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Magnetic properties of the β- and β′-ytterbium hydride phases
Journal of Alloys and Compounds 327 (2001) 11–16
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Magnetic properties of the b- and b9-ytterbium hydride phases W. Iwasieczko, Monika Drulis, H. Drulis* Trzebiatowski Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 1410, 50 -950 Wrocl«aw 2, Poland Received 2 April 2001; accepted 17 April 2001
Abstract Samples of the b-ytterbium hydride phase with compositions 2.2,H / Yb#2.71 were prepared and their magnetic properties studied. Measurements of the magnetization vs. temperature were carried out in the range 1.75–300 K. The magnetization plots proved the presence of the maximum at around 4 K and the Curie–Weiss like behaviour at high temperatures. The magnetic moment per Yb atom exhibits an almost constant value of 3.8560.05 m B for various compositions across the b-ytterbium hydride phase. This effective moment is smaller than the ionic Hund’s rule moment of 4.54 m B expected for trivalent Yb 31 ions and clearly indicates that the Yb atoms stay in an intermediate valence state. The average valence of Yb ions n (Yb)52.7260.02 calculated from magnetic data is independent on the hydrogen concentration and lie between the expected values for the corresponding pure valent Yb 21 and Yb 31 ions. For the first time, the magnetic properties of the b9-ytterbium hydride phase are also measured and discussed as well. The obtained results indicate that the ytterbium atoms in the cubic b9-hydride phase are trivalent like the light lanthanide elements in their hydride phases. 2001 Elsevier Science B.V. All rights reserved. Keywords: Intermediate valence; Magnetic moment; Ytterbium hydrides
1. Introduction The thermodynamical properties of a number of metallic compounds based on Ce, Sm, Eu and Yb cannot be explained on the basis of pure valent rare earth (RE) ions [1,2]. In this class of compounds states of two different occupations of the RE 4f shells have comparable energies so that transitions of electrons between RE 4f shells and band states caused by hybridization interactions are possible. In this situation the ground state of the system will contain RE sites in an intermediate valence (IV) state. It is a quantum mechanical mixture of states corresponding to two different occupations of the 4f shell (valences), leading to a non-integral average number of f-electrons per atom. Experimentally, an intermediate valence state manifests itself, for example, as characteristic anomalies in the specific heat, and magnetic susceptibility [3,4]. The dual nature of the f electrons, an itinerant at low temperatures and a localized at high temperatures in an IV state is an extremely intricate feature. One of the standard methods to measure the degree of valence mixing in intermediatevalent materials is to investigate the effective magnetic *Corresponding author. Tel.: 148-71-343-5021; fax: 148-71-3441029. E-mail address: [email protected] (H. Drulis).
moment. The method might be correct particularly when the thermal energy, kT, is higher than the hybridization energy and the system performs real temporal fluctuations of the valence [5]. Ytterbium metal reacts with hydrogen gas to form a dihydride, a-YbH 2 , phase with an orthorhombic structure. Magnetic susceptibility studies [6] have indicated the divalent, Yb 21 , non-magnetic 4f 14 state of the ytterbium ions in this compound. When the hydride composition is higher than H / Yb.2.2 the system undergoes a phase transition from a-orthorhombic to the two b and b9-cubic crystallographic structures which differ from each other in the lattice constant only [7]. The b9 phase is metastable and exists only in the high temperature range [8]. Since, in all known cubic hydride phases the rare earth elements are trivalent one can expect that also the orthorhombic–cubic transition in the ytterbium hydride will be accompanied by an Yb 21 →Yb 31 valence transition. Recent investigations of the electronic structure of YbH x hydride samples performed by the X-ray line shift (XLS) method have shown that ytterbium changes its valence from 2 in the YbH 2 to a non-integer value 2.66 in the b-cubic phase [9]. To get a more comprehensive and closer insight into the electronic structure of the Yb–H hydride phase the low temperature heat capacity [10] and magnetic susceptibility measurements were studied [11]. The b-
0925-8388 / 01 / $ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 01 )01406-2
W. Iwasieczko et al. / Journal of Alloys and Compounds 327 (2001) 11 – 16
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our previous results [13]. This time we focus our attention on the magnetic moment value interpretation in the framework of the ytterbium intermediate valence (IV) state. For the first time, the magnetic properties of the b9-ytterbium hydride phase will be shown and discussed.
2. Experimental
Fig. 1. XRD patterns for three representative compositions of the ytterbium hydride system.
cubic ytterbium hydride samples are paramagnetic at room temperature with a characteristic maximum being clearly revealed around 4 K. However, no magnetic ordering in the neutron diffraction studies has been found even at the lowest temperatures [12]. In this paper we present new investigations of the magnetic properties of the ytterbium hydrides and discuss
The ytterbium hydride–deuteride samples with composition H / Yb.2.2 were prepared by direct reaction of gaseous hydrogen with ytterbium metal as it is described in Ref. [7]. We assumed that isotope effects in the hydride– deuteride samples are negligible from the magnetic properties point of view. The hydrogen concentration in the samples was determined volumetrically as the amount of gaseous H absorbed during synthesis per formula unit. X-ray diffraction (XRD) analysis (Fig. 1) have shown that the sample with hydrogen concentrations 2.2,H / Yb,2.49 belong to the two-phase range of the Yb–H phase diagram where the a-orthorhombic and b-cubic phases are in equilibrium. The percentage contents of the b-phase in the two-phase sample were calculated from the appropriate XRD line intensity ratio. In turn, the appropriate b-phase compositions were calculated assuming that the a-hydride phase which appears in XRD patterns has a composition of YbH 1.85 [14]. In the sample with compositions H / Yb5 2.49 the X-ray patterns have revealed only the b-cubic phase. The characteristics of all samples are depicted in Table 1. To obtain a sample of the b9-ytterbium hydride phase which exists only at temperatures .2508C [8], a special quenching procedure has been performed during the hydride synthesis. Two samples with effective compositions D/ Yb52.27 and H / Yb52.35 were prepared through rapid quenching of the specimen from 3008C to room temperature. The XRD pattern showed that the sample
Table 1 Crystallographic analysis of the ytterbium hydrides samples Sample
Phase contents b
b-Phase a composition
a Lattice constant ˚ (A)
Normal synthesis YbD 2.26 YbH 2.30 YbH 2.39 YbH 2.49 YbD 2.53 YbH 2.57 YbD 2.71
0.33a10.67b 0.22a10.78b 0.09a10.91b b b b b
YbD 2,46 YbH 2.43 YbH 2.44 YbH 2.49 YbD 2.53 YbH 2.57 YbD 2.71 a Phase composition
5.177 5.187 5.188 5.182 5.187 5.187 5.170 ˚ a Lattice constant (A)
Quenched hydride samples YbD 2.27 0.2b h 10.8b9 YbH 2.35 0.43b h 10.57b9 a b
bh
b9
bh
b9
YbD 2.35 YbH 2.48
YbD 2.25 YbH 2.25
5.178 5.192
5.234 5.249
a- and b9-phase compositions: H / Yb51.85 and 2.25, respectively were accepted from P–T–C diagrams [8,14]. In fractional units.
W. Iwasieczko et al. / Journal of Alloys and Compounds 327 (2001) 11 – 16
Fig. 2. Magnetic susceptibility versus temperature and magnetization dependence on the magnetic field (inset) at 1.75 K for two representative samples consisting of the b-ytterbium hydride phase.
with D/ Yb52.27 consists of 80% of the b9-ytterbium ˚ whereas the hydride phase with lattice constant a55.234 A sample with H / Yb52.35 consists of 57% b9-hydride ˚ The rest of the sample was phase with a55.249 A. identified as the b h -hydride phase with the lattice constants ˚ and 5.192 A, ˚ respectively. X-ray analysis of a55.178 A data are shown in the bottom part of Table 1. Magnetic measurements were performed in the temperature range 1.75–300 K using a Quantum Design magnetometer.
3. Results and discussion
3.1. b -Ytterbium hydrides The magnetization vs. temperature measurements were carried out in the range 1.75–300 K for seven samples
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with compositions of H / Yb52.26, 2.30, 2.39, 2.49, 2.53, 2.57 and 2.71. In Fig. 2, for the sake of clarity, the data for the two border compositions which are representative for the rest of the samples under study are shown. The magnetization plots proved the presence of maxima at around 4 K which are only slightly dependent on the hydrogen concentration and the Curie–Weiss like behaviour at high temperatures. This general shape, involving a maximum at some T5T max followed by Curie–Weiss behaviour at high T and the lack of magnetic ordering may be regarded as very typical of IV metallic materials. The observed low temperature susceptibility anomalies at around 4 K were recently analysed in terms of the f–d hybridization model where a two-peak density of states on the Fermi level was suggested [13,15]. In this paper we are mainly focus on the magnetic moment values of the Yb atoms determined from the high temperature (range 150– 300 K) magnetic susceptibility measurements. The obtained results are collected in Table 2. The magnetic moment per Yb atom calculated from the experimental data (column 3 of Table 2) exhibits an almost constant value of 3.8560.02 m B for the various compositions across the b-ytterbium hydride phase. This effective moment is smaller than the ionic Hund’s rule moment of 4.54 m B expected for trivalent Yb 31 ions (with J 5 7 / 2 and the Lande factor, g 5 8 / 7) and clearly indicates that the Yb atoms stay in an intermediate valence state. The average valence of Yb ions n (Yb)52.7260.02 calculated from our magnetic data lie between the values expected for the corresponding integer valent Yb 21 and Yb 31 ions. The magnitude of the ytterbium valence obtained in these studies is very close to n (Yb)52.6660.02 determined in K line shifts investigations reported several years ago [16]. We have also confirmed our previous observation that the ytterbium valence is independent of the hydrogen concentration in the b-hydride phase in spite of the hydrogen participation in the conduction band depopulation process. The electronic structure of the host metal of any hydride is profoundly affected by the presence of hydrogen. The
Table 2 Magnetic properties and valence state of the Yb atoms in the ytterbium hydride phases
Hydride sample YbD 2.26 YbH 2.30 YbH 2.39 YbH 2.49 YbD 2.53 YbH 2.57 YbD 2.71
Effective mag. moment meff (m B )
Mag. moment / b-phase meff / f.u (m B )
n (Yb) valence state
3.2060.03 3.4860.03 3.6260.03 3.8860.03 3.8060.03 3.8160.03 3.8760.03
3.8660.02 3.9260.02 3.8060.02 3.8860.02 3.8060.02 3.8160.02 3.8760.02
2.7260.02 2.7660.02 2.7060.02 2.7460.02 2.7060.02 2.7060.02 2.7360.02
Quenched hydride samples YbD 2.27 YbH 2.35
3.9660.03 3.1760.03
bh | 0 | 0
b9 4.4360.02 4.4360.02
bh 21 21
b9 | 31 | 31
W. Iwasieczko et al. / Journal of Alloys and Compounds 327 (2001) 11 – 16
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Fermi level in pure ytterbium metal (Yb 21 , 4f 14 ) is well within the 5d6s bands and two electron states are occupied. When ytterbium is hydrogenated up to the dihydride, YbH 2 (a-orthorhombic phase), two hydrogen atoms per unit cell add two extra bands below the Fermi level and also two extra electrons to the system (kind of a chemical doping) [17]. In terms of the anionic (H 2) hydride model these bands with the capacity to hold four valence electrons are filled up with two electrons supplied by hydrogen and the other two by the ytterbium metal conduction band. As a result, the original 5d6s state (conduction band) of the parent metal is completely depleted and the ytterbium dihydride phase becomes a non-magnetic insulator. When the system due to the hydrogen concentration increase over 2, undergoes the phase transition from the orthorhombic to the cubic hydride phase, a new extra hydrogen-like valence band below the Fermi level should appear [17]. To fill up this new band with electrons the conduction band (probably 5d) must be, first of all, refilled (populated) with an extra electrons. The only way to do this is the 4f 14 →4f 13 5d 1 (Yb 21 →Yb 31 ) electronic transition. Simultaneously, with the hydrogen content increasing over H / Yb.2 one may expect a continuous decrease of the conduction electron density implying that each H atom depopulates the conduction band by one electron. The depopulation process of the conduction states within the b-hydride will be continued according to the following sequence (YbH 2 )4f 14 → 4f 13 5d 1 1 H x → (4f 13 5d 12x 1 H 2 x ) (where x . 0.2)
(1)
Finally, in terms of the rigid band model, for the hypothetical composition YbH 3 (x51), the system should be a magnetic (Yb 31 ) insulator again. However, as shown by the experimental data there is not such a simple, linear relationship between the hydrogen content and the ytterbium valence as appears from Eq. (1). The experimentally observed Yb valence is limited to |2.72 across the bhydride phase over the hydrogen concentration range from H / Yb52.44–2.71. A similar phenomenon has been observed in Ce-based IV compounds. It has been reported [18] that in all metallic Ce-based systems the Ce valence is limited by the value n (Ce)#3.25. The same observations have been made in Sm- and Tm-based IV compounds where Sm and Tm valences of v52.6–2.75 have been observed [19,20]. We think that for Yb, as for Ce, Sm and Tm, the valence in IV metallic systems is always ‘trapped’ at a certain value in order to reach a thermodynamically stable intermediate state. The n (Yb) behaviour under hydrogen indicates that this mechanism prevents the 4f 14th level being pushed more than necessary to above EF . Therefore, Yb-based metallic-like hydrides with n (Yb)5 31 cannot exist at all. In Yb the higher valence state is magnetic and every Yb 31 state corresponds to the creation of one electron in the sd band as well as one magnetic ion.
This proves that during the a→b phase transition only about 0.72 electrons are supplied by the 4f state to the sd band and only these electrons are available for hydrogen to form hydridic, H 2 , ions in octahedral sites of b-hydride lattice. It is obvious that the energy of the 4f 13 5d 1 state (arbitrary notation) will be situated very close to or at the Fermi level and the Yb ions will remain in the intermediate-valent state due to a strong hybridization with conduction electron states. The formal relative concentration of 4f 14 and 4f 13 5d 1 configurations are given by experiment as 0.28 and 0.72, respectively.
3.2. b9 -Ytterbium hydride phase The b9-ytterbium hydride phase is metastable and exists only in the high temperature range [7,8]. It is not possible to obtain a pure b9-phase at room temperature because it disproportionates into the orthorhombic dihydride and the b-phase hydride when cooled from high temperatures. Our P–T–C investigations shown in Fig. 3 indicate that the b9-phase appears on the desorption isotherms as a singlephase in the narrow composition range H / Yb52.25–2.29. The in situ XRD studies [14] have confirmed the PTC results and have additionally shown that the b9-phase has a ˚ (Fig. 1). fcc cubic crystal structure with a55.255 A In this paper the magnetic properties of two samples with effective compositions YbD 2.27 and YbH 2.35 consisting of the b9-phase have been studied. Their crystallographic analysis data are shown in Table 1. The magnetic properties as a function of temperature and magnetic field
Fig. 3. Pressure composition isotherms of Yb–H system at high temperatures.
W. Iwasieczko et al. / Journal of Alloys and Compounds 327 (2001) 11 – 16
Fig. 4. Magnetic susceptibility versus temperature and magnetization dependence on the magnetic field (inset) at 1.75 K for the quenched ytterbium hydride samples consisting of b9-phase. To emphasise the differences the susceptibility of pure b-ytterbium hydride phase is also shown.
are illustrated in Fig. 4 and Table 2. There are no anomalies at low temperatures as we saw previously for the b-hydride phase samples. However, below 50 K there is a rapid increase in the susceptibility and a Curie divergence at low temperatures. The low temperature magnetisation curves (inset of Fig. 4) are highly non-linear and look almost ferromagnetic, although they do not saturate in a high field. Having the magnetic data for two samples with different compositions and taking into account their quantitative X-ray phase analysis we were able to affirm that the b9-phase has the composition YbH 2.25 and is a paramagnetic material with almost all (9565%) ytterbium atoms in the Yb 31 valence state. Simultaneously, as a big surprise, we found that the accompanying b-like phase with the composition of YbH 2.35 – 2.48 which we will h call ‘quenched’ or ‘high temperature b -phase’, is totally diamagnetic with ytterbium atoms in the Yb 21 valence state. In this case we probably deal with another isostructural cubic hydride phase which is not exactly the same as the cubic b-phase. It is particularly unusual if we bear in mind that the ‘normal’ b-phase samples we discussed earlier, are magnetically active and have only about 28% of the Yb atoms present as diamagnetic Yb 21 ions. From theoretical band structure calculations of Ce–H and La–H hydrides [21,22] it appeared that octahedral hydrogen (H o ) atoms are almost neutral and are weakly bound to the metal atoms. The weak bonds for H o compared to H t (tetrahedral) were manifested by the pressure–temperature–composition relation [23]. Probably, in the high temperature ranges octahedral hydrogen atoms due to their high thermal energy and fast diffusion through the lattice, form the metal–hydrogen bonding band whose energy levels lie higher than the Fermi energy level, E1s . EF . In such a case appropriate Yb, probably 5de g -like states, are
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also pushed up from the Fermi level. Consequently an electron transfer from the 4f 14 state to the 5d conduction bands usually induced by octahedral hydrogen will not occur and all Yb atoms remain in the Yb 21 valence state. Our observations support earlier reports, which suggested that at high temperatures the cubic divalent ytterbium dihydride phase has sometimes been observed [24]. Contrary to the b h -phase, the b9-ytterbium hydride phase exhibits a magnetic behaviour characteristic for normal light lanthanide trivalent elements. This feature can be expected because the b9-ytterbium hydride has the same crystallographic structure as this group of hydrides and its ˚ is close to that expected for lattice constant a55.255 A trivalent ytterbium hydride estimated from the linear extrapolation of lattice constants across the rare-earth series.
4. Conclusion Whereas the electronic structure of stoichiometric trivalent rare earth hydrides is more or less well understood, there is considerable confusion in the intermediate valence systems where the role of the 4f state must be considered. Usually the specific microscopic IV features are deduced from the coincidence of the narrow 4f band and the Fermi level and this is often applied to interpret the available experimental data. The interpretation of the low energy experimental data, including susceptibility, heat capacity or resistivity data on IV compounds, is based on the assumption that the extremely narrow 4f band is situated in the vicinity of the Fermi level. Using the 4f band width D4f and the 4f level position EF 2 E4f as adjustable parameters, it is possible to achieve agreement between experimental data and model calculations when the relative 4f level population accepts any fixed value from the interval 0 # n rf # 1, i.e. in Yb based IV compounds, any ytterbium valence from the interval 2#v(Yb)#3 can be observed. Unfortunately, at this moment the confrontation of such an approach any with theoretical electron band structure is impossible because, as far as we know, the band structure calculations completely neglected the 4f electrons. The atomic-like 4f electron states are thought not to contribute significantly to the metal–hydrogen bonding. Indeed, in Ce hydrides the Ce 4f electrons and valence of Ce are hardly affected by hydrogen. On the other hand, as we have shown in this paper, hydrogen causes a tremendous valence change in Yb hydrides. This indicates that further theoretical efforts should be made in the field of band structure calculations for the intermediate systems. Also, special attention should be paid to answering the general question of why the average valence of Sm, Tm and Yb in many IV compounds is ‘trapped’ at around v52.6–2.7 and what is the origin of the valence trapping in metallic systems.
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References [1] P. Wachter, in: K.A. Gschneidner, L. Eyring, G.H. Lander, G.R. Choppin (Eds.), Handbook on the Physics and Chemistry of Rare Earth, Vol. 19, North-Holland, Amsterdam, 1994, p. 177. [2] L.L. Hirst, Phys. Cond. Mat. 11 (1970) 255. [3] B.R. Coles, D. Wohlleben and further references, in: Magnetism, V, Shul (Ed.) Academic Press, New York, 1973, p. 3. [4] M.B. Maple, L.E. DeLong, B.C. Sales, in: K.A. Gschneider Jr., L. Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earth, Vol. 1, North Holland, Amsterdam, 1978, p. 797. [5] P. Schlottman, Phys. Rep. 181 (1989) 1. [6] J.C. Warf, K.J. Hardcastle, Inorg. Chem. 5 (1966) 1736. [7] K.J. Hardcastle, J.C. Warf, Inorg. Chem. 5 (1966) 1728. [8] H. Drulis, M. Drulis, W. Iwasieczko, N.M. Suleimanov, J. LessCommon Met. 141 (1988) 201. [9] V.A. Shaburov, A.E. Soviestnov, Yu. L Smirnov, A.W. Tiunis, H. Drulis, M. Drulis, Fiz. Twerd. Tela 40 (1998) 1393. [10] M. Drulis, H. Drulis, B. Stalinski, J. Less-Common Met. 141 (1988) 207. [11] W. Iwasieczko, M. Drulis, H. Drulis, J. Alloys Compd. 259 (1997) 62.
[12] G. Andre, private communication [13] W. Iwasieczko, M. Drulis, P. Gaczynski, H. Drulis, J. Magn. Magn. Mat. 205 (1999) 255. [14] W. Iwasieczko, H. Drulis, R.M. Frak, J. Alloys Compd. 180 (1992) 265. [15] M. Drulis, W. Iwasieczko, P. Gaczynski, H. Drulis, Solid State Commun. 111 (1999) 149. [16] I.A. Smirnov, L.S. Parfen’eva, T.B. Zhukova, K.M. Kholmedov, V.S. Oskot-skii, I.N. Kulikova, V.A. Shaburov, L.G. Karpukhina, H. Drulis, M. Drulis, W. Iwasieczko, Sov. Phys. Solid State 34 (1992) 281. [17] A.C. Switendick, Int. J. Quantum Chem. 5 (1971) 459. ¨ [18] D. Wohlleben, J. Rohler, J. Appl. Phys. 55 (1984) 1904. ¨ [19] J. Rohler, G. Krill, J.P. Kappler, M.F. Ravet, D. Wohlleben, in: P. Wachter, H. Boppart (Eds.), Valence Instabilities, North-Holland, Amsterdam, 1982, p. 215. ¨ [20] B. Batlogg, H.R. Ott, E. Kaldis, W. Thoni, P. Wachter, Phys. Rev. B19 (1979) 247. [21] A. Fujimori, F. Minami, T. Tsuda, Phys. Rev. B 22 (1980) 3573. [22] D.K. Misemer, B.N. Harmon, Phys. Rev. B 26 (1982) 5634. [23] R.N.R. Mulford, C.E. Holley, J. Phys. Chem. 59 (1955) 1222. [24] C.E. Messer, P.C. Gianoukos, J. Less-Common Met. 15 (1968) 377.
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Magnetic properties of the b- and b9-ytterbium hydride phases W. Iwasieczko, Monika Drulis, H. Drulis* Trzebiatowski Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 1410, 50 -950 Wrocl«aw 2, Poland Received 2 April 2001; accepted 17 April 2001
Abstract Samples of the b-ytterbium hydride phase with compositions 2.2,H / Yb#2.71 were prepared and their magnetic properties studied. Measurements of the magnetization vs. temperature were carried out in the range 1.75–300 K. The magnetization plots proved the presence of the maximum at around 4 K and the Curie–Weiss like behaviour at high temperatures. The magnetic moment per Yb atom exhibits an almost constant value of 3.8560.05 m B for various compositions across the b-ytterbium hydride phase. This effective moment is smaller than the ionic Hund’s rule moment of 4.54 m B expected for trivalent Yb 31 ions and clearly indicates that the Yb atoms stay in an intermediate valence state. The average valence of Yb ions n (Yb)52.7260.02 calculated from magnetic data is independent on the hydrogen concentration and lie between the expected values for the corresponding pure valent Yb 21 and Yb 31 ions. For the first time, the magnetic properties of the b9-ytterbium hydride phase are also measured and discussed as well. The obtained results indicate that the ytterbium atoms in the cubic b9-hydride phase are trivalent like the light lanthanide elements in their hydride phases. 2001 Elsevier Science B.V. All rights reserved. Keywords: Intermediate valence; Magnetic moment; Ytterbium hydrides
1. Introduction The thermodynamical properties of a number of metallic compounds based on Ce, Sm, Eu and Yb cannot be explained on the basis of pure valent rare earth (RE) ions [1,2]. In this class of compounds states of two different occupations of the RE 4f shells have comparable energies so that transitions of electrons between RE 4f shells and band states caused by hybridization interactions are possible. In this situation the ground state of the system will contain RE sites in an intermediate valence (IV) state. It is a quantum mechanical mixture of states corresponding to two different occupations of the 4f shell (valences), leading to a non-integral average number of f-electrons per atom. Experimentally, an intermediate valence state manifests itself, for example, as characteristic anomalies in the specific heat, and magnetic susceptibility [3,4]. The dual nature of the f electrons, an itinerant at low temperatures and a localized at high temperatures in an IV state is an extremely intricate feature. One of the standard methods to measure the degree of valence mixing in intermediatevalent materials is to investigate the effective magnetic *Corresponding author. Tel.: 148-71-343-5021; fax: 148-71-3441029. E-mail address: [email protected] (H. Drulis).
moment. The method might be correct particularly when the thermal energy, kT, is higher than the hybridization energy and the system performs real temporal fluctuations of the valence [5]. Ytterbium metal reacts with hydrogen gas to form a dihydride, a-YbH 2 , phase with an orthorhombic structure. Magnetic susceptibility studies [6] have indicated the divalent, Yb 21 , non-magnetic 4f 14 state of the ytterbium ions in this compound. When the hydride composition is higher than H / Yb.2.2 the system undergoes a phase transition from a-orthorhombic to the two b and b9-cubic crystallographic structures which differ from each other in the lattice constant only [7]. The b9 phase is metastable and exists only in the high temperature range [8]. Since, in all known cubic hydride phases the rare earth elements are trivalent one can expect that also the orthorhombic–cubic transition in the ytterbium hydride will be accompanied by an Yb 21 →Yb 31 valence transition. Recent investigations of the electronic structure of YbH x hydride samples performed by the X-ray line shift (XLS) method have shown that ytterbium changes its valence from 2 in the YbH 2 to a non-integer value 2.66 in the b-cubic phase [9]. To get a more comprehensive and closer insight into the electronic structure of the Yb–H hydride phase the low temperature heat capacity [10] and magnetic susceptibility measurements were studied [11]. The b-
0925-8388 / 01 / $ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 01 )01406-2
W. Iwasieczko et al. / Journal of Alloys and Compounds 327 (2001) 11 – 16
12
our previous results [13]. This time we focus our attention on the magnetic moment value interpretation in the framework of the ytterbium intermediate valence (IV) state. For the first time, the magnetic properties of the b9-ytterbium hydride phase will be shown and discussed.
2. Experimental
Fig. 1. XRD patterns for three representative compositions of the ytterbium hydride system.
cubic ytterbium hydride samples are paramagnetic at room temperature with a characteristic maximum being clearly revealed around 4 K. However, no magnetic ordering in the neutron diffraction studies has been found even at the lowest temperatures [12]. In this paper we present new investigations of the magnetic properties of the ytterbium hydrides and discuss
The ytterbium hydride–deuteride samples with composition H / Yb.2.2 were prepared by direct reaction of gaseous hydrogen with ytterbium metal as it is described in Ref. [7]. We assumed that isotope effects in the hydride– deuteride samples are negligible from the magnetic properties point of view. The hydrogen concentration in the samples was determined volumetrically as the amount of gaseous H absorbed during synthesis per formula unit. X-ray diffraction (XRD) analysis (Fig. 1) have shown that the sample with hydrogen concentrations 2.2,H / Yb,2.49 belong to the two-phase range of the Yb–H phase diagram where the a-orthorhombic and b-cubic phases are in equilibrium. The percentage contents of the b-phase in the two-phase sample were calculated from the appropriate XRD line intensity ratio. In turn, the appropriate b-phase compositions were calculated assuming that the a-hydride phase which appears in XRD patterns has a composition of YbH 1.85 [14]. In the sample with compositions H / Yb5 2.49 the X-ray patterns have revealed only the b-cubic phase. The characteristics of all samples are depicted in Table 1. To obtain a sample of the b9-ytterbium hydride phase which exists only at temperatures .2508C [8], a special quenching procedure has been performed during the hydride synthesis. Two samples with effective compositions D/ Yb52.27 and H / Yb52.35 were prepared through rapid quenching of the specimen from 3008C to room temperature. The XRD pattern showed that the sample
Table 1 Crystallographic analysis of the ytterbium hydrides samples Sample
Phase contents b
b-Phase a composition
a Lattice constant ˚ (A)
Normal synthesis YbD 2.26 YbH 2.30 YbH 2.39 YbH 2.49 YbD 2.53 YbH 2.57 YbD 2.71
0.33a10.67b 0.22a10.78b 0.09a10.91b b b b b
YbD 2,46 YbH 2.43 YbH 2.44 YbH 2.49 YbD 2.53 YbH 2.57 YbD 2.71 a Phase composition
5.177 5.187 5.188 5.182 5.187 5.187 5.170 ˚ a Lattice constant (A)
Quenched hydride samples YbD 2.27 0.2b h 10.8b9 YbH 2.35 0.43b h 10.57b9 a b
bh
b9
bh
b9
YbD 2.35 YbH 2.48
YbD 2.25 YbH 2.25
5.178 5.192
5.234 5.249
a- and b9-phase compositions: H / Yb51.85 and 2.25, respectively were accepted from P–T–C diagrams [8,14]. In fractional units.
W. Iwasieczko et al. / Journal of Alloys and Compounds 327 (2001) 11 – 16
Fig. 2. Magnetic susceptibility versus temperature and magnetization dependence on the magnetic field (inset) at 1.75 K for two representative samples consisting of the b-ytterbium hydride phase.
with D/ Yb52.27 consists of 80% of the b9-ytterbium ˚ whereas the hydride phase with lattice constant a55.234 A sample with H / Yb52.35 consists of 57% b9-hydride ˚ The rest of the sample was phase with a55.249 A. identified as the b h -hydride phase with the lattice constants ˚ and 5.192 A, ˚ respectively. X-ray analysis of a55.178 A data are shown in the bottom part of Table 1. Magnetic measurements were performed in the temperature range 1.75–300 K using a Quantum Design magnetometer.
3. Results and discussion
3.1. b -Ytterbium hydrides The magnetization vs. temperature measurements were carried out in the range 1.75–300 K for seven samples
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with compositions of H / Yb52.26, 2.30, 2.39, 2.49, 2.53, 2.57 and 2.71. In Fig. 2, for the sake of clarity, the data for the two border compositions which are representative for the rest of the samples under study are shown. The magnetization plots proved the presence of maxima at around 4 K which are only slightly dependent on the hydrogen concentration and the Curie–Weiss like behaviour at high temperatures. This general shape, involving a maximum at some T5T max followed by Curie–Weiss behaviour at high T and the lack of magnetic ordering may be regarded as very typical of IV metallic materials. The observed low temperature susceptibility anomalies at around 4 K were recently analysed in terms of the f–d hybridization model where a two-peak density of states on the Fermi level was suggested [13,15]. In this paper we are mainly focus on the magnetic moment values of the Yb atoms determined from the high temperature (range 150– 300 K) magnetic susceptibility measurements. The obtained results are collected in Table 2. The magnetic moment per Yb atom calculated from the experimental data (column 3 of Table 2) exhibits an almost constant value of 3.8560.02 m B for the various compositions across the b-ytterbium hydride phase. This effective moment is smaller than the ionic Hund’s rule moment of 4.54 m B expected for trivalent Yb 31 ions (with J 5 7 / 2 and the Lande factor, g 5 8 / 7) and clearly indicates that the Yb atoms stay in an intermediate valence state. The average valence of Yb ions n (Yb)52.7260.02 calculated from our magnetic data lie between the values expected for the corresponding integer valent Yb 21 and Yb 31 ions. The magnitude of the ytterbium valence obtained in these studies is very close to n (Yb)52.6660.02 determined in K line shifts investigations reported several years ago [16]. We have also confirmed our previous observation that the ytterbium valence is independent of the hydrogen concentration in the b-hydride phase in spite of the hydrogen participation in the conduction band depopulation process. The electronic structure of the host metal of any hydride is profoundly affected by the presence of hydrogen. The
Table 2 Magnetic properties and valence state of the Yb atoms in the ytterbium hydride phases
Hydride sample YbD 2.26 YbH 2.30 YbH 2.39 YbH 2.49 YbD 2.53 YbH 2.57 YbD 2.71
Effective mag. moment meff (m B )
Mag. moment / b-phase meff / f.u (m B )
n (Yb) valence state
3.2060.03 3.4860.03 3.6260.03 3.8860.03 3.8060.03 3.8160.03 3.8760.03
3.8660.02 3.9260.02 3.8060.02 3.8860.02 3.8060.02 3.8160.02 3.8760.02
2.7260.02 2.7660.02 2.7060.02 2.7460.02 2.7060.02 2.7060.02 2.7360.02
Quenched hydride samples YbD 2.27 YbH 2.35
3.9660.03 3.1760.03
bh | 0 | 0
b9 4.4360.02 4.4360.02
bh 21 21
b9 | 31 | 31
W. Iwasieczko et al. / Journal of Alloys and Compounds 327 (2001) 11 – 16
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Fermi level in pure ytterbium metal (Yb 21 , 4f 14 ) is well within the 5d6s bands and two electron states are occupied. When ytterbium is hydrogenated up to the dihydride, YbH 2 (a-orthorhombic phase), two hydrogen atoms per unit cell add two extra bands below the Fermi level and also two extra electrons to the system (kind of a chemical doping) [17]. In terms of the anionic (H 2) hydride model these bands with the capacity to hold four valence electrons are filled up with two electrons supplied by hydrogen and the other two by the ytterbium metal conduction band. As a result, the original 5d6s state (conduction band) of the parent metal is completely depleted and the ytterbium dihydride phase becomes a non-magnetic insulator. When the system due to the hydrogen concentration increase over 2, undergoes the phase transition from the orthorhombic to the cubic hydride phase, a new extra hydrogen-like valence band below the Fermi level should appear [17]. To fill up this new band with electrons the conduction band (probably 5d) must be, first of all, refilled (populated) with an extra electrons. The only way to do this is the 4f 14 →4f 13 5d 1 (Yb 21 →Yb 31 ) electronic transition. Simultaneously, with the hydrogen content increasing over H / Yb.2 one may expect a continuous decrease of the conduction electron density implying that each H atom depopulates the conduction band by one electron. The depopulation process of the conduction states within the b-hydride will be continued according to the following sequence (YbH 2 )4f 14 → 4f 13 5d 1 1 H x → (4f 13 5d 12x 1 H 2 x ) (where x . 0.2)
(1)
Finally, in terms of the rigid band model, for the hypothetical composition YbH 3 (x51), the system should be a magnetic (Yb 31 ) insulator again. However, as shown by the experimental data there is not such a simple, linear relationship between the hydrogen content and the ytterbium valence as appears from Eq. (1). The experimentally observed Yb valence is limited to |2.72 across the bhydride phase over the hydrogen concentration range from H / Yb52.44–2.71. A similar phenomenon has been observed in Ce-based IV compounds. It has been reported [18] that in all metallic Ce-based systems the Ce valence is limited by the value n (Ce)#3.25. The same observations have been made in Sm- and Tm-based IV compounds where Sm and Tm valences of v52.6–2.75 have been observed [19,20]. We think that for Yb, as for Ce, Sm and Tm, the valence in IV metallic systems is always ‘trapped’ at a certain value in order to reach a thermodynamically stable intermediate state. The n (Yb) behaviour under hydrogen indicates that this mechanism prevents the 4f 14th level being pushed more than necessary to above EF . Therefore, Yb-based metallic-like hydrides with n (Yb)5 31 cannot exist at all. In Yb the higher valence state is magnetic and every Yb 31 state corresponds to the creation of one electron in the sd band as well as one magnetic ion.
This proves that during the a→b phase transition only about 0.72 electrons are supplied by the 4f state to the sd band and only these electrons are available for hydrogen to form hydridic, H 2 , ions in octahedral sites of b-hydride lattice. It is obvious that the energy of the 4f 13 5d 1 state (arbitrary notation) will be situated very close to or at the Fermi level and the Yb ions will remain in the intermediate-valent state due to a strong hybridization with conduction electron states. The formal relative concentration of 4f 14 and 4f 13 5d 1 configurations are given by experiment as 0.28 and 0.72, respectively.
3.2. b9 -Ytterbium hydride phase The b9-ytterbium hydride phase is metastable and exists only in the high temperature range [7,8]. It is not possible to obtain a pure b9-phase at room temperature because it disproportionates into the orthorhombic dihydride and the b-phase hydride when cooled from high temperatures. Our P–T–C investigations shown in Fig. 3 indicate that the b9-phase appears on the desorption isotherms as a singlephase in the narrow composition range H / Yb52.25–2.29. The in situ XRD studies [14] have confirmed the PTC results and have additionally shown that the b9-phase has a ˚ (Fig. 1). fcc cubic crystal structure with a55.255 A In this paper the magnetic properties of two samples with effective compositions YbD 2.27 and YbH 2.35 consisting of the b9-phase have been studied. Their crystallographic analysis data are shown in Table 1. The magnetic properties as a function of temperature and magnetic field
Fig. 3. Pressure composition isotherms of Yb–H system at high temperatures.
W. Iwasieczko et al. / Journal of Alloys and Compounds 327 (2001) 11 – 16
Fig. 4. Magnetic susceptibility versus temperature and magnetization dependence on the magnetic field (inset) at 1.75 K for the quenched ytterbium hydride samples consisting of b9-phase. To emphasise the differences the susceptibility of pure b-ytterbium hydride phase is also shown.
are illustrated in Fig. 4 and Table 2. There are no anomalies at low temperatures as we saw previously for the b-hydride phase samples. However, below 50 K there is a rapid increase in the susceptibility and a Curie divergence at low temperatures. The low temperature magnetisation curves (inset of Fig. 4) are highly non-linear and look almost ferromagnetic, although they do not saturate in a high field. Having the magnetic data for two samples with different compositions and taking into account their quantitative X-ray phase analysis we were able to affirm that the b9-phase has the composition YbH 2.25 and is a paramagnetic material with almost all (9565%) ytterbium atoms in the Yb 31 valence state. Simultaneously, as a big surprise, we found that the accompanying b-like phase with the composition of YbH 2.35 – 2.48 which we will h call ‘quenched’ or ‘high temperature b -phase’, is totally diamagnetic with ytterbium atoms in the Yb 21 valence state. In this case we probably deal with another isostructural cubic hydride phase which is not exactly the same as the cubic b-phase. It is particularly unusual if we bear in mind that the ‘normal’ b-phase samples we discussed earlier, are magnetically active and have only about 28% of the Yb atoms present as diamagnetic Yb 21 ions. From theoretical band structure calculations of Ce–H and La–H hydrides [21,22] it appeared that octahedral hydrogen (H o ) atoms are almost neutral and are weakly bound to the metal atoms. The weak bonds for H o compared to H t (tetrahedral) were manifested by the pressure–temperature–composition relation [23]. Probably, in the high temperature ranges octahedral hydrogen atoms due to their high thermal energy and fast diffusion through the lattice, form the metal–hydrogen bonding band whose energy levels lie higher than the Fermi energy level, E1s . EF . In such a case appropriate Yb, probably 5de g -like states, are
15
also pushed up from the Fermi level. Consequently an electron transfer from the 4f 14 state to the 5d conduction bands usually induced by octahedral hydrogen will not occur and all Yb atoms remain in the Yb 21 valence state. Our observations support earlier reports, which suggested that at high temperatures the cubic divalent ytterbium dihydride phase has sometimes been observed [24]. Contrary to the b h -phase, the b9-ytterbium hydride phase exhibits a magnetic behaviour characteristic for normal light lanthanide trivalent elements. This feature can be expected because the b9-ytterbium hydride has the same crystallographic structure as this group of hydrides and its ˚ is close to that expected for lattice constant a55.255 A trivalent ytterbium hydride estimated from the linear extrapolation of lattice constants across the rare-earth series.
4. Conclusion Whereas the electronic structure of stoichiometric trivalent rare earth hydrides is more or less well understood, there is considerable confusion in the intermediate valence systems where the role of the 4f state must be considered. Usually the specific microscopic IV features are deduced from the coincidence of the narrow 4f band and the Fermi level and this is often applied to interpret the available experimental data. The interpretation of the low energy experimental data, including susceptibility, heat capacity or resistivity data on IV compounds, is based on the assumption that the extremely narrow 4f band is situated in the vicinity of the Fermi level. Using the 4f band width D4f and the 4f level position EF 2 E4f as adjustable parameters, it is possible to achieve agreement between experimental data and model calculations when the relative 4f level population accepts any fixed value from the interval 0 # n rf # 1, i.e. in Yb based IV compounds, any ytterbium valence from the interval 2#v(Yb)#3 can be observed. Unfortunately, at this moment the confrontation of such an approach any with theoretical electron band structure is impossible because, as far as we know, the band structure calculations completely neglected the 4f electrons. The atomic-like 4f electron states are thought not to contribute significantly to the metal–hydrogen bonding. Indeed, in Ce hydrides the Ce 4f electrons and valence of Ce are hardly affected by hydrogen. On the other hand, as we have shown in this paper, hydrogen causes a tremendous valence change in Yb hydrides. This indicates that further theoretical efforts should be made in the field of band structure calculations for the intermediate systems. Also, special attention should be paid to answering the general question of why the average valence of Sm, Tm and Yb in many IV compounds is ‘trapped’ at around v52.6–2.7 and what is the origin of the valence trapping in metallic systems.
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References [1] P. Wachter, in: K.A. Gschneidner, L. Eyring, G.H. Lander, G.R. Choppin (Eds.), Handbook on the Physics and Chemistry of Rare Earth, Vol. 19, North-Holland, Amsterdam, 1994, p. 177. [2] L.L. Hirst, Phys. Cond. Mat. 11 (1970) 255. [3] B.R. Coles, D. Wohlleben and further references, in: Magnetism, V, Shul (Ed.) Academic Press, New York, 1973, p. 3. [4] M.B. Maple, L.E. DeLong, B.C. Sales, in: K.A. Gschneider Jr., L. Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earth, Vol. 1, North Holland, Amsterdam, 1978, p. 797. [5] P. Schlottman, Phys. Rep. 181 (1989) 1. [6] J.C. Warf, K.J. Hardcastle, Inorg. Chem. 5 (1966) 1736. [7] K.J. Hardcastle, J.C. Warf, Inorg. Chem. 5 (1966) 1728. [8] H. Drulis, M. Drulis, W. Iwasieczko, N.M. Suleimanov, J. LessCommon Met. 141 (1988) 201. [9] V.A. Shaburov, A.E. Soviestnov, Yu. L Smirnov, A.W. Tiunis, H. Drulis, M. Drulis, Fiz. Twerd. Tela 40 (1998) 1393. [10] M. Drulis, H. Drulis, B. Stalinski, J. Less-Common Met. 141 (1988) 207. [11] W. Iwasieczko, M. Drulis, H. Drulis, J. Alloys Compd. 259 (1997) 62.
[12] G. Andre, private communication [13] W. Iwasieczko, M. Drulis, P. Gaczynski, H. Drulis, J. Magn. Magn. Mat. 205 (1999) 255. [14] W. Iwasieczko, H. Drulis, R.M. Frak, J. Alloys Compd. 180 (1992) 265. [15] M. Drulis, W. Iwasieczko, P. Gaczynski, H. Drulis, Solid State Commun. 111 (1999) 149. [16] I.A. Smirnov, L.S. Parfen’eva, T.B. Zhukova, K.M. Kholmedov, V.S. Oskot-skii, I.N. Kulikova, V.A. Shaburov, L.G. Karpukhina, H. Drulis, M. Drulis, W. Iwasieczko, Sov. Phys. Solid State 34 (1992) 281. [17] A.C. Switendick, Int. J. Quantum Chem. 5 (1971) 459. ¨ [18] D. Wohlleben, J. Rohler, J. Appl. Phys. 55 (1984) 1904. ¨ [19] J. Rohler, G. Krill, J.P. Kappler, M.F. Ravet, D. Wohlleben, in: P. Wachter, H. Boppart (Eds.), Valence Instabilities, North-Holland, Amsterdam, 1982, p. 215. ¨ [20] B. Batlogg, H.R. Ott, E. Kaldis, W. Thoni, P. Wachter, Phys. Rev. B19 (1979) 247. [21] A. Fujimori, F. Minami, T. Tsuda, Phys. Rev. B 22 (1980) 3573. [22] D.K. Misemer, B.N. Harmon, Phys. Rev. B 26 (1982) 5634. [23] R.N.R. Mulford, C.E. Holley, J. Phys. Chem. 59 (1955) 1222. [24] C.E. Messer, P.C. Gianoukos, J. Less-Common Met. 15 (1968) 377.