  Stellar ages are an important parameter to study the chemical evolution of
the Galaxy. In recent years, several studies have established the existence of
a relationship between chemical clocks and stellar ages. The [Y/Mg] clock is a
promising technique, but there are still several open questions, such as its
validity for metal-poor stars and differences between the thin and thick disk
populations. Our aim is to study the behaviour of the [Y/Mg] chemical clock
with stellar ages and the effect of metallicity and population on this chemical
clock for a sample of solar-type disk stars. We have derived the precise
stellar atmospheric parameters as well as the elemental abundances of Mg and Y
through line-by-line differential spectroscopic analysis for a sample of 48
metal-poor solar-type stars based on high-quality, high-resolution ESO/HARPS
spectra. From the high-precision Gaia astrometric data, stellar masses and ages
were estimated through isochrone-fitting. A joint analysis of our sample,
together with a sample of 185 solar-twins and analogues from our previous
works, is performed to calibrate the [Y/Mg] chemical clock in the Galactic disk
for $-$0.71 $\leq$ [Fe/H] $<$ +0.34. Open clusters and stars with asteroseismic
ages have been used to validate our relations. Two different populations could
be clearly seen in the [Mg/Fe] - [Fe/H] plane - the thick and thin disks. We
found a metallicity-dependent, strong anti-correlation between the [Y/Mg] ratio
and stellar ages of our sample. For the first time in the literature, we report
similar correlations for the thin and thick disk stars. The [Y/Mg] relation(s)
found here for solar-type stars is compatible with the literature using
solar-twins. Our relation provides higher accuracy and precision of 0.45 and
0.99 Gyr, respectively, comparable with the best accuracy achieved for the
solar-twins till date.
