Theory of the Magnetic and Metal-Insulator Transitions in $R{\mathrm{NiO}}_3$ Bulk and Layered Structures

A slave rotor—Hartree-Fock formalism is presented for studying the properties of the $p\mathrm{\text{−}}d$ model describing perovskite transition metal oxides, and a flexible and efficient numerical formalism is developed for its solution. The methodology is shown to yield, within a unified formulation, the significant aspects of the rare-earth nickelate phase diagram, including the paramagnetic metal state observed for the ${\mathrm{LaNiO}}_3$ and the correct ground-state magnetic order of insulating compounds. It is then used to elucidate ground state changes occurring as morphology is varied from bulk to strained and unstrained thin-film form. For ultrathin films, epitaxial strain and charge transfer to the apical out-of-plane oxygen sites are shown to have significant impact on the phase diagram.

Figure 1

(a) Bulk, (b) 2-layer, and (c) 1-layer phase diagram on the $u\mathrm{\text{−}}\delta d_{pd}$ plane. In (b),(c), the light dotted line indicates the phase boundary obtained without the energy shift on the out-of-layer oxygen. $\Uparrow /\uparrow /0$ denote large moment or small moment or nonmagnetic sites of the magnetic patterns. The pattern of (a) is that of Fig. 2b; in (b),(c) the symbols denote magnetic pattern over the $x\mathrm{\text{−}}z$ plane. Slight charge ordering accompanies the spin ordering for $\delta d_{pd}\ne 0$.

Figure 2

(a) Hopping [Eq. (2)] and geometry of the lattice with rocksalt-pattern distortion. Large light red, large dark blue, and small light gray spheres denote ${\mathrm{Ni}}_{\mathrm{long}}$, ${\mathrm{Ni}}_{\mathrm{short}}$, and O. (b) The magnetic structure of $\Uparrow 0\Downarrow 0$ order in the bulk ${\mathrm{Ni}}_{16}{\mathrm{O}}_{48}$ supercell. ${\mathrm{Ni}}_{\mathrm{short}}$ forms singlets with its neighboring oxygen sites.

Figure 3

Left: Energy of stable solutions of mean-field theory measured relative to ground state of undistorted bulk system. Right: Rotor renormalization and insulating gap for the bulk system at $U=5.3$.

Figure 4

Results for $U=5.3$. Top: $n_{lm}=\sum _{\sigma }⟨n_{lm\sigma }⟩$ for the 1-layer structure. Bottom: $m_{\mathrm{long}}$ magnetic moment for bulk, middle layer of 3-layer, 2-layer, and 1-layer structures.