Crystal structure and properties of phosphate ${\mathrm{PbCu}}_2({\mathrm{PO}}_4{)}_2$ with spin-singlet ground state

Phosphate ${\mathrm{PbCu}}_2({\mathrm{PO}}_4{)}_2$ was found in the $\mathrm{Pb}\text{−}\mathrm{Cu}\text{−}\mathrm{P}\text{−}\mathrm{O}$ system. Its structure parameters were refined by the Rietveld method using synchrotron x-ray diffraction data [space group Pccn (No. 56); $Z=8$; $a=8.03810\left(10\right)\mathrm{\AA }$, $b=15.46574\left(14\right)\mathrm{\AA }$, and $c=10.36820\left(10\right)\mathrm{\AA }$]. ${\mathrm{PbCu}}_2({\mathrm{PO}}_4{)}_2$ is isotypic with ${\mathrm{SrCu}}_2({\mathrm{PO}}_4{)}_2$. Magnetic properties of ${\mathrm{PbCu}}_2({\mathrm{PO}}_4{)}_2$ were investigated by magnetic susceptibility, magnetization up to $65\mathrm{T}$, electron-spin resonance, and specific-heat measurements. Magnetic susceptibilities were fit by a linear four-spin cluster model, $\mathrm{Cu}1\text{−}\mathrm{Cu}2\text{−}\mathrm{Cu}2\text{−}\mathrm{Cu}1$ [Hamiltonian: $-2J_1(S_1{S}_2+S_3{S}_4)-2J_2{S}_2{S}_3]$, with $-2J_1∕k_B=97.0\mathrm{K}$ for $\mathrm{Cu}1\text{−}\mathrm{Cu}2$ and $-2J_2∕k_B=86.5\mathrm{K}$ for $\mathrm{Cu}2\text{−}\mathrm{Cu}2$. The spin gap $(\Delta ∕k_B)$ estimated from the high-field magnetization was $43\mathrm{K}$. The $g$ values of ${\mathrm{PbCu}}_2({\mathrm{PO}}_4{)}_2$, $g_{∕∕}=2.167$ and $g_{\perp }=2.222$, suggest the $3z^2\text{−}{r}^2$ type of the orbital ground state for ${\mathrm{Cu}}^{2+}$ ions. Specific heat showed that ${\mathrm{PbCu}}_2({\mathrm{PO}}_4{)}_2$ does not undergo a long-range magnetic order transition down to $0.45\mathrm{K}$ in agreement with its spin-singlet ground state.

Figure 1

Observed (crosses), calculated (solid line), and difference synchrotron XRD patterns for ${\mathrm{PbCu}}_2({\mathrm{PO}}_4{)}_2$. Bragg reflections are indicated by tick marks for ${\mathrm{PbCu}}_2({\mathrm{PO}}_4{)}_2$ (upper) and ${\mathrm{Pb}}_3{\mathrm{Cu}}_3({\mathrm{PO}}_4{)}_4$ (lower). Inset shows the enlarged fragment.

Figure 2

(Color online) (a) Projection of the structure of ${\mathrm{PbCu}}_2({\mathrm{PO}}_4{)}_2$ along the $a$ axis showing the arrangement of $\mathrm{Cu}1{\mathrm{O}}_{4+1}$ and $\mathrm{Cu}2{\mathrm{O}}_4$ polyhedra. (b) Fragment of the structure of ${\mathrm{PbCu}}_2({\mathrm{PO}}_4{)}_2$ emphasizing the connections between Cu atoms transferred through ${\mathrm{PO}}_4$ groups, $J_1-J_{12}$. $J_{\mathrm{str}}$ denotes the structural dimer unit. $J_1$ and $J_2$ are shown by the double lines.

Figure 3

The $\chi \left(T\right)$ and ${\chi }^{-1}\left(T\right)$ curves for the powder ${\mathrm{PbCu}}_2({\mathrm{PO}}_4{)}_2$ sample. Solid line on the ${\chi }^{-1}\left(T\right)$ curve is the fit to Eq. (1) at $150–400\mathrm{K}$. Solid lines on the $\chi \left(T\right)$ curves are the fits by the dimer and linear-four-spin cluster models. Parameters of the fitting are presented in Table .

Figure 4

High-field magnetization curves at $1.3\mathrm{K}$ for powder ${\mathrm{PbCu}}_2({\mathrm{PO}}_4{)}_2$ and ${\mathrm{SrCu}}_2({\mathrm{PO}}_4{)}_2$ given for comparison.

Figure 5

(Color online) Temperature dependences of $g$ value and the integrated intensity of the powder ${\mathrm{PbCu}}_2({\mathrm{PO}}_4{)}_2$ sample observed by the $X$-band ESR measurements.

Figure 6

(Color online) Typical absorption lines observed at $160\mathrm{GHz}$ for the powder ${\mathrm{PbCu}}_2({\mathrm{PO}}_4{)}_2$ sample. The line-shape analysis (the broken line) is performed. The details can be seen in the text.

Figure 7

(Color online) The $g$ values and linewidths of the powder ${\mathrm{PbCu}}_2({\mathrm{PO}}_4{)}_2$ sample as a function of temperature. The $g$ values and linewidths for $160\mathrm{GHz}$ are obtained by the line-shape analyses as shown in Fig. 6.