std::map: overloading the operator< with a parameter other than the key's class

This is my first post - sorry if I mess any of the site's conventions. Please point out any mistakes I make so i could fix them/not repeat them.

This post may be related

c++ reference: std::map

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I want to be able to use std::map's operator[] by putting an std::string between the brackets - even though the key of the map isn't std::string.

here's the code

class myKey
{
public:
    std::string _name;

    myKey(std::string name)
    {
        _name = name;
    }

    bool operator<(const myKey& other) const
    {
        if (this->_name < other._name)
        {
            return true;
        }
        else
        {
            return false;
        }
    }
};

int main()
{
    std::map<myKey, int> map;
    myKey temp("keyString");
    map[temp] = 1;
    std::cout << map[temp];

    system("pause");
    return 0;
}

So far this works fine - but as you can see, the only thing the operator uses is the std::string _name field of the class. I wan't to be able to look up a value in the map, by only entering a string like so: map["keyString"].

I have tried overloading the operator< of myKey, but it didn't help.

bool operator<(const std::string name) const
{
    if (this->_name < name)
    {
        return true;
    }
    else
    {
        return false;
    }
}

How can it be done?