MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

74 Chapter 3
by Mn +4 2
(S = 3/2). This gives pB = Σ nig 2 si (si +1) = 21. On the Gd/Ca (A)
sublattice, only Gd +3 2
(67% occupied, S = 7/2) has a moment giving pA = 42.
The Gd-Gd interaction is expected to be negligible, and therefore λ AA ≈ 0,
since the Gd 4f electrons are well localized. The Gd atoms are expected to
order due to the significant Gd-Mn interaction which is antiferromagnetic, so
λ BA < 0. In the case of Gd 0.67 Ca 0.33 MnO 3 , there exists a temperature where the
magnetization of the larger, but poorly ordered, Gd moments exactly cancels
that of the Mn sublattice. This temperature is called the compensation
temperature T Comp .
The compensation temperature T Comp can be used to estimate the
molecular field constant λ BA . The weakly coupled Gd approximately act like
free paramagnetic spins reacting to the internal (molecular) field caused by
the ordered Mn moments. In zero applied field this gives
2 2
MA = HmA µ B
pA /3kBT. The internal field on the A sublattice is related to λBA from H mA = λ BA M B . At T = T Comp , there is no net magnetization so M B + M A = 0.
2 2
Combining these relations gives λBA = -3kBTComp /µ B
pA .
Above TN , the susceptibility can be calculated analytically [101] giving a
hyperbola for 1/χ vs. T shown in Figure 5-5. The high temperature asymptote
is a straight, Curie-Weiss like, line which intersects the T axis at
2 4 2 2 2 2
ΘP = (µ B /3kB ) (pB λBB + 2pB pA λBA )/(pB + pA ). For Gd0.67Ca0.33MnO3 , λBA < 0 and
2
λBB > |λBA | so ΘP should be less than but close to 7λBB (µ B /3kB ) which is 1/3 of
the value that would be expected (TC of Mn) if no Gd moments were present.
In this model, the ferrimagnetic Néel temperature is given by
2 2
TN = pB λBB (µ B /3kB )[1/2 + √(1/4 + (pAλBA /pBλBB ) 2 )] [101]. For λBB > |λBA | this is
2 2
only slightly greater than the TC = pB λBB (µ B /3kB ) expected if the Gd moments
were absent. Combining this result with that of the last paragraph gives a