Cubic Heusler Ni-Mn-Ga shape memory alloys are of special attention, because of their structural and magnetic properties. In this kind of Heusler alloys martensitic phase transitions happen in the ferromagnetic state.
To present the phase diagrams of the cubic ferromagnet we take an expression of free energy [1] that contains only order parameter components causing structural and magnetic transitions with the account of external stress along [110] axis. The dimensionless expression for energy in the case *Т*_{М}<*Т*_{С} when a structural transition occurs in a ferromagnetic state is
*F*=*T*(*e*_{3}^{2}+*e*_{2}^{2})/2+sgn(*b*)*e*_{3}(*e*_{3}^{2}-3*e*_{2}^{2})/3+(*e*_{3}^{2}+*e*_{2}^{2})^{2}/4+*B*(2^{1/2}*e*^{2}sin^{2}θcos2φ/2+ 6^{1/2}*e*^{3}(3cos^{2}θ-1)/6)+K(sin^{2}2θ+sin^{4}θsin^{2}2φ)/4+σ(6^{1/2}/6*e*_{3}+1/2ξsin^{2}θsin2φ)
Here *T* is the dimensionless temperature, ξ, *B* is the dimensionless magnetostriction constants, *K* is the dimensionless magnetic anisotropy constant, σ is the dimensionless stress, *е*_{2} and *е*_{3} are the combinations of the strain tensor, θ and φ are the polar and azimuthal angles of magnetization. In this work we consider the case of *B*>0 and *K*>0.
By minimization of free energy (1) with *е*_{2}, *е*_{3}, θ, φ we can obtain the following states.
1. The tetragonal phase T_{1} with magnetization || [001] axes.
2. The orthorhombic phase R_{1} with magnetization || [001] axes.
3. The tetragonal phase T_{2} with magnetization || [110] axes.
4. The tetragonal phase T_{3} with magnetization || [-110] axes.
5. The orthorhombic phase R_{2} with magnetization ∈ (001) plane.
The phase diagram with *b*<0 allows us to describe the experimental sequence of the phase transitions which is observed in [2].
This work was particially sponsored by Human Capital Foundation, RF and CRDF Y2-P-05-19, RFBR 05-08-50341, RFBR 06-02-16266, RFBR and JSPS 05-02-19935, RFBR and NNSF 06-02-39030, RFBR 07-02-96029-r_ural_a, RF President MK-5658.2006.2 grants.
[1] V.D.Buchelnikov et al., JETP, 92, (2001) 1019.
[2] V.V.Kokorin et al., Fiz. Tverd. Tela (Leningrad) 33, 1250-1252. |