  Spangolite (Cu$_6$Al(SO$_4$)(OH)$_{12}$Cl$\cdot$3H$_2$O) is a hydrated
layered copper sulfate mineral whose crystal structure is well described by a
depleted triangular lattice of Cu$^{2+}$ ions in each layer. Experimental
measurements reveal a non-magnetic ground state at $T \sim 8\, \text{K}$ with
magnetization properties dominated by dimerisation. We propose a concrete model
of Cu$^{2+}$ spin-$1/2$ degrees of freedom on this geometrically frustrated and
effectively two-dimensional maple-leaf lattice. The distorted geometry of the
depleted triangular lattice layers results in a spatially anisotropic
Heisenberg model featuring five symmetry inequivalent couplings with
ferromagnetic bonds on hexagons and antiferromagnetic triangular bonds. The
validity of the proposed Hamiltonian is demonstrated by state-of-the-art tensor
network calculations which can assess both the nature of the ground state as
well as low-temperature thermodynamics, including effects of a magnetic field.
We provide theoretical support for a dimerized ground state by calculating the
static spin structure factor as well as the magnetic susceptibility, the latter
is shown to be in good agreement with experiment. We further predict the
emergence of magnetisation plateaus at high values of an external magnetic
field and study their melting with increasing temperature.
