@article{whangbo_xiang_koo_gordon_whitten_2019, title={Electronic and Structural Factors Controlling the Spin Orientations of Magnetic Ions}, volume={58}, ISSN={0020-1669 1520-510X}, url={http://dx.doi.org/10.1021/acs.inorgchem.9b00687}, DOI={10.1021/acs.inorgchem.9b00687}, abstractNote={Magnetic ions M in discrete molecules and extended solids form ML n complexes with their first-coordinate ligand atoms L. The spin moment of M in a complex ML n prefers a certain direction in coordinate space because of spin-orbit coupling (SOC). In this minireview, we examine the structural and electronic factors governing the preferred spin orientations. Elaborate experimental measurements and/or sophisticated computational efforts are required to find the preferred spin orientations of magnetic ions, largely because the energy scale of SOC is very small. The latter is also the very reason why one can readily predict the preferred spin orientation of M by analyzing the SOC-induced highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) interactions of the ML n complexes in terms of qualitative perturbation theory. The strength of this HOMO-LUMO interaction depends on the spin orientation, which is governed by the selection rules based on the minimum |Δ L z| value (i.e., the minimum difference in the magnetic quantum numbers) between the HOMO and LUMO. With the local z axis of ML n chosen as its n-fold rotational axis, the preferred spin orientation is parallel to the z axis (∥ z) when |Δ L z| = 0 but perpendicular to the z axis (⊥ z) when |Δ L z| = 1.}, number={18}, journal={Inorganic Chemistry}, publisher={American Chemical Society (ACS)}, author={Whangbo, Myung-Hwan and Xiang, Hongjun and Koo, Hyun-Joo and Gordon, Elijah E. and Whitten, Jerry L.}, year={2019}, month={Jun}, pages={11854–11874} }
@article{gordon_cheng_kim_cheong_deng_whangbo_2018, title={Nonequivalent Spin Exchanges of the Hexagonal Spin Lattice Affecting the Low-Temperature Magnetic Properties of RInO3 (R = Gd, Tb, Dy): Importance of Spin-Orbit Coupling for Spin Exchanges between Rare-Earth Cations with Nonzero Orbital Moments}, volume={57}, ISSN={["1520-510X"]}, DOI={10.1021/acs.inorgchem.8b01274}, abstractNote={Rare-earth indium oxides RInO3 (R = Gd, Tb, Dy) consist of spin-frustrated hexagonal spin lattices made up of rare-earth ions R3+, where R3+ = Gd3+ (f7, L = 0), Tb3+ (f8, L = 3), and Dy3+ (f9, L = 5). We carried out DFT calculations for RInO3, including on-site repulsion U with/without spin-orbit coupling (SOC), to explore if their low-temperature magnetic properties are related to the two nonequivalent nearest-neighbor (NN) spin exchanges of their hexagonal spin lattices. Our DFT + U + SOC calculations predict that the orbital moments of the Tb3+ and Dy3+ ions are smaller than their free-ion values by ∼2μB while the Tb3+ spins have an in-plane magnetic anisotropy, in agreement with the experiments. This suggests that the f orbitals of each R3+ (R = Tb, Dy) ion are engaged, though weakly, in bonding with the surrounding ligand atoms. The magnetic properties of GdInO3 with the zero orbital moment are adequately described by the spin exchanges extracted by DFT + U calculations. In describing the magnetic properties of TbInO3 and DyInO3 with nonzero orbital moments, however, the spin exchanges extracted by DFT + U + SOC calculations are necessary. The spin exchanges of RInO3 (R = Gd, Tb, Dy) are dominated by the two NN spin exchanges J1 and J2 of their hexagonal spin lattice, in which the honeycomb lattice of J2 forms spin-frustrated ( J1, J1, J2) triangles. The J2/ J1 ratios are calculated to be ∼3, ∼1.7, and ∼1 for GdInO3, TbInO3, and DyInO3, respectively. This suggests that the antiferromagnetic (AFM) ordering of GdInO3 below 1.8 K is most likely an AFM ordering of its honeycomb spin lattice and that TbInO3 would exhibit low-temperature magnetic properties similar to those of GdInO3 while DyInO3 would not.}, number={15}, journal={INORGANIC CHEMISTRY}, author={Gordon, Elijah E. and Cheng, Xiyue and Kim, Jaewook and Cheong, Sang-Wook and Deng, Shuiquan and Whangbo, Myung-Hwan}, year={2018}, month={Aug}, pages={9260–9265} }
@article{gordon_derakhshan_thompson_whangho_2018, title={Spin-Density Wave as a Superposition of Two Magnetic States of Opposite Chirality and Its Implications}, volume={57}, ISSN={["1520-510X"]}, DOI={10.1021/acs.inorgchem.8b01494}, abstractNote={A magnetic solid with weak spin frustration tends to adopt a noncollinear magnetic structure such as a cycloidal structure below a certain temperature and a spin-density wave (SDW) slightly above this temperature. The causes for these observations were explored by studying the magnetic structure of BaYFeO4, which undergoes a SDW and a cycloidal phase transition below 48 and 36 K, respectively, in terms of the density functional theory calculations. We show that a SDW structure arises from a superposition of two magnetic states of opposite chirality, an SDW state precedes a chiral magnetic state because of the lattice relaxation, and whether a SDW is transversal or longitudinal is governed by the magnetic anisotropy of magnetic ions.}, number={16}, journal={INORGANIC CHEMISTRY}, author={Gordon, Elijah E. and Derakhshan, Shahab and Thompson, Corey M. and Whangho, Myung-Hwan}, year={2018}, month={Aug}, pages={9782–9785} }