Magnetic structure of ${\text{Cu}}_2{\text{CdB}}_2{\text{O}}_6$ exhibiting a quantum-mechanical magnetization plateau and classical antiferromagnetic long-range order

In ${\text{Cu}}_2{\text{CdB}}_2{\text{O}}_6$, a quantum-mechanical 1/2 magnetization plateau and classical antiferromagnetic long-range order (AF-LRO) appear. Two crystallographic Cu sites (Cu1 and Cu2) exist and have spin-1/2. It was speculated previously that spins on the Cu1 sites were in a nearly singlet state and that spins on the Cu2 sites formed the long-range order in weak magnetic fields and were almost saturated in fields of the magnetization plateau. As described herein, we report the magnetic structure of ${\text{Cu}}_2{{}^{114}\text{C}\text{d}}^{11}{\text{B}}_2{\text{O}}_6$ as determined using neutron powder-diffraction measurements. Contrary to that previous speculation, both the Cu1 and Cu2 spins have large magnetic moments in the ordered state. We discuss the mechanism which causes the magnetization plateau and AF-LRO.

Figure 1

(Color online) (a) A schematic drawing of ${\text{Cu}}^{2+}$-ion positions in ${\text{Cu}}_2{\text{CdB}}_2{\text{O}}_6$. Red and blue circles represent Cu1 and Cu2 sites, respectively. Red, green, and blue bars represent Cu-Cu bonds 1, 2, and 3, respectively. Parameters of an exchange interaction are defined, respectively, as $J_1$, $J_2$, and $J_3$ in the Cu-Cu bond 1, 2, and 3. Arrows on the Cu sites indicate magnetic moments below $T_{\text{N}}=9.8\text{K}$ determined in the present study. A box on the left side shows the crystallographic unit cell. (b) An illustration of the four-spin system consisting of $S_1–S_4$. We designate a spin pair formed by $S_j$ and $S_{j+1}$ as an ${\alpha }_j$ pair.

Figure 2

(Color online) Temperature dependence of lattice parameters in ${\text{Cu}}_2{{}^{114}\text{C}\text{d}}^{11}{\text{B}}_2{\text{O}}_6$ determined using the synchrotron x-ray diffractometer MS-PD $\left(\lambda =0.4974\text{Å}\right)$.

Figure 3

(Color online) A neutron powder-diffraction pattern of ${\text{Cu}}_2{{}^{114}\text{C}\text{d}}^{11}{\text{B}}_2{\text{O}}_6$ at 15 K (higher than $T_{\text{N}}$) measured using the HRPT diffractometer $\left(\lambda =1.886\text{Å}\right)$. Lines on the observed pattern and at the bottom show a Rietveld refined pattern and difference between the observed and the Rietveld refined patterns. The observed data between $47.2°$ and $48.8°$ were not used in the refinement because a weak reflection of an impurity phase exists. Short vertical lines represent positions of nuclear reflections. The strongest nuclear reflection ($-1$, 0, 2) is indexed. The inset depicts differences between the HRPT patterns measured at 1.5 and 15 K. Two strong magnetic reflections indexed by (0,0,1) and (0,1,1) are, respectively, apparent at $11.4°$ and $13.4°$.

Figure 4

(Color online) Difference between two neutron powder-diffraction patterns of ${\text{Cu}}_2{{}^{114}\text{C}\text{d}}^{11}{\text{B}}_2{\text{O}}_6$ at 1.5 and 15 K recorded using the DMC diffractometer $\left(\lambda =2.458\text{Å}\right)$. Lines on the observed pattern and at the bottom show a Rietveld refined pattern and difference between the observed and the Rietveld refined patterns. Short vertical lines represent positions of magnetic reflections. The strong magnetic reflections (0,1,0), (0,0,1), and (0,1,1) are indexed. The inset shows the temperature dependence of integrated intensity of the magnetic reflection at (0,0,1). The inset also depicts specific heat to indicate the AF transition temperature $\left(T_{\text{N}}\right)$ (Ref. 10).

Figure 5

(Color online) (a) The temperature dependence of the experimental susceptibility (red solid curve) and QMC results of susceptibility (blue dashed curve) less than 300 K. The inset shows the susceptibility less than 40 K. (b) The magnetic field dependence of experimental magnetization (red solid curve) and QMC results of magnetization (blue dashed curve) at 15 K. (c) The magnetic field dependence of experimental magnetization (red solid curve) and QMC results of magnetization (blue dashed curve) at 2.9 K.

Figure 6

(Color online) Schematic drawings portraying the relation between the directions of the ordered magnetic moments (arrows) and oxygen positions in ${\text{Cu}}_2{\text{CdB}}_2{\text{O}}_6$. The red large circles with the short arrow, blue large circles with the long arrow, and green small circles represent Cu1, Cu2, and O sites, respectively.