Dimensional reduction by singlet blockade in the distorted kagome magnet YCa$_3$(CrO)$_3$(BO$_3$)$_4$
The distorted kagome borate YCa$_3$(CrO)$_3$(BO$_3$)$_4$ has a Curie-Weiss temperature of -140 K and shows no magnetic order down to $65$ mK. We determine its Heisenberg Hamiltonian by density-functional energy mapping, obtaining twenty-four symmetry-inequivalent Cr-Cr exchange paths dominated by $J_1=116$ K, and measure the susceptibility, specific heat and ac susceptibility to $50$ mK. The Hamiltonian does not by itself account for the absence of order: simulated classically it orders at $10$ K, a factor of $154$ above the bound. We trace the gap to the site symmetry of the $P6_3$ structure, which divides the exchange network in two: $J_1$ binds two thirds of the Cr into dimers, while the remaining third forms uniform spin-$3/2$ chains along $c$ through a weaker $J_2=33$ K. The chains share no direct bond, and each of the fourteen paths leaving a chain terminates on a spin locked into a dimer singlet of gap $Δ=J_1$. This singlet blockade demotes the interchain coupling to second order; summed over paths with their relative Néel parity it falls to a few tens of millikelvin, against $9.8$ K at first order, and what survives is frustrated on the kagome lattice the chains themselves form. Treating the dimers exactly and the chains by exact diagonalization accounts, without free parameters, for the position of the magnetic specific-heat maximum and the entropy recovered by $100$ K, but not for the susceptibility, which additionally requires a broad distribution of exchange couplings that we attribute to Ca/Y site mixing. That disorder also impacts the thermodynamics at lowest temperatures: below $0.7$ K the magnetic specific heat follows a field-robust $T^2$ law, which excludes one-dimensional chains with gapless excitations, Goldstone modes and spinons alike and implies a linear density of predominantly non-magnetic states, matched by the singlet-triplet gaps the disorder generates.