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Intermediate valence in the ytterbium deuteride — the magnetic susceptibility evidence
Journal of Magnetism and Magnetic Materials 205 (1999) 255}260
Intermediate valence in the ytterbium deuteride * the magnetic susceptibility evidence W. Iwasieczko, M. Drulis*, P. GaczynH ski, H. Drulis Trzebiatowski Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 1410, 50-950 Wroclaw 2, Poland Received 29 March 1999; received in revised form 2 July 1999
Abstract Low-temperature magnetic properties of YbD cubic deuteride phase are reported and interpreted in the model of V intermediate valence system with the ground state consisting of two narrow quasiparticle bands located at the Fermi level. The estimated bandwidth, !"0.3 meV and the gap value, D"1.35 meV for YbD will reproduce the shape of broad maximum in magnetization at around 4.5 K. 1999 Elsevier Science B.V. All rights reserved. Keywords: Magnetic susceptibility; Valence #uctuations; Hybridization; Ytterbium deuterides
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 RE ions [1]. The dual nature of the f electrons, itinerant at low temperatures and localized at high temperatures, is an extremely intriguing feature of these elements. Hirst [2] pointed out that in this class of compounds the states of two di!erent occupations of the RE 4f shells have comparable energies, so transitions of electrons between the RE 4f shells and the band states caused by hybridization interaction are possible. In this situation the ground state of the substance will contain RE sites in an intermediate valence (IV) state, i.e. a quantum mechanical mixture of states corresponding to two
* Corresponding author. Tel.: 0048-71-3435021; fax: 0048-713441029. E-mail address: [email protected] (M. Drulis)
di!erent occupations of the 4f shell (valencies), leading to a non-integral average number of f electrons per atom. Experimentally, an intermediate valence state manifested itself via characteristic anomalies in the speci"c heat and magnetic susceptibility [3,4]. The relatively constant magnetic susceptibility (or #at maximum) typical of IV compounds found at low temperatures is followed at higher temperatures by a Curie-like drop [5]. One of the standard methods to measure the degree of valence mixing in intermediate valent materials is to investigate the magnetic susceptibility and to determine the e!ective magnetic moment. The method is applicable when the thermal energy, k¹, is higher than the hybridization energy, and the system performs real temporal #uctuations of the valence [6]. The hybridization between the local and the conduction band electrons seems to e!ectively quench the moment of the magnetically active valence state when k¹ is less than the hybridization state, and may reduce the size of the e!ective moment at higher temperatures.
0304-8853/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 9 ) 0 0 5 1 4 - 4
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W. Iwasieczko et al. / Journal of Magnetism and Magnetic Materials 205 (1999) 255}260
In this paper we present the magnetic properties of ytterbium deuterides with a high deuterium concentration. Our previous low-temperature heat capacity [7] and photoemission [8] investigations have suggested the presence of an intermediate valence state of Yb ions in these types of interstitial compounds. Ytterbium metal reacts with hydrogen gas to form a dihydride YbH phase with an orthorhom bic structure. Magnetic susceptibility studies [9] indicated the divalent, Yb>, non-magnetic state of ytterbium ions. When the hydride composition is higher than H/Yb'2.2 the system undergoes the phase transition from an orthorhombic to a cubic structure [10]. Since in all known cubic hydride phases the rare earth elements are trivalent, one can expect that an ortho-cubic transition in the ytterbium hydride will also be accompanied by Yb>PYb> electronic transition. Recent investigations of the electronic structure of YbH hydride V samples with x'2.2 by the X-ray line shift (XLS) method [11] have shown that ytterbium changes its valency from 2 in YbH to a non-integral value 2.66 in cubic ytterbium hydride. To get a closer insight into the electronic structure of the hydride phases we have performed magnetic susceptibility measurements [12]. A characteristic maximum has been clearly revealed around 4 K, but no magnetic ordering has been found by neutron di!raction studies at lowest temperatures [13]. Our suggestion that there is an antiferromagnetic ordering therefore has not been con"rmed. There are a number of theoretical results published which deal with intermediate valency and heavy fermion states [14}18]. In most of them a susceptibility is expressed by relations consisting of two terms: (i) Van Vleck-like contribution, which arises from the magnetic moment of the ionic con"guration 4f L! as it is mixed into the ground state by the hybridization, and (ii) the modi"ed Paulilike susceptibility which arises from the conduction band states. The interpretation of s is rather complex because the various electron con"gurations of 4f element, together with spin, must be considered. In this paper we chose the so-called renormalized Sommerfeld model of the quasiparticles in narrow bands assuming the f}d hybridization formalism with double-peak density of states around the Fermi level [19,20].
In our opinion, in this model we can easily reproduce the low-temperature anomalies we have observed in the magnetic properties of ytterbium deuterides.
2. Experimental details The deuteride samples with composition D/Yb '2.35 were prepared by direct reaction of gaseous deuterium with ytterbium metal as described in Ref. [10]. The deuterium concentration in the samples was determined volumetrically as the amount of absorbed D gas per formula unit. X-ray analysis showed that all samples under study were a singlephase of FCC symmetry with parameter a" 5.190}5.182 As , depending on the deuterium composition. Magnetic measurements were performed in the temperature range of 1.75}300 K using a Quantum Design magnetometer. The magnetization measurements in high magnetic "elds up to 14 T have been carried out with the standard Bitter electromagnet in the International Laboratory of High Magnetic Fields in Wroc"aw (Poland).
3. Results and discussion The magnetization versus temperature data for cubic deuteride samples: YbD , YbD and YbD in the range of 1.75}20 K are presented in Fig. 1. To get the correct values of the magnetization, the diamagnetic contribution and the impurity (Yb O ) contribution have been subtracted from the experimental data in the way described in Ref. [12]. Antiferromagnetic Yb O impurities are almost always present in metallic ytterbium compounds. The magnetization plots exhibited a maximum at around 4}5 K which is only slightly dependent on the deuterium concentration. This general shape, involving a maximum at some ¹"¹ followed
by Curie behaviour at high-¹, may be regarded as very typical of IV metallic materials. For the sake of clarity, other magnetic measurements are presented only for the YbD sample as representative of the behavior of the other specimen. In Fig. 2, the
W. Iwasieczko et al. / Journal of Magnetism and Magnetic Materials 205 (1999) 255}260
Fig. 1. Magnetization dependence on the temperature for three deuterided ytterbium samples.
257
Fig. 3. Magnetic susceptibility data and main susceptibility contributions for YbD sample in the temperature range of 1.75}300 K.
Table 1 E!ective magnetic moment of Yb ions, the paramagnetic Curie temperatures and the temperature of maximum of the magnetization determined from the magnetic measurements of the ytterbium deuterides
Fig. 2. Magnetization of YbD deuteride at several magnetic "elds as a function of temperature.
temperature dependence of magnetization at several magnetic "elds is displayed from 1.75}20 K. The magnetic susceptibility as a function of temperature in a wide temperature range of 1.7}300 K is shown in Fig. 3. As can be seen, the measured magnetic susceptibility obeys the Curie}Weiss law at temperatures higher than 50 K with an e!ective magnetic moment and paramagnetic Curie temperature listed in Table 1. The e!ective moments per ytterbium atom are somewhat smaller than the value 4.54 l expected for trivalent Yb ions with J"7/2 and the Lande factor, g"8/7. The average valency of Yb calculated from these data is 2.6}2.7,
Composition
k (l )
H (K)
¹ (K)
YbD YbD YbD
3.45 3.56 3.62
!55.1 !75.6 !69.1
3.63 4.85 4.52
and lies between the expected values for the corresponding pure-valent Yb> and Yb> ions. At temperatures lower than 50 K the variation of susceptibility is partly determined by crystal-"eld e!ects (CFF) which in our case is modeled by a Van Vleck contribution deriving from a ground state doublet ! and ! as the "rst excited state (see full line in Fig. 3), and partly by a Curie}Weiss term modi"ed by the hybridization e!ect represented by the bottom curve in Fig. 3. An interesting "eld dependence of magnetization has been observed at temperatures below and above the ¹ depicted by an arrow in Fig. 1. The
magnetization versus magnetic "eld measured at 1.75 K is displayed in Fig. 4 whereas the same dependence taken at several temperatures above ¹ is shown in Fig. 5. Initially, the magnetization
at 1.75 K is a linear function of the magnetic "eld
258
W. Iwasieczko et al. / Journal of Magnetism and Magnetic Materials 205 (1999) 255}260
Fig. 4. Magnetization versus magnetic "eld at 1.75 K for YbD .
Fig. 5. Field dependence of magnetization for YbD deuter ide at several temperatures above ¹ .
but beginning from about H"25 kOe, a slight upward turn from linearity is observed. Such a behaviour of magnetization of the metallic IV compounds with the applied "eld has been predicted in Ref. [21]. According to the model the magnetization versus applied "eld should obey the relation: p"sH#s H.
(1)
The full line in Fig. 4 is the best "t to the experimental curve with the following parameters: s"2.72;10\ and s "1.95;10\.
Fig. 6. Temperature variation of magnetization contribution connected with an intermediate state of Yb ions in YbD deuteride. The dashed line is a calculated dependence of magnetization according to the model described in the text.
The "eld dependence of magnetization in Fig. 5 is typical of a paramagnetic substance approaching the saturated state under the in#uence of a strong magnetic "eld. The absence of complete saturation of p(H) up to the highest B values may be ascribed to crystal-"eld e!ects. The moment value extrapolated to (1/HP0) is 1.64 l per formula unit. The magnetization curve at 4.2 K "ts a Brillouin function for a ! ground state doublet of Yb> for which the saturation moment is equal to k "1.71 l . To discuss the temperature dependence of the subtracted hybridization contribution shown in Fig. 6, we used a renormalized Sommerfeld model of the quasiparticles which has been proved successful for heavy fermion compounds [22,23]. This crude formalism has described quantitatively, the temperature-dependence of the speci"c heat, the c value and the temperature- and "eld-dependence of the magnetic susceptibility quite well. These thermodynamic properties can be reproduced with only two parameters describing the DOS: the bandwidth, ! and the energy gap, D. We propose a very simple structure for the density of state, N(E ), around the Fermi level; $ a double-Gaussian-band separated by a gap:
! ! N(E )"1/p # , $ E#! (E#D)#!
(2)
W. Iwasieczko et al. / Journal of Magnetism and Magnetic Materials 205 (1999) 255}260
where D is the gap or pseudogap (as de"ned in the inset of Fig. 6). The magnetization dependence on the temperature can be calculated from the following relation:
> 1 p" k N(E )[ f (E!k H!E ) $ $ $ 2 \ !f (E#k H!E )] dE, (3) $ $ where f (E,¹) is the Fermi}Dirac distribution func$ tion, and E is the Fermi energy. $ When we adopt a temperature-independent rigid-band approximation the main in#uence of the temperature is to shift chemical potential k+E . $ The calculated dependence of p(¹) on temperature for the YbD sample is shown as the dashed line in Fig. 6. The comparison with the experiment has been carried out by optimizing a "t with the band width ! and the gap D as free parameters. The "ts of p(¹) turned out to be rather good with !"0.3 meV and D"1.35 meV, respectively. Some visible di!erences between the experimental and theoretical lines can be accounted for by the approximation we have made for CEF e!ects. Now, it is also clear that at low temperatures magnetic saturation cannot be achieved, because the necessary "eld strengths should be at least the size of the hybridization energy (even "elds of 50 T correspond to only 2.9 meV). The electronic structure of the host metal of any hydride is profoundly a!ected by the presence of hydrogen. For pure ytterbium (Yb>) metal the Fermi level is well within the 5d 6s bands and the two states are occupied. When ytterbium is hydrogenated up to the dihydride (orthorhombic phase) the two hydrogen (deuterium) atoms per unit cell, add two extra electrons to the system and also two extra low-lying bands below the Fermi level due to the hybridization of the hydrogen 1s and ytterbium 5d6s states [24]. These bands are "lled with four electrons: two from hydrogen and the other two from the ytterbium conduction band. As a result the original 5d6s states of the parent metal are completely depleted and the dihydride becomes an insulator. When the system undergoes phase transition from the orthorhombic dihydride to the cubic hydride phase due to a hydrogen concentration increase, a new hydrogen-like, low-lying band
259
below the Fermi level is created. Simultaneously, because of the 4fP4f5d electronic transition which accompanied the phase transition, the conduction band (probably 5d) is populated with an extra electron and the DOS at the Fermi level is again "nite. The conduction electrons remain strongly hybridized with 4f electron states. When the hydrogen content exceeds H/Yb"2.25, a further depopulation of the conduction states will occur, and the DOS at the Fermi energy will be gradually lowered. Finally, for the hypothetical composition YbH , the system should be insulating in the IV state with the Fermi level positioned in the energy gap between two sharp peaks in the DOS.
4. Conclusion We have shown that the low-temperature maximum observed in the magnetic susceptibility, s(¹), of the ytterbium deuterides (hydrides) re#ect an intermediate valence state of the ytterbium cations in this material. We have assumed that the temperature-dependence of the susceptibility around anomalies is determined by the temperature-dependence of the Dirac}Fermi distribution function, f (¹). Therefore, we propose to describe the mag$ netic susceptibility with a renormalized Sommerfeld formalism and a two band structure of the density of states at the Fermi level. Even with this very simpli"ed calculation we have got the correct shape of the susceptibility. Narrow quasiparticle bands (!"0.3 meV, D"1.35 meV) can account for the anomalous characteristics at low temperature as well as the Curie}Weiss behavior at high temperature.
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, 19, North-Holland, Amsterdam, 1994, p. 177. [2] L.L. Hirst, Phys.: Condens. Matter 11 (1970) 255. [3] B.R. Coles, D. Wohlleben, and further references in: Shul (Ed.), Magnetism, Vol. V, Academic Press, New York, 1973, p. 3.
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[4] M.B. Maple, L.E. DeLong, B.C. Sales, in: K.A. Gschneidner Jr., L. Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earth, Vol. 1, North-Holland, Amsterdam, 1978, p. 797. [5] A. Bringer, H. Lustfeld, Z. Phys. B 28 (1977) 213. [6] P. Schlottman, Phys. Rep. 181 (1989) 1. [7] M. Drulis, H. Drulis, B. StalinH ski, J. Less-Common Met. 141 (1988) 207. [8] S. Buchler, L. Schlapbach, R. Monnier, L. Degiori, J. Phys. Colloq. C 9 (12) (1987) 947. [9] J.C. Warf, K.J. Hardcastle, Inorg. Chem. 5 (1966) 1736. [10] K.J. Hardcastle, J.C. Warf, Inorg. Chem. 5 (1966) 1728. [11] V.A. Shaburov, A.E. Soviestnov, Yu.L. Smirnov, A.W. Tiunis, H. Drulis, M. Drulis, Fiz. Tverd. Tela 40 (1998) 1393. [12] W. Iwasieczko, M. Drulis, H. Drulis, J. Alloys Compounds 259 (1997) 62.
[13] G. Andre, private communication. [14] N.E. Bickers, D.L. Cox, J.W. Wilkins, Phys. Rev. B 36 (1987) 2036. [15] N. Kawakami, K. Okiji, J. Phys. Soc. Japan 54 (1985). [16] D.M. Newns, A.C. Hewson, J. Phys. F 10 (1980) 2429. [17] V.T. Rajan, Phys. Rev. Lett. 51 (1983) 308. [18] P. Schlottmann, Z. Phys. B 55 (1984) 293. [19] B.H. Brandow, Phys. Rev. B 33 (1986) 215. [20] G.R. Stewart, Rev. Mod. Phys. 56 (1984) 755. [21] H. Lustfeld, A. Bringer, Solid State Commun. 28 (1978) 119. [22] F. Marabelli, P. Wachter, J. Magn. Magn. Mater. 70 (1987) 364. [23] K. Satho, T. Fujita, Y. Maeno, Y. Onuki, T. Komatsubara, T. Ohtsuka, Solid State Commun. 56 (1985) 327. [24] A.C. Switendick, Int. J. Quantum Chem. 5 (1971) 459.
Intermediate valence in the ytterbium deuteride * the magnetic susceptibility evidence W. Iwasieczko, M. Drulis*, P. GaczynH ski, H. Drulis Trzebiatowski Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 1410, 50-950 Wroclaw 2, Poland Received 29 March 1999; received in revised form 2 July 1999
Abstract Low-temperature magnetic properties of YbD cubic deuteride phase are reported and interpreted in the model of V intermediate valence system with the ground state consisting of two narrow quasiparticle bands located at the Fermi level. The estimated bandwidth, !"0.3 meV and the gap value, D"1.35 meV for YbD will reproduce the shape of broad maximum in magnetization at around 4.5 K. 1999 Elsevier Science B.V. All rights reserved. Keywords: Magnetic susceptibility; Valence #uctuations; Hybridization; Ytterbium deuterides
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 RE ions [1]. The dual nature of the f electrons, itinerant at low temperatures and localized at high temperatures, is an extremely intriguing feature of these elements. Hirst [2] pointed out that in this class of compounds the states of two di!erent occupations of the RE 4f shells have comparable energies, so transitions of electrons between the RE 4f shells and the band states caused by hybridization interaction are possible. In this situation the ground state of the substance will contain RE sites in an intermediate valence (IV) state, i.e. a quantum mechanical mixture of states corresponding to two
* Corresponding author. Tel.: 0048-71-3435021; fax: 0048-713441029. E-mail address: [email protected] (M. Drulis)
di!erent occupations of the 4f shell (valencies), leading to a non-integral average number of f electrons per atom. Experimentally, an intermediate valence state manifested itself via characteristic anomalies in the speci"c heat and magnetic susceptibility [3,4]. The relatively constant magnetic susceptibility (or #at maximum) typical of IV compounds found at low temperatures is followed at higher temperatures by a Curie-like drop [5]. One of the standard methods to measure the degree of valence mixing in intermediate valent materials is to investigate the magnetic susceptibility and to determine the e!ective magnetic moment. The method is applicable when the thermal energy, k¹, is higher than the hybridization energy, and the system performs real temporal #uctuations of the valence [6]. The hybridization between the local and the conduction band electrons seems to e!ectively quench the moment of the magnetically active valence state when k¹ is less than the hybridization state, and may reduce the size of the e!ective moment at higher temperatures.
0304-8853/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 9 ) 0 0 5 1 4 - 4
256
W. Iwasieczko et al. / Journal of Magnetism and Magnetic Materials 205 (1999) 255}260
In this paper we present the magnetic properties of ytterbium deuterides with a high deuterium concentration. Our previous low-temperature heat capacity [7] and photoemission [8] investigations have suggested the presence of an intermediate valence state of Yb ions in these types of interstitial compounds. Ytterbium metal reacts with hydrogen gas to form a dihydride YbH phase with an orthorhom bic structure. Magnetic susceptibility studies [9] indicated the divalent, Yb>, non-magnetic state of ytterbium ions. When the hydride composition is higher than H/Yb'2.2 the system undergoes the phase transition from an orthorhombic to a cubic structure [10]. Since in all known cubic hydride phases the rare earth elements are trivalent, one can expect that an ortho-cubic transition in the ytterbium hydride will also be accompanied by Yb>PYb> electronic transition. Recent investigations of the electronic structure of YbH hydride V samples with x'2.2 by the X-ray line shift (XLS) method [11] have shown that ytterbium changes its valency from 2 in YbH to a non-integral value 2.66 in cubic ytterbium hydride. To get a closer insight into the electronic structure of the hydride phases we have performed magnetic susceptibility measurements [12]. A characteristic maximum has been clearly revealed around 4 K, but no magnetic ordering has been found by neutron di!raction studies at lowest temperatures [13]. Our suggestion that there is an antiferromagnetic ordering therefore has not been con"rmed. There are a number of theoretical results published which deal with intermediate valency and heavy fermion states [14}18]. In most of them a susceptibility is expressed by relations consisting of two terms: (i) Van Vleck-like contribution, which arises from the magnetic moment of the ionic con"guration 4f L! as it is mixed into the ground state by the hybridization, and (ii) the modi"ed Paulilike susceptibility which arises from the conduction band states. The interpretation of s is rather complex because the various electron con"gurations of 4f element, together with spin, must be considered. In this paper we chose the so-called renormalized Sommerfeld model of the quasiparticles in narrow bands assuming the f}d hybridization formalism with double-peak density of states around the Fermi level [19,20].
In our opinion, in this model we can easily reproduce the low-temperature anomalies we have observed in the magnetic properties of ytterbium deuterides.
2. Experimental details The deuteride samples with composition D/Yb '2.35 were prepared by direct reaction of gaseous deuterium with ytterbium metal as described in Ref. [10]. The deuterium concentration in the samples was determined volumetrically as the amount of absorbed D gas per formula unit. X-ray analysis showed that all samples under study were a singlephase of FCC symmetry with parameter a" 5.190}5.182 As , depending on the deuterium composition. Magnetic measurements were performed in the temperature range of 1.75}300 K using a Quantum Design magnetometer. The magnetization measurements in high magnetic "elds up to 14 T have been carried out with the standard Bitter electromagnet in the International Laboratory of High Magnetic Fields in Wroc"aw (Poland).
3. Results and discussion The magnetization versus temperature data for cubic deuteride samples: YbD , YbD and YbD in the range of 1.75}20 K are presented in Fig. 1. To get the correct values of the magnetization, the diamagnetic contribution and the impurity (Yb O ) contribution have been subtracted from the experimental data in the way described in Ref. [12]. Antiferromagnetic Yb O impurities are almost always present in metallic ytterbium compounds. The magnetization plots exhibited a maximum at around 4}5 K which is only slightly dependent on the deuterium concentration. This general shape, involving a maximum at some ¹"¹ followed
by Curie behaviour at high-¹, may be regarded as very typical of IV metallic materials. For the sake of clarity, other magnetic measurements are presented only for the YbD sample as representative of the behavior of the other specimen. In Fig. 2, the
W. Iwasieczko et al. / Journal of Magnetism and Magnetic Materials 205 (1999) 255}260
Fig. 1. Magnetization dependence on the temperature for three deuterided ytterbium samples.
257
Fig. 3. Magnetic susceptibility data and main susceptibility contributions for YbD sample in the temperature range of 1.75}300 K.
Table 1 E!ective magnetic moment of Yb ions, the paramagnetic Curie temperatures and the temperature of maximum of the magnetization determined from the magnetic measurements of the ytterbium deuterides
Fig. 2. Magnetization of YbD deuteride at several magnetic "elds as a function of temperature.
temperature dependence of magnetization at several magnetic "elds is displayed from 1.75}20 K. The magnetic susceptibility as a function of temperature in a wide temperature range of 1.7}300 K is shown in Fig. 3. As can be seen, the measured magnetic susceptibility obeys the Curie}Weiss law at temperatures higher than 50 K with an e!ective magnetic moment and paramagnetic Curie temperature listed in Table 1. The e!ective moments per ytterbium atom are somewhat smaller than the value 4.54 l expected for trivalent Yb ions with J"7/2 and the Lande factor, g"8/7. The average valency of Yb calculated from these data is 2.6}2.7,
Composition
k (l )
H (K)
¹ (K)
YbD YbD YbD
3.45 3.56 3.62
!55.1 !75.6 !69.1
3.63 4.85 4.52
and lies between the expected values for the corresponding pure-valent Yb> and Yb> ions. At temperatures lower than 50 K the variation of susceptibility is partly determined by crystal-"eld e!ects (CFF) which in our case is modeled by a Van Vleck contribution deriving from a ground state doublet ! and ! as the "rst excited state (see full line in Fig. 3), and partly by a Curie}Weiss term modi"ed by the hybridization e!ect represented by the bottom curve in Fig. 3. An interesting "eld dependence of magnetization has been observed at temperatures below and above the ¹ depicted by an arrow in Fig. 1. The
magnetization versus magnetic "eld measured at 1.75 K is displayed in Fig. 4 whereas the same dependence taken at several temperatures above ¹ is shown in Fig. 5. Initially, the magnetization
at 1.75 K is a linear function of the magnetic "eld
258
W. Iwasieczko et al. / Journal of Magnetism and Magnetic Materials 205 (1999) 255}260
Fig. 4. Magnetization versus magnetic "eld at 1.75 K for YbD .
Fig. 5. Field dependence of magnetization for YbD deuter ide at several temperatures above ¹ .
but beginning from about H"25 kOe, a slight upward turn from linearity is observed. Such a behaviour of magnetization of the metallic IV compounds with the applied "eld has been predicted in Ref. [21]. According to the model the magnetization versus applied "eld should obey the relation: p"sH#s H.
(1)
The full line in Fig. 4 is the best "t to the experimental curve with the following parameters: s"2.72;10\ and s "1.95;10\.
Fig. 6. Temperature variation of magnetization contribution connected with an intermediate state of Yb ions in YbD deuteride. The dashed line is a calculated dependence of magnetization according to the model described in the text.
The "eld dependence of magnetization in Fig. 5 is typical of a paramagnetic substance approaching the saturated state under the in#uence of a strong magnetic "eld. The absence of complete saturation of p(H) up to the highest B values may be ascribed to crystal-"eld e!ects. The moment value extrapolated to (1/HP0) is 1.64 l per formula unit. The magnetization curve at 4.2 K "ts a Brillouin function for a ! ground state doublet of Yb> for which the saturation moment is equal to k "1.71 l . To discuss the temperature dependence of the subtracted hybridization contribution shown in Fig. 6, we used a renormalized Sommerfeld model of the quasiparticles which has been proved successful for heavy fermion compounds [22,23]. This crude formalism has described quantitatively, the temperature-dependence of the speci"c heat, the c value and the temperature- and "eld-dependence of the magnetic susceptibility quite well. These thermodynamic properties can be reproduced with only two parameters describing the DOS: the bandwidth, ! and the energy gap, D. We propose a very simple structure for the density of state, N(E ), around the Fermi level; $ a double-Gaussian-band separated by a gap:
! ! N(E )"1/p # , $ E#! (E#D)#!
(2)
W. Iwasieczko et al. / Journal of Magnetism and Magnetic Materials 205 (1999) 255}260
where D is the gap or pseudogap (as de"ned in the inset of Fig. 6). The magnetization dependence on the temperature can be calculated from the following relation:
> 1 p" k N(E )[ f (E!k H!E ) $ $ $ 2 \ !f (E#k H!E )] dE, (3) $ $ where f (E,¹) is the Fermi}Dirac distribution func$ tion, and E is the Fermi energy. $ When we adopt a temperature-independent rigid-band approximation the main in#uence of the temperature is to shift chemical potential k+E . $ The calculated dependence of p(¹) on temperature for the YbD sample is shown as the dashed line in Fig. 6. The comparison with the experiment has been carried out by optimizing a "t with the band width ! and the gap D as free parameters. The "ts of p(¹) turned out to be rather good with !"0.3 meV and D"1.35 meV, respectively. Some visible di!erences between the experimental and theoretical lines can be accounted for by the approximation we have made for CEF e!ects. Now, it is also clear that at low temperatures magnetic saturation cannot be achieved, because the necessary "eld strengths should be at least the size of the hybridization energy (even "elds of 50 T correspond to only 2.9 meV). The electronic structure of the host metal of any hydride is profoundly a!ected by the presence of hydrogen. For pure ytterbium (Yb>) metal the Fermi level is well within the 5d 6s bands and the two states are occupied. When ytterbium is hydrogenated up to the dihydride (orthorhombic phase) the two hydrogen (deuterium) atoms per unit cell, add two extra electrons to the system and also two extra low-lying bands below the Fermi level due to the hybridization of the hydrogen 1s and ytterbium 5d6s states [24]. These bands are "lled with four electrons: two from hydrogen and the other two from the ytterbium conduction band. As a result the original 5d6s states of the parent metal are completely depleted and the dihydride becomes an insulator. When the system undergoes phase transition from the orthorhombic dihydride to the cubic hydride phase due to a hydrogen concentration increase, a new hydrogen-like, low-lying band
259
below the Fermi level is created. Simultaneously, because of the 4fP4f5d electronic transition which accompanied the phase transition, the conduction band (probably 5d) is populated with an extra electron and the DOS at the Fermi level is again "nite. The conduction electrons remain strongly hybridized with 4f electron states. When the hydrogen content exceeds H/Yb"2.25, a further depopulation of the conduction states will occur, and the DOS at the Fermi energy will be gradually lowered. Finally, for the hypothetical composition YbH , the system should be insulating in the IV state with the Fermi level positioned in the energy gap between two sharp peaks in the DOS.
4. Conclusion We have shown that the low-temperature maximum observed in the magnetic susceptibility, s(¹), of the ytterbium deuterides (hydrides) re#ect an intermediate valence state of the ytterbium cations in this material. We have assumed that the temperature-dependence of the susceptibility around anomalies is determined by the temperature-dependence of the Dirac}Fermi distribution function, f (¹). Therefore, we propose to describe the mag$ netic susceptibility with a renormalized Sommerfeld formalism and a two band structure of the density of states at the Fermi level. Even with this very simpli"ed calculation we have got the correct shape of the susceptibility. Narrow quasiparticle bands (!"0.3 meV, D"1.35 meV) can account for the anomalous characteristics at low temperature as well as the Curie}Weiss behavior at high temperature.
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