Air carrier Captain reported a de-ice truck hit their aircraft's elevator/stabilizer while they were parked for de-ice application.

Narrative

While being anti-iced at Gate XX in ZZZ; my FO (First Officer) and I were wait for completion of the application of type 4 liquid. The ground crew started delivering our de-icing report over the radio when we felt a sudden shift of the aircraft which lasted for 5-10 seconds; followed by the nose swinging a few degrees to the side. Immediately I assumed we slid a few feet due to jet blast from another aircraft; so I asked ATC if a plane just taxied out of the next door gate. Once ATC informed me that no aircraft's passed behind us; I knew there was a very good chance we were struck by one of the two de-icing trucks as they were pulling away from the aircraft. I asked over the radio if they had hit us; which in return I was not given any information. Since the engines were not running I proceeded to get out of the flight to try and see any damage or of the FWD SERV DOOR. Not able to see anything; I opened the main pax (Passenger) door and walked out to the tail where the damage was spotted. The beam of the de-ice truck had struck our elevator/stabilizer causing significant damage. From here; the chief pilots; Maintenance and the Dispatcher were contacted for further assistance and explanations.Cause: Neither the de-ice truck driver or sprayer were paying attention/could see the trucks beam as it got too close to the aircraft prior to striking the tail.Suggestion: I believe the ground crews should have a spotter when visibility is poor and working within close proximity to an aircraft.