Doping-dependent orbital magnetism in Chromium pnictides

TL;DR

The paper addresses how electron doping tunes orbital magnetism in the Cr pnictide LaCrAsO. It builds a five-band Cr-$d$ tight-binding model from DFT and analyzes spin/charge instabilities with a matrix random-phase approximation, mapping a phase diagram as a function of electron doping $n$. It reveals a sequence of magnetic states—commensurate antiferromagnetism at low $n$, stripe antiferromagnetism at intermediate $n$, and incommensurate magnetic orders at higher $n$—with Lifshitz transitions in the Fermi surface accompanying changes in the nesting vector $Q$ and a shift in orbital dominance from $d_{3z^2-r^2}$ to $d_{xy}$. This demonstrates a crossover from localized to itinerant magnetism controlled by Fermi-surface topology and orbital content, offering a general mechanism relevant to Cr- and Fe-based pnictides and implications for potential spin-fluctuation–driven superconductivity.

Abstract

We present results for the phase diagram of the parent compound LaCrAsO under electron doping using the matrix random-phase approximation. At low doping levels, the system stabilizes an antiferromagnetic state in which different Cr sublattices carry opposite spins, consistent with experimental observations. As the doping concentration increases, a stripe-type antiferromagnetic phase becomes favored. At even higher doping, the system repeats the two former magnetic states, but with incommensurate magnetic ordering vectors. The commensurate magnetic phases are associated with more localized electrons in the Cr $d_{3z^2-r^2}$ orbital, whereas the incommensurate phases are linked to the $d_{xy}$ orbital, whose stronger overlap favors itinerant-electron magnetism.

Figures (5)

• Figure 1: (a) Projected band structure in the $d-$orbitals ($d_{3z^2-r^2}$ in green; $d_{xz}$ in red; $d_{yz}$ in blue; $d_{x^2-y^2}$ in black; $d_{xy}$ in magenta) of the tight-binding ${\rm Cr}$ atoms for ${\rm LaCrAsO}$ along the symmetry lines $\Gamma-X-M-\Gamma$. (b) Density of states (DOS) for ${\rm LaCrAsO}$. In panels (a) and (b), the grey regions indicate the doping studied in this work ($n = 4.0 - 4.55$).
• Figure 2: Panels (a) to (d) shows the contribution of the $d-$orbitals ($d_{3z^2-r^2}$ in green; $d_{xz}$ in red; $d_{yz}$ in blue; $d_{x^2-y^2}$ in black; $d_{xy}$ in magenta) to the Fermi surface pockets for ${\rm LaCrAsO}$ for $n = 4.02, 4.13, 4.40,4.42$, respectively. For ${\rm LaCrAsO}$ and in this doping range, the Lifshitz transition occurs between panels (a) and (b), and panels (c) and (d). The nesting vectors are represented by the grey arrows on each of the panels.
• Figure 3: Panels $(a)$ shows the critical Hubbard interaction strength $U_c^{(s)}$ in the spin channel as a function of electron doping $n$. Colors in the scattered points denote the norm of the magnetic ordering vector at the instability $Q$. For visualization purposes, we indicate the different magnetic instabilities by colored regions of the diagram. In panel $(b)$, we show the magnetic ordering vector $Q$ and the density of states as a function of doping. Panel $(c)$ shows the non-zero components of the magnetic order parameter at the instability $[\Delta_s]_{dd}$ for all orbitals $d$ for the same electron doping values.
• Figure 4: Spin density $[\bar{\Delta}_s]_{pp}(\boldsymbol{r})$ mapping the magnetic texture (spin-up: red; spin-down: blue) at Cr sites (Site A: circle; Site B: square) under varying electron doping concentrations: $n=3.992$ (panel a), $n=4.204$ (panel b), $n=4.219$ (panel c), $n=4.298$ (panel d), $n=4.440$ (panel e), and $n=4.533$ (panel f).
• Figure 5: Superconducting symmetries for different doping levels, $n = 4.17, 4.30, 4.44, 4.53$ respectively in panels (a) to (d).