Two-dimensional triangular-lattice Cu(OH)Cl, belloite, as a magnetodielectric system

Quantum spins on a triangular lattice may bring out intriguing and exotic quantum ground states. Here we report a magnetodielectric system of CuOHCl wherein $S=1/2\mathrm{C}{\mathrm{u}}^{2+}$ spins constitute a two-dimensional triangular lattice with the layers weakly coupled via Cl-H-O bonding. Despite strong magnetic interactions, as expected from the relatively high value of ${\theta }_{\mathrm{CW}}=-100\mathrm{K}$, antiferromagnetic transition occurred at $T_N=11\mathrm{K}$, followed by an uprising turn of the magnetic susceptibility below ∼7 K. Neutron-diffraction experiment revealed a coplanar spin structure on the triangular lattice below the $T_N$, with each spin pointing toward the center of a triangle. Of the three spins on a triangle, two are antiparallel and the third one is angled ${120}^{\circ }$ to the antiparallel spins. A concerted effect of geometric frustration in the triangular lattice and superexchange interactions through a zig-zag path via double Cu-O-Cu and double Cu-Cl-Cu bridges counted for this spin arrangement. Further investigation using dielectric constant and heat capacity measurements, as well as a microscopic probe of muon spin rotation, revealed a magnetodielectric effect and the possibility of multiferroic transition at $T^{*}\sim 5\mathrm{K}$, which is suspected to be in close relation to geometric frustration in this triangular lattice. The present paper presents a magnetodielectric system on a two-dimensional triangular lattice with chemical stoichiometry. It can also serve as a rare reference to the hotly debated quantum spin-orbital liquid compound $\mathrm{LiNi}{\mathrm{O}}_2$.

Figure 1

Neutron powder-diffraction pattern (filled circles) for Cu(OD)Cl at 30 K and the result of Rietveld structure refinements showing the calculated (thick solid line) pattern and the difference (thin solid line on the bottom).

Figure 2

(a) Crystal structure of Cu(OD)Cl. (b) Surrounding environment of $\mathrm{C}{\mathrm{u}}^{2+}$ and spin structure in the magnetically ordered phase. The arrows show the spin directions of the $\mathrm{C}{\mathrm{u}}^{2+}$ (blue). Each $\mathrm{C}{\mathrm{u}}^{2+}$ (blue) is surrounded by three O (red) and three Cl (green) in a deformed octahedral coordination. The zig-zag chains show Cu-Cu couplings through superexchange interactions via Cu-O-Cu and Cu-Cl-Cu.

Figure 3

(a) Temperature dependence of the susceptibilities $\chi$ (open circles, left axis) and the inverse susceptibilities $1/\chi$ (open squares, right axis) for polycrystalline Cu(OH)Cl, measured at 10 kOe. The solid line obeys the Curie-Weiss law, ${\chi }^{-1}\left(T\right)=(T--{\theta }_{\mathrm{w}})/C$, with a Weiss temperature of ${\theta }_{\mathrm{w}}$ of approximately −95 K. The inset plot shows the susceptibilities measured at 1 kOe for a small single crystal approximately along the $c$ axis and within the a-b plane. (b) Specific heat for Cu(OH)Cl depicting a sharp transition at $T_N=11\mathrm{K}$, and a microanomaly below around 5 K. The inset plot on the upper corner shows the dielectric constant changes measured at 100 kHz.

Figure 4

The intensity of magnetic reflections fitted with possible magnetic structures of (a) ${\mathrm{\Gamma }}_1$, (b) ${\mathrm{\Gamma }}_2$, (c) ${\mathrm{\Gamma }}_3$, and (d) ${\mathrm{\Gamma }}_4$ for Cu(OD)Cl.

Figure 5

The $\mathrm{ZF}-\mu \mathrm{SR}$ asymmetry at 18 K for Cu(OH)Cl, showing that the spectrum in the paramagnetic phase is well fitted by the equation including the two-spin model function $G_{2\mathrm{s}}\left(t\right)=\frac{1}{6}\left[1+cos\left(\omega t\right)+2cos\left(\frac{1}{2}\omega t\right)+2cos\left(\frac{3}{2}\omega t\right)\right]$; 79.3(7)% of the implanted muons stopped nearby OH forming $\left(\mathrm{OH}\right)-{\mu }^{+}$ bonding.

Figure 6

Fourier transform for the zero-field $\mu \mathrm{SR}$ asymmetry spectra at typical temperatures for Cu(OH)Cl. The inset plot shows the raw $\mathrm{ZF}-\mu \mathrm{SR}$ spectrum taken at 3.1 K and the fitted curve using nine frequencies.

Figure 7

Analyzed muon spin precession frequency, relaxation rate, and signal fraction for the nine signals observed in Cu(OH)Cl. The double dashed line in the frequency plot (a) is a fitted curve for a representative frequency obeying the formula $f=f_0{\left(1-\frac{T_N}{T}\right)}^{\beta }$ with $f_0=9.04\left(0.06\right)\mathrm{MHz},T_N=10.95\left(0.07\right)\mathrm{K},\beta =0.33\left(0.01\right)$.