Definition from Wiktionary, the free dictionary
- simple past tense and past participle of estrange
- She estranged her husband by not talking to him for over a year.
- Having become a stranger, of one who formerly was close, as a relative, friend, lover, or spouse.
Usage notes 
A relatively formal term, the more colloquial alternative is “to not talk”, as in “I don’t talk to my mother”. A semi-formal alternative is not on speaking terms.