SQLSTATE[HY000]: General error: 1364 Field 'user_id' doesn't have a default value というエラーが出て困っております

SQLSTATE[HY000]: General error: 1364 Field 'user_id' doesn't have a default value (SQL: insert into `user_recipe` (`name`, `url`, `description`, `updated_at`, `created_at`) values (キムチチャーハン, https://yaoply.com/items/sqlstatehy000-general-error-1364-field, な, 2022-01-13 19:52:18, 2022-01-13 19:52:18))

<?php

namespace App\Http\Controllers;
use Illuminate\Http\Request;

/** 必要なモデルをuseする */

use App\Models\Recipe;
use App\Models\User;

class CreateRecipeController extends Controller
{
    //バリデーションのルール
    protected $validationRules = [
        "name" => ["required", "string"],
        "url" => ["nullable", "url"],
        "description" => ["nullable", "string"]
    ];

    function __construct(){
        $this->middleware('auth');
    }

    //レシピ登録フォームを表示
    function create(){
        return view("recipe.recipe_create_form");
    }

    //レシピ登録フォームからの遷移先
    function store(Request $request){
        //入力値の受け取り
        $validatedData = $request->validate($this->validationRules);

        //作成するユーザーIDを設定
        $validatedDate["user_id"] = \Auth::id();

        //レシピの保存
        $new = Recipe::create($validatedData);

        //登録後は登録フォームを表示
        return redirect()->route("create_recipe")
            ->withStatus("レシピ: {$new->name}を作成しました");
    }

}

migrationsディレクトリの2022_01_10_164545_create_recipe_table.php

<?php

use Illuminate\Database\Migrations\Migration;
use Illuminate\Database\Schema\Blueprint;
use Illuminate\Support\Facades\Schema;

class CreateRecipeTable extends Migration
{
    /**
     * Run the migrations.
     *
     * @return void
     */
    public function up()
    {
        Schema::create('user_recipe', function (Blueprint $table) {
            $table->id();

            //レシピ名
            $table->string('name');

            //URL
            $table->string('url')->nullable();

            //説明
            $table->text('description')->nullable();

            //user_id: usersとの連携用
            $table->foreignId('user_id')->constrained("users");

            $table->timestamps();
        });
    }

    /**
     * Reverse the migrations.
     *
     * @return void
     */
    public function down()
    {
        Schema::dropIfExists('user_recipe');
    }
}

resources/views/recipe/recipe_create_form.blade

<x-app-layout>
   <x-slot name="header">
       <h2 class="font-semibold text-xl text-gray-800 leading-tight">
           レシピ登録
       </h2>
   </x-slot>
    <div class="py-12">
        <div class="max-w-7xl mx-auto sm:px-6 lg:px-8">
            <div class="bg-white overflow-hidden shadow-xl sm:rounded-lg">
                @if (session('status'))
                <div class="success mt-5 px-4 text-green-900">
                    {{ session('status') }}
                </div>
                @endif
                <!-- ページ固有要素 -->
                <div class="mt-5 px-4 py-5">
                    <!-- エラー表示 -->
                    <form method="post" action="{{ route('store_recipe') }}">
                        @csrf
                        <div class="mb-4">
                            <label for="recipe_name" class="block mb-2">レシピ名</label>
                            <input type="text" 
                                id="recipe_name" 
                                class="form-input w-full" 
                                name="name"
                                value="{{ old('name') }}"
                                placeholder="レシピ名" />
                            @if ($errors->has('name'))
                            <span class="error mb-4 text-red-900">{{ $errors->first('name') }}</span>
                            @endif
                        </div>
                        <div class="mb-4">
                            <label for="recipe_url" class="block mb-2">URL</label>
                            <input type="text" 
                                id="recipe_url" 
                                class="form-input w-full" 
                                name="url"
                                value="{{ old('url') }}"
                                placeholder="https://xxxxx" />
                            @if ($errors->has('url'))
                            <span class="error mb-4 text-red-900">{{ $errors->first('url') }}</span>
                            @endif
                        </div>
                        <div class="mb-4">
                            <label for="recipe_description" class="block mb-2">説明</label>
                            <textarea type="text" 
                                id="recipe_description" 
                                class="form-input w-full" 
                                name="description"
                                rows="5"
                                >{{ old('description') }}</textarea>
                            @if ($errors->has('description'))
                            <span class="error mb-4 text-red-900">{{ $errors->first('description') }}</span>
                            @endif
                        </div>

                        <div class="mb-4 flex items-center">
                            <input type="submit" value="作成" class="bg-blue-500 text-white font-bold py-2 px-4 rounded" />
                        </div>
                    </form>
                </div>
                <!-- /ページ固有要素 ここまで -->
            </div>
        </div>
    </div>
</x-app-layout>