mongoose 如何返回特定时间段数据

假定数据结构如下：

{
    userid:1111,
    data1:[
        {title:'test',content:'test',createTime:'2019-03-25T09:24:00.000Z'}
        {title:'test',content:'test',createTime:'2019-03-25T09:24:00.000Z'}
    ]
},
{
    userid:2222,
    data1:[
        {title:'test',content:'test',createTime:'2019-03-25T09:24:00.000Z'}
        {title:'test',content:'test',createTime:'2019-03-25T09:24:00.000Z'}
    ]
}

我执行了如下代码但是返回了所有时间段的数据，并不能达到要求

const start = new Date(2019,3,1)
const end = new Date(2019,3,31)
schema.find({userId:req.body.userId,"data1.createTime":{$gte: start,$lt: end}})

小白求助下