric effect in Gd where we find excellent agreement with experiments. Fluctuating moments do not appear to establish naturally over such small regions for some other materials. We show how the DFT-DLM theory can be extended to these materials with the use of the Korringa–Kohn–Rostoker nonlocal coherent potential approximation (KKR-NLCPA) to allow for more extensive, slow magnetic fluctuations. We present the first application of this approach by revisiting the description of the magnetic fluctuations prevalent in the paramagnetic state of nickel. We find that local moments can emerge above T_c and that these form coherently over small clumps of atomic sites (4–8 sites).

We present fully relativistic first principles calculations of the exchange interactions between magnetic impurities deposited on the (1 1 1) surfaces of Cu_xPd_1−x and Cu_xAu_1−x random substitutional alloys, described using the coherent potential approximation. We show that as with pure surfaces of Cu and Au, where Shockley-type surface states mediate an RKKY-type interaction, a surface state and its dispersion can be obtained from studying the Bloch spectral function. In the second part of the paper we show how the details of the interaction are determined by the properties and dispersion of the surface states of the host material. We find an extra exponential decay in the range of the interactions compared to the 1/R² decay on surfaces of pure metals. The similar topology of the Fermi surface of Cu and Au allows us to scale the spin–orbit coupling and to study the Bychkov–Rashba splitting. Alternatively, the entirely different topology of the Cu and Pd Fermi surfaces allows us to study changes in the surface-state dispersion of the RKKY interaction between surface impurities.

The presence of a spin-flip potential at the interface between a superconductor and a ferromagnetic metal allows for the generation of equal-spin spin-triplet Cooper pairs. These Cooper pairs are compatible with the exchange interaction within the ferromagnetic region and hence allow for the long-range proximity effect through a ferromagnet or half-metal. One suitable spin-flip potential is provided by incorporating the conical magnet Holmium (Ho) into the interface. The conical magnetic structure is characterised by an opening angle α with respect to the crystal c-axis and a turning (or pitch) angle β measuring the rotation of magnetisation with respect to the adjacent layers. Here, we present results showing the influence of conical magnet interface layers with varying α and β on the efficiency of the generation of equal-spin spin-triplet pairing. The results are obtained by self-consistent solutions of the microscopic Bogoliubov-de Gennes equations in the clean limit within a tight-binding model of the heterostructure. In particular, the dependence of unequal-spin and equal-spin spin-triplet pairing correlations on the conical magnetic angles α and β are discussed in detail.

Using first-principles calculations we have studied the valence and structural transitions of the rare earth monotellurides RTe (R = Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm and Yb) under pressure. The self-interaction corrected local spin-density approximation is used to establish the ground state valence configuration as a function of volume for the RTe in both the NaCl (B1) and CsCl (B2) structures. We find that in ambient conditions all the RTe are stabilized in the B1 structure. A trivalent (R³⁺) rare earth ground state is predicted for the majority of the RTe, with the exception of SmTe, EuTe, DyTe, TmTe and YbTe, where the fully localized divalent (R²⁺) rare earth configuration is found to be energetically most favourable. Under pressure, the trivalent RTe undergo structural transitions to the B2 structure without associated valence transition. The divalent RTe on the other hand are characterized by a competition between the structural and electronic degrees of freedom, and it is the degree of f-electron delocalization that determines the sequence of phase transitions. In EuTe and YbTe, where respectively the half-filled and filled shells result in a very stable divalent configuration, we find that it is the structural B1 → B2 transition that occurs first, followed by the R²⁺ → R³⁺ valence transition at even higher pressures. In SmTe, DyTe and TmTe, the electronic transition occurs prior to the structural transition. With the exception of YbTe, the calculated transition pressures are found to be in good agreement with experiment.

The nanoparticle phase diagram of an immiscible system is studied at the atomic level. Cu–Ag clusters with sizes 1000 and 2000 atoms, resulting from a global minimum search and belonging to icosahedral and crystalline structural motifs, are considered. We present the statistical analysis of the effect of temperature on the solubility of the two elements based on Metropolis Monte Carlo importance sampling. Our results suggest that the relevance of bulk phase diagrams to nanoparticles is limited to cases where the internal stress distribution does not deviate very much from uniform (e.g. sufficiently large crystalline clusters). In the general case, the principal interdependence between partial phase compositions and the overall cluster composition in nanoparticle phase diagrams need to be taken into account.

We present a theoretical study of electron transport in Ni₄ molecular transistors in the presence of Zeeman spin splitting and magnetic quantum coherence (MQC). The Zeeman interaction is extended along the leads which produces gaps in the energy spectrum which allow electron transport with spin polarized along a certain direction. We show that the coherent states in resonance with the spin up or down states in the leads induces an effective coupling between localized spin states and continuum spin states in the single molecule magnet and leads, respectively. We investigate the conductance at zero temperature as a function of the applied bias and magnetic field by means of the Landauer formula, and show that the MQC is responsible for the appearence of resonances. Accordingly, we name them MQC resonances.

In this work we report the results of theoretical analysis of the effect of the thermal environment on the thermoelectric efficiency of molecular junctions. The environment is represented by two thermal phonon baths associated with the electrodes, which are kept at different temperatures. The analysis is carried out using the Buttiker model within the scattering matrix formalism to compute electron transmission through the system. This approach is further developed so that the dephasing parameters are expressed in terms of relevant energies, including the thermal energy, strengths of coupling between the molecular bridge and the electrodes and characteristic energies of electron–phonon interactions. It is shown that the latter significantly affect thermoelectric efficiency by destroying the coherency of electron transport through the considered system.

Acoustic emission has been measured and statistical characteristics analyzed during the stress-induced collapse of porous berlinite, AlPO₄, containing up to 50 vol% porosity. Stress collapse occurs in a series of individual events (avalanches), and each avalanche leads to a jerk in sample compression with corresponding acoustic emission (AE) signals. The distribution of AE avalanche energies can be approximately described by a power law $p\left(E\right)dE={{E}^{-\varepsilon}}dE~\left(\varepsilon \sim 1.8\right)$ over a large stress interval. We observed several collapse mechanisms whereby less porous minerals show the superposition of independent jerks, which were not related to the major collapse at the failure stress. In highly porous berlinite (40% and 50%) an increase of energy emission occurred near the failure point. In contrast, the less porous samples did not show such an increase in energy emission. Instead, in the near vicinity of the main failure point they showed a reduction in the energy exponent to ~ 1.4, which is consistent with the value reported for compressed porous systems displaying critical behavior. This suggests that a critical avalanche regime with a lack of precursor events occurs. In this case, all preceding large events were 'false alarms' and unrelated to the main failure event. Our results identify a method to use pico-seismicity detection of foreshocks to warn of mine collapse before the main failure (the collapse) occurs, which can be applied to highly porous materials only.

The lattice dynamics of Pb-containing perovskite oxides are investigated theoretically for the transition metal series Ti, Zr, Hf, in order to elucidate their commonalities and their distinctions. For all three compounds, pronounced precursor effects are found to their phase transition temperatures, which get more pronounced the heavier the central transition metal ion is. In addition, a competition between a polar and an antiferrodistortive instability is predicted to take place, which is strongly mass dependent. While in PbTiO₃ the polar instability wins, both instabilities are active in PbZrO₃, whereas in PbHfO₃ the antiferrodistortive phase transition dominates the dynamics. For all three compounds, marked anomalies in the elastic constants are predicted, which are most pronounced in PbHfO₃. Experimental results for elastic anomalies preceding the phase transition, which agree qualitatively with the model calculations are presented for PbHfO₃.

Half-Heusler and Heusler compounds have been of great interest for several decades for thermoelectric, magnetic, half-metallic and many other interesting properties. Among these systems, Zr–Ni–Sn compounds are interesting thermoelectrics which can go from semiconducting half-Heusler (HH) limit, ZrNiSn, to metallic Heusler (FH) limit, ZrNi₂Sn. Recently Makongo et al (2011 J. Am. Chem. Soc.133 18843) found that dramatic improvement in the thermoelectric power factor of HH can be achieved by putting excess Ni into the system. This was attributed to an energy filtering mechanism due to the presence of FH nanostructures in the HH matrix. Using density functional theory we have investigated clustering and nanostructure formation in ZrNi_1+xSn (0 ⩽ x ⩽ 1) systems near the HH (x = 0) and FH (x = 1) ends and have found that excess Ni atoms in HH tend to stay close to each other and form nanoclusters. On the other hand, there is competing interaction between Ni-vacancies occupying different sites in FH which prevents them from forming vacancy nanoclusters. Effects of nano-inclusions on the electronic structure near HH and FH ends are discussed.

Noting that BiI₃ and the well-known topological insulator (TI) Bi₂Se₃ have the same high symmetry parent structures, and that it is desirable to find a wide-band gap TI, we determine here the effects of pressure on the structure, phonons and electronic properties of rhombohedral BiI₃. We report a pressure-induced insulator-metal transition near 1.5 GPa, using high pressure electrical resistivity and Raman measurements. X-ray diffraction studies, as a function of pressure, reveal a structural peculiarity of the BiI₃ crystal, with a drastic drop in c/a ratio at 1.5 GPa, and a structural phase transition from rhombohedral to monoclinic structure at 8.8 GPa. Interestingly, the metallic phase, at relatively low pressures, exhibits minimal resistivity at low temperatures, similar to that in Bi₂Se₃. We corroborate these findings with first-principles calculations and suggest that the drop in the resistivity of BiI₃ in the 1–3 GPa range of pressure arises possibly from the appearance of an intermediate crystal phase with a lower band-gap and hexagonal crystal structure. Calculated Born effective charges reveal the presence of metallic states in the structural vicinity of rhombohedral BiI₃. Changes in the topology of the electronic bands of BiI₃ with pressure, and a sharp decrease in the c/a ratio below 2 GPa, are shown to give rise to changes in the slope of phonon frequencies near that pressure.

The effect of selenium substitution by sulphur on the structural and physical properties of antiferromagnetic TlFe_1.6+δSe₂ has been investigated via neutron, x-ray and electron diffraction, and transport measurements. The $\sqrt{5}a\times \sqrt{5}a\times c$ super-cell related to the iron vacancy ordering found in the pure TlFe_1.6Se₂ selenide is also present in the S-doped TlFe_1.6+δ(Se_1−xS_x)₂ compounds. Neutron scattering experiments show the occurrence of the same long range magnetic ordering in the whole series i.e. the 'block checkerboard' antiferromagnetic structure. In particular, this is the first detailed study where the crystal structure and the $\sqrt{5}a\times \sqrt{5}a$ antiferromagnetic structure is characterized by neutron powder diffraction for the pure TlFe_1.6+δS₂ sulphide over a large temperature range. We demonstrate the strong correlation between occupancies of the crystallographic iron sites, the level of iron vacancy ordering and the occurrence of block antiferromagnetism in the sulphur series. Introducing S into the Se sites also increases the Fe content in TlFe_1.6+δ(Se_1−xS_x)₂ which in turn leads to the disappearance of the Fe vacancy ordering at x = 0.5 ± 0.15. However, by reducing the nominal Fe content, the same $\sqrt{5}a\times \sqrt{5}a\times c$ vacancy ordering and antiferromagnetic order can be recovered also in the pure TlFe_1.6+δS₂ sulphide with a simultaneous reduction in the Néel temperature from 435 K in the selenide TlFe_1.75Se₂ to 330 K in the sulphide TlFe_1.5S₂. The magnetic moment remains high at low temperature throughout the full substitution range, which contributes to the absence of superconductivity in these compounds.

Resistivity ρ(T), Hall coefficient R_H(T), superconducting transition temperature T_c and slopes of the upper critical field dH_c2/dT were studied in (Ba_1−xK_x)Fe₂As₂ (x = 0.218, 0.356, 0.531) single crystals irradiated with fast neutrons. It is found that dT_c/dρ_SC—the rate of decreasing T_c as a function of the ρ_SC (ρ_SC is the resistivity at T = T_c)—linearly increases with concentration x. Slow changes in the Hall coefficient R_H, as well as the quadratic electronic contribution to the resistivity, show that there are no substantial changes in the topology of the Fermi surface caused by irradiation. The slopes of the upper critical field dH_c2/dT in ab and c directions as a function of ρ_SC determined by Hall measurements show a reasonable agreement with a model that suggests constancy of the band parameters.

We report on temperature dependent TmMnO₃ far infrared emissivity and reflectivity spectra from 1910 K to 4 K. At the highest temperature the number of infrared bands is lower than that predicted for centrosymmetric P6₃/mmc $\left(\text{D}_{6\text{h}}^{4}\right)$ (Z = 2) space group due to high temperature anharmonicity and possible defect induced bitetrahedra misalignments. On cooling, at ~1600 ± 40 K, TmMnO₃ goes from non-polar to an antiferroelectric–ferroelectric polar phase reaching the ferroelectric onset at ~700 K.

Room temperature reflectivity is fitted using 19 oscillators and this number of phonons is maintained down to 4 K. A weak phonon anomaly in the band profile at 217 cm⁻¹ (4 K) suggests subtle Rare Earth magneto-electric couplings at ~T_N and below.

A low energy collective excitation is identified as a THz instability associated with room temperature e_g electrons in a d-orbital fluctuating environment. It condenses into two modes that emerge pinned to the E-type antiferromagnetic order hardening simultaneously down to 4 K. They obey power laws with T_N as the critical temperature and match known zone center magnons. The one peaking at 26 cm⁻¹, with critical exponent β=0.42 as for antiferromagnetic order in a hexagonal lattice, is dependent on the Rare Earth ion. The higher frequency companion at ~50 cm⁻¹, with β=0.25, splits at ~T_N into two peaks. The weaker band of the two is assimilated to the upper branch of the gap opening in the transverse acoustical (TA) phonon branch crossing the magnetic dispersion found in YMnO₃. (Petit et al 2007 Phys. Rev. Lett. 99 266604). The stronger second band at ~36 cm⁻¹ corresponds to the lower branch of the TA gap. We assign both excitations as zone center magneto-electric hybrid quasiparticles, concluding that in NdMnO₃ perovskite the equivalent picture corresponds to an instability which may be driven by an external field to transform NdMnO₃ into a multiferroic compound by perturbation enhancing the TA phonon–magnetic correlation.

We report a magnetization study of the compound La_0.75Ba_0.25CoO₃ where the Ba²⁺ doping is just above the critical limit for percolation of ferromagnetic clusters. The field cooled and zero-field cooled (ZFC) magnetization exhibit thermomagnetic irreversibility and the ac susceptibility shows a frequency dependent peak at the ferromagnetic ordering temperature (T_C ≈ 203 K) of the clusters. These features indicate the presence of a non-equilibrium state below T_C. For the non-equilibrium state, the dynamic scaling of the imaginary part of the ac susceptibility and the static scaling of the nonlinear susceptibility clearly establish a spin-glass-like cooperative freezing of ferromagnetic clusters at 200.9(2) K. The assertion of the occurrence of spin-glass-like freezing of ferromagnetic clusters is further substantiated by ZFC ageing and memory experiments. We also observe certain dynamical features which are not present in a typical spin glass, such as: the initial magnetization after ZFC ageing first increases and then decreases with the waiting time; and there is an imperfect recovery of relaxation in negative temperature cycling experiments. This imperfect recovery transforms to perfect recovery for concurrent field cycling. Our analysis suggests that these additional dynamical features have their origin in the inter-cluster exchange interaction and cluster size distribution. The inter-cluster exchange interaction above the magnetic percolation level gives a superferromagnetic state in some granular thin films, but our results show the absence of a typical superferromagnetic-like state in La_0.75Ba_0.25CoO₃.

We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic $\left(J_{1}^{F}\right)$ and antiferromagnetic $\left(J_{1}^{A}\right)$ nearest-neighbor interactions and a ferromagnetic next-nearest-neighbor interaction $\left(J_{2}^{F}\right)$. In this model frustration is present due to the non-zero $J_{2}^{F}$. The model with site spin s behaves like a Haldane spin chain, with site spin 2s in the limit of vanishing $J_{2}^{F}$ and large $J_{1}^{F}/J_{1}^{A}$. We show that the exact ground state of the model can be found along a line in the parameter space. For fixed $J_{1}^{F}$, the phase diagram in the space of $J_{1}^{A}-J_{2}^{F}$ is determined using numerical techniques complemented by analytical calculations. A number of quantities, including the structure factor, energy gap, entanglement entropy and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and potentially important feature of this model is that it can exhibit a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.

We have experimentally investigated the effects of pressure on the magnetoelastic transitions associated with the opening of spin-gaps in Ba₃BiIr₂O₉ and Ba₃BiRu₂O₉. For both compounds, reducing the unit cell volume by either external physical and internal chemical pressure was found to reduce the temperature T^* of the transition and, to a lesser extent, the magnitude of the associated negative thermal volume expansion. The results yield the latent heat associated with the transitions, −3.34(3) × 10² J mol⁻¹ for Ba₃BiIr₂O₉ and −7.1(5) × 10² J mol⁻¹ for Ba₃BiRu₂O₉. The transition in Ba₃BiRu₂O₉ is significantly more robust than in Ba₃BiIr₂O₉, requiring an order of magnitude higher pressures to achieve the same reduction in T^*. The differing responses of the two compounds points to differences between the 4d and 5d metals and hence to the importance of spin-orbit coupling, which is expected to be much stronger in the Ir compound.

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