A method for preparing a bulk or thin-layer single crystal consisting of a scandium, yttrium and/or rare earth sesquioxide cubic matrix doped with at least one element from the series of lanthanides, said single crystal fitting the following formula: R 1 2 O 3:R 2 wherein: - R 1 is at least one metal of valency III selected from among scandium, yttrium, and the elements from the series of lanthanides; - R 2 is at least one element selected from the series of lanthanides; said method being characterized in that it is carried out in a chemically inert crucible and that it comprises the following steps consisting of: 1) preparing a powdery mixture comprising at least: - a solute consisting of a mechanical mixture of at least one sesquioxide of the following formula (IIa) in a molar percentage (1-x) and of at least one sesquioxide of the following formula (IIb) in a molar percentage (x): (R' 1 2 O 3) 1-x (IIa) + (R' 2 2 O 3) x (IIb) wherein R' 1 is identical with R 1, R' 2 is identical with R 2 and 0<x≤25% molar, said solute being present within the mixture MP1 in an amount z such that 5<z≤30% molar, - a synthesis solvent of the following formula: [Li 6 (R" 1 1-x' R" 2 x')(BO 3) 3] wherein: R" 1 and R" 2 are respectively identical with R 1 and with R 2 and x'=x; 2) bringing the powdery mixture MP1 obtained above in step 1), to a temperature T MP1 at least equal to the melting temperature (T F) of said mixture and ≤1250°C, for causing dissolution of the solute in the solvent of formula and for obtaining a liquid solution of said solute in the solvent of formula; 3) maintaining the temperature of the liquid solution at the temperature T MP1 for a period of at least 6 hours, with stirring by means of a solid support subject to rotation around a vertical axis; 4) controlled cooling of the liquid solution from the temperature T MP1 up to a temperature T Exp comprised between the saturation temperature (T sat) of the liquid solution and the critical oversaturation temperature (TC over) of the liquid solution or the bulk setting of the solution, for generating controlled crystallization of the sesquioxide of formula expected on said solid support immersed in said liquid solution and subject to rotation around a vertical axis, said cooling being performed at a maximum rate of 1°C.h -1; 5) withdrawing the solid support from the liquid solution and then controlled cooling of the crystallized sesquioxide of formula on the solid support from the temperature T Exp down to room temperature, a a maximum rate of 50°C.h -1. - R 1 is at least one metal of valency III selected from among scandium, yttrium, and the elements from the series of lanthanides; - R 2 is at least one element selected from the series of lanthanides; 1) preparing a powdery mixture comprising at least: - a solute consisting of a mechanical mixture of at least one sesquioxide of the following formula (IIa) in a molar percentage (1-x) and of at least one sesquioxide of the following formula (IIb) in a molar percentage (x): (R' 1 2 O 3) 1-x (IIa) + (R' 2 2 O 3) x (IIb) wherein R' 1 is identical with R 1, R' 2 is identical with R 2 and 0<x≤25% molar, said solute being present within the mixture MP1 in an amount z such that 5<z≤30% molar, - a synthesis solvent of the following formula: [Li 6 (R" 1 1-x' R" 2 x')(BO 3) 3] wherein: R" 1 and R" 2 are respectively identical with R 1 and with R 2 and x'=x; - a solute consisting of a mechanical mixture of at least one sesquioxide of the following formula (IIa) in a molar percentage (1-x) and of at least one sesquioxide of the following formula (IIb) in a molar percentage (x): (R' 1 2 O 3) 1-x (IIa) + (R' 2 2 O 3) x (IIb) wherein R' 1 is identical with R 1, R' 2 is identical with R 2 and 0<x≤25% molar, said solute being present within the mixture MP1 in an amount z such that 5<z≤30% molar, - a synthesis solvent of the following formula: [Li 6 (R" 1 1-x' R" 2 x')(BO 3) 3] wherein: R" 1 and R" 2 are respectively identical with R 1 and with R 2 and x'=x; R" 1 and R" 2 are respectively identical with R 1 and with R 2 and x'=x; 2) bringing the powdery mixture MP1 obtained above in step 1), to a temperature T MP1 at least equal to the melting temperature (T F) of said mixture and ≤1250°C, for causing dissolution of the solute in the solvent of formula and for obtaining a liquid solution of said solute in the solvent of formula; 3) maintaining the temperature of the liquid solution at the temperature T MP1 for a period of at least 6 hours, with stirring by means of a solid support subject to rotation around a vertical axis; 4) controlled cooling of the liquid solution from the temperature T MP1 up to a temperature T Exp comprised between the saturation temperature (T sat) of the liquid solution and the critical oversaturation temperature (TC over) of the liquid solution or the bulk setting of the solution, for generating controlled crystallization of the sesquioxide of formula expected on said solid support immersed in said liquid solution and subject to rotation around a vertical axis, said cooling being performed at a maximum rate of 1°C.h -1; 5) withdrawing the solid support from the liquid solution and then controlled cooling of the crystallized sesquioxide of formula on the solid support from the temperature T Exp down to room temperature, a a maximum rate of 50°C.h -1.