An engagement ring (regardless of what stone/metal) is a physical sign of a verbal contract to get married. If the man who gives the ring is the one to break it off the woman is not legally bound to return it. However, if it is the woman that breaks off the engagement then she is bound BY LAW to return the ring. Unless she can prove, in court, that he said that she could keep it regardless without any hope of marriage EVER or if she can prove that the ring was a gift that was NOT a sign of a contract to marry.
For example if he gives her the ring on Christmas or her birthday and she can prove that the ring was *just a gift* and not a promise to become his wife then she does NOT HAVE TO GIVE THE RING BACK. But if she leads him to believe that by her acceptance the gift that she would indeed marry him then she HAS TO GIVE IT BACK.
The whole purpose of an engagement ring is a way for the man to offer something of value (ie = future security) to the woman in exchange for her fidelity and promise to legally become his wife.
'Course then there goofballs like me who actually go and GET MARRIED without such a ring.