Two sinks logger as default logger not working

Question

I'm trying to combine two sinks:

    auto console_sink = std::make_shared<spdlog::sinks::stdout_color_sink_mt>();
    console_sink->set_level(spdlog::level::warn);
    console_sink->set_pattern("[multi_sink_example] [%^%l%$] %v");

    auto file_sink = std::make_shared<spdlog::sinks::basic_file_sink_mt>("logs/multisink.txt", true);
    file_sink->set_level(spdlog::level::trace);

    spdlog::logger logger("multi_sink", {console_sink, file_sink});

    logger.warn("this should appear in both console and file");
    logger.info("this message should not appear in the console, only in the file");

And it's working fine, but when I set it as default logger it's only prints to screen without writing anything to file:

    auto console_sink = std::make_shared<spdlog::sinks::stdout_color_sink_mt>();
    console_sink->set_level(spdlog::level::warn);
    console_sink->set_pattern("[multi_sink_example] [%^%l%$] %v");

    auto file_sink = std::make_shared<spdlog::sinks::basic_file_sink_mt>("logs/multisink.txt", true);
    file_sink->set_level(spdlog::level::trace);

    spdlog::logger logger("multi_sink", {console_sink, file_sink});

    spdlog::set_default_logger(std::make_shared<spdlog::logger>(logger));

    spdlog::warn("this should appear in both console and file");
    spdlog::info("this message should not appear in the console, only in the file");

Any idea?