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Competing Magnetic Ground States in Copper-Doped Pb$_{10}$P$_{6}$O$_{25}$

Lin Hou, Kevin Allen, Christopher Lane, Jian-Xin Zhu

Abstract

We investigate the electronic and magnetic properties of copper-doped Pb$_{10}$(PO$_4$)$_6$O using a combination of density functional theory and many-body perturbation theory. The flat half-filled electronic band at the Fermi level is found to give way to an incommensurate antiferromagnetic instability with wave vector $(0.28π,\pm 0.47π,π)$ within the random phase approximation arising predominantly from Cu-$d_{yz}$ and Cu-$d_{xz}$ orbitals. Moreover, the Heisenberg exchange coupling between neighboring copper atoms is estimated to be $\sim 1$ meV. Our results suggest that magnetism in copper-doped Pb$_{10}$(PO$_4$)$_6$O is localized on the impurity copper site, with no long-range ordering. These findings support the picture that copper behaves as a magnetic impurity within the Pb-apatite matrix.

Competing Magnetic Ground States in Copper-Doped Pb$_{10}$P$_{6}$O$_{25}$

Abstract

We investigate the electronic and magnetic properties of copper-doped Pb(PO)O using a combination of density functional theory and many-body perturbation theory. The flat half-filled electronic band at the Fermi level is found to give way to an incommensurate antiferromagnetic instability with wave vector within the random phase approximation arising predominantly from Cu- and Cu- orbitals. Moreover, the Heisenberg exchange coupling between neighboring copper atoms is estimated to be meV. Our results suggest that magnetism in copper-doped Pb(PO)O is localized on the impurity copper site, with no long-range ordering. These findings support the picture that copper behaves as a magnetic impurity within the Pb-apatite matrix.
Paper Structure (9 sections, 11 equations, 4 figures)

This paper contains 9 sections, 11 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Theoretical and Calculation Details
  3. First-principles calculations
  4. Local Projections and Response Function Calculations
  5. Results and discussion
  6. Crystal and Electronic Structure
  7. Magnetic Instabilities
  8. Magnetic Exchange Parameters
  9. Conclusion

Figures (4)

  • Figure 1: (a) Crystal structure of Pb$_9$CuP$_6$O$_{25}$ viewed along the $c$-axis. Black lines denote the primitive unit cell. (b) The associated first Brillouin zone with labeled high-symmetry points. (c) Electronic band structure and corresponding density of states for the non-magnetic phase. The size and color of the dots are proportional to the fractional weight of the various indicated site-resolved orbital projections.
  • Figure 2: Momentum dependence of $\Lambda_F^0(\mathbf{q}, \omega=0)$ for pristine Pb$_9$CuP$_6$O$_{25}$ in the non-magnetic phase for various slices along $q_z$. The white “$\times$” marks denote the critical instability momenta $\mathbf{Q}$. The black dashed line gives the boundary of the Brillouin zone and the gray dotted lines indicate the reciprocal lattice vectors. The color bar indicates the instability strength.
  • Figure 3: Density of instabilities for pristine Pb$_9$CuP$_6$O$_{25}$ in the non-magnetic phase. Shading and lines of various colors (see legend) give the contributions from the total and different instability eigenvalues.
  • Figure 4: Real part of the RPA susceptibility $\chi$ for various combinations of Cu $d$ orbitals at upper left Q point white in Fig\ref{['fig:EigF']}: (a) $\chi^{00}$ charge channel and (b) $\chi^{xx}$ spin channel.