Magnetic Compton Scattering Studies of the Invar Alloy Fe3Pt*

C.J. Yahnke, G. Srajer, D.R. Haeffner, D.M. Mills, and L. Assoufid Experimental Facilities Division

Advanced Photon Source Argonne National Laboratory

9700 South Cass Avenue Argonne, IL 60439, USA

by a contractor of the U.S. Government under contract NO. W-31-104ENG-38 Accordingly, the U. S Government retains a nonexclusive. royalty-free license to publish or reproduce the fnIblished form Ot this contribution, or allow others to do SO, for

February 1995

'This work supported by the U.S. Department of Energy, BES-Materials Sciences, under contract no. W-31-109-ENG-38

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Magnetic Compton Scattering Studies of the lnvar Alloy FePt

C.J. Yahnke, G. Srajer, D.R. Haeff ner, D.M. Mills and L. Assoufid Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439

The magnetic Compton profiles (MCP) for both ordered and disordered Fe3Pt samples have been measured above and below their Curie temperature. These measurements show that the average moment per atom at room temperature is 2.8% f 0.1 for disordered Fe3Pt and 1 .& f 0.1b for ordered Fe3Pt. At temperatures above Tc, we measured a substantial reduction in the moment ( 0 . h f 0.1b for disordered Fe3Pt and 0.6~~ f 0 . 1 ~ ~ for ordered Fe3Pt) and a change in the shape of the MCP. These results indicate a decrease of the d-like moment on the Fe atoms in the disordered phase. The MCP for the ordered phase shows a change in the total moment, yet the momentum distribution is substantially different and cannot be described by this analysis.

Beginning with Guillaume's pioneer work in 1896,' lnvar alloys have been the subject of study by scientists and engineers for nearly 100 years. From Guillaume's initial work on Fe-Ni, the term "Invar" has grown to include a diverse range of systems - one of which is Fe3Pt. As with other lnvar alloys, Fe3Pt displays a small thermal expansion coefficient in a broad range about room temperature. To explain this phenomenon, previous theories have put forward mechanisms such as chemical disorder,2 latent antiferr~magnetism,~ weak ferromagneti~m,~ magnetic inh~mogeneity,~ or short-range-order effects.' Recent exper iment~~~~ have caused these theories to be put aside in favor of the phenomenological Weiss Z~rnodel .~ While this model has been refined and extended,'0*11~12 direct experimental verification of its validity has never been measured. Three excellent reviews of the experimental and theoretical work to date are given by Wa~sermann.'~*'~*'~

To examine the ferromagnetic low-spin state in Fe3Pt, magnetic Compton ~cattering''* '~~'~ (MCS) was used to measure the momentum distribution projected along the scattering vector of the unpaired (or magnetic) electrons in both ordered and disordered Fe3Pt. As MCS is an incoherent process, it lacks site specificity (in general) and is therefore sensitive to only the bulk magnetic ordering of a solid. Thus, the magnetic Compton profile (MCP) is nonzero only for ferro- (or ferri-) magnetically ordered materials. More importantly, however, MCS can shed light on the difference between the two magnetic states of this alloy predicted by the Weiss 2r model (rl and y2).

MCS, which yields information about the momentum distribution of the unpaired electrons, is an excellent test of various band models for spin-dependent wave functions. Such experiments, however, require a circularly polarized x-ray source to have a measurable magnetic contribution to the total cross section. While this contribution is an interference term between the charge and magnetic scattering, it is smaller than pure charge scattering by a factor ticulmoc2, where mo$ is the rest energy of the electron and ti0 is the incident photon energy. To perform these experiments, a high energy source of circularly polarized x-rays is used to maximize the magnetic scattering relative to the charge scattering. High energy (E>SGeV) synchrotron sources coupled with high field wigglers can provide sufficient quantities of high energy x-rays, but these x-rays are generally linearly polarized To accomodate our source requirement for circularly polarized x-rays, we have developed an x-ray phase plate made of single-crystal germanium designed to operate at discrete energies over the range 20-88 keV.Ig The (440) reflection was used to produce 65-keV x-rays with a 90% degree of circular polarization.

In addition to increasing the magnetic cross section and minimizing absorption effects in the sample, the 65-keV incident x-rays used in our experiment kept the scattering well within the impulse approximation. With this approximation;** the magnetic-Compton cross section for a solid, which is the difference of the total Compton cross section for opposite electron spin, can be written a~:'~9'~*'*

where ro is the classical electron radius, ko and k' are the magnitude of the incident and scattered x-ray wave vectors, and Pc is the degree of circular polarization. \y2 contains the scattering geometry (Fig. 1) and is defined as:

fiC Y, = &C( k, COS cx COS ~p - k' COS(C~ - O~))(COSC~ - 1)- m,c2

Here, o is the electron spin (+1/2 or -1/2), cz is the incident angle between the x-ray and the electron spin, and cp is the scattering angle. The momentum distribution of the unpaired electrons projected along the scattering vector (i.e., the magnetic Compton profile) is contained in J' (Jspin):

where the electron momentum density for a given spin orientation is given by n(p). To distinguish the magnetic scattering from the charge scattering background,

measurements are made with opposite sample magnetizations (8) and the results subtracted. The remaining profile is proportional to only the MCP. Alternatively, measurements can be made with elliptical (or circular) polarization of opposite helicity, with the measured profiles subtracted as above. The former approach is experimentally more practical, especially with soft, ferromagnetic samples. This is experimentally achieved by alternately applying a magnetic field through the sample. By constraining the sample magnetization and the incident and scattered wave vectors

to be coplanar (Fig. l), the measured profile depends only upon the scattering from the electron's spin (a).

Experiments were performed at the F2 wiggler beamline at the Cornell High Energy Synchrotron Source (CHESS). A top view of the experimental layout is shown in Fig. 1. A 15-mm-thick carbon filter and a 0.5-mm-thick copper filter were used to remove the lower energy (220) harmonic reflection from the phase plate and also to reduce the effects of heating upon it from the wiggler white beam. The 65-keV circularly polarized exit beam (Pc=O.9M.04) passed through a sealed Xe ion chamber, which acted as a beam monitor, before its incidence at 15' on the Fe3Pt sample. A scattering angle (9) of 165' was chosen to maximize the magnetic Compton cross section within experimental limits. This produced a Compton shift of 13.15 keV with the inelastic peak centered about 51.85 keV.

The sample was mounted in contact between the poles of an electromagnet and saturated with an applied field of 800 Gauss parallel to the sample face. For the high temperature measurements, the sample was placed in a furnace with a built-in electromagnet. The sample temperature was held to within +3K throughout the data collection.

Two sets of data were collected separately for opposite directions of the applied magnetic field in an ABBA sequence using a multichannel analyzer. One A or B step was approximately 2 min. long. Data were collected at room temperature using a germanium solid state detector (Ge SSD) at the rate of 450 countsk (in the electronic Compton peak) for 24 hours. At high temperature, the Ge SSD was moved closer to the sample to compensate for the anticipated loss in count rate due to the decrease in the sample's magnetization. With this geometry, the count rate (in the electronic Compton peak) was 1200 counts/s, which leads to a collection time (to achieve acceptable statistical error) of approximately 24 hours. The profiles were normalized relative to each other by counting versus a monitor (Xe ion chamber). The ordinate of the data has been transformed from energy to momentum in atomic units (a.u.) and folded about pz=O. The horizontal spacing between the points corresponds to the resolution of the Ge SSD (0.8 a.u.). The integral of the profile from -10 a.u. to +10 a.u. is normalized to the number of magnetic electrons or magnetic moment/atom (see Table I below). These values were determined relative to an Fe standard with a known moment.

Currently, there are very few calculations available for Fe3Pt to compare with experiment. In the absence of such calculations, the current MCPs will be compared with calculations for pure Fe by Wakoh and Kubo2' (Fig. 2). The validity of this analysis

is supported by the fact that Pt is, at best, weakly magnetic, while Fe is strongly ferromagnetic. Thus, one would expect Fe to dominate the magnetism of this alloy as it also dominates the chemical composition. This assumption is supported by the MCPs for both ordered and disordered Fe3Pt shown in Figs. 3 - 5. The agreement between Fe theory (when scaled to the correct total magnetic moment/atom) and the room temperature data (open circles) is reasonable.

Wakoh and Kubo performed their calculations using the augmented plane wave method (APW) at 55 E points in 1148th of the Brillouin zone for each spin-state. They used a total of 50 APWs with a maximum number of 6 4 values. The spin-dependent Compton profiles for three major sample orientations were averaged to find the MCP for polycrystalline Fe (Fig. 2). From this, they found that the magnetism could be explained by two components: a broad (in momentum space), ferromagnetic, d-like contribution and one that is due to the negative polarization of the s-p like states. The origin of the s-p polarization was found to be the s-d hybridization, which works to polarize the electrons in the opposite direction to that of the 3d electrons. In their calculations, Wakoh and Kubo show that this negative polarization gives rise to the "dip" in the MCP near the origin (0 a.u. I pz S1.25 a.u.).

In our analysis, we assumed that the MCP for Fe,Pt at a given temperature could be represented by a linear combination of these two components (plus a background). The results of this analysis form the dashed lines shown in Figs. 3 - 5. By integrating each component (d-like, s-p like) separately, the corresponding contribution to the total magnetic moment can be determined. By analyzing the change in each individual component, the difference between the two magnetic states can be examined. The results of this analysis are presented in Table I1 below.

As can be clearly seen from Fig. 5, this analysis is in poor agreement with the measured profile of the ordered sample at 490K. This indicates that the ordered system responds in a different manner to the excitation than does the disordered system. Previous Mossbauer measurements" confirm this general conclusion.

From Table 11, it is seen that there is a large decrease in the magnetic moment/atom of the d-like states. This change in the disordered phase occurs predominantly on the Fe sites as the MCP for the excited state is still well described by the Fe 3d distribution. If the change were instead occurring at the Pt sites, the measured MCP would be narrower than the theory. This can be attributed to the fact that the electrons closest to the Fermi surface (Le., 5d) on Pt are predominantly localized in a region further from the nucleus than the 3d electrons of Fe. Finally, it can be seen that s-p like polarization plays at best a minor role in this phase transition,

however, a more definitive statement is limited at this time by the statistical accuracy of the experiment.

In addition to being the first high-temperature MCP, these data are exciting as it may, for the first time, shed direct experimental evidence on the source of the lnvar effect. To develop a better understanding of this system, it will be necessary to evaluate the contribution of the Pt to the alloy's magnetism. Circular magnetic dichroism (near the Pt L-edge) would be an excellent means by which to probe this.

The magnetic properties of Fe3Pt above and below the Curie temperature were studied using MCS. In addition to measuring the MCP at elevated temperature for the first time, this study has shown that the ferromagnetic excited state of Fe3Pt has a greatly reduced moment. This supports Wassermann's hypothesis and the Weiss 2r model. More importantly, though, the nature of this reduction has, for the first time, been revealed as a sharp decrease of the d-like moment on the Fe sites in the disordered alloy. The nature of the reduction in the ordered alloy could not be explained within the context of this model.

The authors would like to thank E.E. Alp, J. Quintana, and the entire staff at the Cornell High Energy Synchrotron Source for their help. This work is supported by the U.S. DOE-BES under Contract No. W-31-109-ENG-38.

[l] C.E. Guillaume, Compt. Rend. 125, 235 (1896). [2] W.F. Schlosser, J. Phys. Chem. Solids 32,939 (1971). 131 T. Jo, J. Phys. Soc. Jpn. 40, 715 (1976). 141 E.P. Wohlfarth, Phys. Lett. 28A, 569 (1969). [5] M. Shimizu, J. Magn. Magn. Mater. 10, 231 (1979). [6] S.F. Dubinin, S.K. Sidorov, and E.Z. Valiev, Phys. Status Solidi B 46, 337 (1971). [7] E. Kisker, E.F. Wassermann, and C. Carbone, Phys. Rev. Lett. 58, 1784 (1 987). [8] S. Stahler, M. Knulle, G. Schutz, P. Fischer, S. Welzel-Gerth, and B. Buchholz, J.

[9] R.J. Weiss, Proc. Phys. SOC. London 82, 281 (1963). Appl. Phys. 73, 6063 (1 993).

[lo] M. Hillert, unpublished work discussed by P. Miodownik, Calphad 1, 133 (1 977). [l 11 W. Bendick, H. H. Ettwig, and W. Pepperhoff, J. Magn. Magn. Mater. 10, 214

[ 121 M. Matsui and S. Chikazumi, J. Phys. SOC. Japan 45,458 (1 978). [13] E.F. Wassermann, J. Magn. Magn. Mater. 100, 346 (1991). [14] E.F. Wassermann, Physica Scr. T 25, 209 (1989). [15] E.F. Wassermann, Festkorperprobleme - Advances in Solid State Phys. 27, 85

E161 M.J. Cooper, D. Laundry, D.A. Candwell, D.N. Timms, R.S. Holt, and G. Clark,

[I71 N. Sakai and K. Ono, Phys. Rev. Lett. 37, 351 (1976). [ 181 D.M. Mills, Phys. Rev. B 36, 61 78 (1 987). [19] C.J. Yahnke, G. Srajer, D.R. Haeffner, D.M. Mills and L. Assoufid, Nucl. Inst. and

[20] See for example, Cornpton Scattering, edited by B. Williams (Mc-Graw-Hill, New

1211 S. Wakoh and Y. Kubo, J. Magn. Mater. 5,202 (1977). [22] E.E. Alp, M. Ramanathan, S. Salem-Sugui Jr., F. Oliver, V. Stojanoff, and D.P.

(1 979).

(1987).

Phys. Rev. B 34,5984 (1986).

Meth. 347, 128 (1 994).

York, 1977).

Siddons, Rev. Sci. Instrum. 63, 1221 (1992).

Table I. Momentlatom (in Bohr maanetons) for Fe3Pt

Table 11. Momentlatom in Bohr mwetons) fo r individual comoonents of Fe&

Figure 1. Schematic of the experimental setup. The linearly polarized (LP) wiggler white beam is converted to a 65-keV circularly polarized (CP) beam by the phase plate. The degree of circular polarization was measured to be 90%. An incident energy of 65 keV was selected because it avoids K-shell fluorescence from the Pt in the samples and the Pb in the shielding. The incident beam (k,) makes an angle a=15" with the magnetization direction and an angle (p=165" with the scattered photons (k'). The scattered photons were analyzed by a germanium solid state detector (SSD).

Figure 2. MCP for pure Fe as calculated by Wakoh and Kubo, which shows the d-like component (dashed line), the s-p like component (dotted line) and their sum (solid line). The contribution for the core electrons is approximately 10% of the s-p like component and is thus neglected.

Figure 3. MCP for disordered Fe3Pt at room temperature (open circles) and 410 K (open squares). The solid line is the Wakoh-Kubo Fe theory and shows that it dominates the magnetism of the alloy. The dashed lines, as described in the text, represent fits derived from the individual components of this theory.

Figure 4. MCP for disordered Fe3Pt at room temperature (open circles) and 510 K (open squares). The dashed lines, as described in the text, represent fits derived from the individual components of the Wakoh-Kubo Fe theory. Note that the MCP at 510K is still well described by this model.

Figure 5. MCP for ordered Fe3Pt at room temperature (open circles) and 490 K (open squares). The dashed lines, as described in the text, represent fits derived from the individual components of the Wakoh-Kubo Fe theory. While the MCP at room temperature is well described by this model, the MCP at 490K is not.

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