CRITICAL DYNAMICS AND DIPOLAR INTERACTION IN EuO

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CRITICAL DYNAMICS AND DIPOLAR

INTERACTION IN EuO

F. Mezei

To cite this version:

JOURNAL DE PHYSIQUE

Colloque C8, Supplement au no 12, Tome 49, d6cembre 1988

CRITICAL DYNAMICS AND DIPOLAR INTERACTION IN

EuO F. Mezei

Hahn-Meitner-Institut, Pf. 390128, 0 - 1 000 Berlin 39, F. R. G.

Abstract.

-

Recent neutron scattering studies of the critical behaviour of isotropic ferromagnets revealed the apparent contradiction between a good agreement with dynamic scaling at T = T, and drastic deviations from scaling at T

>

Tc. In EuO the experimental findings are consistent with latest theoretical results taking into account dipolar interactions.

The ferromagnetic-paramagnetic phase transition at the Curie point of simple isotropic ferromagnets probably is the most common second order phase tran- sition and a lot of effort has been devoted to its un-

derstanding. The study of static and dynamic scaling properties is crucial in this respect. However, it be- came clear by now that just in this particular case the real critical behaviour can only be observed in a very restricted sense. This is due to what we can call the "dipolar paradox"

.

Namely, the well known demagne- tization effects of magnetostatics (in other words dipo- lar interactions) inevitably become very substantial as the intrinsic susceptibility X : diverges a t the critical wavevector q = 0 on T -+ T,. This simply means that the magnetic fields produced by the critical fluctua- tions tend t o reduce these fluctuations and lead to an apparent susceptibility:

where the X: = C/ (K:

+

q2) Omstein-Zernicke form

has been assumed with C being a constant and nl =

5-I

the inverse correlation length. m is the demagne- tization factor, and the so called "dipolar wavevector" q d = m characterizes the relative strength of the dipolar effects. Equation (1) implies a fundamental breakdown of the scaling hypothesis, since rep- resents a second characteristic length beyond

<.

Thus earlier efforts to establish scaling behaviour at the fer- romagnetic Curie point were rather too optimistic.

Experimentally q, can be calculated from the mea- sured macroscopic susceptibility and n1. For EuO, which is considered to be the best model Heisenberg ferromagnet, qd=0.15

A-'

(see [l] and Refs. therein) is paradoxically so substantial that there is virtually no room left for the true exchange critical regime. (For comparison in Fe q,=0.045

A-'.)

Until recently the dipolar anomaly expressed by equation (1) escaped ob- servation, since in usual critical neutron scattering ex- periments around the forward scattering direction the demagnetization factor m is identically zero. Namely, for the transverse fluctuations t o which neutrons cou-

ple, the magnetization direction M l q stays in the quasi-infinite planes of the wave with wavenumber q. In contrast, around Bragg peaks in single crystals neu- trons can also couple t o the longitudinal fluctuations M

11

q with m = l, and equation (1) has been actu- ally verified in a recent neutron polarization analysis experiment [2].

With finite and constant m, instead of the usual scaling form X : = q2g(nl/q), we can write equa- tion (1) as a "two parameter scaling'' law X, =

q2gL

(nl/q, nl/qd). The same way, instead of normal

dynamic scaling, the behaviour of the relaxation rate

I'

can be expected to be given as

For a given sample this "two parameter scaling" im- plies nothing experimentally relevant, since there are only two parameters (g and T ) anyway. Relevant is if the function f; can be predicted theoretically, as it is the case in the trivial example of equation (1).

Experimentally the dynamics of the transverse fiuc- tuations could only be studied by now, lacking good enough single crystals. Two, rather contradictory fea- tures emerged for both Fe and EuO [l, 3-51: (a) at T = Tc there is no appreciable deviation from the exchange scaling prediction r ( q ) X q5/' in the accessible and

critically relevant q range of qd/8 <q

< 0.3 A-', and

(b) at T

>

Tc there are huge deviations from the scal- ing predictions in the range qd/8 <q

<

qd, as shown in the scaling plot in figure 1. (Intuitively, point (b) illus- trates that with respect to the spin-conserving Heisen- berg exchange interaction, which leads to l? (g) -+ 0 on q + 0, any spin non-conserving interaction, such as

dipolar or spin-orbit, becomes dominant a t small q by giving rise to l? (g = 0) # 0 at T

#

T,).

For quite a few years these observations remained without theoretical explanation. Finally, E e y and Schwabl recently succeeded to evaluate the dynamic effects of dipolar interactions by a mode coupling method [8]. Their results for the function

:

f

in equa- tion (2) reproduces point (a) and are quantitatively consistent with the T > Tc data in EuO, cf. figure l.

The new theoretical results also resolved another controversy. At T = T, triple-axis spectrometer scans

C8

-

1538 JOURNAL DE PHYSIQUE

Fig. 1.

-

Scaling plot of the temperature dependent relax- ation rates of the transverse ( m = 0) fluctuations in EuO [6].

rc

is the relaxation rate a t Tc=69.3 K. Exchange scal- ing theory would require that all data points fall on the lowest line (RP) of reference [7]. The other lines are re- sults of the latest dipolar theory [8]. The data presented were taken in the q range 0.02

-

0.15

A-',

and /cl 0.64 ( T / T ~ - ~ ) ~ . ~ ~

A-'.

a t q

2

0.15

A-'

[5] showed non-Lorentzian inelas- tic lineshapes in agreement with predictions of critical theories [g], while Neutron Spin Echo (NSE) scans at much smaller g's produced Lorentzian lineshapes 141. This is illustrated in figures 2 and 3 by the most pre- cise data obtained by now [6]. (The q = 0.3

W-'

data in figure 3 also show that this wavenumber is already

Fig. 2. - Small wavenumber lineshapes a t T = Tc as di- rectly measured in the time domain by Neutron Spin Echo scans [6]. The lines show the exp

(-r

(g) t) (Lorentzian) lineshape averaged over the rather broad q resolution of the spectrometer, about 0.006

A-'

HWHM. In the inset representative error bars are only indicated once on each curve.

Fig. 3.

-

High resolution triple-axis r~eutron spectrome- ter scans in t h e w domain [6]. The dashed and continu- ous lines show the lineshape predicted by critical theories (e.g. [g]) and the Lorentzian one, respectively, both con- voluted with the instrumental w resolution function (with 0.015 meV HWHM the corrections are hardly detectable).

too large to show undistorted critical behaviour). This lineshape crossover a t Tc has now been shown to be also due to the dipolar ineractions [l.O].

In sum, due to the strong dipolar (i.e. demagneti- zation) effects the critical behaviour in isotropic ferro- magnets violates both static and dynimic scaling. Lat- est theoretical results give gratifyingiy proper account of the observed dynamics in the canonical Heisenberg model system EuO. Note that in Fe the agreement is less good [ll], and other interaction.^, e.g. spin-orbit pseudodipolar effects might also be effective [12].

[l] Mezei, F., J. Magn. Magn. Maier. 45 (1984) 67. [2] Kotzler, J., Mezei, F., Gorlitz,

I).

and Farago, B.,

Europhys. Lett. 1 (1986) 675.

[3] Mezei, F., Phys. Rev. Lett. 49 (1982) 1096. [4] Mezei, F., Physica B 136 (1986) 417.

[5] Boni, P. and Shirane, G., Phys. Rev. B 33 (1986) 3012.

[6] Mezei, F., Farago, B., Hayden, S. M. and Stirling, W . G., Physica B, in press.

[7] Resibois, P. and Piette, C., Phgs. Rev. Lett. 24

(1970).

[8] Frey, E. and Schwabl, F., Phys. Lett. A 123

(1987) 49.

[g] e.g. Folk, R. and Iro, H., Phys. Rev. B 32 (1985) 508.

[l01 Frey, E., Schwabl, F. and Thoma, S., Phys. Lett.

A

129 (1988) 343.

[l11 Frey, E.. and-~chwabl, F., 2. Phrys. B 71 (1988)

355.