What you want is β-Ti3Au which technically is an intermetallic of gold and titanium. Apparently Tony Stark was right about a titanium gold alloy being a good choice for his suits.
The density is similar to titanium. Harder than steel, half the specific gravity.
A sword forged from this stuff would certainly be magical. Lighter, stronger, harder, sharper, corrosion resistant and extremely difficult to forge. It's difficult to form the alloy in the first place, and then you get the α-phase (same hardness as straight titanium). The harder β-phase forms only at extremely high temperatures.
Oh and it's a red-gold colour. You can give it various conflicting backstories of being forged with the blood of dragons and suchlike.
I was thinking about how mediaeval smiths might produce such a thing and you're going to love the answer: in the side of a volcano. And he'll still need coal dust and a fan. How exactly the smith is supposed to survive in such an environment is your problem. I expect that such weapons will have been made by your gods, giving a whole new meaning to "limited edition".
A regular forge won't be hot enough. It will return the material to the α-phase, which is not a horrible material for a sword but won't hold an edge the way the β-phase will. Any reforging of the Sword that was Broken would be an epic quest in itself; you would need to enlist the aid of your world's equivalent to Hephaestus/Vulcan.
Note that being very hard and keeping a superb edge is not the same as unbreakable. With stupid handling such a sword would be easier to break than iron because where iron will bend, this will snap.
It would be within the strength of a big fighter to apply enough torsion to snap it. But this only improves the item from a game perspective because players take care about how they use it, or face the ire of other players for destroying a unique item that's nearly impossible to reforge.
These physical qualities also affect the type of sword. To mitigate the risk of shattering, the blade needs significant depth in the cutting plane — like a scimitar. Long and thin is just begging for failure (but you might start out this way and have Vulcan fix the design flaw if they've been good little players).
Interesting comments. I don't think having half the density of steel represents a problem. Have you ever lifted a real sword? They're heavy! A lighter sword is a speed and stamina advantage.
The tensile strength of mild steel is about 400MPa with a Young's Modulus of 210GPa. By contrast most titanium alloys have a tensile strength from 1000 to 1390MPa and a Young's Modulus of 103GPa .
Straight titanium is similar in hardness to 304 stainless steel, and although I could not find a hardness value for beta βTi3Au it is widely described as "four times harder than titanium" hence my razor blade comments.
Bronze swords were thicker to offset the lower material strength. With half the density you can double the thickness and come out the same weight. While aluminium bronzes can have up to 780MPa tensile strength, the alloys available to the Greeks were about 230MPa.