Method of designing magnetism in compositionally complex oxides

A method of forming a single phase compositionally complex material including a plurality of transition metals, the method comprising:

• creating a magnetic phase diagram to predict magnetic behavior, by calculating expected local magnetic states leading to macroscopic behavior using the formula:
• H
• =
• ∑
• <
• ij
• >
• J
• ij
• ⁢
• S
• i
• ·
• S
• j
• wherein Si are spin values depending on which transition metal is placed at site i, Sj are spin values depending on which transition metal is placed at site j, <ij> refers to next nearest-neighbor sites, and Jij are magnetic exchange values, and calculating the spin structure factor S(k) by Fourier transform, using the formula:
• S
• ⁡
• (
• k
• )
• =
• 1
• N
• ⁢
• ∑
• i
• ,
• j
• 〈
• S
• i
• ·
• S
• j
• 〉
• ⁢
• e
• ik
• ·
• 〈
• r
• i
• -
• r
• j
• 〉
• wherein ri is the vector position of site i, rj is the vector position of site j, k is the wavevector that is set to (0,0,0) and (½,½,½), and <Si·Sj> are the standard spin-spin correlations in real space at all distances;
• obtaining a transition temperature from the spin structure factor;
• selecting the plurality of transition metals and corresponding transition metal composition ratios for the single phase compositionally complex material based on a desired magnetic behavior and the calculated spin structure factor S(k);
• and
• forming the single phase compositionally complex material, wherein the single phase compositionally complex material is a compositionally complex transition metal oxide comprising the plurality of transition metals at the selected composition ratios.