Account of biquadratic exchange in substituted ferrimagnets
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OF
SUBSTITUTED S.
M.
BIQUADRATIC
EXCHANGE
IN
FERRIMAGNETS Zhilyakov
and
E.
P.
Naiden
UDC 538.245
In s e v e r a l c a s e s , the calculated t e m p e r a t u r e dependences of sublattice magnetizations have been reconciled with the r e s u l t s of neutron m e a s u r e m e n t s by taking into account the biquadratic t e r m in the exchange e n e r g y in a n t i f e r r i m a g n e t s and f e r r i m a g n e t s . S a t i s f a c t o r y r e s u l t s have been obtained for NiO, MnO [1], lithium f e r r i t e , and YIG [2]. The biquadratic-exchange concept was used to calculate the t e m p e r a t u r e dependence of the constant of the magnetic c r y s t a l l o g r a p h i c anisotropy, since knowledge of the sublattice magnetic moments is r e quired in this case. In p a r t i c u l a r , the magnetic c r y s t a l l o g r a p h i c anisotropy has been studied, in the
YzFes_xGaxO12 [3], Biz-2xCazxFe~-xVxOi2[4], Li0.sFe2.5_xAlxO4 [5], and other systems. Common to all these studies are a few general features: 1) the same biquadratie-exchange parameter (2/ N 0.04) was used, regardless of the structure and composition; 2) compositions displaying anomalous temperature dependences of the magnetization were fpund [6]; 3) the calculated sublattice magnetizations were not compared with experiment. It was shown in [7] on the basis of a neutron-diffraction s t u d y o f the t e m p e r a t u r e dependence of the sublattice magnetic moments that the biquadratic-exchange p a r a m e t e r Y in the Li0.sFe2.5_xAlxO4 s y s t e m depends strongly on the composition, so that the biquadratic t e r m need not be taken into account in l~he exchange e n e r g y in this s y s t e m at aluminum contents above x = 0.4-0.5. As Neel showed [8], the appearance of an anomalous t e m p e r a t u r e dependence for the spontaneous magnetization is due to the o c c u r r e n c e of an intrasublattice exchange interaction in addition to the intersublattice exchange interaction. The condition f o r the appearance of these dependences in a spinel having a single type of magnetic cation is • --< 1--a ~ ~ 1+~'
(I)
where X and # are the relative n u m b e r s of magnetic cations in t e t r a h e d r a l and oetahedral positions, r e spectively, and ~ and fl a r e m o l e c u l a r - f i e l d coefficients a s s o c i a t e d with interactions of cations within sublattices. This condition is found f r o m an analysis of the transcendental equations d e s c r i b i n g the t e m p e r a t u r e dependences of the sublattice magnetic moments near the Curie t e m p e r a t u r e and near absolute zero. A simple calculation shows that account of biquadratic exchange as in [2-5] cannot in principle yield anomalous m a g n e t i z a t i o n - t e m p e r a t u r e curves. The m o l e c u l a r fields, according to [2], a r e
MA-M8 H A ~ nM B
1 + 7S 2 MAo'MBo] ,
H B = n M A (1 '---~S 2 y A "MB ~ , | MAO.MBO]'
(2) (3)
where n is the m o l e c u l a r - f i e l d coefficient corresponding to the intersublattice interaction; y is the
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