He said to his wife during an argument: This is a separation between me and you

Praise be to Allah.

Firstly: 

Phrases implying divorce may be explicit, which are usually used only in the case of divorce, or implicit, which are used in the case of divorce and other cases. 

In the first case – explicit – divorce takes place even if it was not intended. 

In the second case – implicit – according to the majority of Hanafis, Shaafa’is and Hanbalis, divorce does not take place unless there is the intention of divorce, or there is further evidence that what is intended is divorce, such as when it is done in the case of anger or there being an argument, or if the wife asks for a divorce. In that case divorce takes place even if he did not intend it. Basing the ruling on further evidence to suggest that which is intended is divorce is the view of the Hanafis and Hanbalis. See al-Mawsoo’ah al-Fiqhiyyah (29/26).  

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) favoured the view that implicit phrases did not count as divorce unless that was the intention, even if that was in the case of anger, argument or the wife asking for a divorce. 

See: al-Sharh al-Mumti’ (5/472-473). 

Explicit phrases means using the word of talaaq (divorce) or phrases derived from this word.  

Implicit phrases include such things as saying: Go and stay with your family, or I do not want you, or I have no need of you, or Allah is giving you a break from me. 

And there are phrases concerning which there is a difference of opinion as to whether they are explicit or implicit. This includes the word firaaq (separation). The view of the majority is that this is an implicit phrase. The view of the Shaafa’is and some of the Hanbalis is that it is an explicit phrase. The more correct view is that of the majority, and this is the view favoured by Ibn Qudaamah (may Allah have mercy on him) among the Hanbalis, because: 

although the word firaaq (separation) is mentioned in the Qur’aan in the sense of separation between spouses, it is also mentioned as meaning other things. Allah says:  

“And hold fast, all of you together, to the Rope of Allah (i.e. this Qur’aan), and be not divided among yourselves [wa la tafarraqu]” [Aal ‘Imraan 3:103] 

“And the people of the Scripture (Jews and Christians) differed not [wa ma tafarraqa]…” [al-Bayyinah 98:4]

People also use the word frequently in senses other than divorce."(Al-Mughni  7/294). 

To sum up: Implicit phrases do not mean that divorce has taken place unless that was the intention of the husband. 

Your husband’s saying “This is a separation between me and you” is an implicit phrase. Based on that, if your husband did not intend divorce thereby, then divorce has not taken place. 

And Allah knows best.