Special treatment of youngest member of a group In the German language, there is a term for the youngest member of a family: "Nesthäkchen".

Unfortunately, on Wikipedia I can't find any more details - only the book/film with the same title has a Wikipedia page.

I have seen it several times where the youngest team member gets special treatment. Mostly the older team members are kind to the youngest member, and  thus the youngest member has more freedom/rights than the other team members.

What is this phenomenon called in psychology?

BTW, I guess this phenomena is valid for many mammals.
I'm not aware of any special technical term for such a phenomenon, though colloquially the youngest child may sometimes be called "the baby of the family".  Furthermore, I'm not aware of this phenomenon existing outside of family dynamics - it might be just your personal experience.  In the workplace for example, the youngest members of a team may be treated as inexperienced or incompetent, as competition or threat, or as subordinate or servant.  Favouritism may equally be shown to the eldest, most senior, most productive, or most visionary members of a team.

Within families, a number of surveys have suggested that parents do appear to favour their youngest children.  However, a few interpretations of this phenomenon are possible.  One interpretation is that younger children demand and respond to preferential treatment over their older siblings (eg, Jensen &amp; McHale, 2017).  Another is that younger children are easier to manage than older children, and in fact they receive no better treatment than their older siblings did at the same age (eg, Mumsnet, 2018).  It is also possible that there is a cuteness effect:


  ... human adults react positively to infants who are stereotypically cute.


Also of note: Being the youngest child does not grant any special advantage later in life.