Structural and double magnetic transitions in the frustrated spin-$\frac{1}{2}$ capped-kagome antiferromagnet $\left(\mathrm{RbCl}\right){\mathrm{Cu}}_5{\mathrm{P}}_2{\mathrm{O}}_{10}$

The structural and magnetic properties of the geometrically frustrated spin-$\frac{1}{2}$ capped-kagome antiferromagnet $\left(\mathrm{RbCl}\right){\mathrm{Cu}}_5{\mathrm{P}}_2{\mathrm{O}}_{10}$ are investigated via temperature-dependent x-ray diffraction, magnetization, heat capacity, and ${}^{31}\mathrm{P}$ NMR experiments on a polycrystalline sample. It undergoes a structural transition at around $T_{\mathrm{t}}\simeq 310$ K from a high-temperature trigonal $\left(P\overline{3}m1\right)$ to a low-temperature monoclinic $(C2/c)$ unit cell, where the low-temperature structure features the capped-kagome geometry of ${\mathrm{Cu}}^{2+}$ ions. Interestingly, it shows the onset of two successive magnetic transitions at $T_{\mathrm{N}1}\simeq 20$ K and $T_{\mathrm{N}2}\simeq 7$ K. The shape of the ${}^{31}\mathrm{P}$ NMR spectra unfolds the possible nature of the transitions below $T_{\mathrm{N}1}$ and $T_{\mathrm{N}2}$ to be of incommensurate and commensurate antiferromagnetic type, respectively. A large value of the Curie-Weiss temperature as compared to $T_{\mathrm{N}1}$ sets the frustration parameter $f\simeq 8$, ensuring strong magnetic frustration in the compound. From the ${}^{31}\mathrm{P}$ NMR spin-lattice relaxation rate, the leading antiferromagnetic exchange coupling is estimated to be $J/k_{\mathrm{B}}\simeq 117$ K. These unusual double magnetic transitions make this compound beguiling for further investigations.

Figure 1

(a) Crystal structure of $\left(\mathrm{RbCl}\right){\mathrm{Cu}}_5{\mathrm{P}}_2{\mathrm{O}}_{10}$ projected in the $ac$ plane. The connection of Cu(2,3)${\mathrm{O}}_4$ square planes (plaquettes) and Cu(1)${\mathrm{O}}_5$ square pyramids forming capped-kagome layers. ${\mathrm{PO}}_4$ tetrahedra are connecting these layers along the $c$ direction. (b) A section of the capped-kagome layer in the $ab$ plane. (c) A hexagonal ring showing the bond lengths. (d) Triangular base of the ${\mathrm{OCu}}_4$ tetrahedron with bond lengths and bond angles. (e) The bond lengths and bond angles of the apical Cu atom with basal Cu atoms of the ${\mathrm{OCu}}_4$ tetrahedron.

Figure 2

Powder XRD patterns (open circles) at (a) 400 K, (b) 200 K, and (c) 13 K. The solid lines denote the Rietveld refinement of the data. The Bragg peak positions are indicated by green vertical bars and the bottom solid line indicates the difference between the experimental and calculated intensities. The crystal structure and the corresponding space group at different temperatures are also indicated.

Figure 3

(a) Lattice constants ($a$, $b$, and $c$) as a function of temperature from 13 to 400 K. The lattice constants in the monoclinic phase are scaled with respect to the high symmetry trigonal structure. The areas shaded in yellow, gray, and cyan colors represent the regimes for pure monoclinic, trigonal, and the coexistence of both phases, respectively. (b) Monoclinic angle ($\beta$) and the unit cell volume ($V_{\mathrm{cell}}$) as a function of temperature from 13 to 300 K. The solid line represents the fit of $V_{\mathrm{cell}}\left(T\right)$ using Eq. (1).

Figure 4

(a) Temperature-dependent dc susceptibility $\chi \left(T\right)$ measured at an applied field of ${\mu }_{0}H=0.5$ T. Inset: Thermal hysteresis around the structural transition measured under FCW and FCC conditions. (b) Inverse susceptibility ($1/\chi$) vs $T$ at ${\mu }_{0}H=0.5$ T and the solid line is the CW fit for 200 $\text{K}\le T\le 300$ K, below the structural transition. Inset: $\chi \left(T\right)$ measured at $H=100$ Oe in ZFC and FC protocols.

Figure 5

Real part of ac susceptibility ${\chi }^{\prime }$ vs $T$ at different frequencies. The arrows point to the magnetic anomalies.

Figure 6

(a) $C_{\mathrm{p}}\left(T\right)$ of RCCPO measured in zero field. Inset: $C_{\mathrm{p}}/T$ vs $T^2$ in zero field, showing the linear regime below $T_{\mathrm{N}2}$. The solid line is the linear fit. (b) $C_{\mathrm{p}}/T$ vs $T$ measured in different applied fields in the low-temperature region, around $T_{\mathrm{N}1}$.

Figure 7

(a) Temperature evolution of ${}^{31}\mathrm{P}$ NMR spectra measured at a radio frequency $f=49.6$ MHz, above $T_{\mathrm{N}1}$. The vertical dashed line corresponds to the ${}^{31}\mathrm{P}$ nonmagnetic reference field position. (b) ${}^{31}\mathrm{P}$ NMR spectra below $T_{\mathrm{N}1}$. The peak at the right side corresponds to the signal of ${}^{87}\mathrm{Rb}$ present in the sample.

Figure 8

Temperature-dependent ${}^{31}\mathrm{P}$ NMR isoshift $K_{\mathrm{iso}}$ measured at 49.6 MHz. Upper inset: $K_{\mathrm{iso}}$ vs $\chi$ (measured at 3 T). The solid line is the straight line fit. Lower inset: Full width at half maximum (FWHM) vs $T$.

Figure 9

(a) Longitudinal magnetization recovery curves for 120.6 MHz at four selective temperatures measured on the ${}^{31}\mathrm{P}$ nuclei and the solid lines are fits using Eq. (5). (b) ${}^{31}\mathrm{P}$ NMR spin-lattice relaxation rate ($1/T_1$) vs $T$ measured at 49.6 and 120.6 MHz. The downward arrows point to $T_{\mathrm{N}1}\simeq 23.5$ K and $T_{\mathrm{N}2}\simeq 9.5$ K. The solid line represents $T^3$ behavior below $T_{\mathrm{N}2}$. Inset: Exponent $\beta$ as a function of $T$ for both the frequencies.

Figure 10

(a) Transverse magnetization recovery curves as a function of $\tau$ at four different temperatures. The solid lines show the fit using Eq. (7). (b) ${}^{31}\mathrm{P}$ NMR spin-spin relaxation rate ($1/T_2$) vs $T$ measured at 49.6 and 120.6 MHz. The downward arrows mark the transition temperatures at $T_{\mathrm{N}1}\simeq 23.5$ K and $T_{\mathrm{N}2}\simeq 9.5$ K.