  Context. Penumbral microjets are elongated jet-like brightenings observed in
the chromosphere above sunspot penumbrae. They are transient events that last
from a few seconds to several minutes and are thought to originate from
magnetic reconnection processes. Previous studies have mainly focused on their
morphological and spectral characteristics, and more recently on their
spectropolarimetric signals during the maximum brightness stage. Studies
addressing the temporal evolution of PMJs have also been carried out, but they
are based on spatial and spectral time variations only.
  Aims. Here we investigate the temporal evolution of the polarization signals
produced by short-lived PMJs (lifetimes $<$ 2 minutes) to infer how the
magnetic field vector evolves in the upper photosphere and mid-chromosphere.
  Methods. We use fast-cadence spectropolarimetric observations of the Ca II
854.2 nm line taken with the CRisp Imaging Spectropolarimeter at the Swedish
1-m Solar Telescope. The weak-field approximation (WFA) is used to estimate the
strength and inclination of the magnetic field vector.
  Results. The WFA reveals larger magnetic field changes in the upper
photosphere than in the chromosphere during the PMJ maximum brightness stage.
In the photosphere, the magnetic field inclination and strength undergo a
transient increase for most PMJs, but in 25$\%$ of the cases the field strength
decreases during the brightening. In the chromosphere, the magnetic field tends
to be slightly stronger during the PMJs.
  Conclusions. The propagation of compressive perturbation fronts followed by a
rarefaction phase in the aftershock region may explain the observed behavior of
the magnetic field vector. The fact that such behavior varies among the
analyzed PMJs could be a consequence of the limited temporal resolution of the
observations and the fast-evolving nature of the PMJs.
