Anthony Milan Ross, 45, is said to have shot dead 38-year-old Iris Mr Ross and their young children Nigel, 11, and Anora, 10 months, on Monday. He was also charged with multiple counts of aggravated assault and assault against a police officer.
Police responding to a report of gunfire arrived at a block of flats in Phoenix, Arizona, to find Ms Ross' body outside. They later found the children's bodies inside the apartment where their father had barricaded himself.
Officers tried to talk to Mr Ross when he was inside the unit, Sgt Jonathan Howard said. Several hours later, Mr Ross indicated he had killed the two children and began shooting at officers, said authorities. After a brief gunfight, he was taken into custody.
Mr Ross was not hurt, Sgt Howard said. One officer was injured by shrapnel and taken to hospital in stable condition.
Mr Ross is a vegan cook, author and motivational speaker who promotes a plant-based lifestyle using his middle name. He claims to have lost some 100kg in weight after cutting out meat and dairy products.
On Christmas Day, hours before the shooting, he posted a video of himself singing "Santa Claus Is Coming To Town" with his son, filmed the day before.
Mary Wogas, Iris Ross' sister, told ABC15: "I received a text yesterday about 2.52pm. Two messages, first one saying 'I just killed Iris and the kids'. The second message was 'with a gun'.
"I knew that man was very unstable. I knew he had a very, very dark side. I didn't know it was this dark."
Police had initially indicated Mr Ross no longer lived at the complex in Phoenix and was visiting the area for the holidays, but court documents listed the apartment address as his residence.
Officers did not give a motive for the shooting, which they said they were investigating as a domestic violence incident. Mr Ross is due in court on 3 January.
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