  Magnetic fields in galaxies and galaxy clusters are believed to be the result
of the amplification of intergalactic seed fields during the formation of
large-scale structures in the universe. However, the origin, strength, and
morphology of this intergalactic magnetic field (IGMF) remain unknown. Lower
limits on (or indirect detection of) the IGMF can be obtained from observations
of high-energy gamma rays from distant blazars. Gamma rays interact with the
extragalactic background light to produce electron-positron pairs, which can
subsequently initiate electromagnetic cascades. The $\gamma$-ray signature of
the cascade depends on the IGMF since it deflects the pairs. Here we report on
a new search for this cascade emission using a combined data set from the Fermi
Large Area Telescope and the High Energy Stereoscopic System. Using
state-of-the-art Monte Carlo predictions for the cascade signal, our results
place a lower limit on the IGMF of $B > 7.1\times10^{-16}$ G for a coherence
length of 1 Mpc even when blazar duty cycles as short as 10 yr are assumed.
This improves on previous lower limits by a factor of 2. For longer duty cycles
of $10^4$ ($10^7$) yr, IGMF strengths below $1.8\times10^{-14}$ G
($3.9\times10^{-14}$ G) are excluded, which rules out specific models for IGMF
generation in the early universe.
