Use a chainsaw or axe to cut the stump as close to the ground as possible. The more stump you can remove, the less time and effort is needed to kill the remaining tree stump.
Pour enough Epson salt or rock salt to cover the top of the hybrid poplar stump and any exposed roots. Lightly spray the salt with water. The stump will absorb the salt, killing it. Repeat Epsom salt application on the stump and roots every week to 10 days for at least one month.
Drill multiple holes into the top of the stump. The holes need to be made with the largest drill bit you have and as deep as you can drill. Fill the holes with the Epsom salt for faster absorption. The advantage of using salt over high nitrogen or chemicals is that the salt will quickly kill the roots of the stump. When a poplar tree has been cut down, the roots will begin generating saplings to survive.
Pull, cut or dig out all poplar saplings that sprout from the roots while your tree stump is dying. Hand-pull or use a spade or shovel to remove the saplings. Remove poplar saplings before they have developed eight leaves. At that point, the sapling has formed its own roots and will begin sending food to the original mother plant roots, hindering your stump and root killing.
Check and remove all saplings weekly. You can eliminate saplings in your lawn by mowing. Diligent monitoring of hybrid poplar saplings and removing them immediately will eventually eliminate all volunteer trees.