  The emission of the upper atmosphere of the Sun is closely related to
magnetic field concentrations at the solar surface.
  It is well established that this relation between chromospheric emission and
magnetic field is nonlinear. Here we investigate systematically how this
relation, characterised by the exponent of a power-law fit, changes through the
atmosphere, from the upper photosphere through the temperature minimum region
and chromosphere to the transition region.
  We used spectral maps from IRIS: MgII and its wings, CII, and SiIV together
with magnetograms and UV continuum images from SDO. We performed a power-law
fit for the relation between each pair of observables and determine the
power-law index (or exponent) for these.
  While the correlation between emission and magnetic field drops monotonically
with temperature, the power-law index shows a hockey-stick-type variation: from
the upper photosphere to the temperature-minimum it drops sharply and then
increases through the chromosphere into the transition region. This is even
seen through the features of the MgII line, this is, from k1 to k2 and k3. It
is irrespective of spatial resolution or feature types on the Sun.
  In accordance with the general picture of flux-flux relations from the
chromosphere to the corona, above the temperature minimum the sensitivity of
the emission to the plasma heating increases with temperature. Below the
temperature minimum a different mechanism has to govern the opposite trend of
the power-law index with temperature. We suggest four possibilities, in other
words, a geometric effect of expanding flux tubes filling the available
chromospheric volume, the height of formation of the emitted radiation, the
dependence on wavelength of the intensity-temperature relationship, and the
dependence of the heating of flux tubes on the magnetic flux density.
