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First observations of a magnetic exchange induced valence transition
Journal of Magnetism and Magnetic Materials 52 (1985) 91-95 North-Holland, Amsterdam
INVITED
91
PAPER
FIRST OBSERVATION
OF A MAGNETIC
W. R E I M , H. B O P P A R T
a n d P. W A C H T E R
EXCHANGE
INDUCED
VALENCE
TRANSITION
Laboratorium ff~r FestkOrperphysik, Eidgen~ssische Technische Hochschule Z~trich, 8093 Z~rich, Switzerkmd
In the pseudobinary alloy system Tml_xEuxSe the compounds for x > 0.25 are semiconductors with a spontaneous magnetic moment. For 0.25 < x < 1 the energy gap Tm 4f 13-5d is less than 200 meV and this gap closes spontaneously below Ty due to the exchange induced splitting of the conduction band (red shift), causing a semiconductor-metal transition. This is monitored by the magneto-optical Kerr effect of the Eu 4f 7 - 5 d transition. The metallic state is intermediate valent and induces a votume collapse up to about 1% which is measured as a function of temperature. Within the pseudobinary system T m l _ x E u x S e the substitution of the Eu ions by the smaller T m ions leads to a reduction of the lattice constant. Compounds with 0.25 < x ~<'1 are semiconductors and at x = 0.2 a compositionally induced semiconductor to metal transition (SMT) has been observed [1,2]. For 0 ~< x < 0.2 the compounds are intermediate valent (IV). For semiconducting compositions the energy gap is determined by the separation in energy of the TmZ+4f t3 level and the 5d conduction band. The EuZ+4f 7 state is lying about 1.85 eV below the conduction band (fig. 1) [3]. The magnitude of the semiconducting gap Eg has been determined from the exponential variation of the electrical resistivity with hydrostatic pressure, showing a l n ( p ) - p dependence up to the pressure induced SMT [4]. This indicates a linear closing of the gap with external pressure. The gap Eg is also found to decrease linearly with composition x from about 200 meV for x = 0.85 down to about 40 meV at x = 0.29 near the compositionally induced SMT [4]. In this paper we report for the first time on a magnetic exchange induced SMT, which we found to occur in T m l _ x E u x S e for 0.25 ~< x ~< 0.85. It will be shown that via the exchange splitting of the 5d conduction band, which is studied by optical absorption, reflectivity and the polar magnetooptical Kerr effect, the semiconducting gap becomes closed followed by a valence change of the T m ions from 2.0 to 2.15. The transition into the intermediate valence phase manifests itself in a volume collapse of about 1%. In the case of EuSe (and of course the other ferromagnetically ordering Eu chalcogenides) it is well known that the energy of the 4f 7 --~4f65dt2g transition becomes reduced when the sample gets magnetized (magnetic red shift) [5]. In a simple model which, however, describes the physics of this effect quite well, the mag0304-8853/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
netic red shift is explained by an exchange splitting of the 5d band [5] (for more complex models refer to ref. [6]). The spin polarized subbands are separated in energy by 2 A E = b J r d ( S i S s ) / S 2, with the intra-atomic f d exchange Jfd, the spin correlation function ( S i S j ) / S 2 and b a scaling factor. For EuSe A E = 130 meV in 1.45 T [5] and 160 meV in 4 T, which is the same order of magnitude as Eg in T m t _ , E u x S e and hence it suggests a possible closing of the gap Eg with temperature if A E is sufficiently large also in this system.
(eV)
Tml_xEuxSe
~
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t2g 4f 13 T m ~ O
Eu m
4f z -2
-4
4p
Fig. 1. Energy level scheme of Tm 1_~ Eu ~Se.
144 Reim et al. / Magnetic exchange induced valence transition
92
A direct study of the Tm2+4f 1-~---, 4fl25dt2g transition, however, is difficult because of substantial free carrier absorption in this energy range. The composition with the lowest free carrier concentration is Tm0.15 Eu0.ssSe and by careful selection of a large enough single crystal from this batch together with a lucky handling of the thinning procedure we have been able to measure optical transmission in the infrared as a function of temperature. This is shown in fig. 2 where the absorption coefficient is plotted versus the photon energy. At 300 K we observe an absorption edge and a free carrier absorption, resulting in a m i n i m u m of the absorption coefficient. With lower temperature, but still in the paramagnetic temperature range, this m i n i m u m deepens. At 100 K we can extract an absorption edge Eg of about 200 meV, substracting a fitted Drude absorption tail due to free carriers. We also realize that in this temperature range the free carrier absorption is decreasing in accordance with the semiconducting behavior of this compound. At temperatures below about 30 K, at the onset of the spin correlation function (about 2 to 3 times TN) we discern a red shifting knee in the absorption spectrum (the T m concentration is only 15%) and at the same time below about 10 K an increase of the free carrier absorption, i.e. the gap closes faster than k T with decreasing temperature: d E g / d T < O . This is in
agreement with conclusions drawn on the basis of electrical resistivity and carrier concentration measurements on the same composition [7]. At temperatures below 4.5 K the gap is practically closed (see fig. 2) and no transmission is anymore possible. Instead, the reflectivity could be measured on a cleaved crystal of the same batch and it is displayed in fig. 3. Between 300 and 6 K the reflectivity is unchanged and near 10% indicating semiconducting behavior. Only at 4 and 2 K the reflectivity increases sharply towards o~-~ 0 because of the plasma edge of the free carriers, indicating metallic behavior. In fig. 3 we show also the reflectivity of a cleaved crystal of composition Tm0.sEu0.sSe for selected temperatures. Here we observe already at room temperature a plasma edge in the infrared because of the smaller g a p Eg. At temperatures below 8 K we observe a large shift of the plasma edge towards higher energies indicating a significant increase of the free carrier concentration. A generally applicable method to monitor the SMT also on more Tm containing compositions is to use the Eu2+4f 7 ~ 4f65dt2g transition as a probe to study the energy and exchange splitting of the 5d band. A high resolution measurement of the 4f 7 excitation is achieved
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93
HIt Reim et al. / Magnetic exchange induced ~'alence transition
exchange induced S M T in semiconducting T m t -x E u , Se for 0.25 ~< x ~< 0.85. The S M T should go c o n c o m i t a n t with a transition to intermediate valence of the T m ion. Fig. 5b postulates the largest valence change for x = 0.5 with the b o t t o m of the conduction b a n d 140 meV below E v at 2 K. A simple estimate of the m a g n i t u d e of the valence change assuming a c o n d u c t i o n electron density of states of 1 e / e V spin gives a valence change of 0.15. It is k n o w n from volume versus pressure measurem e n t s [4] that the conversion of 15% T m 2+ into T m 3+ in the average is a c c o m p a n i e d by a volume collapse of 1%. T h u s in order to verify our interpretation of fig. 5b we have performed length change m e a s u r e m e n t s using a capacitance dilatometer having a sensitivity of 10-8 a n d an accuracy of _+2%. Fig. 6 displays A l / l for different semiconducting ( x = 0.85, 0.50, 0.38) and metallic ( x = 0 . 1 ~ compositions of T m 1 xEuxSe and shows for comparison the length change of EuS, measured with the same apparatus. T h e indicated ordering temperatures have been determined from low field susceptibility data
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by the polar magneto-optical Kerr effect OK measured on cleaved single crystals. Fig. 4 displays typical curves at temperatures above a n d below the magnetic ordering t e m p e r a t u r e of 13 K for Tm0.tsEu0.85Se indicating A E = 190 meV in 4 T. A t room t e m p e r a t u r e the onset energy of the 4f 7 _.., 4f65dt2~ excitation in OK a m o u n t s to 2.08 eV in EuSe ( s o m e w b a t larger t h a n the gap of 1.85 eV determined by optical a b s o r p t i o n [5]) a n d decreases linearly with x d o w n to 1.92 eV for x = 0.38. Subtracting the respective m a g n i t u d e s of Eg [4] from these energies yields the position of the T m 2 + 4f 13 state relative to the Eu 2 + 4f 7 level, which comes out to be i n d e p e n d e n t of composition x (fig. 5a). The onset energy at temperatures well below the magnetic ordering temperature, on the o t h e r h a n d , is reduced by the observed magnetic red shift A E (fig. 5b). It comes to a surprise that A E for 0.29 ~< x ~< 0.85 is larger t h a n in EuSe itself. A s s u m i n g a temperature i n d e p e n d e n t separation in energy of the T m 2 + a n d E u 2 + 4 f states, a crossing of the lower 5d b a n d edge with the Tm2+4f 13 level occurs for x ~< 0.85. In other words this low t e m p e r a t u r e energy level scheme predicts an
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Fig. 5. (a) Onset energy of the Eu2+4f 7--) 4f65dt2g transition in Tm 1 xEuxSe at 300 K as a function of x from the polar Kerr effect. The subtraction of the respective semiconducting gap energy Eg yields the position of the Tm2+4f 13 state relative to the Eu2+4f v level; (b) onset energy of the same Eu 2+ excitation at 2 K. Compared to the value at 300 K, this energy is smaller by the size of the magnetic red-shift AE. The energy separation of the Eu 2+ and Tm2+4f states is kept constant•
W. Reim et al. / Magnetic exchange induced valence transition
94
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20 30 40 50 TEMPERATURE (K) Fig. 5. Thermal expansion h l / l of semiconducting (x = 0.85, 0.50, 0.38) and intermediate valent (x = 0.11) compositions of Tm 1 ,.EuxSe in the temperature range near magnetic ordering. EuS has been measured for comparison. The influence of an applied magnetic field of 4 kG on Al/I is also shown.
on the identical samples. For the reference material EuS A l / l displays the expected behavior of a volume magnetostriction (exchange striction) with maximum slope of A l / l (or a peak in the expansion coefficient a = 1 / l ( d l / d T ) ) at the magnetic ordering temperature and a magnetic contraction of A V / V = 1.2 × 10 -3 [8]. The most contrasting behavior shows Tm0.sEu0.sSe with clearly no relation between maximum slope and TN: (The compounds 0.25 ~< x ~< 0.85 are canted antiferromagnets with spontaneous magnetic moments [4].) In addition this compound shows the largest volume collapse of 1.1%, 10 times larger than EuS. A similar behavior is found for x = 0.38, whereas the sample with the largest gap, x = 0.85, but also the compositionally induced intermediate valent compound x = 0.11 display
much smaller contractions by factors of 30 and 300, respectively. The observed variation of 21V/V with temperature in semiconducting T m 1 xEu~Se can hardly be related to exchange striction as in EuS. Apart from the missing relationship between T N and maximum thermal expansion, this statement is supported by the variation of A V / V by a factor of 300 in this system, although TN changes only by a factor of 3. Since the magnitude of the exchange striction is proportional to the internal magnetic energy Um, which in turn can be calculated from the magnetic coupling parameter J12 the exchange striction is proportional to T N [9]. However, the observed volume reductions are in excellent agreement with fig. 5b. For x = 0.15 the exchange splitting of the conduction band just equals Eg. Because A E follows the spin correlation function [5], the bottom of the 5d band approaches the Tm2+4f 13 state only at T<< Ty which leads to minor changes in A V / V below TN/2, corresponding to a valence change of < 0.02. In the case of Tm0.sEu05Se, on the other hand, A E ( T ) equals Eg already at higher temperatures, but still well below T N, while for x = 0.38 the gap becomes closed near T N because of the reduced magnitude of the semiconducting gap. Fig. 7 displays the energy of the bottom of the 5dt2g band relative to the TmZ+4f 13 level as determined from the temperature dependence of the magnetic red shift AE(T). In addition, the valence of the Tm ions is shown, calculated form AV/V. It is remarkable that the valence for Tm0.sEu0.sSe changes only by 0.01 until the
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.... o; - -/- ,
,
,
30
40
,
215
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10
20
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T E M P E R A T U R E (K) Fig. 7. Temperature dependence of the lower 5d band edge as derived from magneto-optics and magnetization measurements at 4 kG for Tmo.sEu0.sSe. The temperature variation of the Tm valence is calculated from the measured volume change using Vegards law.
HA Reim et al. / Magnetic exchange induced valence transition gap is closed, although the magnetization has raised to half of its saturation value. However, as soon as the gap is closed, the Tm valence alters rapidly with te~nperature. For the compositionally induced intermediate valent compound x = 0.11, the T m valence at room temperature is estimated from lattice constant data to be 2.6. Both spin polarized 5d subbands are now partly occupied already at room temperature which can be extracted from the conduction electron spin polarization of TmSe of 30% [10]. However, if both 5d subbands are partly occupied, the temperature variation of 2 A E only induces a change in the occupation numbers of these subbands, but the numbers of conduction electrons and hence the valence of T m is nearly independent of temperature. The observed A V / V = 10 -4 is attributed to a pure magnetostrictive effect, similar as for TmSe, which displays a volume magnetoelastic effect of the same order of magnitude [11]. Since the compound with x = 0.11 is metallic over the whole investigated temperature range, A l / l and a is different in the paramagnetic region from the semiconducting compositions 0.25 ~< x ~< 0.85 as can be seen from fig. 6. It should be mentioned that the spontaneous magnetization decreases with (1 - x ) and becomes zero at the compositionally induced SMT. Therefore the influence of a magnetic field on A E increases with (1 - x), which in fact has been observed (fig. 6). We have shown that a magnetic exchange induced S M T occurs in semiconducting T m l_:,EuX for 0.25 ~< x ~< 0.85. It could be demonstrated that the hybridization of d and f wave functions is negligible as long as the semiconducting gap is present. This behavior contrasts the observation of substantial valence mixing in TmSe 1_~,Tex already for semiconducting compositions x [12]. In the latter system the substitution of Te with the smaller Se creates lattice pressure on the T m ions. In the
95
former system the substitution of Eu with the smaller T m creates no lattice pressure on the Tm ion, only the gap Eg becomes reduced. The Eu ions, however, are responsible for the enhanced magnetic exchange. The authors are grateful to Dr. E. Kaldis for the growth and chemical characterization of the single crystals and to Dr. J. Schoenes for some critical discussions. We acknowledge the assistance of L. Frey and K. Mattenberger in part of the experiments. H.P. Staub has developed the dilatometer and performed the length change experiments without which this paper could not have been written.
References [1] B. Batlogg, E. Kaldis and P. Wachter, J. de Phys. 40-C5 (1979) 370. [2] E. Kaldis and B. Fritzler, J. de Phys. 41-C5 (1980) 135. [3] B. Batlogg, Phys. Rev. B23 (1981) 650. [4] H. Boppart and P. Wachter, in: Physics of Solids under High Pressure, eds. J.S. Schilling and R.N. Shelton (North-Holland, Amsterdam, 1981) p. 301. [5] P. Wachter, in: Handbook on the Physics and Chemistry of Rare Earths, vol. 2, eds. K.A. Gschneidner and L. Eyring (North-Holland, Amsterdam, 1979) p. 509. [6] W. Nolting, Phys. Star. Sol. (b) 79 (1977) 573. [7] H, Boppart and P. Wachter, J. Appl. Phys. 52 (1981) 2161. [8] F. Levy, Physik Kondens. Mater. 10 (1969) 71. [9] B.E. Argyle, N. Miyata and T.D. Schultz, Phys. Rev. 160 (1967) 413. [10] W. Reim, O.E. H~sser, J. Schoenes, E. Kaldis and P. Wachter, J. Appl. Phys. 52 (1984) 2155. [11] B. Batlogg, E. Kaldis and H.R. Ott, Phys. Lett. 62A (1977) 270. [12] H. Boppart and P. Wachter, Phys. Rev. kett. 53 (1984) 1759.
INVITED
91
PAPER
FIRST OBSERVATION
OF A MAGNETIC
W. R E I M , H. B O P P A R T
a n d P. W A C H T E R
EXCHANGE
INDUCED
VALENCE
TRANSITION
Laboratorium ff~r FestkOrperphysik, Eidgen~ssische Technische Hochschule Z~trich, 8093 Z~rich, Switzerkmd
In the pseudobinary alloy system Tml_xEuxSe the compounds for x > 0.25 are semiconductors with a spontaneous magnetic moment. For 0.25 < x < 1 the energy gap Tm 4f 13-5d is less than 200 meV and this gap closes spontaneously below Ty due to the exchange induced splitting of the conduction band (red shift), causing a semiconductor-metal transition. This is monitored by the magneto-optical Kerr effect of the Eu 4f 7 - 5 d transition. The metallic state is intermediate valent and induces a votume collapse up to about 1% which is measured as a function of temperature. Within the pseudobinary system T m l _ x E u x S e the substitution of the Eu ions by the smaller T m ions leads to a reduction of the lattice constant. Compounds with 0.25 < x ~<'1 are semiconductors and at x = 0.2 a compositionally induced semiconductor to metal transition (SMT) has been observed [1,2]. For 0 ~< x < 0.2 the compounds are intermediate valent (IV). For semiconducting compositions the energy gap is determined by the separation in energy of the TmZ+4f t3 level and the 5d conduction band. The EuZ+4f 7 state is lying about 1.85 eV below the conduction band (fig. 1) [3]. The magnitude of the semiconducting gap Eg has been determined from the exponential variation of the electrical resistivity with hydrostatic pressure, showing a l n ( p ) - p dependence up to the pressure induced SMT [4]. This indicates a linear closing of the gap with external pressure. The gap Eg is also found to decrease linearly with composition x from about 200 meV for x = 0.85 down to about 40 meV at x = 0.29 near the compositionally induced SMT [4]. In this paper we report for the first time on a magnetic exchange induced SMT, which we found to occur in T m l _ x E u x S e for 0.25 ~< x ~< 0.85. It will be shown that via the exchange splitting of the 5d conduction band, which is studied by optical absorption, reflectivity and the polar magnetooptical Kerr effect, the semiconducting gap becomes closed followed by a valence change of the T m ions from 2.0 to 2.15. The transition into the intermediate valence phase manifests itself in a volume collapse of about 1%. In the case of EuSe (and of course the other ferromagnetically ordering Eu chalcogenides) it is well known that the energy of the 4f 7 --~4f65dt2g transition becomes reduced when the sample gets magnetized (magnetic red shift) [5]. In a simple model which, however, describes the physics of this effect quite well, the mag0304-8853/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
netic red shift is explained by an exchange splitting of the 5d band [5] (for more complex models refer to ref. [6]). The spin polarized subbands are separated in energy by 2 A E = b J r d ( S i S s ) / S 2, with the intra-atomic f d exchange Jfd, the spin correlation function ( S i S j ) / S 2 and b a scaling factor. For EuSe A E = 130 meV in 1.45 T [5] and 160 meV in 4 T, which is the same order of magnitude as Eg in T m t _ , E u x S e and hence it suggests a possible closing of the gap Eg with temperature if A E is sufficiently large also in this system.
(eV)
Tml_xEuxSe
~
ee5d
t2g 4f 13 T m ~ O
Eu m
4f z -2
-4
4p
Fig. 1. Energy level scheme of Tm 1_~ Eu ~Se.
144 Reim et al. / Magnetic exchange induced valence transition
92
A direct study of the Tm2+4f 1-~---, 4fl25dt2g transition, however, is difficult because of substantial free carrier absorption in this energy range. The composition with the lowest free carrier concentration is Tm0.15 Eu0.ssSe and by careful selection of a large enough single crystal from this batch together with a lucky handling of the thinning procedure we have been able to measure optical transmission in the infrared as a function of temperature. This is shown in fig. 2 where the absorption coefficient is plotted versus the photon energy. At 300 K we observe an absorption edge and a free carrier absorption, resulting in a m i n i m u m of the absorption coefficient. With lower temperature, but still in the paramagnetic temperature range, this m i n i m u m deepens. At 100 K we can extract an absorption edge Eg of about 200 meV, substracting a fitted Drude absorption tail due to free carriers. We also realize that in this temperature range the free carrier absorption is decreasing in accordance with the semiconducting behavior of this compound. At temperatures below about 30 K, at the onset of the spin correlation function (about 2 to 3 times TN) we discern a red shifting knee in the absorption spectrum (the T m concentration is only 15%) and at the same time below about 10 K an increase of the free carrier absorption, i.e. the gap closes faster than k T with decreasing temperature: d E g / d T < O . This is in
agreement with conclusions drawn on the basis of electrical resistivity and carrier concentration measurements on the same composition [7]. At temperatures below 4.5 K the gap is practically closed (see fig. 2) and no transmission is anymore possible. Instead, the reflectivity could be measured on a cleaved crystal of the same batch and it is displayed in fig. 3. Between 300 and 6 K the reflectivity is unchanged and near 10% indicating semiconducting behavior. Only at 4 and 2 K the reflectivity increases sharply towards o~-~ 0 because of the plasma edge of the free carriers, indicating metallic behavior. In fig. 3 we show also the reflectivity of a cleaved crystal of composition Tm0.sEu0.sSe for selected temperatures. Here we observe already at room temperature a plasma edge in the infrared because of the smaller g a p Eg. At temperatures below 8 K we observe a large shift of the plasma edge towards higher energies indicating a significant increase of the free carrier concentration. A generally applicable method to monitor the SMT also on more Tm containing compositions is to use the Eu2+4f 7 ~ 4f65dt2g transition as a probe to study the energy and exchange splitting of the 5d band. A high resolution measurement of the 4f 7 excitation is achieved
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93
HIt Reim et al. / Magnetic exchange induced ~'alence transition
exchange induced S M T in semiconducting T m t -x E u , Se for 0.25 ~< x ~< 0.85. The S M T should go c o n c o m i t a n t with a transition to intermediate valence of the T m ion. Fig. 5b postulates the largest valence change for x = 0.5 with the b o t t o m of the conduction b a n d 140 meV below E v at 2 K. A simple estimate of the m a g n i t u d e of the valence change assuming a c o n d u c t i o n electron density of states of 1 e / e V spin gives a valence change of 0.15. It is k n o w n from volume versus pressure measurem e n t s [4] that the conversion of 15% T m 2+ into T m 3+ in the average is a c c o m p a n i e d by a volume collapse of 1%. T h u s in order to verify our interpretation of fig. 5b we have performed length change m e a s u r e m e n t s using a capacitance dilatometer having a sensitivity of 10-8 a n d an accuracy of _+2%. Fig. 6 displays A l / l for different semiconducting ( x = 0.85, 0.50, 0.38) and metallic ( x = 0 . 1 ~ compositions of T m 1 xEuxSe and shows for comparison the length change of EuS, measured with the same apparatus. T h e indicated ordering temperatures have been determined from low field susceptibility data
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by the polar magneto-optical Kerr effect OK measured on cleaved single crystals. Fig. 4 displays typical curves at temperatures above a n d below the magnetic ordering t e m p e r a t u r e of 13 K for Tm0.tsEu0.85Se indicating A E = 190 meV in 4 T. A t room t e m p e r a t u r e the onset energy of the 4f 7 _.., 4f65dt2~ excitation in OK a m o u n t s to 2.08 eV in EuSe ( s o m e w b a t larger t h a n the gap of 1.85 eV determined by optical a b s o r p t i o n [5]) a n d decreases linearly with x d o w n to 1.92 eV for x = 0.38. Subtracting the respective m a g n i t u d e s of Eg [4] from these energies yields the position of the T m 2 + 4f 13 state relative to the Eu 2 + 4f 7 level, which comes out to be i n d e p e n d e n t of composition x (fig. 5a). The onset energy at temperatures well below the magnetic ordering temperature, on the o t h e r h a n d , is reduced by the observed magnetic red shift A E (fig. 5b). It comes to a surprise that A E for 0.29 ~< x ~< 0.85 is larger t h a n in EuSe itself. A s s u m i n g a temperature i n d e p e n d e n t separation in energy of the T m 2 + a n d E u 2 + 4 f states, a crossing of the lower 5d b a n d edge with the Tm2+4f 13 level occurs for x ~< 0.85. In other words this low t e m p e r a t u r e energy level scheme predicts an
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Fig. 5. (a) Onset energy of the Eu2+4f 7--) 4f65dt2g transition in Tm 1 xEuxSe at 300 K as a function of x from the polar Kerr effect. The subtraction of the respective semiconducting gap energy Eg yields the position of the Tm2+4f 13 state relative to the Eu2+4f v level; (b) onset energy of the same Eu 2+ excitation at 2 K. Compared to the value at 300 K, this energy is smaller by the size of the magnetic red-shift AE. The energy separation of the Eu 2+ and Tm2+4f states is kept constant•
W. Reim et al. / Magnetic exchange induced valence transition
94
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20 30 40 50 TEMPERATURE (K) Fig. 5. Thermal expansion h l / l of semiconducting (x = 0.85, 0.50, 0.38) and intermediate valent (x = 0.11) compositions of Tm 1 ,.EuxSe in the temperature range near magnetic ordering. EuS has been measured for comparison. The influence of an applied magnetic field of 4 kG on Al/I is also shown.
on the identical samples. For the reference material EuS A l / l displays the expected behavior of a volume magnetostriction (exchange striction) with maximum slope of A l / l (or a peak in the expansion coefficient a = 1 / l ( d l / d T ) ) at the magnetic ordering temperature and a magnetic contraction of A V / V = 1.2 × 10 -3 [8]. The most contrasting behavior shows Tm0.sEu0.sSe with clearly no relation between maximum slope and TN: (The compounds 0.25 ~< x ~< 0.85 are canted antiferromagnets with spontaneous magnetic moments [4].) In addition this compound shows the largest volume collapse of 1.1%, 10 times larger than EuS. A similar behavior is found for x = 0.38, whereas the sample with the largest gap, x = 0.85, but also the compositionally induced intermediate valent compound x = 0.11 display
much smaller contractions by factors of 30 and 300, respectively. The observed variation of 21V/V with temperature in semiconducting T m 1 xEu~Se can hardly be related to exchange striction as in EuS. Apart from the missing relationship between T N and maximum thermal expansion, this statement is supported by the variation of A V / V by a factor of 300 in this system, although TN changes only by a factor of 3. Since the magnitude of the exchange striction is proportional to the internal magnetic energy Um, which in turn can be calculated from the magnetic coupling parameter J12 the exchange striction is proportional to T N [9]. However, the observed volume reductions are in excellent agreement with fig. 5b. For x = 0.15 the exchange splitting of the conduction band just equals Eg. Because A E follows the spin correlation function [5], the bottom of the 5d band approaches the Tm2+4f 13 state only at T<< Ty which leads to minor changes in A V / V below TN/2, corresponding to a valence change of < 0.02. In the case of Tm0.sEu05Se, on the other hand, A E ( T ) equals Eg already at higher temperatures, but still well below T N, while for x = 0.38 the gap becomes closed near T N because of the reduced magnitude of the semiconducting gap. Fig. 7 displays the energy of the bottom of the 5dt2g band relative to the TmZ+4f 13 level as determined from the temperature dependence of the magnetic red shift AE(T). In addition, the valence of the Tm ions is shown, calculated form AV/V. It is remarkable that the valence for Tm0.sEu0.sSe changes only by 0.01 until the
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T E M P E R A T U R E (K) Fig. 7. Temperature dependence of the lower 5d band edge as derived from magneto-optics and magnetization measurements at 4 kG for Tmo.sEu0.sSe. The temperature variation of the Tm valence is calculated from the measured volume change using Vegards law.
HA Reim et al. / Magnetic exchange induced valence transition gap is closed, although the magnetization has raised to half of its saturation value. However, as soon as the gap is closed, the Tm valence alters rapidly with te~nperature. For the compositionally induced intermediate valent compound x = 0.11, the T m valence at room temperature is estimated from lattice constant data to be 2.6. Both spin polarized 5d subbands are now partly occupied already at room temperature which can be extracted from the conduction electron spin polarization of TmSe of 30% [10]. However, if both 5d subbands are partly occupied, the temperature variation of 2 A E only induces a change in the occupation numbers of these subbands, but the numbers of conduction electrons and hence the valence of T m is nearly independent of temperature. The observed A V / V = 10 -4 is attributed to a pure magnetostrictive effect, similar as for TmSe, which displays a volume magnetoelastic effect of the same order of magnitude [11]. Since the compound with x = 0.11 is metallic over the whole investigated temperature range, A l / l and a is different in the paramagnetic region from the semiconducting compositions 0.25 ~< x ~< 0.85 as can be seen from fig. 6. It should be mentioned that the spontaneous magnetization decreases with (1 - x ) and becomes zero at the compositionally induced SMT. Therefore the influence of a magnetic field on A E increases with (1 - x), which in fact has been observed (fig. 6). We have shown that a magnetic exchange induced S M T occurs in semiconducting T m l_:,EuX for 0.25 ~< x ~< 0.85. It could be demonstrated that the hybridization of d and f wave functions is negligible as long as the semiconducting gap is present. This behavior contrasts the observation of substantial valence mixing in TmSe 1_~,Tex already for semiconducting compositions x [12]. In the latter system the substitution of Te with the smaller Se creates lattice pressure on the T m ions. In the
95
former system the substitution of Eu with the smaller T m creates no lattice pressure on the Tm ion, only the gap Eg becomes reduced. The Eu ions, however, are responsible for the enhanced magnetic exchange. The authors are grateful to Dr. E. Kaldis for the growth and chemical characterization of the single crystals and to Dr. J. Schoenes for some critical discussions. We acknowledge the assistance of L. Frey and K. Mattenberger in part of the experiments. H.P. Staub has developed the dilatometer and performed the length change experiments without which this paper could not have been written.
References [1] B. Batlogg, E. Kaldis and P. Wachter, J. de Phys. 40-C5 (1979) 370. [2] E. Kaldis and B. Fritzler, J. de Phys. 41-C5 (1980) 135. [3] B. Batlogg, Phys. Rev. B23 (1981) 650. [4] H. Boppart and P. Wachter, in: Physics of Solids under High Pressure, eds. J.S. Schilling and R.N. Shelton (North-Holland, Amsterdam, 1981) p. 301. [5] P. Wachter, in: Handbook on the Physics and Chemistry of Rare Earths, vol. 2, eds. K.A. Gschneidner and L. Eyring (North-Holland, Amsterdam, 1979) p. 509. [6] W. Nolting, Phys. Star. Sol. (b) 79 (1977) 573. [7] H, Boppart and P. Wachter, J. Appl. Phys. 52 (1981) 2161. [8] F. Levy, Physik Kondens. Mater. 10 (1969) 71. [9] B.E. Argyle, N. Miyata and T.D. Schultz, Phys. Rev. 160 (1967) 413. [10] W. Reim, O.E. H~sser, J. Schoenes, E. Kaldis and P. Wachter, J. Appl. Phys. 52 (1984) 2155. [11] B. Batlogg, E. Kaldis and H.R. Ott, Phys. Lett. 62A (1977) 270. [12] H. Boppart and P. Wachter, Phys. Rev. kett. 53 (1984) 1759.