I always have the same student which appears after each recording

When I add a recording, I always have the same student which appears ???

I think the problem is perhaps in my function index() ?

public function index(Request $request)
  {   
     $user = $request->user();
     $payments = Payment::query()
     ->when($user->hasRole('admin') !== true, function (Builder $query) use ($user) {
     $query->where('email', $user->email);
     })
     ->when($request->has('search'), function (Builder $query) use ($request) {
    $query->where('name', 'like', '%' . $request->input('search') . '%');
         })->with('students:id,name') 
    ->paginate(5);

    return view('admin.payments.index', compact('payments'))
    ->with('display_search', $user->hasRole('admin'));
    }

For information my table students has 3 fields (id, name, email) and the table payments has 6 fields (id, date_payment, number_seance, price, total, fk_student).

My relationships:

Model Student:

protected  $fillable = ['user_id', 'name', 'email', 'payment_id'];

public function payments(){

        return $this->hasMany('App\Payment', 'fk_student');
    }

  public function user()
    {
        return $this->belongsTo('App\User', 'id', 'payment_id');
    }

Model Payment:

protected  $fillable = ['date_payment', 'fk_student', 'number_seance',  'price', 'total'];
    
    public function students(){

    return $this->belongsTo('App\Student', 'fk_student');
    }

    public function user()
    {
        return $this->belongsTo('App\User', 'id', 'payment_id');
    }

Model User

public function students()
    {
        return $this->hasOne('App\Student', 'user_id', 'id');
    }

    public function payments()
    {
        return $this->hasOne('App\Student', 'payment_id', 'id');
    }

Index blade

<th>Date payment</th>
<th>Number seance</th>
<th>Price</th>
<th>Total</th>
 <th>Name</th>

</tr>
</thead>
@foreach($payments as $payment)
<tr>
   <td> {{$payment->date_payment->format('d/m/Y') }}</td>
   <td> {{$payment->number_seance}}</td>
   <td> {{$payment->price}}</td>
   <td> {{$payment->total}}</td>
   <td> {{$payment->students->first()->name}}</td> 
   <td>

Thank you for your help.