FirebaseDatabase doesn't write data to realtime database

[0x2f0713]

Hi, I want to implement FirebaseDatabase into my application but it doesn't write anything although I enable Realtime Database, init FirebaseApp
Here is my main.dart code

import 'package:firebase_core/firebase_core.dart';
import 'package:firebase_database/firebase_database.dart';
import 'package:flutter/material.dart';
import 'package:iot4home/ui/login.dart';
import 'package:sizer/sizer.dart';

void main() {
  WidgetsFlutterBinding.ensureInitialized();
  runApp(MyApp());
}

class MyApp extends StatelessWidget {
  // This widget is the root of your application.
  @override
  Widget build(BuildContext context) {
    return Sizer(builder: (context, orientation, deviceType) {
      return MaterialApp(
        title: 'Flutter Demo',
        theme: ThemeData(
          // This is the theme of your application.
          //
          // Try running your application with "flutter run". You'll see the
          // application has a blue toolbar. Then, without quitting the app, try
          // changing the primarySwatch below to Colors.green and then invoke
          // "hot reload" (press "r" in the console where you ran "flutter run",
          // or simply save your changes to "hot reload" in a Flutter IDE).
          // Notice that the counter didn't reset back to zero; the application
          // is not restarted.
          primarySwatch: Colors.blue,
        ),
        home: MyHomePage(title: 'IoT for Home'),
      );
    });
  }
}

class MyHomePage extends StatefulWidget {
  MyHomePage({Key? key, required this.title}) : super(key: key);

  // This widget is the home page of your application. It is stateful, meaning
  // that it has a State object (defined below) that contains fields that affect
  // how it looks.

  // This class is the configuration for the state. It holds the values (in this
  // case the title) provided by the parent (in this case the App widget) and
  // used by the build method of the State. Fields in a Widget subclass are
  // always marked "final".

  final String title;

  @override
  _MyHomePageState createState() => _MyHomePageState();
}

class _MyHomePageState extends State<MyHomePage> {
  final Future<FirebaseApp> _initialization = Firebase.initializeApp();

  @override
  Widget build(BuildContext context) {
    print(Theme.of(context).platform);
    return FutureBuilder(
      // Initialize FlutterFire:
      future: _initialization,
      builder: (context, AsyncSnapshot<FirebaseApp> snapshot) {
        // Check for errors
        if (snapshot.hasError) {
          return Text("Something went wrong");
        }

        // Once complete, show your application
        if (snapshot.connectionState == ConnectionState.done) {
          final FirebaseDatabase database = FirebaseDatabase(app: snapshot.data);
          DatabaseReference _messagesRef = database.reference().child('messages');
          _messagesRef.set("Hello World");
          return Scaffold(
              appBar: AppBar(
                // Here we take the value from the MyHomePage object that was created by
                // the App.build method, and use it to set our appbar title.
                title: Text(widget.title),
              ),
              body: LoginUI());
        }

        // Otherwise, show something whilst waiting for initialization to complete
        return Scaffold(
            body: Center(
          child: CircularProgressIndicator(),
        ));
      },
    );
  }
}

Sorry for my bad English