Does ssh-keygen -t rsa work if only set for root user

i.e, if the username on local system is sodium and i generate the key using the above said command and on the remote system if i place the key in /root/.ssh authorized_keys ,this works.

But on the remote system if the key is placed in /home/natrium/.ssh authorized_keys

This still prompts for a password.Is this the expected behavior or is that some thing wrong in the above procedure

Thanks..