It does work the way you tried in your code with just "AppendText". But, the link works only if the document is in read mode and client property "Make Internet URL ... into Hotspots" is set.
UPDATE:
AppendItemValue
doesn't work for RichTextItems.
Append the link direct to your field "Details" or if it doesn't exist then create it. Your code should look like this:
Dim rtItem As NotesRichTextItem
If doc.Hasitem("Details") Then
Set rtitem = doc.Getfirstitem("Details")
Else
Set rtitem = doc.Createrichtextitem("Details")
End if
Call rtitem.AddNewLine( 1 )
Call rtItem.AppendText ("http://www.google.com")