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Transport properties provide important access to a solid's quasiparticles,such as quasiparticle density, mobility, and scattering. The transport of heatcan be particularly revealing because, in principle, all types of excitationsin a solid may contribute. Heat transport is well understood for phonons andelectrons, but relatively little is known about heat transported by magneticexcitations. However, during the last about two decades, the magnetic heattransport attracted increasing attention after the discovery of large andunusual signatures of it in low-dimensional quantum magnetic cuprate materials.Today it constitutes an important probe to otherwise often elusive, topologicalquasiparticles in a broader class of quantum magnets. This review summarizesthe experimental foundation of this research, i.e. the state of the art for themagnetic heat transport in the mentioned cuprate materials which hostprototypical low-dimensional antiferromagnetic $S=1/2$ Heisenberg models. Thesecomprise, in particular, the two-dimensional square lattice, andone-dimensional spin chain and two-leg ladder spin models. It is shown, howstudying the heat transport provides direct access to the thermal occupationand the scattering of the already quite exotic quasiparticles of these modelswhich range from spin-1 spin wave and triplon excitations to fractionalizedspin-1/2 spinons. Remarkable transport properties of these quasiparticles havebeen revealed: the spin-heat transport often is highly efficient and in somecases even ballistic, in agreement with theoretical predictions.

Heat transport of cuprate-based low-dimensional quantum magnets with strong exchange coupling