What rare earth metal is commonly used in household smoke detectors?

Americium-241

http://large.stanford.edu/courses/2011/ph241/eason1/

Americium, specifically the isotope Am-241.

https://en.wikipedia.org/wiki/Americium#Ionization_detectors

https://en.wikipedia.org/wiki/Rare_earth_element
This site lists all seventeen rare earth elements, but Americium is not one of them. Nor is a smoke detector listed as an application of any of them. Rare earth elements or rare earth metals are a collection of seventeen chemical elements in the periodic table, specifically the fifteen lanthanoids plus scandium and yttrium.

From the site linked above:

"The name americium (after the Americas) and the symbol Am are suggested for the element on the basis of its position as the sixth member of the actinide rare-earth series, analogous to europium, Eu, of the lanthanide series."

None of the proper rare earth elements are used in smoke detectors, so this tangential definition gives the best answer I could find to the question, which may have been based on slightly erroneous information.

You are both correct. Americium is the element I had in mind when I composed the question and it is of course not a rare earth metal but a transuranic metal.

This is what you get when you let an old organic chemist with a faulty memory compose questions about the bottom of the periodic table.