That is not enough - she has to wear a 'khimaar' which covers the head and chest. The scarf is not loose fitting and does not cover enough. Yes, that is the 'khimaar'. It is a wide cover covering the head and shoulders. When we say that it covers the chest, then it covers the shoulders since it is wide.
Many people hold that the khimaar' is a covering for the face.
That is ignorance with regard to the language. This is ignorance regarding the language. That is not permissible. It involves resembling the Disbelieving Women or the wicked women. It has its origin among the Jewish women before Islaam.