The paper considers a 2D problem associated with a porous magneto thermoelastic material under the effect of gravity in the context of the Three Phase Lag (3PHL) model and a ‘memory dependent derivative frame. It has been assumed that during the initial stages, the medium is in an inactive state for the half space (thermoelastic) the surface of this half space is subjected to mechanical force and has a constant heat flux. The paper presents graphical illustrations of the variables under consideration as they vary along with the vertical distance. A number of figures are used to draw out several comparisons for the thermophysical quantities as they greatly assist in studying the effects of the gravity field, mechanical force, time, and thermal memories (relaxation times).