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We present the first determination of the galaxy luminosity function (LF) atz~4, 5, 6 and 7 in the rest-frame optical at lambda_rest~900 nm (z' band). Therest-frame optical light traces the content in low-mass evolved stars (~stellarmass - Mstar), minimizing potential measurement biases for Mstar. Moreover itis less affected by nebular line emission contamination and dust attenuation,is independent of stellar population models, and can be probed up to z~8through Spitzer/IRAC. Our analysis leverages the unique full depth Spitzer/IRAC3.6um-to-8.0um data over the CANDELS/GOODS-N, CANDELS/GOODS-S andCOSMOS/UltraVISTA fields. We find that at absolute magnitudes M_z' fainter than>-23 mag, M_z' linearly correlates with M_UV,1600. At brighter M_z', M_UV,1600presents a turnover, suggesting that the stellar mass-to-light ratioMstar/L_UV,1600 could be characterised by a very broad range of values at highstellar masses. Median-stacking analysis recovers a Mstar/L_z' roughlyindependent on M_z' for M_z'>-23 mag, but exponentially increasing at brightermagnitudes. We find that the evolution of the LF marginally prefers a pureevolution in luminosity over a pure evolution in density, with thecharacteristic luminosity decreasing by a factor ~5x between z~4 and z~7.Direct application of the recovered Mstar/L_z' generates stellar mass functionsconsistent with average measurements from the literature. Measurements of thestellar-to-halo mass ratio at fixed cumulative number density show that it isroughly constant with redshift for Mh>10^12Msun. This is also supported by thefact that the evolution of the LF at 4<z<7 can be accounted for by a rigiddisplacement in luminosity corresponding to the evolution of the halo mass fromabundance matching.

The rest-frame optical (900nm) galaxy luminosity function at z~4-7: abundance matching points to limited evolution in the Mstar/Mhalo ratio at z>4