Here is My Shorty Sock pattern which is for free.

This pattern is written for use of DPNs as this is what I use to make my socks. I have tried using magic loop, flyers and all sorts of other methods but DPNs work best for me. You should be able to adapt this pattern to work for magic loop, my advice would be to run through the pattern in full before starting and making a note of any changes you may need to make.

The pattern can be worked with contrasting cuff, heel and toe like the images but you can also work the whole sock in one colour. Look out for the useful ‘Notes’ to indicate where you should change colour if wanting contrasts.

Any sock yarn should work as long as you get the gauge noted.
Grams noted below are approximate amounts for size M.
I used Blue Fern Yarns hand dyed platinum sock yarn in colours;
Petals on the pavement 25g,
Rose 10g,
Blackberry 10g.

This pattern has not been tested but if you have a query about the pattern at all, please get in touch.