Ultralow-Field Triplon Condensation in a Spin-Ladder Magnet
We realise the first ultralow-field Bose-Einstein condensation of triplons in a spin-ladder magnet, uncovering a quantum critical point at only $\mu_0 H_{c1}=0.17$ T in Henmilite ($\mathrm{Ca_2Cu(OH)_4[B(OH)_4]_2}$). Unlike dimer magnets, a ladder retains extended one-dimensional correlations in its gapped parent state, making this limit strongly fluctuation dominated. Thermodynamic, magnetoelastic, $\mu$SR, and neutron-diffraction measurements overturn the previous assignment of zero-field antiferromagnetic order, establishing a quantum-disordered coupled-ladder parent state with persistent low-energy dynamics. The weak low-temperature anomaly instead marks a gap-controlled crossover from the correlated ladder regime into the activated quantum-disordered state. These measurements further reveal an exceptionally asymmetric ordered dome extending to $\mu_0 H_{c2}\simeq 8.2$ T. Quantum Monte Carlo simulations for the relevant spin Hamiltonian place Henmilite just on the gapped side of the zero-field ladder-ordering instability, naturally accounting for the strong separation between the exchange and residual-gap scales and the tiny critical field. Our findings extend ultralow-field triplon condensation beyond the dimer paradigm and establish Henmilite as a platform for controlled tuning across quantum criticality in a fluctuation-dominated spin ladder.