GIANT GRUNEISEN PARAMETER OF SPIN FLUCTUATIONS IN CHROMIUM

(1)

HAL Id: jpa-00229280

https://hal.archives-ouvertes.fr/jpa-00229280

Submitted on 1 Jan 1988

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

GIANT GRUNEISEN PARAMETER OF SPIN

FLUCTUATIONS IN CHROMIUM

Eric Fawcett

To cite this version:

(2)

JOURNAL DE PHYSIQUE

Colloque C8, SupplCment au no 12, Tome 49, dCcembre 1988

GIANT GRUNEISEN PARAMETER OF SPIN FLUCTUATIONS IN CHROMIUM

Eric Fawcett

Physics Department and Scarborough College, University of Toronto, Toronto M5S 1A7, Canada

Abstract. - Thermal expansion and bulk modulus data for pure Cr and for dilute antiferromagnetic Crloo-,Vx al-

loys, in the paramagnetic phase close to the NCel temperature, are used to determine the Gruneisen parameter,

ry

=

-d In TsF (w) /dw, TSF (w) being the temperature (energy) parameter characteristic of the spin fluctuations. In Cr the giant Gruneisen parameter, I?? = -155, is about three times larger than the value,

ry

= -55, in Cr

+

0.510.67 at.% V.

Inelastic neutron scattering in Cr provides clear evidence for spin fluctuations in the paramagnetic (P) phase [I, 21. The thermal expansivity ,B, and bulk modulus B, also show magnetic contributions up to at least twice the N6el temperature, TN = 311 K.

I describe elsewhere [3,4], where references are given to experimental work on

P ,

B, and the specific heat C, in Cr (and also in dilute Crloo-,V, alloys) how Gruneisen parameters, corresponding to the logarith- mic derivatives with respect t o volume of the characteristic magnetic energies in various temperature ranges, may be determined from the magnetic contributions to p, B, and C in Cr, measured by comparing Cr with the paramagnetic alloy Cr95V5. I focus atten- tion here on the temperature range above TN. There is some difficulty in principle with the use of Crs5V5 as a non-magnetic reference material in the P-phase, however, since inelastic neutron scattering shows that spin fluctuations, termed spin-density wave (SDW) paramagnons, occur in Crs5V5 itself [5]. Scattering due to SDW paramagnons is, however, about two orders of magnitude weaker than that in paramagnetic Cr close to TN, SO that in practice Cr95V5 is still a satisfactory

reference material.

We obtain [3, 41 from the magnetic free energy,

limit can be put on the magnitude of

I?;

[4]. The linear plot of Ap (t) versus AB (t) for t

>

1 gives [4], however, an accurate measure of the giant Gruneisen parameter, = -d In TSF (w) /dw = -155.

A clue t o the origin of the extraordinarily strong volume dependence of the spin fluctuations in the P-phase of Cr is provided by the observation that, in dilute Crloo-,V, alloys, the magnetic contributions Ap (t)

and AB (t) [6] above TN are significantly smaller than

in Cr, as shown in figures 1 and 2.

Unfortunately, data for both ,B and B on the same dilute Crloo-,V, alloy are not yet available. I have combined the /3 data [4] for Cr

+

0.5 at. % V (TN = 267 K) with the B data [6] for Cr

+

0.67 at.% V (TN = 245 K)

,

by plotting both against reduced temperature, t = T/TN. The resultant linear plot of Ap (t)

versus AB (t) at the same values oft, shown in figure 3,

gives, when the slope of the line is substituted in equation (2), with appropriate average values for BN and

n TN, the value,

I?+

= -55.

When seeking an explanation for the fact that the Gruneisen parameter :I? in the P-phase of Cr is about a factor 3 larger than in dilute antiferromag-

AF (t) =

f

[t (w)] ; t (w) = TITSF (w)

,

(1) the magnetic Gruneisen parameters,

A@ (t)

r:

= BN lim - a

rn

-

1 AB (t) lim

-

2-1 AC (t) +

-

-m

t-1 Ap ( t )

'

(2) in the approximation (which is valid for the characteristic temperature parameter TN (w) for Cr in the ordered phase [3]) that the spin-fluctuation characteristic temperature TSF (w) is linear in volume strain w, and that

f"

<<

f'

close to TN.

In principle,

:

?

I

and : I? may be determined by using Cr95V5 as reference material by defining the magnetic contribution to each thermophysical property X,

AX (t) =

X

(Cr) -X (Cr~gV5)

.

₍₃₎

In practice, AC (t) is so small for Cr that only a lower

Temperoture ( K)

Fig. 1.

-

The temperature dependence of the magnetic contribution Ap to the thermal expansivity defined as in

equation (3) for Cr and for Cr

+

0.5 at.% V.

(3)

C8

-

226 JOURNAL DE PHYSIQUE

0 103 203 500 400 500 600 703

Temperature T ( K 1

Fig. 2. - The temperature dependence of the bulk modulus of Cr, Crg5Vs, and two dilute antiferromagnetic Crloo-,V, alloys [6].

I

I 2 3 4

-ap( t NIO-~K-' )

Fig. 3.

-

Plot of the magnetic contributions AB (t) and

AD (t) to the bulk modulus and thermal expansivity, re-

spectively, with reduced temperature t as variable parameter for Cr

+

0.5/0.67 at.% V samples (see text).

netic Crloo-,V, alloys, one remarks a striking differ- ence between the inelastic neutron scattering in the two cases. The SDW paramagnon scattering seen [5] in Cr

+

0.5 at. % V is an order of magnitude weaker than, and of a quite different nature from, the so-called commensurate-diffuse (CD) scattering seen [I] in the P-phase of Cr.

The fact that the addition of V to Cr changes the nature of the magnetic excitations in the P-phase is undoubtedly related to the dramatic changes seen in the thermophysical properties. In the P-phase, the gi-

ant Gruneisen parameter for Cr indicating a strong magnetoacoustic coupling is evidently associated with the CD scattering. Its magnitude is a factor 3 smaller in dilute Crloo-,V, alloys, where the magnetic excitations are SDW paramagnons, Furthermore, the weak first-order N6el transition seen in Cr becomes a con- tinuous transition with the addition of as little as 0.2 at. % V [7, 81, while the strong attenuation peak of a longitudinal sound wave seen at the N6el transition in Cr is greaty reduced in dilute C ~ I ~ ~ - , V , alloys [2, 91.

I recommend t o theorists the problems of explaining why the CD scattering in the P-phase of Cr is so extraordinarily volume-dependent, and why its suppres- sion in Crloo-,V, results in a fundamental change in the nature of the Nee1 transition.

Endorsement

It is the author's wish that no agency should ever derive military benefit from the publication of this pa- per. Authors who cite this work in support of their own are requested to qualify similarly the availability of their results.

Acknowledgement

This work was supported by the Natural Sciences and Engineering Research Council of Canada.

[I] Grier, B. H., Shirane, G. and Werner, S. A., Phys. Rev. B 31 (1985) 2882.

[2] Fawcett, E., Rev. Mod. Phys. 60 (1988) 209. [3] Muir, W. C., Perz, J. M. and Fawcett, E., J. Phys.

F

17 (1987) 2431.

[4] Fawcett, E., J. Phys. F 19 (1988) in press. [5] Fawcett, E., Werner, S. A., Goldman, A. and

Shirane, G., Phys. Rev. Lett. 61 (1988) 558; Proc. Int. Conf. on Neutron Scattering, Greno- ble, Physica (1988) in press.

[6] de Camargo, P. C. and Brotzen, F. R., J. Magn. Magn. Mater. 27 (1982) 65.

[7] Fawcett, E., Roberts, R. B. and White, G. K., Europhys. Lett. 1 (1986) 473.

[8] de Camargo, P. C., Castro, E. P. and Fawcett, E., J. Phys. F 18 (1988) L209.