A high energy Compton scattering study of magnetocaloric HoAl2

Radiation Physics and Chemistry 96 (2014) 148–152

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Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem

A high energy Compton scattering study of magnetocaloric HoAl2 H.S. Mund a, Jagrati Sahariya b, B.L. Ahuja a,n a b

Department of Physics, M. L. Sukhadia University, Udaipur 313001, Rajasthan, India Department of Physics, Manipal University, Jaipur 303007, Rajasthan, India

H I G H L I G H T S








Measured first ever experimental Compton profile (CP) of HoAl2. Highlighted CP method for finding charge reorganisation in compounds. Computed first ever energy bands and DOS of HoAl2 using SPR-KKR method. Predicted charge transfer in HoAl2 using CPs and integrated DOS. Discussed state-of-art charge transfer method using differences in DOS.

art ic l e i nf o

a b s t r a c t

Article history: Received 12 June 2013 Accepted 25 September 2013 Available online 3 October 2013

We present the first-ever Compton profile of HoAl2 at an intermediate resolution of 0.36 a.u. using a 740 GBq 137Cs Compton spectrometer. Charge reorganization on the formation of compound is depicted by significant deviation between the experimental Compton profile of HoAl2 and superposition profile (deduced from individual Compton measurements of Ho and Al). Further analysis of experimental momentum densities of HoAl2 shows a charge transfer of 0.32 7 0.03e‾ from Al-Ho. The electronic occupancies obtained from the present measurements are very close to those computed using spinpolarized relativistic Korringa–Kohn–Rostoker method. Electronic properties of HoAl2 are also explained on the basis of energy bands and integrated density of states. & 2013 Elsevier Ltd. All rights reserved.

Keywords: X-ray scattering Intermetallic compounds Electronic structure

1. Introduction RAl2 (R¼Rare earth element) compounds have a cubic MgCu2 type structure and most of them show ferromagnetic behavior. As far as the nature of constituents is concerned, the rare earth elements are mostly magnetic while Al is magnetically neutral. Since the HoAl2 compound depicts magnetocaloric effects, it is a promising material in magnetic refrigeration. Moreover, HoAl2 is more environmental friendly as compared to other gases used in refrigeration. Among earlier studies, Millhouse et al. (1972) have reported temperature dependent elastic neutron diffraction of TbAl2 and HoAl2. They have investigated the ordered magnetic structures, form factors and saturation magnetic moments in these compounds. Rao et al. (1983) have studied the dependencies of lattice constants on temperature along with a study of the thermal expansion coefficients of CeAl2 and HoAl2. Using inelastic neutron scattering technique, Rhyne and Koon (1983) have reported inelastic neutron scattering to examine the spin dynamics of HoAl2 at 4 K. Schelp et al. (1984, 1985) have investigated the

n

specific heat and ground state spin wave excitation energies of HoAl2 under different magnetic fields and temperatures. Using the Faraday method, the temperature-dependent magnetic susceptibilities of RAl2 compounds (R¼Gd, Dy, Ho, and Er) have been reported by Kuvandikov and Shakirov (2004). Campoy et al. (2006) have discussed the magnetoresistivity of RAl2 (R¼Pr, Nd, Tb, Dy, Ho, Er) compounds while Oliveira et al. (2007) have employed a microscopic model Hamiltonian to explore the spin reorientation and magnetocaloric effect in HoAl2. Very recently, Chatterji et al. (2013) have studied the low energy nuclear spin excitations in HoAl2. It is well established that Compton scattering (CS) is a powerful tool to study the ground state properties of electrons in a variety of materials (Cooper et al., 2004; Ahuja, 2010). CS is sensitive to change in the ground state wave functions of materials. The Compton profile (CP), J(pz), is a one-dimensional projection of the electron momentum density onto the scattering vector (z-axis). Within the criteria of impulse approximation (Kaplan et al., 2003), J(pz) can be deduced from the double differential scattering cross-section. Mathematically, 2

Correspoding author. Tel.: þ 91 94 143 17048; fax: þ 91 294 2411950. E-mail address: [email protected] (B.L. Ahuja).

0969-806X/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.radphyschem.2013.09.012

d s ¼ Cðω1 ; ω2 ; ϕ; pz ÞJðpz Þ dΩdω2

ð1Þ

H.S. Mund et al. / Radiation Physics and Chemistry 96 (2014) 148–152

and 2

Jðpz Þ ¼ ∬ jχðpÞj dpx dpy :

ð2Þ

In Eq. (1), ω1 and ω2 are the energies of incident and scattered photons. The function Cðω1 ; ω2 ; ϕ; pz Þ depends upon the experimental set-up (Cooper et al., 2004), ϕ is the scattering angle and pz is the component of electron momentum along the scattering vector. Further, in Eq. (2), χ(p) is the electron wave function in the momentum space which is obtained by the Fourier transformation of the real space wave function. Since different valence bands have their characteristic Compton line shapes, transfer of an electron from one band to another is clearly reflected in the CPs. This aspect of CS gives us a reliable estimation of charge transfer in the compounds/alloys. CS is a unique probe which does not require a long electron-mean free-path as in case of the de Hass–van Alphen experiment. Moreover, applicability of CS is not limited to systems with low defects or impurities. CS, unlike photoemission or electron scattering experiments, is free from drawbacks like surface sensitivity (Cooper et al., 2004). To the best of our knowledge, any data on CS of HoAl2 is not yet available in the literature. In this paper, we present the first-ever experimental momentum density of HoAl2 using CS technique. To study the charge transfer on the formation of HoAl2 compound, we have also measured the CP of Al using the same Compton spectrometer. The charge reorganization in HoAl2 is also confirmed using theoretical calculations based on atomic-sphere approximation (ASA) as embodied in spin-polarized relativistic Korringa–Kohn– Rostoker (SPR-KKR) methodology.

2. Experiment The polycrystalline HoAl2 sample used in the present study was prepared by melting high purity (4 99.9%) constituent elements. For attaining proper homogeneity in the sample, the melting process was repeated three times in a water-cooled copper hearth using an arc furnace. This was followed by grinding of the HoAl2 buttons to get a uniform pellet of thickness 0.30 cm and diameter 2.00 cm. X-ray diffraction measurement was then undertaken to confirm the MgCu2 type crystal structure of the compound. The experimental set-up comprises of a 740 GBq (20 Ci) 137Cs Compton spectrometer and a high purity planar Ge detector (Ahuja et al., 2006, 2012a, 2012b). The collimation of the incident and scattered radiations led to a scattering angle of 160 70.61. The incident radiations of 661.65 keV were allowed to fall vertically on the sample mounted in the scattering chamber. Using 57Co and 133 Ba calibration sources, the electronic drift in the detection system was found to be negligible during the measurements. Both Al and HoAl2 samples were exposed to γ-rays for about 185 and 377 h, respectively, which led to an accumulation of 1.7  107 and 4.2  107 counts (integrated) under CPs. The resolution of the detecting system was 0.36 a.u. (Gaussian full width at half maximum) which is much better in comparison to the conventional 241 Am spectrometer [see, for example, Raykar et al., 2013]. The data processing included subtraction of background (which was measured separately for 94 h) as well as corrections for energy dependent detector efficiency, instrumental resolution, sample absorption, scattering cross-section, multiple scattering, etc. (Felsteiner et al., 1974; Timms, 1989). The instrumental resolution correction was restricted to stripping off the low energy tail from the Compton data. In the present data, contribution of multiple scattering (up to triple scattering) in the momentum range  10 to þ10 a.u. was found to be 16.32% for HoAl2, 7.7% for Ho (Ahuja and Sharma, 2005) and 0.1% for Al. The experimental CPs were

149

normalized to respective free atom (FA) CP in the momentum range 0–10 a.u. (Biggs et al., 1975).

3. Theory To get a clear insight on the electronic states in HoAl2, we have also computed the energy bands and density of states (DOS) using the SPR-KKR method (Gonis, 1992; Ebert et al., 2011). This method is based on a single particle Green's function within the ASA instead of electronic wave functions and eigen values. The ASA is a mean field approximation where the homogeneity of a disordered system restores its translational symmetry using an averaged quantity. We have treated the exchange and correlation effects using the local spin density approximation (LSDA) with the parameterization of Vosko et al. (1980). To achieve the self consistency (SCF), the k-space integration was performed using the tetrahedron method on a grid of 834k points in an irreducible part (1/48) of the Brillouin zone (BZ). The SCF mixing parameter was set to 0.2, which helped in achieving faster convergence. Accuracy of the energy convergence was 0.01 mRy.

4. Results and discussion In Fig. 1(a), we have plotted the energy bands of HoAl2 as computed using the SPR-KKR calculations. It can be seen that several energy bands cross the Fermi level (EF) which depicts a metallic behavior of the HoAl2 compound. The energy bands are mainly comprised of two groups of almost linear bands lying in the energy range of  3.15 to  2.23 eV and  0.48 to 0.43 eV. Since the SPR-KKR calculations involve relativistic effects, splitting of several energy bands is also quite evident. Differences in DOS (ΔDOS) of Al and Ho (calculated by subtraction of Al/Ho DOS in bulk Al/Ho environment from Al/Ho DOS in HoAl2 environment) are presented in Fig. 1(b). From Fig. 1(b), it is evident that ΔDOS of Al (in HoAl2 environment—in bulk Al form) is negative for 3s and 3p electrons. This shows a presence of larger number of valence electrons in bulk Al than in the HoAl2 compound and hence a feasibility of charge transfer from 3s and 3p states of Al after the formation of the compound. Moreover, it is seen that the overall amplitude of ΔDOS (up to EF) of Ho is positive, which depicts an excess of charge (number of valence electrons) in Ho on the formation of HoAl2. The ΔDOS for Ho shows more changes in the electronic states of 4f electrons than in the other states. To deduce the charge transfer quantitatively, we have computed the integrated DOS (IDOS) of Ho in bulk and in compound form up to EF (occupied level). This integration provides us the number of valence electrons in Ho in the HoAl2 environment and that in its bulk form. The difference between the IDOS values of bulk Ho and Ho within HoAl2 compound gives a quantitative value of the charge transfer. While going from bulk to compound environment, the respective changes in the IDOS for f and p electrons of Ho were found to be 0.24 and 0.14e–. For s and d electrons, the change in IDOS values was found to be –0.25 and 0.25e–, respectively. This leads to an overall excess of 0.38e– on Ho site after the formation of HoAl2 compound. Present experimental Compton data of HoAl2 and Al along with those available for Ho (Ahuja and Sharma, 2005) are shown in Fig. 2(a). It is worth noting that the CP of Ho (Ahuja and Sharma, 2005) was also measured earlier by our group using the same experimental set-up. The FA CP of HoAl2 (Biggs et al., 1975) and the superposition profile for HoAl2 are also shown in Fig. 2(a). The superposition profile J Sup Expt: of HoAl2 was calculated using the

150

H.S. Mund et al. / Radiation Physics and Chemistry 96 (2014) 148–152

22

4 2

20

HoAl2 (FA)

18

HoAl2 (Expt.)

J(pz )(e /a.u.)

16

Energy (eV)

0

-2 EF

HoAl2 (Sup.)

14

Ho (Expt.)

12

Al (Expt.)

10

Error

8 6

-4

4 2

-6

0 0

2

-8

4

6

10

8

pz (a.u.)

-10 W

L

X

K 5

k

Comp. JFA

J(pz)(e /a.u.)

4

_

0

DOS (states/eV f.u.)

-1 Al Al_3s Al_3p

-2

I

Error

3 2 1 0 -1 -2

2.5

0

1.5 1.0 0.5

2

4

6

Comp. JFA

I

0.0

J(pz)(e /a.u.)

-0.5

_

-1.0 -6

10

0.4 0.3

-8

8

pz(a.u.)

Ho Ho_6s Ho_6p Ho_5d Ho_4f

2.0

-1.5

Comp. - JExpt.

-4 -2 Energy (eV)

0

2

4

Fig. 1. (a) Energy bands of HoAl2 along high symmetry directions computed using SPR-KKR calculations and (b) differences in density of states (ΔDOS) of Ho (Al) within HoAl2 environment and that in bulk phase of Ho (Al). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Comp. - JExpt.

Error

0.2 0.1 0.0 -0.1 -0.2

0

2

4

6

8

10

pz(a.u.) following relation, Ho Al J Sup Expt: ðpz Þ ¼ J Expt: ðpz Þ þ 2J Expt: ðpz Þ:

ð3Þ

Al Here J Ho Expt: and J Expt: are the respective experimental Compton profiles of Ho and Al as shown in Fig. 2(a). Differences between the FA and absolute experimental CPs of HoAl2 are shown in Fig. 2(b). It may be noted that to incorporate the effect of experimental broadening, the FA profile was convoluted with the experimental resolution. As expected, the experimental profile is found to be in

Fig. 2. (a) Absolute experimental, free atom and superposition Compton profiles of HoAl2 compound along with absolute experimental profiles of Ho (taken from Ahuja and Sharma, 2005) and Al (b) difference between the free atom (FA) and absolute experimental Compton profiles of HoAl2 and (c) the differences between the experimental and superposition profiles of HoAl2 compound. Statistical error (7 s) is shown for a few points. Solid lines are drawn to guide the eyes. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

reasonable agreement with the FA profile in the high momentum region (pz Z3 a.u.). It is understandable due to dominance of core electrons in the high momentum region which are well-defined by

H.S. Mund et al. / Radiation Physics and Chemistry 96 (2014) 148–152

their respective FA wave functions. A reasonable agreement between the FA and experimental CPs in high momentum region shows the correctness of our data acquisition and implementation of various data correction routines as mentioned in Section 2. Very large differences between the FA and the experimental profiles in the vicinity of pz ¼ 0 a.u. (Fig. 2(b)) show a failure of the FA model in predicting the momentum densities of high Z compounds like HoAl2. Since the core electrons are not affected by the formation of compounds, the difference between the experimental and superposition profiles gives information about change in the valence electronic states on the formation of the compound. This means that in case the valence electronic states remain unchanged (i.e. there is no charge reorganization on the compound formation), there should not be any difference in the experimental and superposition profiles. To investigate the feasibility of charge transfer (CP based) between constituents of HoAl2, the differences Sup between J Comp Expt: and J Expt: are shown in Fig. 2(c). It is clear from Fig. 2 (c) that the superposition profile for HoAl2 is broader than its experimental profile. Since the experimental Compton profile of the compound does not concur with its superposition profile, the possible use of rigid band model in explaining the electronic properties of magnetocaloric compounds, like HoAl2, seems to be unacceptable. The broadening in the superposition profile leads to the possibility of charge transfer in HoAl2 on the formation of compound. In Fig. 3, we have presented the experimental valence CP (calculated by subtracting the convoluted free atom core profile from absolute experimental profile) of HoAl2 compound. Since the CP is sensitive to the electron momentum density built from the contribution of different electrons, the Compton line can be analyzed in terms of relative contribution from different sites by decomposing it into individual contributions of participating electrons. This aspect has been successfully used in determining the site specific spin moments in variety of magnetic materials like shape memory alloys (Sahariya et al., 2011), manganites and ferrites (Ahuja et al., 2011, 2012a, 2012b). In Ho–Al system, the electron momentum densities and hence valence CPs of Ho and Al are characteristically different. This particular character of CP facilitates fitting of individual experimental valence profiles to the experimental valence profile of the compound. We have used the following least square relation to fit the experimental valence

6

J(pz)(e /a.u.)

Table 1 Charge transfer determined from the analysis of valence band Compton profiles (CPs) of HoAl2 compound. Charge reorganization calculated from the integrated density of states using SPR-KKR is also included. Multiplicity of Al, as required in HoAl2 compound, is equal to 2. Definition

(a) Present experiment Al (valence band) Ho (valence band) Average charge transfer* (Al-Ho) (b) Present SPR-KKR based IDOS calculations n

Area under CPs Before fitting

After fitting

3.10e  6.30e 

2.81e  6.64e 

0.32 70.03e– (Al-Ho) 0.38e  (Al-Ho)

Average of 0.34e– (6.64–6.30e–) and 0.29e– (3.10–2.81e–).

Compton data of HoAl2 with that of Ho and Al, 2  Ho Al 2 S ¼ ∑ J HoAl Expt: ðpz Þ  mJ Expt: ðpz Þ  nJ Expt: ðpz Þ pz

ð4Þ

In Eq. (4), the summation index was taken up to pz ¼10.0 a.u. and the weight coefficients m and n were calculated for the best fit to the experimental CP of HoAl2. The area under the fitted component profile gives the corresponding number of electrons participating in the Compton phenomena. To calculate the charge transfer, we have taken the difference between areas of CPs of Ho and Al before and after the least square curve fitting. The synthesized (fitted) profile, as depicted in Fig. 3, shows a reasonable agreement with the experimental valence CP of HoAl2. In Table 1, we have presented the total number of valence electrons of Ho and Al before (in bulk form) and after (in HoAl2 environment) the curve fitting. The contributions of valence electrons of Ho and Al in the HoAl2 environment are 6.64 and 2.81e–, respectively, while the respective valence charges on Ho and Al before the fitting were 6.30 and 3.10e–. A systematic reorganization of charge on Al or Ho in HoAl2 environment shows an average charge transfer of 0.3270.03e‾ from Al-Ho as shown in Table 1. Thus the charge transfer derived from IDOS using SPR-KKR method (0.38e– from Al-Ho) is in reasonable agreement with that obtained from the present experimental data on momentum densities.

5. Conclusions

7 Ho (Valence)

5

Al (Valence)

4

Fitted

HoAl2 (Valence)

3 2 1 0

151

0

2

4

6

8

10

The experimental Compton profile of HoAl2 is found to be in disagreement with the experimental superposition profile, which rules out the possibility of rigid band model in such compounds. The experimental profiles of HoAl2 together with those of constituent Ho and Al show a charge transfer of 0.3270.03e– from Al-Ho. In this trend setting work, the charge transfer obtained from integrated density of states using SPR-KKR calculations (0.38e–, Al-Ho) is found to be in accordance with the experimental investigations. We also conclude that the Compton scattering technique can be treated as an excellent tool for determination of charge transfer/bonding in heavy magnetocaloric compounds, where other spectroscopic techniques may have limitations. To understand the magnetocaloric properties, temperature and field dependent magnetic Compton profiles using circularly polarized synchrotron radiations may be attempted.

pz (a.u.) Fig. 3. Decomposition of experimental valence Compton profiles of HoAl2 compound into the valence-band Compton profiles of Ho and Al. The area under the individual valence profile is equal to the number of corresponding electrons. Errors in the experimental profiles are within the size of symbols used. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Acknowledgements Authors are thankful to the group of Prof. H. Ebert for providing the SPR-KKR package. They are also grateful to SERB, New Delhi, India for providing financial support (Grant No. SR/S2/CMP-40/2011).

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