Understanding the structural underpinnings of magnetism is of great fundamental and practical interest. Se_{1-x}Te_{x}CuO_{3} alloys are model systems for the study of this question, as composition-induced structural changes control their magnetic interactions. Our work reveals that this structural tuning is associated with the position of the supposedly dummy atoms Se and Te relative to the super-exchange (SE) Cu--O--Cu paths, and not with the SE angles as previously thought. We use density functional theory, tight-binding, and exact diagonalization methods to unveil the cause of this surprising effect and hint at new ways of engineering magnetic interactions in solids.
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