In ferromagnetic (FM) Heusler alloys the structural transition from high temperature cubic phase to low temperature tetragonal one takes place. The experiments show that in Ni_{2}MnX (X=In, Sn, Sb) alloys the next sequence of phase transitions occurs: paramagnetic (PM) cubic phase → FM cubic one → PM tetragonal one → FM tetragonal one [1]. This magnetic behavior can be explained by the existence in these alloys the inversion of exchange interaction [2]. In this work with the help of the Ginzburg-Landau theory the phase diagrams of Heusler alloys with inversion of exchange interaction are theoretically investigated. We used the expression for the Ginzburg-Landau functional from works [2,3]
*F*=α*m*^{2}/2+β*m*^{2}cosφ/2-γ*m*^{4}cosφ/4+δ_{1}*m*^{4}cos^{2}φ/4+δ_{2}*m*^{4}/4-ω_{1}*m*^{2}(*e*_{2}^{2}+ *e*_{3}^{2})/2-
ω_{2}*m*^{2}(*e*_{2}^{2}+ *e*_{3}^{2})cosφ/2+*a*(*e*_{2}^{2}+ *e*_{3}^{2})/2+*be*_{3}(*e*_{3}^{2}-3*e*_{2}^{2})/3+*c*(*e*_{2}^{2}+ *e*_{3}^{2})^{2}/4 (1)
where *m* is the normalized magnetization; φ is the angle between the magnetizations of two ferromagnetic sublattices; *e*_{2,3} are the linear combinations of the strain tensor; α, β, δ_{1}, δ_{2}, γ are the exchange interaction parameters; ω_{1}, ω_{2} are the magnetoelastic constants; *a*, *b*, *c* are the linear combinations of the 2^{nd}-, 3^{rd}-, and 4^{th}-order elastic moduli. After minimization energy with respect to the order parameters *m*, *φ*, *e*_{2,3} we constructed the phase diagrams on the (β-*a*) plane. The analysis shows that in general case twelve phases exist: three paramagnetic, three ferromagnetic and six antiferromagnetic phases. At certain values of functional parameters (1) we obtained the same sequence of phase transitions as in experimental work [1].
This work was supported by grants RF and CRDF Y2-P-05-19, RFBR 05-08-50341, 06-02-16266, 07-02-96029-r-ural, 06-02-39030-NNSF, 05-02-19935-YaF_a RFBR and JSPS, RF President MK-5658.2006.2 and Human Capital Foundation.
1. T. Krenke, M. Acet, E.F. Wasserman et al., Phys. Rev. B 72 (2005) 014412.
2. C. Kittel, Phys. Rev. 120 (1960) 335.
3. M.A. Fradkin, Phys. Rev. B 50 (1994) 16326. |