Wanting to use only Free fully functional recovery software means your data is not valuable to you.
The software I installed was a free Trial
it wont let me actually recover anything until I pay for it...
I have recently tried the following data recovery tools:
On a formatted partition with good results. But some files were corrupted or lost.There are many more free programs most are a cut down version of a commercial package.
A few recover a limited number of files for free or show you what could be recovered if you Pay for a license.
Based on my experience, though those tools are paid, they are more professional and find more good results than free ones.
I would recommend to you:
iBoysoft Data Recovery
Please note that If you look for an unformat option if you have not written to the formatted partition since it happened (although windows will write to the drive anyway ). Because how successful they will depend on how much has been written to the drive since formatting. Therefore, you'd better use another hard disk eg USB, SATA, or over a network to a hard drive to recover the data.
This post will be helpful: https://iboysoft.com/data-recovery/recover-data-from-formatted-hard-drive.html
Moreover, depending on the value of data ask for professional help or carry on recovery yourself.