Coexisting charge and magnetic orders in the dimer-chain iridate $\mathrm{B}{\mathrm{a}}_5\mathrm{AlI}{\mathrm{r}}_2{\mathrm{O}}_{11}$

We have synthesized and studied single-crystal $\mathrm{B}{\mathrm{a}}_5\mathrm{AlI}{\mathrm{r}}_2{\mathrm{O}}_{11}$ that features dimer chains of two inequivalent octahedra occupied by tetravalent $\mathrm{I}{\mathrm{r}}^{4+}\left(5d^5\right)$ and pentavalent $\mathrm{I}{\mathrm{r}}^{5+}\left(5d^4\right)$ ions, respectively. $\mathrm{B}{\mathrm{a}}_5\mathrm{AlI}{\mathrm{r}}_2{\mathrm{O}}_{11}$ is a Mott insulator that undergoes a subtle structural phase transition near $T_S=210\mathrm{K}$ and a magnetic transition at $T_M=4.5\mathrm{K}$; the latter transition is surprisingly resistant to applied magnetic fields ${\mu }_{o}H\le 12\mathrm{T}$ but more sensitive to modest applied pressure $\left(d{T}_M/dp\approx +0.61\mathrm{K}/\mathrm{GPa}\right)$. All results indicate that the phase transition at $T_S$ signals an enhanced charge order that induces electrical dipoles and strong dielectric response near $T_S$. It is clear that the strong covalency and spin-orbit interaction (SOI) suppress double exchange in Ir dimers and stabilize a novel magnetic state that is neither $S=3/2$ nor $J=1/2$, but rather lies in an “intermediate” regime between these two states. The novel behavior of $\mathrm{B}{\mathrm{a}}_5\mathrm{AlI}{\mathrm{r}}_2{\mathrm{O}}_{11}$ therefore provides unique insights into the physics of SOI along with strong covalency in competition with double-exchange interactions of comparable strength.

Figure 1

Crystal structure: The single-crystal structure generated based on the x-ray data for (a) the $ac$ plane, (b) the $ab$ plane, and (c) a representative single crystal of $\mathrm{B}{\mathrm{a}}_5\mathrm{AlI}{\mathrm{r}}_2{\mathrm{O}}_{11}$. Note that the dimers are connected via $\mathrm{Al}{\mathrm{O}}_4$ tetrahedra (yellow), forming dimer chains along the $b$ axis.

Figure 2

The temperature dependence of the lattice parameters of single-crystal $\mathrm{B}{\mathrm{a}}_5\mathrm{AlI}{\mathrm{r}}_2{\mathrm{O}}_{11}$: (a) the $a$ axis, $b$ axis, and $c$ axis ($A=a,b$, or $c$ axis; $A_{300}=$ the lattice parameter at $300\mathrm{K}$), (b) the unit cell $V$, (c) the Ir1-Ir2 distance $(\mathrm{S}1=\mathrm{sample}1\mathrm{and}\mathrm{S}2=\mathrm{sample}2)$, and (d) the thermal displacement $U$ for $90\mathrm{K}<T<300\mathrm{K}$. Note the pronounced changes at $T_S=210\mathrm{K}$ in the Ir1-Ir2 distance and thermal displacement $U$.

Figure 3

Temperature dependence of (a) the $b$-axis electrical resistivity ${\rho }_b$ and (b) the dielectric constant for the $a$ axis and $b$ axis, ${\varepsilon }_a^{\prime }$ and ${\varepsilon }_b^{\prime }$, respectively. The inset in (a) shows ln ${\rho }_b$ vs $1/T$; the inset in (b) shows ${\varepsilon }_b^{\prime }$ vs. $T$ for lower temperatures.

Figure 4

A sketch of the proposed configurations of electrical dipoles ($E$, red arrows) and magnetic moments ($M$, black arrows) for (left) the $ac$ plane and (right) the $ab$ plane based on the data collected for this study. This is a simplified illustration that does not include possible magnetic moment canting.

Figure 5

Temperature dependence of (a) the magnetization for the $a,b$, and $c$ axes, $M_a,M_b$, and $M_c$, at ${\mu }_{\mathrm{o}}H=7\mathrm{T}$, (b) the $b$-axis magnetic susceptibility ${\chi }_b$ at various fields, and (c) $M_b$ at various pressures and ${\mu }_{\mathrm{o}}H=7\mathrm{T}$. The inset shows enlarged $M_b$ near $T_S$.

Figure 6

Temperature dependence of (a) the specific heat $C\left(T\right)$ at ${\mu }_{\mathrm{o}}H=0$ and $9\mathrm{T}$ and entropy at ${\mu }_{\mathrm{o}}H=0\mathrm{T}$ (right scale) and (b) $C\left(T\right)$ for $140\mathrm{K}<T<300\mathrm{K}$.