Spin-$\frac{1}{2}$ chain compound ${\mathrm{Ba}}_2{\mathrm{Cu}}_2{\mathrm{Te}}_2{\mathrm{P}}_2{\mathrm{O}}_{13}$: Magnetization, specific heat, and local-probe NMR

We present synthesis and characterization of ${\mathrm{Ba}}_2{\mathrm{Cu}}_2{\mathrm{Te}}_2{\mathrm{P}}_2{\mathrm{O}}_{13}$ (BCTPO) via x-ray diffraction, magnetic susceptibility, heat capacity, and ${}^{31}\mathrm{P}$ nuclear magnetic resonance (NMR) measurements. BCTPO crystallizes in a monoclinic structure with ${\mathrm{Cu}}^{2+}$ ions forming coupled chains. In magnetization $M\left(T\right)$ measurements, a broad maximum is observed around 53 K. Upon the application of magnetic fields, a sharp anomaly evolves around 4 K in the heat capacity $C_P\left(T\right)$ data, indicative of long-range order, while it is absent in zero field. The ${}^{31}\mathrm{P}$ NMR line shift at about 93.954 kOe tracks the spin susceptibility, whereas the line broadening evidences the onset of magnetic order at about 4 K or lower. The inferred isotropic and axial components of the hyperfine coupling constant are $A_{hf}^{\mathrm{iso}}\simeq$ 3635 $\text{Oe}/{\mu }_B$ and $A_{hf}^{ax}\simeq$ 479 $\text{Oe}/{\mu }_B$, respectively. The ${}^{31}\mathrm{P}$ NMR spin-lattice relaxation rate $1/T_1$ shows a pronounced divergence for $T⟶0$. We assign this behavior to critical fluctuations on the verge of order.

Figure 1

XRD pattern of ${\mathrm{Ba}}_2{\mathrm{Cu}}_2{\mathrm{Te}}_2{\mathrm{P}}_2{\mathrm{O}}_{13}$ measured at 300 K with a wavelength of 1.54182 Å. The red circles are experimental data, and the solid black line is the theoretically calculated fit by Rietveld analysis. The solid green line is the difference between the experimental and theoretically calculated patterns. The vertical blue bars are the expected Bragg positions for BCTPO.

Figure 2

The crystal structure of BCTPO is shown. (a) The unit cell of BCTPO. (b) Two-dimensional projection of the crystal structure of BCTPO in the $a\text{–}c$ plane. The solid line shows the intrachain exchange interaction $J_1$, and the dashed line shows the interchain exchange interaction $J_2$. (c) Paths of intrachain and interchain interaction among ${\mathrm{Cu}}^{2+}$ ions in the $a\text{–}c$ plane. (d) Interplanar interaction among ${\mathrm{Cu}}^{2+}$ ions in BCTPO by exchange coupling constant $J_3$ and its path. (e) Distribution of three ${\mathrm{Cu}}^{2+}$ ions around P in BCTPO.

Figure 3

The magnetic susceptibility $\chi \left(T\right)$ of BCTPO is shown as a function of temperature at 10 kOe, and the fitting is done by the 1D HAF chain model as explained in the text. Bottom inset: The inverse of the susceptibility due to extrinsic paramagnetic impurities is plotted as a function of $T$, and to extract ${\theta }_p$, a linear fit in the $T$ range of 2–5 K is shown. Top inset: $\frac{d\chi }{dT}$ is shown as a function of $T$ in various applied fields.

Figure 4

The heat capacity $C_p\left(T\right)$ as a function of temperature in zero field together with a fit by a combination of one Debye and two Einstein terms $(1\mathrm{D}+2\mathrm{E})$ for BCTPO is shown. Top inset: The magnetic heat capacity $C_m$ in zero field is shown along with a fit to the uniform HAF chain model (see text). Bottom inset: $C_m/T$ as a function of $T$ at different applied magnetic fields is shown.

Figure 5

Magnetic heat capacity $C_m\left(T\right)$ as a function of temperature for BCTPO at different applied magnetic fields is shown, and a power law (see text) fitting is done below the ordering temperature for different applied magnetic fields. Bottom inset: An enlarged view of the power law fits (log-log scale) is shown at various magnetic fields. Top inset: The change in magnetic entropy $\mathrm{\Delta }{S}_m\left(T\right)$ as a function of $T$ at different applied magnetic fields is plotted for BCTPO.

Figure 6

The temperature-dependent ${}^{31}\mathrm{P}$ NMR spectrum of BCTPO at a fixed magnetic field of 93.954 kOe is shown at different temperatures from 4 to 300 K. The reference position for ${}^{31}\mathrm{P}$ is shown by a vertical dashed line.

Figure 7

The FWHM $\mathrm{\Delta }\nu$ and the FWHM $\mathrm{\Delta }H$ for the ${}^{31}\mathrm{P}$ spectrum are plotted as a function of $T$ on the left and right $y$ axes, respectively, for BCTPO (in semilog scale).

Figure 8

The right $y$ axis shows the susceptibility as a function of temperature. The left $y$ axis shows the temperature-dependent isotropic ${}^{31}\mathrm{P}$ NMR shift as a function of temperature. Inset: The variation of the isotropic ${}^{31}\mathrm{P}$ NMR shift is shown as a function of the magnetic susceptibility $\chi \left(T\right)$ by taking the temperature to be implicit parameter, and its linear fit is shown by the solid line.

Figure 9

Axial ${}^{31}\mathrm{P}$ NMR shift $K_{ax}\left(T\right)$ for BCTPO is shown as a function of temperature. It shows a broad maximum around 50 K. Inset: $K_{ax}\left(T\right)$ is plotted as a function of $\chi \left(T\right)$ with temperature being an implicit parameter, and the solid line is a linear fit to the data.

Figure 10

On the left $y$ axis the spin-lattice relaxation rate $1/T_1$ is plotted, and on the right $y$ axis $1/\left(K_{\mathrm{iso}}{T}_{1}T\right)$ is plotted as a function of temperature. Inset: The recovery of the longitudinal nuclear magnetization of ${}^{31}\mathrm{P}$ as a function of time delays $t_d$ is presented in semilog scale for some selected temperatures. Here $m_t$ is magnetization at time delay $t_d$, and $m_0$ is the saturation magnetization.