Calculations of the EPR g-tensor using unrestricted two- and four-component relativistic approaches within the HF and DFT frameworks

ABSTRACT

Approaches and programs for calculations of the EPR g-tensor in the framework of the two- and four-component methods are still very rare. There are three main reasons for this: the wider community's unawareness of the importance of second- and higher order spin–orbit effects on the g-tensor, the methodological problems associated with performing such calculations and the lack of understanding of these problems. This paper reports on the implementation of a method for calculation of the g-tensor in the framework of the relativistic unrestricted two- and four-component Hartree–Fock and density functional theory approaches based on the Kramers pair formalism. This implementation allows us to analyse problems which arise when the g-tensor is calculated via Kramers pairs in the unrestricted framework.     

Investigation of magnetic transitions through ultrasonic measurements in double-layered CMR manganite La1.2Sr1.8Mn2O7

A polycrystalline, double-layered, colossal magnetoresistive manganite La_1.2Sr_1.8Mn₂O₇ is synthesized by sol-gel process and its magnetic and ultrasonic properties were investigated in the temperature range 80–300 K. The sample has Curie temperature at 124 K, where the sample exhibits a transition from paramagnetic insulator to ferromagnetic metallic state. The longitudinal sound velocity measurements show a significant hardening of sound velocity below T_C, which may be attributed to the coupling between ferromagnetic spins and longitudinal acoustic phonons. The magnetization and ultrasonic studies reveal the presence of secondary transition at ≈ 260 K in this sample. The present sound velocity measurement results confirm the reliability of ultrasonic investigations as an independent tool to probe magnetic transitions in manganites.     

Molecular g-tensors from analytical response theory and quasi-degenerate perturbation theory in the framework of complete active space self-consistent field method

The molecular g-tensor is an important spectroscopic parameter provided by electron para magnetic resonance (EPR) measurement and often needs to be interpreted using computational methods. Here, we present two new implementations based on the first-order and second-order perturbation theories to calculate the g-tensors within the complete-active space self-consistent field (CASSCF) wave function model. In the first-order method, the quasi-degenerate perturbation theory (QDPT) is employed for constructing relativistic CASSCF states perturbed with the spin–orbit coupling operator, which is described effectively in one-electron form with the flexible nuclear screening spin–orbit approximation introduced recently by us. The second-order method is a newly reported approach built upon the linear response theory which accounts for the perturbation with respect to external magnetic field. It is implemented with the coupled–perturbed CASSCF (CP-CASSCF) approach, which provides an equivalent of untruncated sum-over-states expansion. The comparison of the performances between the first-order and second-order methods is shown for various molecules containing light to heavy elements, highlighting their relative strength and weakness. The formulations of QDPT and CP-CASSCF approaches as well as the derivation of the second-order Douglas–Kroll–Hess picture change of Zeeman operators are given in detail.     

Jahn–Teller and coupled Jahn–Teller/Renner–Teller effects in the calculation of adiabatic-to-diabatic transformation angle for the lowest three 2A′ states of NH2 (NHH)

We report here on the first study of topological effects for the NHH system, as carried out by treating simultaneously the two dominant effects of this system, namely, the Jahn–Teller (JT) effect and the Renner–Teller (RT) effect. Both the effects were treated rigorously as demanded by the Born–Oppenheimer approach. No approximations were made and in those cases where convergence was required, it was achieved by including the required number of states. The study concentrates on calculating the privileged adiabatic-to-diabatic transformation (ADT) angle γ_12, along closed contours, which is the only needed angle to carry out the ADT in the case of relatively low energies. For this purpose, three coupled A′-states are usually considered and only in the last two extreme cases, where the area in configuration space becomes relatively large, namely 15–35 Ų, we had also to include an A^″ state (the second Δ-state), a situation that enforces the more elaborate (JT/RT) effect. In this paper, we also report on potential energies as calculated along the above-mentioned contours. Among them are considered the energies associated with the two adiabatic Δ-states, 1A′ and 1A^″, of different symmetry and therefore are responsible for the RT effect. These states are expected to be degenerate along the collinear axis. It was revealed that these states, in contrast to the Renner theory, are not degenerate along a finite interval of the collinear axis at the vicinity of the JT conical intersection (JT-CI). In other words, the JT-CI annihilates the RT degeneracy along this interval.     

Ultrasonic evidence for short-range charge-ordering state in the low-doping regime of La1– x Sr x FeO3 (1/3 ≤ x ≤ 0.45)

The longitudinal ultrasonic velocity (V) and attenuation at a frequency of 10?MHz, as well as magnetization and resistivity, have been measured in the single-phase polycrystalline La_{1– x} Sr _x FeO₃ (x?=?1/3, 0.4, 0.45). Upon cooling down from high temperature, a slight softening in V and dramatic stiffening are observed in all samples, and this stiffening is coincided with a big attenuation peak. The relative increase of V is proportional to the Sr concentration, which implies that this anomaly is strongly correlated with Fe⁴⁺. However, no obvious changes in magnetic and electric properties are found at this temperature range. The analysis suggests that this feature may be caused by the Jahn–Teller effect of Fe⁴⁺ and correspond to the formation of short-range charge-ordering state.     

Dynamic Jahn-teller effect in a Fe-N6 cage molecule

Mössbauer spectroscopic studies of [Fe(di(amH)-sar)](NO₃)_4·H₂O where di(amH)-sar represents 1,8 diamino 3,6,10,13,16,19-hexaza bicyclo [6,6,6] icosane in the temperature range of 4.2 to 300 K suggest that it undergoes a dynamic Jahn-Teller effect as revealed from the plots of temperature dependent quadrupole coupling constant, chemical shift and line width values. The spectrum down to 4.2 K, shows a quadrupole doublet with no magnetic hyperfine splitting.     

Magnetization of interacting electrons in anisotropic quantum dots with Rashba spin–orbit interaction

Magnetization of anisotropic quantum dots in the presence of the Rashba spin–orbit interaction has been studied for three and four interacting electrons in the dot for non-zero values of the applied magnetic field. We observe unique behaviors of magnetization that are direct reflections of the anisotropy and the spin–orbit interaction parameters independently or concurrently. In particular, there are saw-tooth structures in the magnetic field dependence of the magnetization, as caused by the electron–electron interaction, that are strongly modified in the presence of large anisotropy and high strength of the spin–orbit interactions. We also report the temperature dependence of magnetization that indicates the temperature beyond which these structures due to the interactions disappear. Additionally, we found the emergence of a weak sawtooth structure in magnetization for three electrons in the high anisotropy and large spin–orbit interaction limit that was explained as a result of merging of two low-energy curves when the level spacings evolve with increasing values of the anisotropy and the spin–orbit interaction strength.     

True spin and pseudo spin entanglement around Dirac Points in graphene with Rashba spin–orbit interaction

We analytically obtained the Schmidt decomposition of the entangled state between the pseudo spin and the true spin in graphene with Rashba spin–orbit coupling. The entangled state has the standard form of the Bell state, where the SU(2) spin symmetry is broken. These states can be explicitly expressed as the superposition of two nonorthogonal, but mirror symmetrical spin states entangled with the pseudo spin states. Because of the closely locking between the pseudo spin and the true spin, it is found that the orbit curve in the spin-polarization parameter space for the fixed equi-energy contour around Dirac points has the same shape as the $\delta \overrightarrow{k}$-contour. Due to the spin–orbit coupling that cause the topological transition in the local geometry of the dispersion relation, the new equi-energy contours around the new emergent Dirac Points can be obtained by squeezing the one around the original Dirac point. The spin texture in the momentum space around the Dirac points is analyzed under the Rashba spin–orbit interaction and it is found that the orientation of the spin polarization at each crystal momentum $\overrightarrow{k}$ is independent of the Rashba coupling strength.     

Pu+4的几何构型和Jahn-Teller效应

在Pu原子的相对论有效原子实势下,用密度泛函B3LYP方法计算得到Pu +4分子离子的6种稳定的几何构型.计算表明Pu+4的Td构型不能稳定存在,详细讨论了 Td构型的Jahn-Teller效应,讨论结果显示它们的各种畸变方式都符合群的分解原理, 从而证明Pu+4分子离子的Td构型的Jahn-Teller效应非常明显.D4h 构型也存在Jahn-Teller效应.     

Theoretical investigations on the g factors and local structures for Cu2+ in the ZnX (X= O,S and Se) nanocrystals

ABSTRACT

The g factors and local structures for Cu²⁺ in the ZnX (X = O, S and Se) nanocrystals at room temperature are theoretically investigated by the perturbation calculations for a tetragonally distorted tetrahedral 3d⁹ cluster in a consistent way, and the isotropic g factor is predicted for the ZnS:Cu²⁺ nanocrystals at room temperature. The bond angles θ between the four equivalent Cu²⁺?X^2? bonds and the C₄ axis are found to be about 1.26°, 1.24° and 1.07°, respectively, larger in the ZnO, ZnS and ZnSe nanocrystals than that (θ₀ ≈ 54.74°) for an ideal tetrahedron, inducing tetragonally compressed tetrahedra. The declining tendency (ZnO > ZnS > ZnSe) of the tetragonal angular distortion Δθ (= θ ? θ₀) can be ascribed to the decreasing strength of the dynamic Jahn–Teller effect via the vibration interactions of the [CuX₄]^6? groups due to the weakening Cu²⁺?X^2? bonding. The isotropic g factors are attributable to the appropriate Δθ due to the dynamic Jahn–Teller effect and the internal stress. The slightly increasing (ZnO < ZnS < ZnSe) g factors can be illustrated by the declining cubic field parameter Dq, angular distortion Δθ and covalency factor N of the systems.     

Spin and charge Nernst effect in a four-terminal double-dot interferometer

We investigate the spin and charge Nernst effect of a four-terminal Aharonov–Bohm interferometer with Rashba spin–orbit interaction (RSOI). It is shown that a pure spin Nernst effect or a fully spin-polarized Nernst effect can be obtained by modulating the magnetic flux phase ? and the RSOI induced phase φ. It is also demonstrated that some windows of ? (or φ) for maintaining an almost fully spin-polarized Nernst effect exist and their width is under the control of the other phase. Moreover, for the charge Nernst coefficient $N_c$ and spin Nernst coefficient $N_s$ the relationship $N_c(?,\phi )=?N_s(\phi ,?)$ always holds. These results suggest that our proposal may act as a controllable thermospin generator.     

Influence of spin–orbit interaction,Zeeman effect and light polarisation on the electronic and optical properties of pseudo-elliptic quantum rings under magnetic field

ABSTRACT

We theoretically investigated the influences of the magnetic field and light polarisation on the electronic and optical properties of a GaAs/GaAlAs pseudo-elliptic quantum ring, modelled by an outer ellipsis and an inner circle, in the presence of the Rashba and Dresselhaus spin–orbit interactions and Zeeman effect. We show that Aharonov-Bohm oscillations of the energy spectrum are not affected by the presence of the Zeeman effect alone but, in the presence of Rashba and Dresselhaus spin–orbit couplings, the periodicity of certain levels becomes hardly definite. The Zeeman effect generally enhances/diminishes the separation levels produced by Rashba/Dresselhaus interactions (SOI) and when both types of SOI are considered, the effect depends on their relative strength. The magnetic field can trigger spin-flip for each type of spin–orbit interaction and Zeeman effect or their combination through anticrossings in the energy spectra. Our results reveal that the absorption spectra are very sensitive to the magnetic field and light polarisation. For all polarisations considered, the magnetic field increment leads to the redshift or blueshift of some particular peaks (an effect of this ring geometry) and a better separation of the peaks. The x-polarised light determines spectra with many small, but separated peaks while the circular polarised light leads to spectra with large peaks of high amplitude.     

Effects of electron–electron interaction on the collinear indirect exchange coupling in graphene nanoflakes

Using the Hubbard model in the framework of the tight-binding formulation, we studied the effects of the electron–electron (e–e) interaction on the indirect magnetic exchange coupling between the magnetic impurities embedded in triangular graphene nanoflakes. The results show that the magnitude of the coupling enhances in the presence of the e–e interaction and Rashba spin–orbit interaction (RSOI). The RKKY coupling magnitude depends on the impurity positions in nanoflake and the size of the system, as well.