Add this after your line:
AuthenticationManager.SignOut(DefaultAuthenticationTypes.ApplicationCookie);
// Expire the cookie by setting its expiration date to a past date
var cookie = new HttpCookie("YourAuthCookieName")
{
Expires = DateTime.UtcNow.AddDays(-1)
};
// Add the expired cookie to the response to update the client's cookie
Response.Cookies.Add(cookie);
Make sure to replace "YourAuthCookieName" with the actual name of your authentication cookie.