Electronic – Vacuum relay vs silicon

You can certainly use an electromechanical switch, but at these current levels it's called a contactor https://en.wikipedia.org/wiki/Contactor. You'll need a fairly hefty circuit to drive its coil, too, so you won't be able to just connect it to your MCU.

In your case, you only need the simplest form of contact arrangements, single pole, single throw (SPST).

The obvious alternative to a contactor is a solid state relay (SSR), and some good information about using them is here http://www.sos.sk/a_info/resource/Crydom/Selecting%20a%20solid%20state%20relay.pdf. You can get current ratings in excess of 100 amps, so that's not a problem. If you do decide to go this route, be aware that you MUST use a DC-rated SSR, NOT an AC-rated unit. If you mistakenly use an AC SSR you will not be able to turn it off.

Rolling your own is possible, using commercially-available MOSFETs. Just be aware that dealing with 50 amps has its own peculiar set of problems. Things like getting enough copper trace on a pc board to keep from burning your traces. Things like making contact with the load-carrying wires mechanically strong enough (the wires are thick and unwieldy) to be reliable. And being absolutely certain that you get enough gate drive to turn the MOSFETs fully on. It's certainly doable, but not necessarily on the first try. It's a classic case of doing it yourself or paying someone else for their experience in how to do it right.

Thanks Ignacio Vazquez-Abrams and Spehro Pefhany for your advices!

So, I have reconnected all wires and seems one relay I got is broken now (I suppose I have done short circuit)...

Now, when the signal is ON I have connection between NC and COM.