Prediction of Intrinsic Valley Polarization in Single‐Layer GdX₂ (X = Br, Cl) from a First‐Principles Study

Abstract

The key to manipulating valley degrees of freedom is to achieve valley polarization. Intrinsic valley polarization materials provide a new platform for the development of valleytronics. Herein, it is found that single‐layer (SL) GdX2 (X = Br, Cl) are ferrovalley materials. Their valley polarization values are 79 and 35 meV by first‐principles calculations. In addition, SL GdBr2 is taken as an example and its valley physical properties are studied. Its valley polarization can be effectively tuned by the external strains. When tensile strain 4% is applied, the valley polarization value of a SL of GdBr2 can reach 107 meV. Moreover, by reversing the spin orientation of SL GdBr2, the valley polarization of the SL GdBr2 can be reversed. This is very necessary for using the electron′s valley degree of freedom to encode and process information. In addition, the doping of electrons and holes has a significant effect on the valley polarization of SL GdBr2. The results provide a new family of ferrovalley materials GdX2 (X = Br, Cl).

Monolayer gadolinium halides, GdX2 (X = F, Cl, Br): intrinsic ferrovalley materials with spontaneous spin and valley polarizations

“…As listed in Table 2, all of the K 1 values of GdF 2 , GdCl 2 , and GdBr 2 are found to be positive and predominant upon fitting the angular dependence of MAE, in agreement with the fact that MLs GdX 2 exhibit an out-of-plane preference for magnetization. The MAEs at θ = 90° reach 351, 268, and 30 μeV per Gd atom for MLs GdF 2 , GdCl 2 , and GdBr 2 , respectively, agreeing with the recent reported theoretical values of 229.63 μeV per Gd for GdCl 2 35 as well as of −3.75 and −75 μeV per Gd for GdBr 2 35,37 at the same functional level. Our obtained values are about one to two orders greater than those of cubic Fe (1.4 μeV per atom) and Ni (2.7 μeV per atom), 55 which are also comparable to the experimental values of the Fe monolayer deposited on the Rh (111) substrate (80 μeV per atom) and the Co monolayer on the Pt (111) substrate (100 μeV per atom).…”

“…With this definition, the Δ E s of MLs GdF 2 , GdCl 2 , and GdBr 2 are found respectively to be around −55, 38, and 82 meV, in agreement with those available for MLs GdCl 2 (35 meV) and GdBr 2 (79 meV) at the same functional level. 37 Also, it can been observed from Fig. 6 that the valley states at the + K and − K points are mainly contributed by the degenerate Gd-5d xy and Gd-5d x 2 − y 2 orbitals which form the hybridization with the Gd-5d z 2 orbital.…”

“…For MLs GdCl 2 and GdBr 2 , our calculated lattice parameters and exchange energies are consistent with recent reported theoretical values at the same functional level. 35,37 Bader charge analysis reveals that there is a significant amount of electron transfer from Gd to X atoms, reaching 1.59 e in GdF 2 , 1.44 e in GdCl 2 , and 1.38 e in GdBr 2 , respectively. Although the Bader charge analysis generally underestimates the amount of charge transfer, 48 its prediction agrees with the fact that from the F to Br atom, the electronegativity reduces, and therefore the ability to attract electrons correspondingly reduces.…”

“…The PBE+ U method 42 with U eff = 8.0 eV is adopted to account for the strong correlation effects of the Gd-4f orbitals, where U eff = U − J with U is equal to 9.2 eV and J to 1.2 eV. 34, 35, 36, 37 The more accurate HSE06 hybrid functional with the Hartree–Fock mixing coefficient set as the default value of 0.25 43 is used in the calculation of band structures to check the reliability of band dispersion by the PBE+ U functional. Phonon dispersion spectra are determined by means of the PHONOPY package 44 based on density functional perturbation theory.…”

Gadolinium Halide Monolayers: A Fertile Family of Two-Dimensional 4f Magnets

“…The first part will describe the studies on 2D FM GdX2 (X=I, Br, Cl and F). [46][47][48][49][50] The second part will recall Gd dihalide based Janus monolayers, including GdClF, GdBrCl, GdICl and GdIBr. 51,52 The third part will introduce 2D GdI3 and GdCl3 monolayers, as well as their variants with metal atom intercalation.…”