FileNotFoundException (permission denied) when try

As you can notice from title, I have a problem with writing file to sdcard in Android. I've checked this question but it didn't help me. I want to write file that will be in public space on sdcard so that any other app could read it.

First, I check if sdcard is mounted:

Environment.getExternalStorageState();

Then, I run this code:

File baseDir = Environment.getExternalStoragePublicDirectory(Environment.DIRECTORY_DOWNLOADS);
    baseDir.mkdirs();
    File file = new File(baseDir, "file.txt");
    try {
        FileOutputStream out = new FileOutputStream(file);
        out.flush();
        out.close();
        Log.d("NEWFILE", file.getAbsolutePath());
    } catch (IOException e) {
        e.printStackTrace();
    }

I have:

<manifest>
    <uses-permission android:name="android.permission.WRITE_EXTERNAL_STORAGE" />

<application>
...
</application>
</manifest>

in my AndroidManifest.xml.

Exact error is this:

java.io.FileNotFoundException: /storage/1510-2908/Download/secondFile.txt: open failed: EACCES (Permission denied)

I'm testing my code on emulator (emulating Nexus5 API 23). My minimum required SDK version is 19 (4.4 Kitkat).

Also, everything works fine with writing files to private folder on sdcard with same code so I'd say former code should work too:

File newFile = new File(getExternalFilesDir(Environment.DIRECTORY_DOWNLOADS), "esrxdtcfvzguhbjnk.txt");
    newFile.getParentFile().mkdirs();
    try {
        FileOutputStream out = new FileOutputStream(newFile);
        out.flush();
        out.close();
        Log.d("NEWFILE", newFile.getAbsolutePath());
    } catch (IOException e) {
        e.printStackTrace();
    }

Does anyone have any clue what could be the problem? Could it be that somehow KitKat 4.4 just doesn't allow writing to public space in sdcard anymore or?

Everything works fine with writing files to private folder on sdcard

Beginning with Android 4.4, these permissions are not required if you're reading or writing only files that are private to your app. For more information, see saving files that are app-private.

FileNotFoundException (permission denied) when trying to write file to sdcard in Android

As you are trying to write the file in emulator having API 23(Marshmallow), You need to Request WRITE_EXTERNAL_STORAGE permission at runtime also. Check this and this for more detail.