Magnetic interaction and the critical dynamics above the curie point

Volume 47A, number 2

PHYSICS LETTERS

11 March 1974

MAGNETIC INTERACTION AND THE CRITICAL DYNAMICS ABOVE THE CURIE POINT S.V. MALEEV Leningrad Nuclear Physcis Institute, USSR Received 21 January 1974 It is shown that near Tc, where 4ir~~‘ I magnetic interaction completely change the long-wave critical dynamics of the ferromagnets and the new dynamic critical exponent is = (5 — — 1.

Usually, critical dynamics of ferromagnets is investigated under the assumption of pure exchange interaction. This interaction conserves the total spin of the system and, therefore is insufficient for an explanation of the relaxation of the uniform magnetization and the long-wave absorption of the electromagnetic field. In the cubic ferromagnets the main interaction, which violates this conservation law, is the dipolar magnetic interaction. This interaction is anisotropic and above the Curie point the spin Green’s function contains terms perpendicular and parallel to the momentum k. Owing to the long-range character of the dipolar forces this two parts are connected by the Krivoglaz relation [11: G1~(k,w)G1(k,w)[l +w0 G1(k,w)]~

~

(1)

~

and w0 G1(k, w) = 4ir~(k,w) where ~(k, w) is the usual retarted magnetic susceptibility. If4ir~(O,O)~ 1 the difference between 4irX G1 and1 G1~is small. In this temperature range the magnetic interaction may be considered as the the difference between G 1,G perturbation. If 1 and is large. In the region 4ir~ 1 G11 w~ 1 and the perturbation theory for the magnetic forces is wrong. If we use for G1 the Ornstein-Zernike relation we obtain from (1), that in the region 1 the difference between G1 andand G11 ‘rexists forT~)/T~). the momenta which are lower 2~ 4~r~ R~,(Rc= ar~is the correlation lenght = (T thanThe q0critical = a~(w0/T~)’i dynamics is determined by the value of the damping constant: ~‘

~‘

~

Fk

1

=

—1

~G

.

.

—1

1 (k,O) lim (iw)

[XLL

(w)

XLL

(O)]

w-~O

where = dSk/dt and [21. HeLkobtained that

4irx ~ 1) XLL

is the generalized susceptibility. Huber evaluated F0 in the exchange region (

w~T~1r-3v(1_7~)/2 w~ ~ r~1. In the dipolar region the main contribution to the L gives the magnetic interaction and we have: L°

N112 ~

k~e~ S~k

2. (3) 1(k1 Sk1 )k~ The susceptibility XLL is the analytic continuation of the corresponding temperature function. For this function we have diagrams [31which are shown on the fig. 1 where the upper lines correspond to G 1 and the lower lines to G~. The main contribution to XLL comes from the intermediate momenta k12 q0. Now we can analyse the critical dynamics in the dipolar region by the method of work [4]. If the momentum k> q0 we have the usual exchange dynamical scaling with the critical exponent Ze = (5 77)12. But if k
—

—

111

Volume 47A, number 2

PHYSICS LETTERS

~

II March 1974

± 2

2

Hg. I.

w1~(~/w~)1~4f (ka)~ 1 q0 Fk

=

~ k ~

K.

q0a)(Ka)~C~°f(k/K)

(4)

w~(T~/w0)f2T,

K ~

k

where J~ f2 1. We see that F0 decrease if r tends to zero. It is not surprising because the uniform4iry niagnetizaI the tion is the order parameter and the decreasing of F0 is the usual critical slowing down. In the region quantity F 0 has the maximum.

References 111 MA. Krivoglaz, Liz. Tverd. Tela, 5 (1963) 3437 121 DL. Huber, J. Phys. Chem. Solids 32 (1971) 2145. 131 V.G. Yaks, Al. Larkin and S.A. Pikin. Zh. Eksp. i Teor. Liz., 53 (1967) 1089. (Soviet Phys. JETP. 26 (1968) 647).

141

112

S.V. Maleev. Zh. Eksp. i Teor. Fiz.,65 (1973) 1237.