Nature of the magnetic coupling in infinite-layer nickelates versus cuprates

Armin Sahinovic, Benjamin Geisler, and Rossitza Pentcheva

Phys. Rev. Materials 7, 114803 – Published 6 November 2023

Abstract

In contrast to the cuprates, where the proximity of antiferromagnetism (AFM) and superconductivity is well established, first indications for AFM interactions in superconducting infinite-layer nickelates were only recently obtained. Here, we explore, based on first-principles simulations, the nature of the magnetic coupling in ${NdNiO}_{2}$ as a function of the on-site Coulomb and exchange interaction, varying the explicit hole doping and the treatment of the Nd $4 f$ electrons. The $U − J$ phase diagrams for undoped nickelates and cuprates indicate $G$ -type ordering, yet show opposite $U$ dependency. By either Sr hole doping or explicit treatment of the Nd $4 f$ electrons, we find a transition to a Ni $C$ -type AFM ground state. We trace back the effect of Sr doping to a distinct accommodation of the holes by the Ni versus Cu $e_{g}$ orbitals. The interaction between Nd $4 f$ and Ni $3 d$ states stabilizes $C$ -type AFM order on both sublattices. Though spin-orbit interactions induce a band splitting near the Fermi energy, the bad-metal state is retained even under epitaxial strain. These results establish the distinct role of the magnetic interactions in the nickelates versus the cuprates and suggest the former as a unique platform to investigate the relation to unconventional superconductivity.

Received 6 June 2023
Accepted 10 October 2023

DOI:https://doi.org/10.1103/PhysRevMaterials.7.114803

Physics Subject Headings (PhySH)

Electronic structure Epitaxial strain Magnetic interactions Spin-orbit coupling Superconductivity

Nickelates Transition metal oxides

DFT+U Density functional theory

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Armin Sahinovic¹, Benjamin Geisler ^1,2,3,*, and Rossitza Pentcheva ^1,†

¹Department of Physics and Center for Nanointegration (CENIDE), Universität Duisburg-Essen, Lotharstraße 1, 47057 Duisburg, Germany
²Department of Physics, University of Florida, Gainesville, Florida 32611, USA
³Department of Materials Science and Engineering, University of Florida, Gainesville, Florida 32611, USA

^*benjamin.geisler@ufl.edu
^†rossitza.pentcheva@uni-due.de

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Vol. 7, Iss. 11 — November 2023

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Images

Figure 1
Modeling the $A B O_{2}$ infinite-layer structure in $\sqrt{2} a \times \sqrt{2} a \times 2 c$ supercells (a) permits us to consider four different magnetic orderings (b) independently at the $A$ - and $B$ -site sublattices. (c)–(e) Magnetic phase diagrams for ${NdNiO}_{2}, {LaNiO}_{2}$ , and ${CaCuO}_{2}$ show the ground-state order at the Ni/Cu sublattice for a range of $U$ and $J$ values (the dotted line marking $U = J$ ), which suggests a profound $G$ -type order in all three compounds. Closer inspection unravels a fundamentally distinct $U$ dependence of the Ni/Cu magnetic coupling in ${NdNiO}_{2}$ and ${LaNiO}_{2}$ versus ${CaCuO}_{2}$ , displayed in panel (i). The evolution of the corresponding Ni/Cu magnetic moments is shown in panel (j). The black and gray dashed lines in panels (i) and (j) confirm these trends by using the vasp code and the PBE and SCAN exchange-correlation functionals, respectively. (f) Surprisingly, the explicit treatment of the Nd $4 f$ electrons (so far FM ordered) reveals a $C$ -type magnetic ground state of the Ni ions in ${NdNiO}_{2}$ , demonstrating a strong coupling of the sublattices. A possible mechanism is illustrated in panel (k). (g), (h) The explicitly hole-doped ${Nd}_{0.75} {Sr}_{0.25} {NiO}_{2}$ exhibits $C$ -type AFM order as well, which is additionally stabilized by a full consideration of the Nd $4 f$ states.
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Figure 2
(a) Magnetic phase diagram of ${NdNiO}_{2}$ with explicit treatment of the Nd $4 f$ electrons in their ground-state AFM $C$ -type order. Comparison with Fig. 1 reveals that the AFM $C$ -type ground state at the Ni sites is preserved. The same is observed for the explicitly hole-doped Ni system achieved by doubling the supercell in vertical direction [panel (c); see also Fig. 1]. (b) The site-averaged Ni magnetic moments of undoped and hole-doped ${NdNiO}_{2}$ monotonically rise with $U$ ; hole doping results in a sizable additional increase of their magnitude. In contrast, they are quasi-independent of the Nd magnetic order.
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Figure 3
(a) Spin-resolved band structure of undoped and hole-doped ${CaCuO}_{2}$ ( $G$ -type; left) and ${NdNiO}_{2}$ (Ni $C$ -type, Nd FM; right). The Cu/Ni $3 d_{x^{2} - y^{2}}$ , Cu/Ni $3 d_{z^{2}}$ , Nd $5 d$ , and Nd $4 f$ orbitals are depicted by blue, pink, green, and orange, respectively. In stark contrast to the infinite-layer cuprates, where the hole doping strongly affects the oxygen $2 p_{x}, 2 p_{y}$ system (represented by the black valence bands) and slightly reduces the Cu magnetic moment via the $3 d_{x^{2} - y^{2}}$ orbital, exclusively the Ni states accommodate the doped holes in the infinite-layer nickelates, resulting in a depleted Ni- $3 d_{z^{2}}$ -derived flat band and significantly enhanced Ni magnetic moments. (b) This is also reflected in the density difference plots, which visualize the areas of increased hole density due to doping (isosurface value $n_{c} = 0.006$ a.u. $^{- 3}$ for ${CaCuO}_{2}$ and 0.012 a.u. $^{- 3}$ for ${NdNiO}_{2}$ ).
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Figure 4
Band structure of ${NdNiO}_{2}$ in the Ni $C$ -type, Nd $C$ -type AFM ground state from (a) $DFT + U$ and (b) $DFT + U + SOC$ . Orange, red, and green bands indicate Nd $4 f$ , Ni $3 d$ , and Nd $5 d$ orbital character, respectively. The corresponding Fermi surface is localized in the $k_{x}, k_{y}$ plane (inset).
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Figure 5
Strain-dependent band structure of fully $C$ -type AFM ${NdNiO}_{2}$ around the Fermi level. (a) Spin-orbit coupling results in hybridization and avoided crossings between Ni- $3 d$ -derived (red) and Nd- $5 d$ -derived (green) bands. (b) Nevertheless, neither compressive ( $a_{LAO}, a_{STO}$ ) nor tensile epitaxial strain ( $a_{DSO}$ ) drive a metal-to-insulator transition. Instead, a weakly conducting metal is retained. Merely a strong response of the normally depleted Nd- $5 d$ -derived electron pocket at the $Γ$ point can be observed.
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