I am posting this because it's deeply impressive from an engineering standpoint. The goal of their experiment was to learn about magnetic recording heads by building and testing a wire recorder. This requires understanding the relationship between recording current and playback voltage, the number of turns used in the coil for the recording head, and the speed of the moving wire among other variables.
Unfortunately the experiment recommends starting with vintage recording wire. This will be difficult to find, probably be oxidized, and more than likely already contain a recording. So the experiment will in destroy a 60-year old recording. Please don't do that.
Any steel or iron wire will certainly work. Aluminum, copper and brass wire will not work, it needs to be a ferrous metal. Also avoid Austenitic Stainless steel as that is by definition non-magnetic. Avoid wound wire, which owing to it's irregular surface, will produce inconsistent contact with the recording head and therefore low fidelity.
The original wire Postwar wire was was very thin. Poulsen's early model, the Telegraphone (1898) used .01-inch (0.25 mm) wire, but later models used a diameter of .004 to .006 in (0.10 to 0.15 mm) which was standard into the mid 1940s. You can find it online as a jewelry making supply.