  Breaking of spatial inversion symmetry (SIS) induces unique phenomena in
condensed matter. Besides the classic examples such as natural optical activity
and piezoelectricity, the spin-orbit interaction further enriches the effect of
SIS breaking, as exemplified by the Rashba effect. In particular, by combining
this symmetry with magnetic fields or another type of time-reversal symmetry
(TRS) breaking, noncentrosymmetric materials can be made to exhibit
nonreciprocal responses, which are responses that differ for rightward and
leftward stimuli. For example, resistivity becomes directionally dependent;
that is to say, rectification appears in noncentrosymmetric materials in a
magnetic field. However, the effect of SIS breaking on thermal transport
remains to be elucidated. Here we show nonreciprocal thermal transport in the
multiferroic helimagnet TbMnO3. The longitudinal thermal conductivity depends
on whether the thermal current is parallel or antiparallel to the vector
product of the electric polarization and magnetization. This phenomenon is
thermal rectification that is controllable with external fields in a uniform
crystal. This discovery may pave the way to thermal diodes with controllability
and scalability.
