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 Ni₂MnX (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=αm²/2+βm²cosφ/2-γm⁴cosφ/4+δ₁m⁴cos²φ/4+δ₂m⁴/4-ω₁m²(e₂²+ e₃²)/2-

ω₂m²(e₂²+ e₃²)cosφ/2+a(e₂²+ e₃²)/2+be₃(e₃²-3e₂²)/3+c(e₂²+ e₃²)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, δ₁, δ₂, γ are the exchange interaction parameters; ω₁, ω₂ 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.

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