Specific heat jump in metals under quantizing magnetic fields

The specific heat is calculated for a three-dimensional electron gas in metals under quantizing magnetic fields taking into account magnetic interactions between conduction electrons (the Shoenberg effect). Under the conditions of the nonlinear de Haas-van Alphen (dHvA) effect the temperature jump in specific heat at a diamagnetic phase transition is calculated. The jump occurring at the magnetic field corresponding to the centre of the dHvA period is about of a few percent of the specific heat in the absence of magnetic field. In gold and copper it is predicted to be larger than the maximal value of the change observed during a.c. temperature measurements in heat capacity of beryllium in a magnetic field. It is shown that the jump substantially increases with increasing magnetic field. Limiting fields for existence of diamagnetic phase transitions at any temperature; as well as transition temperatures in gold and copper at certain fields, are estimated and it is found that the latter coincide with the measured values.