Laravel Eloquent：寻找缺少关系的对象

I have a Posts object, that may or may not have a Link object (Link belongsTo Post and Post hasOne Link).

I'm trying to find Posts that were created after a certain date that don't have a Link created yet.

I have the following but it doesn't work:

$posts = Post::where('post_date', '>', 'xxxx')->whereIsNull('link.id'); // which is how I would write it with an OUTER JOIN.

What am I missing here?

Use Laravel eager loading and loop through the results to find posts without links.

$posts = Post::with('link') -> get();
// loop with foreach and extract posts with no links
$not_linked_posts = array();
foreach ($posts as $k => $post){
  // if link is not set
  if (!isset($post -> link)){
       // add it to array
       $not_linked_posts[$k] = $post -> toArray(); //convert post to array
  }
}

Hope this help.