Effect of biquadratic exchange on the Curie temperature

Abstract

in wh ich first t e r m is t h e usual b i l inear exchange t e rm, and the second one is t he b iquadra t ic exchange t e r m wi th an ad jus t ab le p a r a m e t e r a (0 ~ a ~ 1). The above Hami l t on i an r ep resen t s Heisenberg a n d Is ing models for n = 1 a n d 0, respect ive ly . The necess i ty of inc lud ing a smal l nega t ive b iquad ra t i c exchange t e r m in t he H a m i l t o n i a n in real magne t i c mate r ia l s was po in t ed out b y HARRlS and 0 w ~ (~) a n d RODBELL et al. (2), to expla in the i r da ta on p a r a m a g n e t i c resonance of Mn 2+ in Mg0 . A theore t i ca l basis for such a t e r m was es tab l i shed b y ANDERSON (3) a n d HUANG a n d 0RBACH (4) in t he i r calcula t ions of t he superexchange in te rac t ion in M n 0 . A n o t h e r possible origin of b iquadra t i c exchange m e n t i o n e d b y ALL~N and BETTS (5) is t he fac t t h a t t h e exchange opera to r for S = 1 for par t i c les i a n d j is