I will echo what others have mentioned: this kind of thing is generally a bad idea, but I also understand that you sometimes have to work with legacy code in ways you'd prefer not to. All that said, you can turn HTML loaded from outside Angular into Angular-bound views with the $compile service. Here's how you might rewrite your current example to make it work with $compile:
// We have to set up controllers ahead of time.
myApp.controller('AfterCtrl', function($scope) {
$scope.loaded = 'Is now loaded';
});
//loads html and afterwards creates a controller
$('button').on('click', function() {
$.get('ajax.html', function(data) {
// Get the $compile service from the app's injector
var injector = $('[ng-app]').injector();
var $compile = injector.get('$compile');
// Compile the HTML into a linking function...
var linkFn = $compile(data);
// ...and link it to the scope we're interested in.
// Here we'll use the $rootScope.
var $rootScope = injector.get('$rootScope');
var elem = linkFn($rootScope);
$('.content').append(elem);
// Now that the content has been compiled, linked,
// and added to the DOM, we must trigger a digest cycle
// on the scope we used in order to update bindings.
$rootScope.$digest();
}, 'html');
});
Here is an example: http://plnkr.co/edit/mfuyRJFfA2CjIQBW4ikB?p=preview
It simplifies things a bit if you can build your functionality as a directive instead of using raw jQuery--you can inject the $compile and $rootScope services into it, or even use the local scope inside the directive. Even better if you can use dynamic binding into an <ng-include> element instead.