Captcha non working on module

Hi, I have a captcha field in an application form, that correctly works, and one in the login form of the Users module, that does not work. In the login form I wrote:

<?= $form->field($user, 'captcha')->widget(\yii\captcha\Captcha::className(), [
    'captchaAction' => 'user/captcha',  // Important, otherwise no image shown.
    'template' => '...',
]); ?>

In the User model I wrote:

class User extends ActiveRecord implements IdentityInterface
{
    public $captcha;

    public function rules()
    {
        return [
            ...
            ['captcha','captcha'],
        ];
    }

In the actions() method of the UserController I wrote:

public function actions()
{
    return [
        'captcha' => [
            'class' => 'yii\captcha\CaptchaAction',
        ],
    ];
}

I also added this code in the behaviors() method:

public function behaviors()
{
   return [
        'access' => [
            'class' => AccessControl::className(),
            'rules' => [
                [
                    'actions' => ['captcha'],
                    'allow' => true,
                ],
            ],
        ]
   ];
}

Any idea?

Thanks