var app = angular.module('plunker', ['firebase']);

app.constant('FIREBASE_URL', 'https://newname.firebaseio.com/');
app.run(['$rootScope', 'authService', function($rootScope, authService){
	authService();
	$rootScope.$watch('auth.authenticated', function() {
		isAuthenticated = $rootScope.auth.authenticated;
	});
}]);

app.factory('authService', [
	'$rootScope',
	'$timeout',
	'angularFireAuth',
	'FIREBASE_URL',

	function($rootScope, $timeout, angularFireAuth, FIREBASE_URL) {
  		return function() {
  			angularFireAuth.initialize(new Firebase(FIREBASE_URL), {
  				scope: $rootScope,
  				name: 'user'
  			});
    		$rootScope.auth = {
       			authenticated: false,
       			user: null,
       			name: null
    		};

		    $rootScope.$on('angularFireAuth:login', _set);
		    $rootScope.$on('angularFireAuth:error', _unset);
		    $rootScope.$on('angularFireAuth:logout', _unset);

		    function _set(evt, user) {
		    	$timeout(function() {
			        $rootScope.auth = {
			            authenticated: true,
			            user: user.id,
			            provider: user.provider
			           };
			    });
		     }

		    function _unset() {
		        $timeout(function() {
		    	    $rootScope.auth = {
		        	    authenticated: false,
		            	user: null,
		            	provider: $rootScope.auth && $rootScope.auth.provider
		           	};
		        });
		    }
		}
	}
]);



app.controller('MainCtrl', function($scope, authService, angularFireAuth) {
  $scope.name = 'World';
  
  $scope.login = function(){
    angularFireAuth.login('facebook');
  }
  
  $scope.logout = function(){
    angularFireAuth.logout();
  }
  console.log($scope.auth);
});
<!DOCTYPE html>
<html ng-app="plunker">

  <head>
    <meta charset="utf-8" />
    <title>AngularJS Plunker</title>
    <script>document.write('<base href="' + document.location + '" />');</script>
    <link rel="stylesheet" href="style.css" />
    <script data-require="angular.js@1.0.x" src="https://ajax.googleapis.com/ajax/libs/angularjs/1.0.7/angular.js" data-semver="1.0.7"></script>
    <script src='https://cdn.firebase.com/v0/firebase.js'></script>
	  <script src='https://cdn.firebase.com/v0/firebase-simple-login.js'></script>
	  <!--<script src="https://cdnjs.cloudflare.com/ajax/libs/angularFire/0.2.0/angularfire.min.js"></script>-->
    <script src="https://cdn.firebase.com/libs/angularfire/0.3.0/angularfire.min.js"></script>
    <script src="app.js"></script>
  </head>

  <body ng-controller="MainCtrl">
    <p>Hello {{name}}!</p>
    
    <div ng-show="auth.authenticated">
      <button ng-click="logout()">logout</button>
    </div>
    
    <div ng-show="!auth.authenticated">
      <button ng-click="login()">login</button>
    </div>
    
    Check it in console. $scope.auth in controller always return null datas
  </body>

</html>
/* Put your css in here */