Mixing of 3d and Excited Orbitals of an Iron Group Ion in a Tetrahedral Field and Its Effect on Orbital Momentum and Spin-Orbit Coupling Coefficient

1972 ◽  
Vol 53 (2) ◽  
pp. 711-722 ◽  
Author(s):  
C. Basu ◽  
D. Majumdar ◽  
U. S. Ghosh

The theory of magnetic anisotropy and susceptibility of Fe 2+ in Tutton salts has been worked out on the basis of Abragam & Pryce’s method. It is found that the anisotropic part of the crystal field changes with temperature owing to the thermal expansion of the crystal lattice. The spin-orbit coupling coefficient has to be decreased by ~ 20 % from its free ion value of - 103 cm -1 which indicates some amount of overlap between the 3 d -Fe 2+ and 8 - and p -O 2- charge clouds. The agreement of the theoretical values with the experiment is good within the limitations of the approximations involved.


The He I photoelectron spectra of the chlorides, bromides and iodides of Na, K, Rb and Cs have been recorded in the vapour state by a molecular beam technique. The spectra exhibit features which have been interpreted on the basis of a completely ionic model in keeping with the treatments usually applied to ionic solids. To explain structure in the spectra of the lighter molecules it has been necessary to discuss polarization of the halogen atoms by the alkali metal ions. For the heavier molecules such as KI, RbI and Csl the spectra of the monomers consist of two fairly broad bands corresponding to ionization of the X­­­­ˉmoiety to its 2 P 3/2 and 2 P ½ states. These have a 2/1 intensity ratio and a separation equal to 3/2 times the appropriate spin-orbit coupling coefficient. In the case of NaI the 2 P 3/2 state is split by the strong electrostatic field of the Na + ion into states possessing 2 ∏ 3/2 and 2 ∏ ½ character. This is accompanied by a shift of the 2 P ½ state to higher energies as it gradually assumes 2 ∑ character. The result is an increase of the mean 2 P 3/2 – 2 P ½ separation to a value greater than that to be expected from spin-orbit coupling alone. This increase becomes more pronounced for the bromides and chlorides where the spin-orbit coupling coefficient is smaller. For NaCl the separation of the 2 P 3/2 and 2 P ½ bands shows clearly that the 2 P½ band possesses considerable 2 ∑ character. In terms of partial ionic character, increased polarization of the halogen atom is related to increased covalent character of the MX bond. The lighter molecules can therefore be said to be the least ionic in this description. The proportion of dimers to monomers observed in the spectra is found to fall as the molecules become more ionic, i. e. as the halogen atoms become less polarized.


2019 ◽  
Vol 116 (10) ◽  
pp. 4006-4011 ◽  
Author(s):  
H.-H. Kung ◽  
A. P. Goyal ◽  
D. L. Maslov ◽  
X. Wang ◽  
A. Lee ◽  
...  

The protected electron states at the boundaries or on the surfaces of topological insulators (TIs) have been the subject of intense theoretical and experimental investigations. Such states are enforced by very strong spin–orbit interaction in solids composed of heavy elements. Here, we study the composite particles—chiral excitons—formed by the Coulomb attraction between electrons and holes residing on the surface of an archetypical 3D TI,Bi2Se3. Photoluminescence (PL) emission arising due to recombination of excitons in conventional semiconductors is usually unpolarized because of scattering by phonons and other degrees of freedom during exciton thermalization. On the contrary, we observe almost perfectly polarization-preserving PL emission from chiral excitons. We demonstrate that the chiral excitons can be optically oriented with circularly polarized light in a broad range of excitation energies, even when the latter deviate from the (apparent) optical band gap by hundreds of millielectronvolts, and that the orientation remains preserved even at room temperature. Based on the dependences of the PL spectra on the energy and polarization of incident photons, we propose that chiral excitons are made from massive holes and massless (Dirac) electrons, both with chiral spin textures enforced by strong spin–orbit coupling. A theoretical model based on this proposal describes quantitatively the experimental observations. The optical orientation of composite particles, the chiral excitons, emerges as a general result of strong spin–orbit coupling in a 2D electron system. Our findings can potentially expand applications of TIs in photonics and optoelectronics.


2019 ◽  
Vol 31 (18) ◽  
pp. 185802 ◽  
Author(s):  
Sayantika Bhowal ◽  
Shreemoyee Ganguly ◽  
Indra Dasgupta

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Woo Seung Ham ◽  
Abdul-Muizz Pradipto ◽  
Kay Yakushiji ◽  
Kwangsu Kim ◽  
Sonny H. Rhim ◽  
...  

AbstractDzyaloshinskii–Moriya interaction (DMI) is considered as one of the most important energies for specific chiral textures such as magnetic skyrmions. The keys of generating DMI are the absence of structural inversion symmetry and exchange energy with spin–orbit coupling. Therefore, a vast majority of research activities about DMI are mainly limited to heavy metal/ferromagnet bilayer systems, only focusing on their interfaces. Here, we report an asymmetric band formation in a superlattices (SL) which arises from inversion symmetry breaking in stacking order of atomic layers, implying the role of bulk-like contribution. Such bulk DMI is more than 300% larger than simple sum of interfacial contribution. Moreover, the asymmetric band is largely affected by strong spin–orbit coupling, showing crucial role of a heavy metal even in the non-interfacial origin of DMI. Our work provides more degrees of freedom to design chiral magnets for spintronics applications.


APL Materials ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 060704
Author(s):  
Mei Fang ◽  
Wenchao Zhang ◽  
Xiaoyu Wu ◽  
Wang Guo ◽  
Huayan Xia ◽  
...  

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