Spin-liquid behavior of the three-dimensional magnetic system ${\mathrm{Ba}}_3{\mathrm{NiIr}}_2{\mathrm{O}}_9$ with $S=1$

The quantum spin liquid (QSL) is an exotic phase of magnetic materials where the spins continue to fluctuate without any symmetry breaking down to zero temperature. Among the handful reports of QSL with spin $S\ge$ 1, examples with magnetic ions on a three-dimensional (3D) magnetic lattice are extremely rare since both larger spin and higher dimension tend to suppress quantum fluctuations. In this work, we offer a new strategy to achieve 3D QSL with high spin by utilizing two types of transition metal ions; both are magnetically active but located at crystallographically inequivalent positions. We design a 3D magnetic system ${\mathrm{Ba}}_3{\mathrm{NiIr}}_2{\mathrm{O}}_9$ consisting of interconnected corner-shared ${\mathrm{NiO}}_6$ octahedra and face-shared ${\mathrm{Ir}}_2{\mathrm{O}}_9$ dimer, both having triangular arrangements in a-b plane. X-ray absorption spectroscopy measurements confirm the presence of ${\mathrm{Ni}}^{2+}$ ($S=1)$. Our detailed thermodynamic and magnetic measurements reveal that this compound is a realization of gapless QSL state down to at least 100 mK. Ab initio calculations find a strong magnetic exchange between Ir and Ni sublattices and in-plane antiferromagnetic coupling between the dimers, resulting in dynamically fluctuating magnetic moments.

Figure 1

(a) Unit cell of $6H{A}_{3}M{M}_2^{\prime }{\mathrm{O}}_9$ without any disorder. (b), (c) The triangular lattice arrangement of $M_2^{\prime }{\mathrm{O}}_9$ dimers, $M{\mathrm{O}}_6$ octahedra, respectively, in a-b plane. (d) $M$-O-$M\prime$ connectivity forms buckled honeycomb lattice. $A, M$, and $M^{\prime }$ correspond to Ba, Ni, and Ir, respectively, for BNIO. Different magnetic exchange pathways ($J_i$) are also shown in (a)–(d). (e) Observed and refined powder XRD pattern of BNIO. (f) XAS spectrum of Ni $L_{3,2}$-edge of BNIO along with NiO and ${\mathrm{NdNiO}}_3$ for comparison. The XAS data for ${\mathrm{NdNiO}}_3$ have been adapted from Ref. [31].

Figure 2

(a) Fitting of $\rho$ by 3D VRH model for BNIO. Inset shows $\rho$ vs $T$. (b) $\chi$ vs $T$ on the left axis and $1/(\chi -{\chi }_0)$ along with fitting on the right axis. (c) M-H at 2 K.

Figure 3

(a) $C_p$ vs $T$ curves at various fields. (b) Magnetic-specific heat ($C_m$) extracted by subtracting lattice contribution. (c) Low temperature part of $C_m$ is plotted in a log-log plot. (d) Magnetic entropy for zero field.

Figure 4

(a) Asymmetry vs time curves at various temperatures taken at zero magnetic field and fitted curve (solid line) using Eq. (2). (b) Variation of $\nu$ with temperature (thick curve is a guide to the eye). Inset shows variation of $\nu$ with applied LF at 100 mK.