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The phrase "a thin margin" is correct and usable in written English.
It can be used to describe a small difference or a narrow range between two values, often in contexts like finance, competition, or decision-making.
Example: "The company was able to turn a profit, but it was only achieved with a thin margin, leaving little room for error."
Alternatives: "a narrow margin" or "a slight margin".
Exact(49)
Modern elections are fought over a thin margin in the middle.
In 2014, she was re-elected by a thin margin after an especially divisive campaign.
However, last‐minute polls give Mr. Prouty only a thin margin.
In 2001, he was elected by a thin margin and with less than 30% of the vote.
This meant that the already strained Mets bullpen had to do more heavy lifting with a thin margin for error.
Moreover, Putin faces three new constraints that augur stagnation and increasing turbulence: his relative weakness, the emergence of an opposition and a thin margin of error.
Similar(9)
-Thin Mints are, by a thin margin, America's favorite Girl Scout cookie.
Whereas deregulation turned a cosy and profitable business into a thin-margin snakepit, e-commerce could restore trucking's glory days.
In a thin-margin industry, that's a tough cost to bear.
But soon after the initial public offering, Schrader foresaw that the consumer service was becoming a thin-margin commodity.
With Fab.com, Goldberg realised that the growth needed to succeed as a thin-margin e-commerce marketplace was just not going to happen.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com