A La(OH).sub.3/La.sub.2O.sub.3/CaSiO.sub.3/g-C.sub.3N.sub.4 particulate crystalline nanocomposite including: a hexagonal lanthanum hydroxide (La(OH).sub.3) crystalline phase; a lanthanum oxide (La.sub.2O.sub.3) crystalline phase; a monoclinic calcium silicate (CaSiO.sub.3) crystalline phase; and, a graphitic carbon nitride (g-C.sub.3N.sub.4) crystalline phase, wherein at least a fraction of the g-C.sub.3N.sub.4 is in the form of mesoporous nanosheets.

A La(OH).sub.3/La.sub.2O.sub.3/CaSiO.sub.3/g-C.sub.3N.sub.4 particulate crystalline nanocomposite including: a hexagonal lanthanum hydroxide (La(OH).sub.3) crystalline phase; a lanthanum oxide (La.sub.2O.sub.3) crystalline phase; a monoclinic calcium silicate (CaSiO.sub.3) crystalline phase; and, a graphitic carbon nitride (g-C.sub.3N.sub.4) crystalline phase, wherein at least a fraction of the g-C.sub.3N.sub.4 is in the form of mesoporous nanosheets.

A metal-supported material including a transition metal excluding Group 4 elements supported on a binary composite oxide. The composite oxide includes a metal element expressed by A.sub.nX.sub.y, where A represents a lanthanoid that is in a partially or entirely trivalent state, X represents an element that is a Group-2 element in a periodic table selected from the group consisting of Ca, Sr, and Ba, or a lanthanoid, and that is different from A, n satisfies 0<n<1, y satisfies 0<y<1, m satisfies 0m<1, and n+y=1. The composite oxide includes a solid solution that is a tetragonal crystal or a cubic crystal, and a ratio of a value (D.sub.ads) of a dispersion degree of the transition metal obtained by an H.sub.2 pulse chemical adsorption method to a value (D.sub.TEM) of the dispersion degree predicted from an average particle diameter of particles of the transition metal obtained from a TEM image satisfies 0<D.sub.ads/D.sub.TEM<1.

A metal-supported material including a transition metal excluding Group 4 elements supported on a binary composite oxide. The composite oxide includes a metal element expressed by A.sub.nX.sub.y, where A represents a lanthanoid that is in a partially or entirely trivalent state, X represents an element that is a Group-2 element in a periodic table selected from the group consisting of Ca, Sr, and Ba, or a lanthanoid, and that is different from A, n satisfies 0<n<1, y satisfies 0<y<1, m satisfies 0m<1, and n+y=1. The composite oxide includes a solid solution that is a tetragonal crystal or a cubic crystal, and a ratio of a value (D.sub.ads) of a dispersion degree of the transition metal obtained by an H.sub.2 pulse chemical adsorption method to a value (D.sub.TEM) of the dispersion degree predicted from an average particle diameter of particles of the transition metal obtained from a TEM image satisfies 0<D.sub.ads/D.sub.TEM<1.

A method for extracting a rare earth from a rare earth sample using magnetic-based concentration and separation of an ore containing a selected rare earth from a lanthanide series of elements. The method steps include selecting and grinding a rare earth sample into particle size from the lanthanide series of elements, treating the rare earth sample to variable weak electromagnets, treating the rare earth sample to a variable strong electromagnets and separating non-magnetic minerals. Then heating the rare earth sample in a thermal decomposition oven and then treating the rare earth sample to second variable strong electromagnets for a magnetic gradient ion exchange fixed bed separation. Finally, creating high grade rare earth oxides for further production of rare earth contained products.

A method for extracting a rare earth from a rare earth sample using magnetic-based concentration and separation of an ore containing a selected rare earth from a lanthanide series of elements. The method steps include selecting and grinding a rare earth sample into particle size from the lanthanide series of elements, treating the rare earth sample to variable weak electromagnets, treating the rare earth sample to a variable strong electromagnets and separating non-magnetic minerals. Then heating the rare earth sample in a thermal decomposition oven and then treating the rare earth sample to second variable strong electromagnets for a magnetic gradient ion exchange fixed bed separation. Finally, creating high grade rare earth oxides for further production of rare earth contained products.