Laravel Ajax live search relationship - ajax

Question

Laravel ajax live search does not work. In the console browser, he writes a 500 error. The problem is this relationships. If I do not use it relationship, the ajax live sarch is work. How do I edit my code to work?
Here the code, to be precise:
$contract->typzakazky->nazov_typu.
My model:
public function typzakazky()
{
return $this->belongsTo('App\ContractsType','contracts_type_id');
}
Controller:
public function index()
{
return view('contracts.index');
}
public function search(Request $request)
{
if ($request->ajax()) {
$output = "";
$contracts = DB::table('contracts')->where('nazov', 'LIKE', '%' . $request->search . "%")->get();
if ($contracts) {
foreach ($contracts as $key => $contract) {
$output .= '<tr>' .
'<td>' . $contract->poradove_cislo . '</td>' .
'<td>' . $contract->nazov . '</td>' .
'<td>' . $contract->typzakazky->nazov_typu. '</td>' .
'<td>' . $contract->datumodovzdania. '</td>' .
'</tr>';
}
return Response($output);
}
}
}
View:
...
<script type="text/javascript">
$('#search').on('keyup',function(){
$value=$(this).val();
$.ajax({
type : 'get',
url : '{{URL::to('search')}}',
data:{'search':$value},
success:function(data){
$('tbody').html(data);
}
});
})
</script>
<script type="text/javascript">
$.ajaxSetup({ headers: { 'csrftoken' : '{{ csrf_token() }}' } });
</script>
How to use it properly relationship in ajax? Very thank you.