The biggest challenge of our Mars journey is the journey time (9 months). Now I have seen news coming stating that atomic or nuclear rockets would cut the journey time in half. Is that right? When I googled for nuclear rocket, I found that this technology has been known since the 1960s. What took it so long to be considered a better technology than the chemical rockets?
The biggest challenge of our Mars journey is the journey time (9 months).
Well, maybe. More likely, the biggest challenge is making it economically worthwhile to support a viable colony. But if you're just talking about the problems of transport, assuming the will to do it, sure, that's plausible enough.
Now I have seen news coming stating that atomic or nuclear rockets would cut the journey time in half. Is that right?
It's right, or even understating the advantage, but this is not news at all. This has been known since the designs were drawn up in the first place, and the advantages fairly well understood.
When I googled for nuclear rocket, i found that this technology has been known since the 1960s. What took it so long to be considered a better technology than the chemical rockets?
Very simply, it didn't take so long. It's always been considered technologically superior, and several concepts are comparatively straightforward to develop or have already been mostly worked out (Orion, in particular, got quite far before being shut down hard, and Timberwind/NERVA got even farther). The problem has been that no one wants to deal with the risks, public perception, or definite hazards associated with putting high-powered nuclear reactors in space. Or even putting nuclear reactors in space at all. (Let's not even mention nuclear bombs every second, Orion/Medusa style.)
Until you can say "1 MW nuclear-thermal engine" to a US senator without them reaching for their smelling salts or their shotgun, this is a non-starter.
See also Are nuclear-powered engines the way to go for space exploration? for a slightly different perspective on the issues.
Cut the journey in half compared to what? As far as I’m aware there is no physical limit for chemical rocket velocity or acceleration (except for the speed of light of course). With a huge enough rocket, thrust and enough stages you could go as fast as you want.
Nuclear rockets have a much higher efficiency of about ~800s of specific impulse compared to the ~400s of chemical rockets. So it’s true that it would take about half as much fuel for the same change in velocity. However, the most limiting factor in rocket flight is cost  and I doubt that a nuclear rockets would be very competitive in that regard.
Current flights from the Earth to Mars are routes that take the least amount of fuel (energy) to get there. If you have plenty of fuel (money) you could fly a route that goes directly to Mars, no need to wait for a launch window or anything.