Solid State Communications, Vol. 31, pp. 703-704. Pergamon Press Ltd. 1979. Printed in Great Britain. ON FERROMAGNETISM AND FERROELECTRICITY COEXISTENCE IN SYSTEMS WITH ELECTRON-HOLE PAIRING V.K. Dugayev, V.I. Litvinov and K.D. Tovstyuk Semiconducting Materials Science Department, Academy of Science of UkSSR, Chernovtsy, Zhovtneva 5, 274001, USSR (Received 3 April 1979 by E.A. Kaner) The example of two-band system with interband hybridization unstable with respect to charge density wave (CDW) formation has been considered. It has been shown that at the appearance of CDW with real order para- meter (ferroelectric transition), magnetic moment induced by the spon- taneous electric field arises in the electron system. IT IS KNOWN that in two-band systems with electron- hole coupling, ferromagnetism is quite possible provided CDW and spin density wave co-exist, since presence of corresponding order parameters A s and A t removes spin degeneration in the electron spectrum of initial semi- metal system [ 1]. That is why on the phase diagram the ferromagnetic is that region of thermodynamical stab- ility of the mixed state A s 4: 0, A t :# 0. The dielectric phase transition with CDW formation is studied in [2] for the A4B6 type materials, since A4B6 semiconductors are close to semi-metals of V¢ Ee is gap at k = 0, mz and m± are components of bare effective mass, Vz and V± are real constants. The spectrum consists of two bands twofold degenerated on spin. The Coulomb interaction in the self-consistent approximation is known to bring about the exciton instability. This interaction taken into account, there appear some additional terms in the Hamilton±an corres- ponding to the non-zero A s (the matrix parameter A t is assumed to have lower critical temperature than As). Now the Green function is eOoE k 0 G-I(K, 60) = 0.9 - - Ek ~ --As --iKzVz i(Kx --iKy)V± ~i(Kx +±Ks)V± --As--iKzV z -- As + iK~ V~ i(Kx -- iK, )ViN~ -i(Kx+iKv)V±w+Ek - - A s o i K z V z ) 0 w+E~ / (2) group. In [2] the simplified model is used in which spin is not taken into account. Once spin-orbit interaction is small this simplification is quite justified. However taking into account spin in a model which closer corresponds to reality, as will be shown below, leads to principally new consequences, namely, the existence of spin-orbit terms in the Hamiltonian makes it possible to remove spin de- generation while only CDW (and no SDW) appears in the system provided CDW is corresponded by the real order parameter. Let us consider the Dimmock model as a more adequate one of electron spectrum ofA4B6. Energetical matrix, built in Luttinger-Khon basis is shown [3], and one particle spectrum has the form EI,2 = -+(Ek 2 +Kz2Vz 2 +K±2VI2) v2 where = + K: + 2 2mz 2m±' and electron spectrum is the system of four non- degenerate by spin bands El,2 o = + (Ek 2 + Kz 2 Vz 2 + K± 2 I112 31- As2 +_ 2KI VIAs)I/2 (3) where o = ]', $ corresponds to the sign + or - under root in (3). The basic wave functions in (2) are taken as real. Magnetic moment is defined as follows M = -- il~n ~ Sp,Gu(K, t = -- 0) (4) Ki where G, is matrix by spin Green function, i is the band index and/aB Bohr magneton. The Green function from (2) being substituted into (4) (the chemical potential assumed to be within the conductivity band) one obtains 703