This paper presents an approximate yet practical methodology for calculating two-photon absorption (TPA) cross sections with time-dependent density functional theory (TDDFT), including spin–orbit coupling (SOC). The approach is based on the second-order perturbative sum-over-states (SOS) expression for the TPA cross section and is referred to as the SOS-SOC-TDDFT method. To investigate the influence of SOC on TPA, we apply our approach to the calculation of TPA cross sections that include singlet and triplet states in fac-Ir(ppy)3, which is a phosphorescent complex known for its strong SOC effects. Due to the high angular momentum orbitals in Ir, SOC induces substantial mixing between many singlet and triplet states, although the ground state is predominantly of singlet character. Our evaluation of the TPA cross section involves constructing transition dipole matrix elements between SOC excited states by transforming the dipole matrix elements of singlet and triplet excited states obtained from scalar-relativistic TDDFT calculations, using the excited-state wavefunctions from SOC-included calculations. Our TPA results reveal that SOC leads to spectral broadening, redistribution of TPA intensities, and activation of spin-forbidden transitions. In particular, the presence of intermediate states with mixed spin character allows new excitation pathways to triplet-dominated two-photon excited states, which are inaccessible in spin-pure calculations. This highlights the importance of including SOC for accurate modeling of TPA for heavy-element systems, with results that are more sensitive to relativity than for one-photon excitation, providing insights for using the present approach in future studies of relativistic effects in nonlinear optical properties.
more »
« less
Odd-Parity Magnetism Driven by Antiferromagnetic Exchange
Realizing odd-parity, time-reversal-preserving, nonrelativistic spin splitting is a central goal for spintronics applications. We propose a group-theory-based microscopic framework to induce odd-parity spin splitting from coplanar antiferromagnetic (AFM) states without spin-orbit coupling (SOC). We develop phenomenological models for 421 conventional period-doubling AFM systems in nonsymmorphic space groups and construct minimal microscopic models for 119 of these. We find that these AFM states can attain three possible competing ground states. These ground states all break symmetries in addition to those broken by the usual AFM order. Specifically, they give rise to either odd-parity spin-splitting, nematic order, or scalar odd-parity order related to multiferroicity. Our microscopic theories reveal that the oddparity spin-splitting energy scale is generically large and further reveal that the scalar odd-parity order gives a nonzero Berry curvature dipole without SOC. We identify 67 materials in the Magndata database for which our theory applies. We provide density-functional theory (DFT) calculations on Fe-based materials that reveal an h-wave spin splitting consistent with our symmetry arguments and apply our microscopic model to determine the nonrelativistic Edelstein response for CeNiAsO.
more »
« less
- Award ID(s):
- 2323857
- PAR ID:
- 10637137
- Publisher / Repository:
- Physical Review Letters
- Date Published:
- Journal Name:
- Physical Review Letters
- Volume:
- 135
- Issue:
- 4
- ISSN:
- 0031-9007
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)Spin-orbit coupling (SOC) is a relativistic effect, where an electron moving in an electric field experiences an effective magnetic field in its rest frame. In crystals without inversion symmetry, it lifts the spin degeneracy and leads to many magnetic, spintronic, and topological phenomena and applications. In bulk materials, SOC strength is a constant. Here, we demonstrate SOC and intrinsic spin splitting in atomically thin InSe, which can be modified over a broad range. From quantum oscillations, we establish that the SOC parameter α is thickness dependent; it can be continuously modulated by an out-of-plane electric field, achieving intrinsic spin splitting tunable between 0 and 20 meV. Unexpectedly, α could be enhanced by an order of magnitude in some devices, suggesting that SOC can be further manipulated. Our work highlights the extraordinary tunability of SOC in 2D materials, which can be harnessed for in operando spintronic and topological devices and applications.more » « less
-
Abstract Energy bands in antiferromagnets are supposed to be spin degenerate in the absence of spin–orbit coupling (SOC). Recent studies have identified formal symmetry conditions for antiferromagnetic crystals in which this degeneracy can be lifted, spin splitting,even in the vanishing SOC (i.e., non‐relativistic) limit. Materials having such symmetries could enable spin‐split antiferromagnetic spintronics without the burden of using heavy‐atom compounds. However, the symmetry conditions that involve spin and magnetic symmetry are not always effective as practical material selection filters. Furthermore, these symmetry conditions do not readily disclose trends in the magnitude and momentum dependence of the spin‐splitting energy. Here, it is shown that the formal symmetry conditions enabling spin‐split antiferromagnets can be interpreted in terms of local motif pairs, such as octahedra or tetrahedra, each carrying opposite magnetic moments. Collinear antiferromagnets with such a spin‐structure motif pair, whose components interconvert by neither translation nor spatial inversion, will show spin splitting. Such a real‐space motif‐based approach enables an easy way to identify and design materials (illustrated in real example materials) having spin splitting without the need for SOC, and offers insights into the momentum dependence and magnitude of the spin splitting.more » « less
-
From a leading-order unbiased renormalization group analysis we here showcase the emergence of superconductivity (including the topological ones) from purely repulsive electron-electron interactions in two-dimensional doped Dirac insulators, featuring a Fermi surface. Otherwise a simply connected Fermi surface becomes annular deep inside the topological regime. In the absence of chemical doping, such systems describe quantum anomalous or spin Hall and normal insulators. By considering all symmetry allowed repulsive local four-fermion interactions, we show that the nature of the resulting superconducting states at low temperature follows certain Clifford algebraic selection rules, irrespective of the underlying Fermi surface topology. Within the framework of a microscopic Hubbard model, on-site repulsion among fermions with opposite orbitals (spin projections) typically favors odd-parity topological 𝑝-wave (conventional even-parity 𝑠-wave) pairing. Theoretically predicted superconductivity can in principle be observed in experiments once the promising candidate materials for quantum anomalous and spin Hall insulators are doped to foster Fermi surfaces, realizable in quantum materials and on optical lattices of cold atoms.more » « less
-
Altermagnets exhibit spontaneously spin-split electronic bands in the zero spin-orbit coupling (SOC) limit arising from the presence of collinear compensated magnetic order. The distinctive magnetocrystalline symmetries of altermagnets ensure that these spin splittings have a characteristic anisotropy in crystal momentum space. These systems have attracted a great deal of interest due to their potential for applications in spintronics. In this paper, we provide a general Landau theory that encompasses all three-dimensional altermagnets where the magnetic order does not enlarge the unit cell. We identify all crystal structures that admit altermagnetism and then reduce these to a relatively small set of distinct possible Landau theories governing such systems. In the zero SOC limit, we determine the possible local multipolar orders that are tied to the spin splitting of the band structure. We make precise the connection between altermagnetism as defined at zero SOC (“ideal” altermagnets) and the effects of weak SOC. In particular, we examine which response functions allowed by symmetry when SOC is present are guaranteed by the spin-orbit free theory and spell out the distinctive properties of altermagnets in comparison with conventional collinear antiferromagnets. Finally, we show how these ideas can be applied by considering a number of altermagnetic candidate materials.more » « less
An official website of the United States government

