Frustrated Ising chains on the triangular lattice in ${\mathrm{Sr}}_3{\mathrm{NiIrO}}_6$

Inelastic neutron scattering study on the spin-chain compound ${\mathrm{Sr}}_3{\mathrm{NiIrO}}_6$ reveals gapped quasi-1D magnetic excitations. The observed one-magnon band between 29.5 and 39 meV consists of magnon modes of the ${\mathrm{Ni}}^{2+}$ ions. The fitting of the spin wave spectrum reveals strongly coupled Ising-like chains along the $c$ axis that are weakly coupled into a frustrated triangular lattice in the $ab$ plane. The magnetic excitations survive up to 200 K well above the magnetic ordering temperature of $T_N\sim 75$ K, also indicating a quasi-1D nature of the magnetic interactions in ${\mathrm{Sr}}_3{\mathrm{NiIrO}}_6$. Our microscopic model is in agreement with ab initio electronic structure calculations and explains the giant spin-flip field observed in bulk magnetization measurements.

Figure 1

Crystal structure of ${\mathrm{Sr}}_3{\mathrm{NiIrO}}_6$, showing the ${\mathrm{NiO}}_6$ trigonal prism (light green) and ${\mathrm{IrO}}_6$ octahedra (dark green). The white vertical bonds are the first-neighbor anisotropic exchange interactions $J_{xy}$ and $J_z$; the zigzag bonds with three different colors denote the three inequivalent interchain couplings $J_{3a},J_{3b}$, and $J_{3c}$. The red vertical arrows show the exchange coupling between Ir-Ir, $J_{2a}$, and Ni-Ni, $J_{2b}$, along the chain direction.

Figure 2

Imaginary part of the magnetic dynamical susceptibility of ${\mathrm{Sr}}_3{\mathrm{NiIrO}}_6$ measured using inelastic neutron scattering on a polycrystalline sample collected with incident neutron energy of 80 meV and after the subtraction of the nonmagnetic background. The signal is in absolute units. (a) Data cuts measured at 5 K and integrated for different $Q$ ranges. (b) Data cuts measured at different temperatures and integrated between 2 and $3{\AA }^{-1}$. Note that the slightly negative signal is an artifact of the background subtraction.

Figure 3

Momentum transfer dependence of the integrated inelastic magnetic signal denoted by blue dots. Red and green lines denote the squared $\langle j_0\rangle$ magnetic form factor of ${\mathrm{Ni}}^{2+}$ and ${\mathrm{Ir}}^{4+}$ ions [30].

Figure 4

(a) The magnetic scattering of ${\mathrm{Sr}}_3{\mathrm{NiIrO}}_6$ at 5 K obtained after subtracting phonon scattering. The strong scattering below 10 meV is due to the incoherent background. (b) The simulated spin wave cross section at 5 K was calculated using the parameters of the best-fitting hexagonal structure. Intensity is scaled with a factor of 0.8 to fit the data; the solid peak at the bottom shows the instrumental energy resolution at 32.5 meV. (c) Cuts at different $Q$ ranges of both the data (color circles) and simulation (black lines). (d) The complete spin wave spectrum; blue and red areas show the intensity of spin waves localized on iridium and nickel ions, respectively.

Figure 5

Phase diagram of the triangular lattice Ising model with interactions up to the second neighbor. $J_{\text{tri}}$ is the effective coupling between the Ni-Ir chains (see text) and $J_{tri2}$ is the effective coupling between second-neighbor chains. Gray and white circles denote spins with opposite directions.

Figure 6

Magnetic structures used for the modeling of the (a) hexagonal structure and (b) stripy structure. The underlying gray parallelepipeds show the equivalent Ising model with black and white spheres for the down and up spins.

Figure 7

Elastic signal of the sample integrated between 2 Å${}^{-1}$ and 4 Å${}^{-1}$ momentum transfer. The red line denotes the resolution function model using a linear combination of different Lorentzian and Gaussian functions on each side.