The phase diagrams with influence of biquadratic exchange coupling on martensitic–austenitic transformations for core–surface nanoparticles

• The phase diagrams have been observed for HM- and CM-NPs with martensitic (M) and austenitic (A) phases.
• The thermal hysteresis loops have also been plotted for CM-NPs.
• The four separate regions in phase diagrams called first-order phase transition (1st), martensitic/austenitic transition (M–A), second-order phase transition (2nd) and TCid have been observed.

Recently, origin of the martensite–austenite transitions in core–surface type magnetic nanoparticles has been investigated theoretically and it has been indicated that repulsive biquadratic exchange coupling (K<0.0) causes the coexisting martensite and austenite phases. In the present paper, the phase diagrams of homogeneous and composite nanoparticles in the kBT/J0−D/J0 plane are studied for the presence and absence of attractive biquadratic exchange interaction in addition to repulsive biquadratic exchange interaction. Significant changes in the phase diagram points are discussed in the presence of martensitic and austenitic transformations. Four regions in the phase diagrams are found as second-order, martensitic–austenitic, TCid and first-order phase transition regimes.

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