  We study the high-energy emission of the Galactic black hole candidate GX
339-4 using INTEGRAL/SPI and simultaneous RXTE/PCA data. By the end of January
2007, when it reached its peak luminosity in hard X-rays, the source was in a
bright hard state. The SPI data from this period show a good signal to noise
ratio, allowing a detailed study of the spectral energy distribution up to
several hundred keV. As a main result, we report on the detection of a variable
hard spectral feature (>150 keV) which represents a significant excess with
respect to the cutoff power law shape of the spectrum. The SPI data suggest
that the intensity of this feature is positively correlated with the 25 - 50
keV luminosity of the source and the associated variability time scale is
shorter than 7 hours. The simultaneous PCA data, however, show no significant
change in the spectral shape, indicating that the source is not undergoing a
canonical state transition. We analyzed the broad band spectra in the lights of
several physical models, assuming different heating mechanisms and properties
of the Comptonizing plasma. For the first time, we performed quantitative model
fitting with the new versatile Comptonization code BELM, accounting
self-consistently for the presence of a magnetic field. We show that a
magnetized medium subject to pure non-thermal electron acceleration provides a
framework for a physically consistent interpretation of the observed 4 - 500
keV emission. Moreover, we find that the spectral variability might be
triggered by the variations of only one physical parameter, namely the magnetic
field strength. Therefore, it appears that the magnetic field is likely to be a
key parameter in the production of the Comptonized hard X-ray emission.
