Computational Study of Ga NMR Shielding in Metallic Gallides

We present first-principles calculations of the isotropic NMR Ga shielding in metallic MGa2 with M = Ca, Sr, Ba and MGa4 with M = Na, Ca, Sr and Ba. We show that the experimentally observed trend of Ga NMR shifts is as expected driven mainly by the spin part of the response, but the orbital contribution must not be neglected. For all analyzed compounds the spin contact term constitute the major component of the response, except for BaGa2, where the spin-dipolar contribution is unusually large. This spin-dipolar contribution is related to the difference of the Ga-4pz and 4px,y partial density of states (PDOS) at the Fermi level, which is large only for BaGa2. It is related to the honeycomb-like Ga-lattice and the distances between Ga atoms. The spin-contact term is determined to a large extend by Ga-4s PDOS at the Fermi level, because the magnetic field leads to a small spin-splitting and a reoccupation of spin-up and spin-down states. This Ga-4s PDOS is related to the local atomic structure around the Ga atoms and results in fact from an overlap with the neighboring Ga-4p orbitals, therefore more symmetric local arrangements of atoms around Ga result in higher Ga-4s PDOS. However, we noticed that for very low Ga-4s PDOS the spin contact term does not tend to zero but changes sign and becomes diamagnetic. This can be explained by the energy dependence of the Ga-4s radial wave function near the nucleus, leading to a contraction/expansion of 4s densities, respectively. This effect is also present in all insulating materials; however, it has been neglected so far in literature. ■ INTRODUCTION First-principles calculations of NMR shielding for insulating solids are now relatively easy and routinely carried out to aid the interpretation of measured spectra. Such calculations are much more complicated for metallic systems and therefore less common. In this case, the nuclear spin interacts not only with the electron orbit but also with its spin. So far only shieldings for metallic elements have been computed. The difficulty is, however, not related to the more complicated nature of the screening of the nuclear spin, but mainly to technical issues like slow convergence of the shielding with respect to the Brillouin zone sampling and the sensitivity to the approach applied to determine the occupancy of the electronic states close to the Fermi level. If these facts are carefully considered, reliable parameters can be computed. In this work we focus on computing the isotropic shielding at the Ga nucleus in intermetallic MGa2, with M = Ca, Sr, Ba, and MGa4, with M = Na, Ca, Sr and Ba compounds. Ga, residing near the Zintl border in the Periodic Table of Elements, forms compounds with electropositive elements characterized by attractive Ga−Ga interactions with short Ga−Ga contacts, as proposed by the Zintl concept. They possess metallic conductivity. The Ga local atomic structure and the number of Ga−Ga contacts interlinking the Ga atoms proves to be quite flexible. The degree of the interlinking increases with Ga content. For instance, isolated Ga atoms are found in Ca28Ga11, 7 2or 3-fold bonded Ga clusters are observed in Sr8Ga7 or Ba8Ga7. 8 3-fold coordinated Ga atoms, forming twodimensional networks, are seen in various MGa2, 9 whereas 4and 5-fold bonded atoms and three-dimensional interlinking are characteristic in MGa4. 10 To reflect this flexibility, Ga atoms are referred to as Ga(3b), Ga(4b), and Ga(5b), indicating 3-, 4-, and 5-fold coordination. Here, the term bonded is not used in the sense of two-electron−two-center bonds, but describe interatomic distances that are smaller than the average Ga−Ga distance in elemental a-Ga (2.70 Å). MGa4, with M = Na, Sr, and Ba, crystallizes in the BaAl4 structure (Table 1), with one Ga(4b) and one Ga(5b) site, shown in Figure 1a,b. The Ga(4b) sites are coordinated by four equidistant Ga(5b), forming a distorted tetrahedron with two angles slightly different from ideal tetrahedral 109.5°. The Ga(5b) local atomic structure is a pyramid with a square base of Ga(4b) and a Ga(5b) at the top. The atomic structure of CaGa4 is a monoclinic distortion of the BaAl4 type. 12 For the Ga(4b) site the four Ga(5b) are not equidistant but slightly split into two shorter and two longer distances. MGa2 crystallize in the AlB2-type structure with a 2D honeycomb-like Ga layer shown in Figure 1c. The layer is flat showing some corrugation for CaGa2. 13 Considering the different interatomic distances within and between the layers, Received: November 8, 2016 Published: December 9, 2016 Article