Quantum phase transition in $\left(\text{CuCl}\right)\text{La}{\left({\text{Nb}}_{1-x}{\text{Ta}}_x\right)}_2{\text{O}}_7$

We demonstrate the synthesis and magnetic properties of a quasi-two-dimensional frustrated quantum spin system $\left(\text{CuCl}\right)\text{La}{\left({\text{Nb}}_{1-x}{\text{Ta}}_x\right)}_2{\text{O}}_7$. We observed persistence of the spin-singlet state in $\left(\text{CuCl}\right){\text{LaNb}}_2{\text{O}}_7$ up to $x\sim 0.4$, accompanied by a slight reduction in the spin gap with increasing $x$. In spite of unaltered cell parameters and a preserved CuCl plane, $\left(\text{CuCl}\right){\text{LaTa}}_2{\text{O}}_7$ exhibits collinear antiferromagnetic (CAF) order with $T_{\text{N}}\sim 7\text{K}$ as observed in $\left(\text{CuBr}\right){\text{LaNb}}_2{\text{O}}_7$. In the intermediate region $\left(0.4<x<1\right)$, we observed CAF order with a significantly reduced magnetic moment but with a nearly constant $T_{\text{N}}$, suggesting that the CAF state coexists with the spin-singlet state in agreement with recent $\mu \text{SR}$ results.

Figure 1

(Color online) (a) Schematic view of the crystal structure of $\left(\text{CuCl}\right)\text{La}{B}_2{\text{O}}_7$ $\left(B=\text{Nb},\text{Ta}\right)$. (b) TEM image and [(c) and (d)] the corresponding EDS maps of the $x=0.8$ sample, where blue and red dots represent Nb and Ta, respectively.

Figure 2

(Color online) Magnetic susceptibilities of $\left(\text{CuCl}\right)\text{La}{\left({\text{Nb}}_{1-x}{\text{Ta}}_x\right)}_2{\text{O}}_7$ measured at $H=2\text{T}$.

Figure 3

(Color online) Magnetization curves $M$ of $\left(\text{CuCl}\right)\text{La}{\left({\text{Nb}}_{1-x}{\text{Ta}}_x\right)}_2{\text{O}}_7$ at $T=1.3\text{K}$. The normalized magnetization for $\left(\text{CuBr}\right){\text{LaNb}}_2{\text{O}}_7$ (broken line) was obtained from the data in Ref. 10 as its saturation field equals to that of $x=1.0$ $\left(\sim 23\text{T}\right)$. Circles and triangles represent fitted curves to the $x=0.6$ and 0.8 data, respectively (see text for details). Inset is an enlarged plot for $x=0$, 0.2 and 0.4, highlighting the critical fields $H_{\text{c}}$, which were assigned to the fields of the inflection points in $dM/dH$. The very slow increases in magnetization below $H_{\text{c}}$ are due to tiny amount of defect and/or unknown magnetic impurity as mentioned in Refs. 7, 9.

Figure 4

[(a)–(c)] Neutron diffraction profiles of $x=1.0$, 0.8, and 0.6 around the ($\frac{1}{2}$, 0, $\frac{1}{2}$) magnetic reflection. Open and closed circles represent the data collected at 1.7 and 17 K, respectively, and solid lines are a guide to the eyes. A broken line in (c) represents the background. [(d)–(e)] Temperature dependence of the intensity of the ($\frac{1}{2}$, 0, $\frac{1}{2}$) reflection. The lines are a guide to the eyes. (f) Temperature dependence of the difference between intensity of the ($\frac{1}{2}$, 0, $\frac{1}{2}$) reflection and the background. The lines are a guide to the eyes.

Figure 5

Results of inelastic neutron scattering measurements for $x=0$ (closed circles) (Ref. 6) and 0.3 (open circles). (a) The difference $I\left(1.7\text{K}\right)-I\left(20\text{K}\right)$ for $x=0$ and $I\left(3.3\text{K}\right)-I\left(20\text{K}\right)$ for $x=0.3$. The curve represents a least-squares fit to a Gaussian. (b) Peak intensities of the transition from the singlet ground state to the one-triplet excited state as a function of $Q$ obtained at $E=2.1\text{meV}$ for $x=0$ and at $E=2.0\text{meV}$ for $x=0.3$. The solid lines represent the fits according to the equation written in Ref. 6.

Figure 6

(Color online) (a) Antiferromagnetic volume fraction $\alpha$ obtained using neutron powder diffraction (NPD) (closed circles), high-field magnetization (HFM) (closed triangles), and $\mu \text{SR}$ (Ref. 12) (open circles). $\mathrm{S}$ stands for the spin-singlet state. The solid line is a guide to the eyes. (b) Magnetic phase diagram of $\left(\text{CuCl}\right)\text{La}{\left({\text{Nb}}_{1-x}{\text{Ta}}_x\right)}_2{\text{O}}_7$ as a function of temperature and concentration. $\mathrm{P}$ stands for the paramagnetic state. Closed squares represent the zero-field gap obtained by inelastic neutron scattering (INS). $\mathrm{S}$ stands for the spin-singlet state. Closed and open circles denote the transition temperatures obtained by NPD and $\mu \text{SR}$ (Ref. 12).