Is breaking off an engagement to the fiancée considered an injustice to her, despite no fault on her part, when one's heart is attached to another woman?

An engagement is a promise of marriage. It is commendable to fulfill it, permissible to break it for a valid reason, and disliked without justification. If you wish to break the engagement because you desire to propose to the other girl you have grown fond of, there is no blame upon you. However, if you have already solemnized the marriage contract with the second girl, she has become your wife, and if you divorce her, you owe her half of the agreed upon Mahr.