  This article reviews low-temperature heat transport studies of spin-gapped
quantum magnets in the last few decades. Quantum magnets with small spins and
low dimensionality exhibit a variety of novel phenomena. Among them, some
systems are char-acteristic of having quantum-mechanism spin gap in their
magnetic excitation spectra, including spin-Peierls systems, S = 1 Haldane
chains, S = 1/2 spin ladders, and spin dimmers. In some particular spin-gapped
systems, the XY-type antiferromagnetic state induced by magnetic field that
closes the spin gap can be described as a magnon Bose-Einstein condensation
(BEC). Heat transport is effective in probing the magnetic excitations and
magnetic phase transitions, and has been extensively studied for the
spin-gapped systems. A large and ballistic spin thermal conductivity was
observed in the two-leg Heisenberg S = 1/2 ladder compounds. The characteristic
of magnetic thermal transport of the Haldane chain systems is quite
controversial on both the theoretical and experimental results. For the
spin-Peierls system, the spin excitations can also act as heat carriers. In
spin-dimer compounds, the magnetic excitations mainly play a role of scattering
phonons. The magnetic excitations in the magnon BEC systems displayed dual
roles, carrying heat or scattering phonons, in different materials.
