Chrsyler originally, back in the old oil days of 2006 when they printed the owners manuals, said to use a 10w30.
Maybe any good full syn 5w30 or even Mobil1 0w40 at walmart would be best here.
I'm not sure I would go to M1 0w20 as you are doing, but it should be fine. Going thinner is not necessarily bad, although the timing chains could suffer some. We just don't know for sure.
No timing chains on this engine. I have a bunch of 0w20 to use up from an old AZ clearance, figured winter would be a fine time to use some as the Chrysler does mostly short trips. We don't have particularly awful winters here, but it will get down to 0 or the single digits a handful of times.
Oddly, I have gotten stellar UOA results in winter using 5w-20 in my Maxima, when a 30 weight is called for. That engine does have timing chains. I don't think a 20 weight is going to hurt anything, but will likely have a UOA performed to see if anything unusual pops up.