Magnetization Process of Atacamite: A Case of Weakly Coupled $S=1/2$ Sawtooth Chains

We present a combined experimental and theoretical study of the mineral atacamite ${\mathrm{Cu}}_2\mathrm{Cl}(\mathrm{OH}{)}_3$. Density-functional theory yields a Hamiltonian describing anisotropic sawtooth chains with weak 3D connections. Experimentally, we fully characterize the antiferromagnetically ordered state. Magnetic order shows a complex evolution with the magnetic field, while, starting at 31.5 T, we observe a plateaulike magnetization at about $M_{\mathrm{sat}}/2$. Based on complementary theoretical approaches, we show that the latter is unrelated to the known magnetization plateau of a sawtooth chain. Instead, we provide evidence that the magnetization process in atacamite is a field-driven canting of a 3D network of weakly coupled sawtooth chains that form giant moments.

Figure 1

(a) Crystal structure of atacamite ${\mathrm{Cu}}_2\mathrm{Cl}(\mathrm{OH}{)}_3$. (b) Visualization of the dominant magnetic exchange paths in atacamite forming a sawtooth pattern. Also shown is the magnetic structure together with the nuclear and the magnetic unit cell (black solid lines). (c) Cu-Cu exchange couplings of atacamite, $J_i$, with $i=1,2,\dots$ denoting first, second, $\dots$ neighbor. The vertical line indicates the $U$ value at which the couplings $J_1=1.3$, $J_2=-9.6$, $J_3=102$, $J_4=336$, $J_{11b}=15.6$, $J_{13}=1.1\mathrm{K}$ match the experimental Curie-Weiss temperature; for details, see text.

Figure 2

(a) Specific heat $c_p/T$, (b) magnetic susceptibility $\chi$, and normalized intensity of the $(1/201/2{)}_M$ neutron scattering reflection as function of (c) temperature and (d) magnetic field ($\mathbf{H}\parallel b$ axis). Data in (b) are shifted for clarity by values denoted in the plot; lines in (d) are guides to the eye; dashed line indicates the plateau field.

Figure 3

(a) Magnetostriction and (b) magnetization of atacamite in magnetic fields $\mathbf{H}\parallel b$ axis at different temperatures. (c) Magnetization versus $h$ via iTEBD for the $\mathrm{\Delta }$ chain for different $J^{\prime }/J$ at $T=0$. Note that, for $J\sim 336\mathrm{K}$, a unit of $h$ corresponds to $\sim 250\mathrm{T}$. Inset: magnetization at $J^{\prime }/J=0.3$ for maximal Schmidt rank ${\chi }_m=80(100)$ lines (crosses) and imaginary time $\tau =n_{\tau }d\tau$, $d\tau =0.01/J$. (d) MFA for 3D coupled $\mathrm{\Delta }$ chains.

Figure 4

Magnetic phase diagram of atacamite for $\mathbf{H}\parallel b$; for details, see text. Data points at 31.5 T from pulsed-field experiments as measured, not corrected for magnetocaloric effect [60].