Superposition of symmetry-protected topological order and Neel order in a spin-1/2 coupled ladder antiferromagnet near a quantum critical point

We present a comprehensive study of the S=1/2 coupled two-leg ladder antiferromagnet C₉H₁₈N₂CuBr₄ (DLCB for short) by means of bulk thermodynamics, neutron scattering, and high-resolution electron spin resonance (ESR) measurements on single-crystal samples. In this study, the Néel order below the ordering temperature T_N=2.0 K was confirmed by specific heat, susceptibility, and neutron diffraction measurements. However, ESR below T_N reveals anomalous magnetic excitations that cannot be described as antiferromagnetic resonance modes but rather as transitions induced between components of the S=1 triplet, unambiguously pointing to a macroscopic spin singlet as an essential ingredient of the ground state. Supported by numerical results demonstrating the adiabatic transformation between the S=1 antiferromagnetic (AFM) chain and the AFM S=1/2 ladder system [1], we conclude that the spin gap in DLCB is not entirely due to a spin anisotropy but also related to that of the Haldane gap of S=1 AFM Heisenberg chains in the topologically nontrivial phase [2]. Additional evidence in support of this conclusion is provided by magnetization measurements below T_N and inelastic neutron scattering across T_N. Our findings point to the ground state of DLCB being a quantum superposition of a Néel-ordered phase and a symmetry-protected Haldane phase. To our knowledge, this is the first time such a state has been found in a macroscopic system.

References

[1] P. Sompet et al., Nature 606, 484 (2022).

[2] F. D. M. Haldane, Phys. Rev. Lett. 50, 1153 (1983).