Interplay of magnetism and dimerization in the pressurized Kitaev material $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$

We present magnetization measurements on polycrystalline $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ under hydrostatic pressures up to 3 GPa and construct the temperature-pressure phase diagram of this material. Our data confirm that magnetic order breaks down in a first-order phase transition at $p_{\mathrm{c}}\approx 1.4$ GPa and additionally reveal a steplike feature—magnetic signature of structural dimerization—that appears at $p_{\mathrm{c}}$ and shifts to higher temperatures upon further compression. Following the structural study by L. S. I. Veiga et al. [Phys. Rev. B 100, 064104 (2019)], we suggest that a partially dimerized phase with a mixture of magnetic and nonmagnetic ${\mathrm{Ir}}^{4+}$ sites develops above $p_{\mathrm{c}}$. This phase is thermodynamically stable between 1.7 and 2.7 GPa according to our ab initio calculations. It confines the magnetic ${\mathrm{Ir}}^{4+}$ sites to weakly coupled tetramers with a singlet ground state and no long-range magnetic order. Our results rule out the formation of a pressure-induced spin-liquid phase in $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ and reveal peculiarities of the magnetism collapse transition in a Kitaev material. We also show that a compressive strain imposed by the pressure treatment of $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ enhances signatures of the 100 K magnetic anomaly at ambient pressure.

Figure 1

Nondimerized ($Fddd$), partially dimerized ($P{2}_1/n$), and fully dimerized ($C2/c$) phases of $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ under pressure, with the crystal structures taken from Ref. [22]. Red Ir–Ir bonds denote the dimerized ${\mathrm{Ir}}^{4+}$ ions.

Figure 2

Temperature-dependent magnetic susceptibility $\chi \left(T\right)$ of $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ measured under various pressures from 2 to 300 K in the 1 T magnetic field. (a), (c), (e) Data from three different runs. (b), (d), (f) Magnifications of the steplike features due to the dimerization transition at $T_d$ shown by the black arrows. A hysteresis loop is clearly seen at 1.51 GPa in (b) upon cooling and warming.

Figure 3

Curie-Weiss analysis of the susceptibility data. (a) Magnetic susceptibility $\chi$ and inverse susceptibility ${(\chi -{\chi }_0)}^{-1}$ measured at 1.51 and 1.77 GPa in run No. 1. The dashed line shows the Curie-Weiss fitting at 1.51 GPa. (b) The paramagnetic effective moment and Curie-Weiss temperature ${\theta }_{\mathrm{CW}}$ extracted from the Curie-Weiss fits for the low-temperature part of the magnetic susceptibility.

Figure 4

Temperature-pressure phase diagram of $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ inferred from the magnetic susceptibility data. $T_{\mathrm{N}}$ marks the antiferromagnetic transition temperature of the nondimerized phase, whereas $T_{\mathrm{d}}$ stands for the dimerization transition temperature of the high-pressure phase.

Figure 5

Zero-field-cooled and field-cooled magnetic susceptibility of $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ measured at 1.77 GPa in the applied field of 0.1 T (run No. 2). No FC/ZFC splitting is observed around 15–20 K where the volume fraction of static spins increases according to $\mu \mathrm{SR}$ [20].

Figure 6

(a) Temperature-dependent magnetic susceptibility $\chi \left(T\right)$ of pristine $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ measured upon cooling in various magnetic fields. Note that the 100 K anomaly observed in low fields is fully suppressed already at 0.2 T. (b) Normalized inverse magnetic susceptibility of pristine $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$, samples of run No. 1 after decompression, and samples of run No. 2 after decompression, respectively.

Figure 7

Comparison of the nondimerized ($Fddd$), partially dimerized ($P{2}_1/n$), and fully dimerized ($C2/c$) phases: (a) volume dependence of energy; (b) pressure dependence of enthalpy.

Figure 8

Density of states corresponding to the Ir $t_{2g}$ bands in the three phases of $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$. Note that the partially dimerized phase ($P{2}_1/n$) shares features of both dimerized and nondimerized phases. The calculations are performed on the DFT$+$SO level without taking Coulomb correlations into account.

Figure 9

Partially dimerized phase of $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ with nonmagnetic Ir2–Ir4 dimers and magnetic Ir1–Ir3–Ir3–Ir1 tetramers. $J_{it}$ is the coupling between the tetramers.

Figure 10

Rietveld refinements versus high-resolution XRD data. Tick marks show reflection positions for the $Fddd$ structure of nondimerized $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$. The refinement residuals are $R_I=0.028$ and $R_p=0.067$ for the sample from run No. 1 and $R_I=0.018$ and $R_p=0.080$ for the pristine sample.