Structural origin of the $J_{\mathrm{eff}}=1/2$ antiferromagnetic phase in Ga-doped ${\mathrm{Sr}}_2\mathrm{Ir}{\mathrm{O}}_4$

${\mathrm{Sr}}_2\mathrm{Ir}{\mathrm{O}}_4$ hosts a novel $J_{\mathrm{eff}}=1/2$ Mott state and quasi-two-dimensional antiferromagnetic order, providing a unique avenue of exploring emergent states of matter and functions that are extraordinarily sensitive to any structural variations. Although the correlation between the physical property and the lattice structure in ${\mathrm{Sr}}_2\mathrm{Ir}{\mathrm{O}}_4$ has been a focused issue in the past decade, a common perception assumes that the magnetic ordering is essentially determined by the Ir-O-Ir bond angle. Therefore, a delicate modulation of this angle and, consequently, a major modulation of the magnetic ordering by chemical doping, such as Ga at the Ir site, has been extensively investigated and well believed. In this paper, however, we present a whole package of structure and magnetism data on a series of single-crystal and polycrystalline ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Ga}}_x{\mathrm{O}}_4$ samples, revealing the substantial difference in the Néel temperature $T_N$ between the two types of samples, and the $T_N$ value for the polycrystalline sample $x=0.09$ is even 64 K higher than that of the single-crystal sample $x=0.09$ ($\mathrm{\Delta }{T}_{\mathrm{N}}\sim 64\mathrm{K}$ at $x=0.09$). Our systematic investigations demonstrate the crucial role of the c/a ratio in tuning the interlayer coupling and thereby the Néel point $T_N$, i.e., a higher $T_N$ can be achieved as c/a is reduced. The notable differences in structural parameters between the two groups of samples are probably caused by additional strain due to the massive grain boundaries in polycrystalline samples. The present paper suggests an additional ingredient of physics that is essential in modulating the emergent properties in ${\mathrm{Sr}}_2\mathrm{Ir}{\mathrm{O}}_4$ and probably other iridates.

Figure 1

(a) Rietveld refinement of a ${\mathrm{Sr}}_2\mathrm{Ir}{\mathrm{O}}_4$ single crystal. Evaluated lattice parameters: (b) $a$, (c) $c$, (d) variation in cell volume ΔV, (e) the c/a ratio, (f) the Ir-O2-Ir bond length $l$, (g) the Ir-O2-Ir bond angle ϕ, and (h) the rotation angle φ of oxygen octahedra for the polycrystalline (blue squares) and single crystal (red dots) ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Ga}}_x{\mathrm{O}}_4$.

Figure 2

(a) and (b) show SEM images of the single-crystal and polycrystalline ${\mathrm{Sr}}_2{\mathrm{Ir}}_{0.93}{\mathrm{Ga}}_{0.07}{\mathrm{O}}_4$, respectively. The inset in (b) shows a magnified image for the polycrystalline sample with $x=0.07$ and the corresponding elemental mappings of Sr, Ir, Ga, and O are shown in (c)–(f), respectively. An EDS spectra of a sample with $x=0.07$ is show in (g). (h) Measured Ga content $x_{\mathrm{EDS}}$ as a function of nominal value $x_{\mathrm{nominal}}$.

Figure 3

Measured XPS spectra for samples with $x=0$, 0.05, and 0.09. The spectra are fitted with multiple valance states of Ir.

Figure 4

Temperature dependence of magnetization for (a) single-crystal ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Ga}}_x{\mathrm{O}}_4$ ($0\le x\le 0.09$) and (b) for polycrystalline samples with $0\le x\le 0.15$. (c) The Néel temperature $T_N$ as a function of Ga-content $x$ for both groups of samples.

Figure 5

Measured magnetization as a function of H at $T=10\mathrm{K}$. (a) In-plane magnetization $M_a\left(H\right)$ and (b) out-of-plane magnetization $M_c\left(H\right)$ of the single crystals. (c) M(H) curves for the polycrystalline samples. (d) $x$ dependence of measured magnetization $M_{\mathrm{s}}$ at $H=5\mathrm{T}$.

Figure 6

Temperature dependence of ρ for (a) the single crystals and (b) the polycrystalline samples. (c) Estimated ρ as a function of $x$ at $T=50\mathrm{K}$ for both groups of samples.

Figure 7

(a) The c/a ratio as a function of doping content $x$ for several groups of samples with different dopants. The data of Ca- and Ba-doped ${\mathrm{Sr}}_2\mathrm{Ir}{\mathrm{O}}_4$ were taken from Refs. [28, 35]. (b) $\mathrm{\Delta }{T}_{\mathrm{N}}$ as a function of the Δ(c/a) ratio. $\mathrm{\Delta }{T}_{\mathrm{N}}$ and Δ(c/a) represent the difference in $T_N$ and c/a between the polycrystalline and the single-crystal samples, respectively.

Figure 8

Measured in-plane magnetization $M_a$ as a function of T for the samples with (a) $x=0.05$ and (b) $x=0.09$. The resintered polycrystals were obtained from corresponding single crystals. $T_N$ is indicated by an arrow. The full data are shown in the insets of the figures.