The 660-kilometre seismic discontinuity is the boundary between the Earth’s lower mantle and transition zone and is commonly interpreted as being due to the dissociation of ringwoodite to bridgmanite plus ferropericlase (post-spinel transition)1–3. A distinct feature of the 660-kilometre discontinuity is its depression to 750 kilometres beneath subduction zones4–10. However, in situ X-ray diffraction studies using multi-anvil techniques have demonstrated negative but gentle Clapeyron slopes (that is, the ratio between pressure and temperature changes) of the post-spinel transition that do not allow a significant depression11–13. On the other hand, conventional high-pressure experiments face difficulties in accurate phase identification due to inevitable pressure changes during heating and the persistent presence of metastable phases1,3. Here we determine the post-spinel and akimotoite–bridgmanite transition boundaries by multi-anvil experiments using in situ X-ray diffraction, with the boundaries strictly based on the definition of phase equilibrium. The post-spinel boundary has almost no temperature dependence, whereas the akimotoite–bridgmanite transition has a very steep negative boundary slope at temperatures lower than ambient mantle geotherms. The large depressions of the 660-kilometre discontinuity in cold subduction zones are thus interpreted as the akimotoite–bridgmanite transition. The steep negative boundary of the akimotoite–bridgmanite transition will cause slab stagnation (a stalling of the slab’s descent) due to significant upward buoyancy14,15.