Magnetization and ESR studies on $\mathrm{C}{\mathrm{u}}_4{\left(\mathrm{OH}\right)}_6\mathrm{FCl}$: An antiferromagnet with a kagome lattice

We have synthesized a spin-1/2 antiferromagnet, $\mathrm{C}{\mathrm{u}}_4{\left(\mathrm{OH}\right)}_6\mathrm{FCl}$, containing kagome lattices. The magnetic susceptibility gives a Curie-Weiss temperature ${\theta }_{\mathrm{CW}}=-135\mathrm{K}$, nearest-neighbor exchange $J=-166\mathrm{K}$, and two magnetic anomalies at $T_1=15\mathrm{K}$ and $T_2=4.8\mathrm{K}$ with weak ferromagnetism. However, the specific heat curve does not exhibit λ-like peaks expected for long-range magnetic order. The high-field ESR data are strongly correlated with the magnetism. There are a gapless mode ${\omega }_1$ observed at all temperatures and two gapped modes, ${\omega }_2$ and ${\omega }_3$, corresponding to different temperature regions: $T<T_1(=15\mathrm{K})$ and $T<T_2(=4.8\mathrm{K})$, respectively. The possible origins of the gapped modes are discussed.

Figure 1

Crystal structure of $\mathrm{C}{\mathrm{u}}_4{\left(\mathrm{OH}\right)}_6\mathrm{FCl}$. (a) Unit cell. (b) A view of the structure along the $c$ axis. The symbols are Cu, blue; O, red; H, salmon; F, silver; Cl, green. The interkagome Cu2 site is an average of three equivalent positions. (c) Observed and calculated XRD powder patterns of $\mathrm{C}{\mathrm{u}}_4{\left(\mathrm{OH}\right)}_6\mathrm{FCl}$. The green vertical bars are the expected Bragg reflection positions.

Figure 2

$\chi \left(T\right)$ curve measured in 0.1 T for $\mathrm{C}{\mathrm{u}}_4{\left(\mathrm{OH}\right)}_6\mathrm{FCl}$. The solid line stands for the fitted curve using tenth-order high-temperature series expansion (HTSE) [28]. The inset shows the inverse ${\chi }^{-1}\left(T\right)$ curve as well as the high-temperature Curie-Weiss fit.

Figure 3

ZFC heating and FC cooling $M\left(T\right)$ curves measured at different magnetic fields.

Figure 4

Temperature dependence of the specific heat at zero field. The inset shows the magnetic specific heat $C_{\mathrm{mag}}$ after subtracting the background and the magnetic entropy integrated from 2 to 30 K, which is normalized as a fraction of the total value per Cu spin.

Figure 5

The magnetization normalized to the saturated magnetic moment of $\mathrm{C}{\mathrm{u}}^{2+}$ spins. The open squares are the nonlinear part of the magnetization obtained by subtracting the linear term at higher field. The solid red line is a fit of the data to the Brillouin function. The inset shows an enlarged view in the low-field range.

Figure 6

(a) Temperature dependence of the integrated intensity $I_{\mathrm{ESR}}$ of the ESR resonance for $\mathrm{ZnC}{\mathrm{u}}_3{\left(\mathrm{OH}\right)}_6\mathrm{FBr}$. The $\chi \left(T\right)$ curve is also shown for calibrating the value of $I_{\mathrm{ESR}}$. The inset shows the several representative ESR spectra at 170 GHz. The DPPH resonance line is a field marker. (b) The Frequency-field ($f\text{−}H$) relation at 2 and 4.2 K.

Figure 7

Temperature-dependent ESR spectra measured 210 GHz for $\mathrm{C}{\mathrm{u}}_4{\left(\mathrm{OH}\right)}_6\mathrm{FCl}$.

Figure 8

Frequency-dependent ESR spectra and the corresponding $f\text{−}H$ relations measured at 20, 10, and 2 K for $\mathrm{C}{\mathrm{u}}_4{\left(\mathrm{OH}\right)}_6\mathrm{FCl}$. The red line is the calculated curve based on the FM-like resonance. In (f), the asterisks stand for the data for the barlowite. The black and blue lines are guides to the eyes for AFM-like resonances with easy-plane anisotropy (see text).