Since XPath 1.0 spec doesn't support default namespace (and since PHP SimpleXML use libxml, which as far as I know, implements 1.0 spec), we need to register the default namespace first for xpath to work properly.
So $xml->registerXPathNamespace('atom', 'http://www.w3.org/2005/Atom')
first, then we can do $xml->xpath('atom:link[@rel="self"]');
successfully.