Aliphatic chains as physical realizations of one-dimensional spin chains supporting magnetically silent spin waves.

Spin waves are collective spin excitations that propagate through lattices with nearest-neighbor interactions. They are conventionally observed in magnetically ordered solids using inelastic scattering techniques or ferromagnetic resonance. Here, we show that analogous spin dynamics can occur in solution-state nuclear magnetic resonance (NMR) of molecules containing aliphatic chains. We show that singlet-triplet population imbalances of nuclear spins can propagate coherently along aliphatic chains. These dynamics correspond to spin waves that carry no net magnetization and are therefore referred to as magnetically silent. When J-couplings along the chain exhibit translational symmetry, the spin Hamiltonian factorizes into subspaces that are formally equivalent to the one-dimensional XY model of spin chains. This enables analytical expressions for eigenstates and eigenenergies, leading to a form of spectroscopy that we term spin-chain zero-quantum NMR. Beyond spectroscopy, the emergence of collective dynamics in molecular systems provides a platform for exploring spin transport, which can be addressed using quantum simulations when classical computational approaches become intractable.