I looked into that a little, using googly on the internet. Mars is stated as having a magnetic field, but weaker than Earth. But it is a smaller planet, in a different orbit, etc. Also, this isn’t my theory, it has to stand on its own two feet, I’m totally cool with that :)
It has actually a scattered field as I understand it, with stronger pieces and weaker pieces, but not a uniform field aroudn the planet, according to the surveyor, its not constant at all.
The prevailing theory as I understand it is that Mars used to have one, possibly because of a large moon that the planet captured which spun the planet at a much higher velocity that it does today, because mars alone while comparable in size, is not comparable in mass with the Earth.
The theory further purports that this massive satellite eventually crashed into mars, most likely in the northern hemisphere creating the distict differences northern and southern hemispheres of mars.
Also without this satellite to keep it spinning fast, the dynamo collapsed, and with it the marsian atmosphere that the dynamo created and protected.
Again, I am not saying this current theory is wrong, just that mars seems to stand in stark contrast to it.