Mother of Tears

The film begins with members of the Catholic Church digging up the body of a 19th-century church official, whose casket has a box-shaped urn chained to it. Inside the box they discover artifacts belonging to Mater Lachrymarum (Moran Atias), the last surviving member of the Three Mothers; an ancient trio of powerful black witches. In particular, the box contains a magic cloak that, when worn by Mater Lachrymarum, increases her powers significantly.
The urn is shipped to the Museum of Ancient Art in Rome where Sarah Mandy (Asia Argento), an American studying art restoration, works. Sarah is dating the curator Michael Pierce, a single father who is away from the museum that night. With help from the assistant curator, Sarah opens the box and finds the cloak, a dagger, and three statues representing the three witches. Sending Sarah to her office to retrieve tools to help her translate the text on the artifacts, the curator is promptly attacked by the demonic agents of Mater Lachrymarum. Sarah arrives too late to save her boss (who is being disembowelled by the monsters) and starts to flee the museum. Unfortunately, she is pursued by Mater Lachrymarum's familiar (a baboon) and is only able to escape when a disembodied voice magically throws open a series of locked doors keeping her trapped inside the museum. Sarah tells the police what happened as she spends the night with Michael and his son. Michael visits the Cardinal who sent him the urn only to find out that, shortly after mailing the urn to him, he had a severe stroke and is now in a coma. An assistant of the priest gives Michael a piece of paper, which the Cardinal was writing on before collapsing. On it is scrawled the name "Mater Lachrymarum". As he leaves the hospital, a pair of witches observe Michael leaving the building.
Back in Rome, chaos descends as a wave of mass suicides, murder, and violence engulfs the city. Sarah continues her own research only to be summoned by Michael to his apartment. The witches have kidnapped his young son and won't return the boy to him unless he stops his investigation. Sarah begs him to call the police (who are tailing Sarah, ever since the murder at the museum) but Michael refuses to and instead opts to visit a local priest who is a trained exorcist. This goes badly for Michael; the two witches see him and he is soon captured and murdered, along with his son, whose body is cannibalized by the rapidly expanding coven. However, before he is killed, Michael calls Sarah and begs for her to come and help him. As she makes her way through a crowded train station, Sarah is spotted by a gang of witches who, like so many other witches, have arrived in Rome in order to pledge their loyalty to Mater Lachrymarum. Pursued by the witches and the police, the disembodied voice from before instructs Sarah on how to magically make herself invisible. She uses this to avoid the police detective, though she is forced to kill a witch, Katerina, who catches and corners her on the train.
At the priest's home, Sarah meets Marta, a fellow white witch and friend of Sarah's deceased mother. Realizing that Sarah's mother is the voice guiding her, Marta reveals details to Sarah about her parents. Her mother was a powerful white witch who dared to challenge and severely wound Mater Suspiriorum, the eldest and wisest of the Three Mothers. In response to this, Suspiriorum caused the fatal car crash that killed Sarah's parents. Though Mater Suspiriorum and her sister Mater Tenebrarum are now dead, their sibling Mater Lachrymarum has emerged from the shadows to bring about the second age of magic, with the fall of Rome as her coming out party. They talk to the priest, only for him to be killed before he can give the two a copy of a book that would explain Mater Lachrymarum's backstory to them by a patient of his. Escaping back to the city, Sarah goes to her own home but finds Mater Lachrymarum's goons waiting for her. She heads to Marta's house, but once again Mater Lachrymarum's minions strike and Marta and her lesbian lover are murdered. Fleeing, Sarah spots Michael, who takes her back to his apartment. Unfortunately, Sarah soon realizes that Michael is dead and that Mater Lachrymarum is animating his body in an attempt to kill her. As she burns her lover's still-animate body, the ghost of her mother intervenes one final time to grab Michael and banish him (and possibly herself) to Hell.
Sarah locates a powerful alchemist, who Marta mentioned as her only hope to learn how to fight Mater Lachrymarum. After being briefly paralyzed by the alchemist (so that he could perform a test on her to see if she was a white witch or an evil witch), the alchemist gives Sarah the only help he has in locating Mater Lachrymarum's dwelling. Sarah is given a copy of "The Three Mothers" to read, and from this (and from following a group of witches) Sarah finds Mater Lachrymarum's lair; a now run-down and disrepaired mansion. At this point, she is joined by one of the police detectives hunting her and the two go into the catacombs to find Mater Lachrymarum. However, the two become separated, and the detective is tortured alongside the alchemist and his assistant, who dies after his arm is chopped off by one of Mater Lachrymarum's minions. Sarah is caught and brought before Mater Lachrymarum, who offers Sarah up to her cannibal followers. Sarah, having healed the detective's wounds, uses a spear to pull the cloak off Mater Lachrymarum and tosses it into a nearby fire. This causes the mansion to collapse as a pillar falls and impales Mater Lachrymarum. With the Mother's followers crushed as the caves collapse, Sarah and the detective laugh in horror and shock as they reach the surface, as they realize that the threat of the Three Mothers has been defeated once and for all.

Question: What type of garment increased Mater Lachrymarum' powers significantly when worn?
Answer: A cloak