taĉmento

There is no -ment- suffix in Esperanto. This is worth stating flatly, because taĉmento looks like taĉm- plus a suffix and English speakers have a -ment reflex from government, movement, agreement. Esperanto has none. The words that end that way - momento, monumento, dokumento, instrumento, taĉmento - are single borrowed roots with the Latin ending already fossilised inside them, exactly like the -iv in ekskluziva two ranks back. Where Esperanto wants the idea English spells -ment, it uses -ad- for the action (movado) or -aĵ- for the thing produced (aranĝaĵo).

A detachment is defined by what it left. The sense is precise and it is not just "a small group": a taĉmento is a body of troops detached from a larger force for a particular job, which is why it needs a armeo behind it to make sense. A grupo is any group, a trupo is a body of soldiers as such, and a taĉmento is a slice cut off one and sent somewhere. Taĉmentestro is its commander.

Register. This is military and administrative vocabulary. In ordinary prose you will meet it in war reporting, in adventure fiction and in the older literature, and almost nowhere else. If you want a detachment in the emotional sense - being uninvolved, standing back - taĉmento is the wrong word entirely: that is sendependeco, indiferenteco or malinteresiĝo, depending on which kind of standing back you mean.