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.
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