Evolution of the structural, magnetic, and electronic properties of the triple perovskite ${\mathrm{Ba}}_3\mathrm{Co}{\mathrm{Ir}}_2{\mathrm{O}}_9$

We report a comprehensive investigation of the triple perovskite iridate ${\mathrm{Ba}}_3\mathrm{Co}{\mathrm{Ir}}_2{\mathrm{O}}_9$. Stabilizing in the hexagonal $P{6}_3/mmc$ symmetry at room temperature, this system transforms to a monoclinic $C2/c$ symmetry at the magnetic phase transition. On further reduction in temperature, the system partially distorts to an even lower symmetry ($P2/c$), with both these structurally disparate phases coexisting down to the lowest measured temperatures. The magnetic structure as determined from neutron diffraction data indicates a weakly canted antiferromagnetic structure, which is also supported by first-principles calculations. Theory indicates that the ${\mathrm{Ir}}^{5+}$ carries a finite magnetic moment, which is also consistent with the neutron data. This suggests that the putative $J=0$ state is avoided. Measurements of heat capacity, electrical resistance noise, and dielectric susceptibility all point toward the stabilization of a highly correlated ground state in the ${\mathrm{Ba}}_3\mathrm{Co}{\mathrm{Ir}}_2{\mathrm{O}}_9$ system.

Figure 1

A schematic of the crystal structure of the ${\mathrm{Ba}}_{3}M{\mathrm{Ir}}_2{\mathrm{O}}_9$ triple perovskite. Here, blue and yellow octahedra represent cobalt and iridium sites, respectively, with the barium atoms being represented by green circles. The structure is comprised of a single $M{\mathrm{O}}_6$ octahedron sharing corners with ${\mathrm{Ir}}_2{\mathrm{O}}_9$ dimers, which in turn are formed by two face-sharing ${\mathrm{IrO}}_6$ octahedra.

Figure 2

Main panel: Rietveld refinement of the synchrotron powder diffraction pattern of ${\mathrm{Ba}}_3\mathrm{Co}{\mathrm{Ir}}_2{\mathrm{O}}_9$ at 295 K. The compound crystallizes in a 6H-hexagonal perovskite with space group ($P{6}_3/mmc$). The calculated and observed diffraction profiles are shown as red and black markers, respectively. The vertical green lines indicate the calculated Bragg positions. The blue line at the bottom is the difference between observed and calculated intensities. Inset: SEM images of the system exhibiting clear hexagonal facets shown on the right. The XPS fit for the Ir $4f$ core level is depicted on the left. Black circles are the data points and the red line is the fit. The solid and dashed blue lines depict the deconvolution of the $4f_{7/2}$ and $4f_{5/2}$ contributions, respectively.

Figure 3

(a) Temperature-dependent magnetization of ${\mathrm{Ba}}_3\mathrm{Co}{\mathrm{Ir}}_2{\mathrm{O}}_9$ as measured in the zero-field-cooled (ZFC) and field-cooled (FC) protocols with an applied magnetic field of $100\mathrm{Oe}$. Part (b) depicts the heat capacity as measured for this system, with a peak characterizing the magnetic transition. Part (c) depicts the MH isotherm as measured at $5\mathrm{K}$, with a finite opening of the loop indicating a finite ferromagnetic contribution to the otherwise antiferromagnetic system.

Figure 4

Schematic representation of Ir dimers and cobalt octahedra at 295 K (left) and 80 K (right). The cobalt octahedra has only one Co-O bond at high temperatures, which splits into three pairs of Co-O bonds at $80\mathrm{K}$. Similarly, Ir has two different bonds associated with Ir face sharing and corner sharing O atoms in the high-symmetry structure, which transforms into six different pairs of Ir-O bonds below the magnetostructural transition. The bond lengths with equal magnitudes are represented with the same color for the sake of clarity.

Figure 5

Neutron powder diffraction pattern of ${\mathrm{Ba}}_3\mathrm{Co}{\mathrm{Ir}}_2{\mathrm{O}}_9$ measured at 80 K using the WISH diffractometer. The calculated and observed diffraction profiles are shown in red and black, respectively. The upper and lower vertical blue marks represent the positions of nuclear and magnetic reflections, respectively, and the green line at the bottom is the difference between observed and calculated intensities. The fit was for Ireps ${\mathrm{\Gamma }}_1$, and the symmetry operators and magnetic basis vectors are (1) $x,y,z[u,v,w]$, (2) $-x,y,-z+1/2[-u,v,-w]$, (3) $-x,-y,-z[u,v,w]$, and (4) $x,-y,z+1/2[-u,v,-w]$ for iridium at 8($\mathit{f}$) and (1) and (2) for the more symmetric site 4($\mathit{a}$) for cobalt. Here, $u, v$, and $w$ indicate the components of the magnetic moment.

Figure 6

Schematic of the magnetic structure of the monoclinic ($C2/c$) phase at $80\mathrm{K}$ from (a) the Rietveld analysis of neutron diffraction data, and (b) using first-principles GGA $+ U +$ SOC calculations. Here, the blue solid circles and the small red arrows represent cobalt and iridium atoms, respectively.

Figure 7

(a) Resistivity ($\ln \rho$) plotted as a function of temperature ($T^{-1/4}$). The blue line is the linear fit to the high-temperature region using the variable range hopping formalism. (b) The derivative of $\ln \rho$ exhibits a peak close to 107 K marking the onset of the magnetostructural transition. Part (c) depicts the fitting to the low temperature specific heat data.

Figure 8

The calculated band structure at various theoretical hierarchies: (a) GGA, (b) GGA $+ U$ ($U_{\mathrm{Co}}=3$ and $U_{\mathrm{Ir}}=2.4$ eV), (c) GGA $+$ SOC, and (d) GGA $+ U +$ SOC for ${\mathrm{Ba}}_3\mathrm{Co}{\mathrm{Ir}}_2{\mathrm{O}}_9$. While the GGA $+ U +$ SOC ($U_{\mathrm{Co}}=3$ and $U_{\mathrm{Ir}}=2.4$ eV) results correctly predict a Mott insulating electronic structure along with the correct magnetic solution, all other calculations predict a metallic band structure. These calculations together indicate the interplay between the Coulomb interaction $U$ and spin-orbit coupling.

Figure 9

(a) Rietveld refinement of synchrotron powder diffraction pattern of ${\mathrm{Ba}}_3\mathrm{Co}{\mathrm{Ir}}_2{\mathrm{O}}_9$ at $60\mathrm{K}$. The calculated and observed diffraction profiles are shown as red and black markers, respectively. The vertical green lines indicate the calculated Bragg positions for the monoclinic $C2/c$ (top) and $P2/c$ (bottom) phases. The blue line at the bottom depicts the difference between observed and calculated intensities. The inset (b) depicts the temperature dependence of the main peaks, with the onset of the magnetostructural transition seen below 110 K. The inset (c) shows an expanded view of the main peak fitted using the two-phase model at 60 K.

Figure 10

Schematic crystal structures exhibited by ${\mathrm{Ba}}_3\mathrm{Co}{\mathrm{Ir}}_2{\mathrm{O}}_9$ across the temperature range of our investigations. Here, the blue and yellow octahedra represent the cobalt and iridium sites, respectively. The high-symmetry $P{6}_3/mmc$ structure (a) transforms to a monoclinically distorted $C2/c$ structure (b) at the magnetostructural transition. On further reduction in temperature, a part of the system transforms to an even lower symmetry $P2/c$ (c), with both of these monoclinic phases coexisting down to the lowest measured temperatures.

Figure 11

Variation of the lattice parameters of ${\mathrm{Ba}}_3\mathrm{Co}{\mathrm{Ir}}_2{\mathrm{O}}_9$ as a function of temperature. The error bars are of the order of the symbol sizes. The three regions correspond to three different structural phases. Region I, $P{6}_3/mmc$; II, $C2/c$; and III, $C2/c+P2/c$.

Figure 12

The main panel depicts the low-temperature specific heat $C_p/T^3$ as a function of temperature as measured in ${\mathrm{Ba}}_3\mathrm{Co}{\mathrm{Ir}}_2{\mathrm{O}}_9$. The inset depicts the temperature evolution of the two monoclinic phases as determined from the analysis of structural data, with the uncertainty being of the order of the symbol sizes.

Figure 13

(a) The temperature-dependent normalized resistance noise evaluated at $1\mathrm{Hz}$ for ${\mathrm{Ba}}_3\mathrm{Co}{\mathrm{Ir}}_2{\mathrm{O}}_9$ at different magnetic fields. The inset (b) depicts the scaling of the voltage noise magnitude $S_V$ with the applied current $I$ at a fixed temperature of $50\mathrm{K}$. Part (c) depicts the temperature dependence of the frequency exponent for the zero-field data, and a comparison to the calculated values using the DDH model. Part (d) depicts the temperature dependence of the real part of the dielectric susceptibility as measured in frequencies ranging from $2\mathrm{KHz}$ to $4\mathrm{MHz}$.