Is there any detail in Tolkien's work indicating what the One Ring was made of?
Some other magical material?
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It was gold.
It may not be clear from LOTR itself whether it's actually gold (the metal) or just golden (color), but History of Middle-Earth clarifies the matter, and also explains why Sauron chose gold:
Sauron's power was not (for example) in gold as such, but in a particular form or shape made of a particular portion of total gold. Morgoth's power was disseminated throughout Gold, if nowhere absolute (for he did not create Gold) it was nowhere absent. (It was this Morgoth-element in matter, indeed, which was a prerequisite for such 'magic' and other evils as Sauron practised with it and upon it.)
For example, all gold (in Middle-earth) seems to have had a specially 'evil' trend - but not silver.
[History of Middle-Earth vol. X, Morgoth's Ring, Myths Transformed - text VII 'Notes on motives in the Silmarillion' (ii); hardcover p. 400]
As far as I'm aware, Tolkien never mentioned what the One Ring's material was.
We only know 2 things about it:
It looks like it's made of gold (so platinum/mithril/silver are out).
It's not destructible other than in the Orodruin volcano. But this is likely a magical property instead of physical/chemical one, so can't tell us what the material is.
One further circumstantial confirmation that The One was made of gold:
Seven Rings given to Dwarves were made of gold:
It is said that the foundation of each of the Seven Hoards of the Dwarf-kings of old was a golden ring. (Source: The Silmarillion)
And all the rings made by Sauron (including the Seven Dwarven and The One) seemed to have been made using the same technology, as per the consensus of the answers to this SFF question (" Were there any differences between the Rings of power given to the Dwarves and the Men? " )
Gandalf, who probably knows as much about the Rings as anyone, refers several times to the Ring as being made of gold.
Fellowship, p. 53
"'Oh, are you indeed, my love,' said Sméagol; and he caught Déagol by the throat and strangled him, because the gold looked so bright and beautiful."
Fellowship, p. 60
"Your small fire, of course, would not melt even ordinary gold. This Ring has already passed through it unscathed..."
Isildur thought the same, though he had less ring-lore than Gandalf, but in this case Tolkien is using him as an exposition device, so perhaps we can give his words something near to a narrator's weight. Fellowship again, p. 253:
...and maybe were the gold made hot again, the writing would be refreshed.
There are also a few places where the narrator defines the material of the ring. For example in the Prologue, Fellowship p. 11:
He possessed a secret treasure that had come to him long ages ago, when he still lived in the light: a ring of gold that made its wearer invisible.
And p. 60 again:
Frodo drew the ring out of his pocket again and looked at it. It now appeared plain and smooth, without mark or device that he could see. The gold looked very fair and pure, and Frodo thought how rich and beautiful was its colour
There are other mentions of 'gold' in relation to the ring, but these are the clearest that they're referring to its material, not its colour. I think the second Gandalf quote is the closest to a slam-dunk we're going to get without someone casting a Speak with Dead spell on Professor Tolkien himself.