CRYSTAL-FIELD EXCITATIONS IN THE LIGHT RARE EARTHS - Rare Earth Magnetism: Structures and Excitations - page 358

Fig. 7.11. Experimental measurements of the first harmonic of the
magnetization on the hexagonal sites in Pr, deduced from the intensities
of neutron-diffraction peaks at 1.5 K, compared with a MF calculation
for the J =4ion.

where the matrix element

O 2 | J η | M 22 ≡ < 1 a | 1 a > = − < 1 a | 1 a > = − 10 ,

in Pr. ∆ ξ differs from ∆ by the same amount, but with the opposite sign.
At the incipient ordering wave-vector Q along the η -axis, the excitations
are purely transverse or longitudinal, J ξ or J η modes. The critical ratio
R 0 , defined by eqn (7.1.6), for the optical longitudinal mode at Q is then
determined by

R 0 ( t 11 )= R 0 (0)∆ / ∆ η ( t 11 ) .
Hence the application of the stress alters the critical ratio, and it attains
the threshold value 1 when

T 11 = {

1 − R 0 (0) } ∆

c γ N/V, (7 . 4 . 4)

M 22 B γ 2

where c γ N/V =4 c 66 . With the following values of the parameters;
R 0 (0) = 0 . 92, ∆ = 3 . 52 meV, B γ 2 10 10 N/m 2 ,

the effective ( J = 1)-model predicts that the critical stress necessary
for inducing magnetic ordering in Pr at zero temperature is T 11 =

12 meV, and c 66 =1 . 6 ·

− 1 . 5

kbar. However, the | 3 s > -state lies just above the magnetic excitons