Electronic and magnetic properties of a quasi-one-dimensional spin chain system ${\text{Sr}}_3{\text{NiRhO}}_6$

We investigate the electronic structure of ${\text{Sr}}_3{\text{NiRhO}}_6$, a quasi-one-dimensional spin chain system using ab initio band-structure calculations. Spin polarized calculations within generalized gradient approximation (GGA) reveal that Ni and Rh have finite moments, and they are antiferromagnetically coupled along the chain axis in the ground state. While these results that are obtained within the local spin-density approximations provide remarkable representation of the magnetic phase, the experimentally observed insulating behavior could not be captured within this method. $\text{GGA}+U$ calculations show that the opening up of an insulating gap requires on-site Coulomb interaction strength among the $\text{Rh}4d$ electrons, $U_{dd}^{\text{Rh}}\approx 2.5\text{eV}$, and the correlation strength among $\text{Ni}3d$ electrons, $U_{dd}^{\text{Ni}}\approx 4.5\text{eV}$, suggesting this system to be a Mott insulator. Electron correlation among $d$ electrons leads to significant enhancement of the $\text{O}2p$ character of the energy bands in the vicinity of the Fermi level and the $d$ bands appear at lower energies. Energy gap in the up-spin density of states appears to be significantly small $\left(\sim 0.12\text{eV}\right)$ while it is $>2\text{eV}$ in the down-spin density of states, suggesting a possibility of spin-polarized conduction in the semiconducting phase.

Figure 1

(Color online) The unit cell of ${\text{Sr}}_3{\text{NiRhO}}_6$. Sr is represented by largest symbols (black). Gradually decreasing sized symbols represent Ni (pink), Rh (blue), and O (green), respectively.

Figure 2

(Color online) The PDOS corresponding to $d_{z^2}$ ($d_0$; thin solid lines), $d_{xz}+d_{yz}$ ($d_{\pm 1}$; dashed lines), and $d_{xy}+d_{x^2-y^2}$ ($d_{\pm 2}$; thick solid lines) orbitals for (a) Ni and (b) Rh, obtained from spin-polarized GGA calculation when Ni and Rh are ferromagnetically coupled. (c) $\text{O}2p$ PDOS.

Figure 3

(Color online) The PDOS corresponding to $d_{z^2}$ ($d_0$; thin solid lines), $d_{xz}+d_{yz}$ ($d_{\pm 1}$; dashed lines), and $d_{xy}+d_{x^2-y^2}$ ($d_{\pm 2}$; thick solid lines) orbitals for (a) Ni and (b) Rh, obtained from spin-polarized GGA calculation when intrachain Ni and Rh are antiferromagnetically coupled. (c) $\text{O}2p$ PDOS.

Figure 4

(Color online) On-site Coulomb interaction among $\text{Ni}3d$ $\left(U_{dd}^{\text{Ni}}\right)$ and $\text{Rh}4d$ $\left(U_{dd}^{\text{Rh}}\right)$ electrons vs insulating gap for (a) up-spin and (b) down-spin channels. Two cases are considered: (i) $U_{dd}^{\text{Rh}}$ is fixed at 3 eV and $U_{dd}^{\text{Ni}}$ varied from 3.5 to 5.5 eV (solid circles), and (ii) $U_{dd}^{\text{Ni}}$ is fixed at 5.5 eV and $U_{dd}^{\text{Rh}}$ varied from 3 to 5 eV (open circles).

Figure 5

(Color online) The PDOS corresponding to $d_{z^2}$ ($d_0$; thin solid lines), $d_{xz}+d_{yz}$ ($d_{\pm 1}$; dashed lines), and $d_{xy}+d_{x^2-y^2}$ ($d_{\pm 2}$; thick solid lines) orbitals for (a) Ni and (b) Rh, obtained from spin-polarized $\text{GGA}+U$ calculation ($U_{dd}^{\text{Ni}}=5\text{eV}$ and $U_{dd}^{\text{Rh}}=3\text{eV}$) when intrachain Ni and Rh are antiferromagnetically coupled. (c) $\text{O}2p$ PDOS.

Figure 6

Dispersion curves along different symmetry directions of the first Brillouin zone for both the spin channels. Fermi level is denoted by zero in the energy scale.

Figure 7

(Color online) Schematic energy-level diagram of $d_0$, $d_{\pm 1}$, and $d_{\pm 2}$ orbitals for ${\text{Ni}}^{2+}$ and ${\text{Rh}}^{4+}$, obtained from (a) nonmagnetic (Nonmag) and FM calculations, and (b) Nonmag and IAFM calculations. Solid and dashed arrows indicate the occupied and unoccupied states, respectively.