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MODEL FOR MAGNETOELASTIC INTERACTIONS
IN CHROMIUM AND ITS AFM ALLOYS
E. Castro, P. de Camargo, G. Marques
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C8, Supplkment au no 12, Tome 49, dkcembre 1988
MODEL FOR MAGNETOELASTIC INTERACTIONS IN CHROMIUM AND ITS
AFM ALLOYS
E. P. Castro, P. C. de Camargo and G . E. Marques
Departamento de Fisica, UFSCar, P.O. Box 676, 13560, SBo Carlos, SP, Brazil
Abstract. - A theoretical model for the ultrasonic attenuation and elastic constants in chromium and its alloys, near the Neel transition is proposed. The model is based on the thermodynamics of a magnetic system under applied acoustic field. The calculated attenuation and longitudinal elastic constant show a good agreement with the experimental values.
The peculiar itinerant incommensurate antiferro- magnetic (AFM) state in chromium and its dilute al- loys have an extensive literature on experimental and theoretical aspects, however, many basic questions still remain unresolved [I].
At present, none of the available theories explain the observed ultrasonic attenuation near the Neel temper- ature, neither for chromium nor for its alloys. It is the aim of this paper t o propose a model with a simple mechanism which describes resonably well, not only the ultrasonic attenuation, but also the elastic con- stant. Experimental data is shown for chromium, Cr-
0,67 % V and Cr-1,5 % V samples.
tion V.J,=Bp,
/
a t which defines a current of mag- netic order. Current J, contains a drift term, (-pH),
plus a diffusion term ( D Vp,),
where p (D) is the mo- bility (Diffusion constant).The solution of the wave equation, together with the above considerations, is found by taking into account only linear terms. The elastic constant 4 1 and the
ultrasonic attenuation a are then given by:
Its is well known by neutron diffraction that and wc
chromium and its AFM alloys form a itinerant spin- w r-
a = - R W
density-wave (SDW) which is transversaly polarized 2
'0 r 2 + ( 2 L + P ) (2)
for temperatures between 123 K and 311 K. wo
The magnetic structure consists of domains of the type (Qi, Sj)
,
where Qi = (27r/
a) (1 f 6) is a wave vector perpendicular t o the spin directions Sj and par- allel t o the cube axis.Ultrasonic studies [2, 31 revealed that only longitudi- nal stress waves parallel t o Q are significantly affected by the magnetoelastic coupling around TN. There- fore, we consider only one dimensional interaction [4] between the elastic deformation and the AFM-SDW system.
From a macroscopic thermodynamical point of view, we propose a mechanism which takes into account the interaction of an ultrasonic longitudinal stress plane wave with the SDW based on the steps: i) the per- turbing elastic wave modulates the magnetic order- ing, i.e., the ultrasound modulates the staggered mag- netic field (H) and its correspondent magnetization (M) a t temperatures close to
TN
; ii) the constitutive equations for the stress, a (E, H ),
and magnetization, M ( E , H),
where E is the strain, define the coupling between magnetic and elastic systems; iii) Poisson's equation, V.M= -p,, defines a density of carriers of magnetic order p,, together with the continuity equa-where, R = e2
/
2 ~ and : r ~= ~1-
Ivd /voI
p = density of materialvo = ultrasonic velocity on PM state w = ultrasonic frequency
x
= (SM/
bH), magnetic susceptibility e =-
(bM/
a&),, magnetoelastic constantv d = -pH drift velocity
CII
= longitudinal elastic constant along [loo] in the PM statep, = density of carriers of magnetic order. These are the usual form for a wave propagating in a dissipative medium. Here, the lattice itself is not considered t o dissipate energy, but the magnetoe- lastic coupling with the SDW system is what causes
0
the energy losses. The frequencies w, = pp,
/
x
and wo = v:/
D represent the relaxation due to local stag- gered field Hand frequency of fluctuations due to gra- dient of carriers, respectively. The expressions (1) and (2) were examined t o find the best parameters w, andw o SO that the attenuation (a) vs. r would resem- ble the experimental result a us. temperature, close
JOURNAL DE PHYSIQUE
Fig. 1. - Left side shows attenuation and righ side Cll. Chromium (a), 0,67 % V (b), 1,5 % V (c). Crosses experimental data and continous line the theoretical calculation. Arrows show a temperature interval of 10 K and attenuation in (b) shows 5 K.
(XI
the t o TN. The next step is to define a proper scale whichwould convert ( r ) on a Kelvin scale. This was done as-
suming that the local field (H) would be proportional to IT - TNI
,
close to TN. Once the temperature scale is found, the velocity is calculated by using the same parameters.Figure 1 shows experimental data [5, 61 together with theoretical results on attenuation and on elas- tic constant Cl1 as a function of T - TN for chromium and the alloys.
The experimental values show deviations as T gets away from TN, because the proposed mechanism is good only within limits where the stress wave can mod- ulate the magnetic order.
Table I shows the fitting parameters wo and w, with
TN
for chromium and alloys.It is worth notice that wo is the most sensitive pa- rameter indicating that the diffusion coefficient D is the contribution which dominates the behaviour close to TN.
Table I. - Parameters for Crl-,Vx .
It is striking that from D = 2 x.10~ m2/s for Cr the diffusion coefficient drops to 12,3 m2/s for the al- loy 0,67 % V. This can be explained by pinning effects due to the vanadium random distribution. The lat- ter increase on D for larger vanadium concentration is attributed to the lower temperature where TN occurs. In conclusion, we have proposed a simple mechanism which describes both ultrasonic attenuation and elas- tic constants for chromium and its antiferromagnetic alloys
.
An estimate of the behaviour of attenuation and elastic constant for other compositions can be made by interpolation of wo and w,.
Acknowledgments 1.5
%v
3.00 x lo3 4.00x
10' 1.23 x lo3 165 Parameters w, (MHz) wo (MHz) D (m2/s) TN (K)The authors wish to thank the financial support of brazilian agencies CNPq and FAPESP.
[I] Fawcett,
E.,
Rev. Mod. Phys. 60 (1988) 210. [2] de Camargo, P. C. and Brotzen, F. R., J. Magn.Magn. Mater. 27 (1982) 65.
[3] Palmer, S.
B.
and Lee, E. W., Philos. Mag. 24(1971) 311.
141 Muir, W. C., Fawcett, E. and Perz, J. M., J.
Magn. Magn. Mater. 69 (1987b) 133.
[5] de Camargo,
P.
C. and Brotzen, F. R., J. Magn.Magn. Mater. 27 (1982) 65.
[6] Castro,
