[1] The idea of elementary magnets originated from the Swiss physicist Walther Ritz, who tried to explain atomic spectra.
Just like elementary charges, this was supposed to give rise to discrete values of the total magnetic moment per atom.
[2] In 1909, Weiss performed measurements of the saturation magnetization at the temperature of liquid hydrogen in the laboratory of Heike Kamerlingh Onnes in Leiden.
In 1911, Weiss announced that the molar moments of nickel and iron had the ratio of 3:11, from which he derived the value of a magneton.
[4] But once the old quantum theory was a bit better understood, no theoretical argument could be found to justify Weiss's value.