Matthew Barney has filed a lawsuit at New York's Brooklyn Supreme Court in the hope of working out a fairer custody share of the girl, nicknamed Doa.

According to New York Post gossip column Page Six, Barney states in the lawsuit that Bjork is "effectively sacrificing Doa's emotional well-being in favour of her own selfish desires... in part, from her belief that as Doa's mother, she has far greater rights than I do as Doa's father; and, in part, from her insistence that I am solely to blame for the breakdown of our relationship and the end of our intact family."

He also insists it is essential for the child's "needs and desires" that her time is split equally between both parents.

Their 13-year relationship ended acrimoniously in 2013 and the singer recently took aim at Barney on her 2015 album Vulnicura.