Laravel foreign key referencing table in external database?

I am new to laravel and databases in general and I am writing a web application for student evaluations. I have an existing mysql database that contains everything I need already; however, I am using laravel's auth user table and trying to add a foreign key that references the teacher table in the mysql database. I keep getting the following error:

php artisan migrate:fresh

In Connection.php line 664:                                                       
SQLSTATE[HY000]: General error: 1215 Cannot add foreign key constraint 
(SQL: alter table `users` add constraint `users_teacher_id_foreign` 
foreign key (`teacher_id`) references `p4j`.`teacher` (`teacher_id`))                      

In Connection.php line 458:
SQLSTATE[HY000]: General error: 1215 Cannot add foreign key constraint 

My code is as follows.

config/database.php:

   'mysql' => [
          'driver' => 'mysql',
        'host' => env('DB_HOST', '127.0.0.1'),
        'port' => env('DP_PORT', '3306'),
        'database' => env('DB_DATABASE', 'p4j'),
        'username' => env('DB_USERNAME', 'root'),
        'password' => env('DP_PASSWORD', '**mypassword**'),
        'charset' => 'utf8',
        'collation' => 'utf8_unicode_ci',
        'prefix' => '',
    ],

database/migrations/2014_10_12_000000_create_users_table.php:

    public function up()
{
    Schema::create('users', function (Blueprint $table) {

        $table->increments('id');
        $table->string('name');
        $table->string('email')->unique();
        $table->string('password');
        $table->integer('teacher_id')->unsigned();
        $table->rememberToken();
        $table->timestamps();
    });

    Schema::table('users', function (Blueprint $table) {
          $table->foreign('teacher_id')->references('teacher_id')->on('p4j.teacher');
    });
}

app/User.php

    protected $fillable = [
    'name', 'email', 'password', 'teacher_id'
];

/**
 * The attributes that should be hidden for arrays.
 *
 * @var array
 */
protected $hidden = [
    'password', 'remember_token',
];

via Chebli Mohamed