Journal of Magnetism and Magnetic Materials 31-34 (1983) 295-296 295

S P A T I A L C O R R E L A T I O N O F M A G N E T I S A T I O N I N T H E P A R A M A G N E T I C P H A S E S O F I R O N A N D N I C K E L

P.J. B R O W N +, H. C A P E L L M A N N +, J. D E P O R T E S *, D. G I V O R D * and K.R.A. Z I E B E C K ÷

+ lnstitut Laue-Langevin, 156X Centre de Tri, 38042 Grenoble C~dex, France • Laboratoire Louis N~el, CNRS-USMG, B.P. 166X, 38042 Grenoble C~dex, France

The diffuse scattering of polarised neutrons with polarisation analysis has revealed the presence of ferromagnetic short range order in the paramagnetic phases of iron and nickel. Unlike the residual long range correlations which occur close to T c, the short range order arises from the itinerant nature of magnetic electrons.

1. Introduction

The magnetism of transition metals, in which the magnetic carriers are itenerant electrons, contained in partly filled bands and participating in the Fermi surface, is still a controversial topic. There is no general agreement as to which fluctuations are responsible for the transition between the magnetically ordered and paramagnetic states, or even on the nature of the paramagnetic state itself [1-3]. Experimental evidence exists for a qualitative difference in the paramagnetic phases of itinerant and localised systems.

In inelastic neutron scattering measurements [4,5] have shown the existence of propagating spin wave excitations of wavelengths up to 20 ~, well above T c in both iron and nickel. Paramagnetic scattering of polarised neutrons from itinerant magnetic systems demonstrates the existence of short range order far above T c [6].

2. Experiment and results

The paramagnetic scattering of neutrons presents a direct method of studying the space and time correla- tions of electron spins. If polarisation analysis is used a

-2s ~-20

Fe- $atT'. SI //

-15

-1o f

0 O O o O ~ o • | ! !

O CA -s ]

Fig. 1. Paramagnetic scattering observed in a single crystal of Fe-5 at% Si, along [hhO] at 1273 K.

unique separation of the magnetic component from other contributions to the scattering can be obtained. The wavevector dependence of the pararnagnetic scattering M ( Q ) from iron in both the u and ~, phases and from nickel were measured. The a phase of iron was stabilised at these temperatures by the addition of 5 at% Si. The wavevector dependence of the paramagnetic scattering measured [7] on a single crystal at 1273 K, i.e. 1.25Tc, is shown in fig. 1. The principle features are an enhancement of the scattering in the forward direction and around the nuclear Bragg peaks and a low level of scattering observed towards the zone boundary. These results are in agreement with the original measurements of total scattering from iron [8].

The spatial correlations giving rise to the enhanced forward scattering are ferromagnetic in nature and ex- tend over distances up to -- 15 A. Significant reduction in the observed scattering as a function of increasing temperature was observed only at the smallest scattering vectors namely _< 0.4 A - ~. Thus, the influence of resid- ual long range magnetic order which occurs in the vicinity of T c effects primarily the small wavevector components. The characteristic length describing the short range magnetic order was therefore found to be only slightly dependent on temperature. This character- istic length describing the short range order must not be confused with the correlation length which appears in the Ornstein-Zernicke description of long range order.

At small wavevectors corresponding to the correlated regions the observed scattering was found to be pre- dominantly at low frequencies much less than k T c. A

series of energy scans at different wavevectors throughout the zone and extending upto 100 meV k T c

confirmed that the experiment effectively integrated over all thermal fluctuations of the system. At large wavevec- tors, towards the zone boundary the scattering was found to remain at a low level up to the highest energy transfers employed i.e. 100 meV. Integration of the paramagnetic response throughout the first Brillouin zone enabled the moment per Fe atom to be established as 1.3#B, essentially temperature independent. Care should be taken when interpreting this value since it

0 3 0 4 - 8 8 5 3 / 8 3 / 0 0 0 0 - 0 0 0 0 / $ 0 3 . 0 0 © 1983 N o r t h - H o l l a n d

296 P.J. Brown et aL / Magnetic correlations in paramagnetic Fe and Ni

20

15

10

0

0

s

• | - F e 1 3 2 0 K

o Ni 700 K

I 0.5

+ +

++

( I I

'1.0 '1.5

Fig. 2. Paramagnetic scattering observed in 7-Fe and nickel.

represents an average over the characteristic time of the neutron scattering experiment -- 10-13 s and does not contain components of the magnetisation density which fluctuate faster than this.

Similar results to those described above were ob- tained on pure iron, in both the a and "r phases [9]. Ferromagnetic correlations are observed to characterize the paramagnetism of the -/-phase as well as that of the a-phase, stable for instance at 1320 K (fig. 2). These results are in contrast with the belief that "r-Fe should order antiferromagneticaUy. The average Fe moment deduced is 1.3(1)/~ a for the a-phase and 0.9(1)# B for the -/-phase. Finally, measurements on pure nickel show the same general features as in iron. Results obtained with a polycrystaUine sample at 700 K (1.15Tc) are shown in fig. 2. The enhancement of the scattering occurs only below 0.4 A - i suggesting that the length of correlations is larger in nickel than in iron. However, the lack of accuracy, related to the small magnetic signal in nickel does not allow us to deduce the correlation length for nickel. Measurements on a single crystal around the Bragg reflection [111], up to 1.5T c, show the scattering

at small wavevector to decrease as temperature in- creases. Nevertheless, as in iron, significant short range order is shown to persist beyond 1.5T c.

3. D i s c u s s i o n

The present results indicate that the magnetic prop- erties of alpha iron and nickel above T c are dominated by strong ferromagnetic correlations. They indicate how the exchange splitting of itinerant electrons in the 3d band may be maintained by short range order in the disordered magnetic phase. The large values of "effec- tive" moments obtained in static susceptibility measure- ments can be attributed to magnetic correlations which persist far into the paramagnetic region. The existence of correlated regions enables an understanding of how short wavelength spin waves can propagate above T c. Furthermore, the general features of the observed scattering indicate conclusively the inadequacies of the Heisenberg model often applied to iron. Any model must consider the itinerant nature of the electrons re- sponsible for the magnetism in an iron and nickel, and account for the short range order which fluctuates on a time scale < h ( k T c ) - i . Faster fluctuations of the spin density upto h / W s where W is the band width may account for the low level of scattering observed at large wavevectors. The results presented here are a general feature observed in all itinerant magnets and are in agreement with models proposed recently for such sys- tems at finite temperatures.

Finally, it is well known that the magnetic order in ~-Fe cannot be obtained since the fee-phase is not stable at low temperatures. The observation of ferro- magnetic correlations suggest that if v-iron were stable at low temperatures it would order ferromagnetically. Any description of Invar effect systems, for which -/-Fe is a prototype, must take into considerations the pres- ence of these ferromagnetic spatial correlations.

R e f e r e n c e s

[1] H. Capellmann, Z. Phys. B34 (1979) 29. [2] V. Korenmann, J.L. Murray and R.E. Prange, Phys. Rev.

B16 (1977) 4032, 4048, and 4058. [3] T. Moriya, J. Magn. Magn. Mat. 14 (1979) 1. [4] H.A. Mook and R.M. Nicklow, Phys. Rev. B7 (1973) 336. [5] J.W. Lynn, Phys. Rev. Bll (1975) 2624. [6] P.J. Brown, J. Deportes, D. Givord and K.R.A. Ziebeck, J.

Appl. Phys. 52 (1981) 2074. [7] P.J. Brown, H. CapeUmann, J. D6portes~.D. Givord and

K.R.A. Ziebeck, J. Magn. Magn. Mat. 30 (1982) 243. [8] M.K. Wilkinson and C.G. Shull, Phys. Rev. 103 (1956) 516. [9] P.J. Brown, H. Capellmann, J. Deportes, D. Givord and

K.R.A. Ziebeck, J. MaSh. Magn. Mat. 30 (1983) in press.