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Possibility of Kondo effect in Gd-intermetallic-compound
Physica B 281&282 (2000) 178}180
Possibility of Kondo e!ect in Gd-intermetallic-compound A. Yazdani*, Rajaie Khorassani Tarbiat Modares University, P.O. Box 14155-4838, Tehran, Iran
Abstract Based on the crystal and magnetic structural properties of some Gd intermetallic compounds, it is shown that with increasing condition electron concentration (c.e.c) Gd experiences electronic and magnetic instability, and that these behaviors point to the appearance of the Kondo Lattice. We suggest that the conduction electrons have gained local character. It is shown that the Kondo e!ect should be observed at around x"0.4. Resistivity studies con"rm the calculation. A Kondo temperature of around 50 K was found for Gd Au Al . ( 2000 Elsevier Science B.V. All 2 0.4 0.6 rights reserved. Keywords: Kondo lattices; Electron localization
The theory of magnetic moment formation in intermetallic compounds has been a controversial subject for many decades [1,2]. One of the major points of dispute has been whether a model based on localized or itinerant is the most appropriate or rather which of the concepts of electron #uctuation, hybridization or electron localization are dominant. We considered how magnetic instability in itinerant intermetallic system arises. We chose as the subject of our study rare earth magnets with very stable 4f electrons, in particular Gd, with the aim of investing the possibility of the Kondo e!ect (Kondo lattice) in Gd Au Al inter2 x 1~x metallic compounds. Investigation of the magnetic and structural behavior of Gd Au Al compounds reveals the following ob2 x 1~x servations which show a dependency of crystal and magnetic structure and instability on c.e.c 1. X-ray studies of the lattice parameters show a nonlinear dependency on c.e.c and a deviation from Vegards rule [3]. 2. Shape dependency (powder &p' and needle &n') of magnetic behavior and the gap between the &p' and &n' samples at x"0.2}0.6 (in the same range where the
* Corresponding author. Fax: #98-21-8006544. E-mail address: [email protected] (A. Yazdani)
deviation from Vegards rule is exhibited) reveal the existence of a hidden magnetic energy [3]. A low value of s(¹) accompanied by a spreading in the magnetic phase transition (not a sharp transition) is also exhibited at x"0.4. With the c.e.c (decrease in x) the gap increases. The above shows magnetic moment #uctuation and high entropy which make the alignment of the moments impossible. These behaviors along with a low value of k could be %&& due to a canted system or absorbing electrons that reduce the ferromagnetic moments. The latter can even result in moment compensation. However, in the case of Gd 2 Al}Au compounds the absorption of electrons is not possible as Al and Gd atoms have "lled electron shells, and for Au it is not observable in Y Au [4]. 2 These observations point to the conduction electrons becoming bound. Resistivity studies con"rmed our line of thought and showed the Kondo e!ect for Gd Au Al (Fig. 1). 2 0.4 0.6
1. Method of calculations The "rst aim of our calculation was to anticipate the c.e.c at which the Kondo e!ect should manifest (for what compound should this e!ect be observed?). We also wished to calculate the e!ective mass of the conduction
0921-4526/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 1 2 2 - 9
A. Yazdani, R. Khorassani / Physica B 281&282 (2000) 178}180
179
Table 1 R !R for Gd I, Gd II and their nearest-neighbors where i j x"!0.473x#0.96 and z"0.067x#0.75 Gd
n.n"
R !R i j
Gd II
1 2 3 4 5 6
((x!0.66)2a2#0.25b2#(z!0.57)2c2 (0.25a2#(2z!0.5)2c2)1.@1 ((x!0.84)2a2#(z!1.07)2c2)1@2 ((x!1.16)2a2#0.25b2#(z!0.07)2c2)1@2 (2.25a2#(2z!0.5)2c2)1@2 ! ((x!1.34)2a2#(z!0.34)2c2)1@2
Gd I
1 2 3 4 5
((x!0.66)2a2#0.25b2#(0.34!z)2c2)1@2 ((x!1.16)2a2#0.25b2#(0.07!z)2c2)1@2 (0.109a2#0.25b2#c2)1@2 ((0.84!x)2a2#(0.07!z)2c2)1@2 ((1.34x)2a2#(z!0.43)2c2)1@2
Fig. 1. Variation of resistivity with ¹ for Gd Au Al . 2 0.4 0.6
electrons in that compound, which is an important parameter in addition to nonVegard rule behavior showing the extent of electron localization in heavy fermion study. 1. Because of the competition between interionic RKKY [5] regime and the Kondo e!ect we expect the Kondo e!ect to show itself where J is at a minimum (as ij a function of x). J is a function of separation of the ij magnetic ions DR !R D which itself can be calculated i j as a function of the lattice parameters and through them as a function of x(c.e.c) [6], z2F(2k DR !R D) & i j J J ij E & where 1 F(w)" (w cos w!sin w) with w"2k DR !R D. & i j u4 Gd has 5 and Gd has 6 nearest-neighbors [5]. I II DR !R D has been calculated for these nearest-neighi j bor ion pairs (Table 1). Using the above relations we considered the di!erent ion pairs, and calculated the x(c.e.c) corresponding to the minimum J for each ij pair (Table 2). For di!erent ion pairs the minimum J occurs at di!erent x. The only pair constitutes from ij two Gd II ions (R !R ) shows a minimum for G$II 5 J at x"0.46 (Fig. 2 shows the variation of J with ij ij x for R !R and the minimum is seen at G$II 5 x"0.46).Thereby we expect the Kondo e!ect at around x"0.46, which was con"rmed by our experimental work (Fig. 1). 2. One of the parameters which can show a measure of electron localization is the e!ective mass. Based on the above calculations and experimental result we were led to calculate the electron e!ective mass for Gd Au Al (x"0.4). 2 0.4 0.6
!This ion pair gave the minimum in J corresponding ij x "0.46 (Fig. 2). .*/ "Nearest-neighbor.
Table 2 The values of x for the nearest-neighbor ion pairs .*/ Type of Gd ions
R !R j i
x .*/
II-I II-II II-I II-I II-II II-I I-II I-II I-I I-II I-II
R !R G$II 1 R !R G$II 2 R !R G$II 3 R !R G$II 4 R !R G$II 5 R !R G$II 6 R !R G$I 1 R !R G$I 2 R !R G$I 3 R !R G$I 4 R !R G$I 5
0.55 1.57 0.90 0.37 0.46! 1.27 2.76 0.37 0.5 1.42 1.27
!The acceptable value for x
.*/
.
Fig. 2. Variation of J with x. ij
Our experimental result (Fig. 1) shows the observed Kondo temperature for Gd Au Al to be around 2 0.4 0.6 50 K. From the observed Kondo temperature (¹ ) J(0)s, K the exchange integral between the conduction electrons
180
A. Yazdani, R. Khorassani / Physica B 281&282 (2000) 178}180
and the localized 4f orbital electrons, can be calculated by
A
B
E 1 ¹ " & exp " k K g(E )J(0) & where J(0) can also be calculated by 2<2 J(0)" . E !E & 4& By varying mH in the above relations until the two J(0)s are equal we were able to calculate the e!ective mass. For mH"29m }35m the J(0)s for the two relations coincided. 0 0
References [1] R.M. Martin, Phys. Rev. Lett. 48 (1982) 362. [2] T. Brugger et al., Phys. Rev. Lett. 71 (1993) 248. [3] Yazdani, J.St. Gardner, Phys. Stat. Sol. B 208 (1998) 465. [4] J.K. Yakinthos, P.F. Ikonomou, T.A. Topolos, J. Magn. Magn. Mater. 8 (1978) 308. [5] T. Kasuya, Theor. Phys. 115 (1978) 45. [6] A. Yazdani, A. Ramazani, J. Sci. Iran 9 (3) (1998) 273.
Possibility of Kondo e!ect in Gd-intermetallic-compound A. Yazdani*, Rajaie Khorassani Tarbiat Modares University, P.O. Box 14155-4838, Tehran, Iran
Abstract Based on the crystal and magnetic structural properties of some Gd intermetallic compounds, it is shown that with increasing condition electron concentration (c.e.c) Gd experiences electronic and magnetic instability, and that these behaviors point to the appearance of the Kondo Lattice. We suggest that the conduction electrons have gained local character. It is shown that the Kondo e!ect should be observed at around x"0.4. Resistivity studies con"rm the calculation. A Kondo temperature of around 50 K was found for Gd Au Al . ( 2000 Elsevier Science B.V. All 2 0.4 0.6 rights reserved. Keywords: Kondo lattices; Electron localization
The theory of magnetic moment formation in intermetallic compounds has been a controversial subject for many decades [1,2]. One of the major points of dispute has been whether a model based on localized or itinerant is the most appropriate or rather which of the concepts of electron #uctuation, hybridization or electron localization are dominant. We considered how magnetic instability in itinerant intermetallic system arises. We chose as the subject of our study rare earth magnets with very stable 4f electrons, in particular Gd, with the aim of investing the possibility of the Kondo e!ect (Kondo lattice) in Gd Au Al inter2 x 1~x metallic compounds. Investigation of the magnetic and structural behavior of Gd Au Al compounds reveals the following ob2 x 1~x servations which show a dependency of crystal and magnetic structure and instability on c.e.c 1. X-ray studies of the lattice parameters show a nonlinear dependency on c.e.c and a deviation from Vegards rule [3]. 2. Shape dependency (powder &p' and needle &n') of magnetic behavior and the gap between the &p' and &n' samples at x"0.2}0.6 (in the same range where the
* Corresponding author. Fax: #98-21-8006544. E-mail address: [email protected] (A. Yazdani)
deviation from Vegards rule is exhibited) reveal the existence of a hidden magnetic energy [3]. A low value of s(¹) accompanied by a spreading in the magnetic phase transition (not a sharp transition) is also exhibited at x"0.4. With the c.e.c (decrease in x) the gap increases. The above shows magnetic moment #uctuation and high entropy which make the alignment of the moments impossible. These behaviors along with a low value of k could be %&& due to a canted system or absorbing electrons that reduce the ferromagnetic moments. The latter can even result in moment compensation. However, in the case of Gd 2 Al}Au compounds the absorption of electrons is not possible as Al and Gd atoms have "lled electron shells, and for Au it is not observable in Y Au [4]. 2 These observations point to the conduction electrons becoming bound. Resistivity studies con"rmed our line of thought and showed the Kondo e!ect for Gd Au Al (Fig. 1). 2 0.4 0.6
1. Method of calculations The "rst aim of our calculation was to anticipate the c.e.c at which the Kondo e!ect should manifest (for what compound should this e!ect be observed?). We also wished to calculate the e!ective mass of the conduction
0921-4526/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 1 2 2 - 9
A. Yazdani, R. Khorassani / Physica B 281&282 (2000) 178}180
179
Table 1 R !R for Gd I, Gd II and their nearest-neighbors where i j x"!0.473x#0.96 and z"0.067x#0.75 Gd
n.n"
R !R i j
Gd II
1 2 3 4 5 6
((x!0.66)2a2#0.25b2#(z!0.57)2c2 (0.25a2#(2z!0.5)2c2)1.@1 ((x!0.84)2a2#(z!1.07)2c2)1@2 ((x!1.16)2a2#0.25b2#(z!0.07)2c2)1@2 (2.25a2#(2z!0.5)2c2)1@2 ! ((x!1.34)2a2#(z!0.34)2c2)1@2
Gd I
1 2 3 4 5
((x!0.66)2a2#0.25b2#(0.34!z)2c2)1@2 ((x!1.16)2a2#0.25b2#(0.07!z)2c2)1@2 (0.109a2#0.25b2#c2)1@2 ((0.84!x)2a2#(0.07!z)2c2)1@2 ((1.34x)2a2#(z!0.43)2c2)1@2
Fig. 1. Variation of resistivity with ¹ for Gd Au Al . 2 0.4 0.6
electrons in that compound, which is an important parameter in addition to nonVegard rule behavior showing the extent of electron localization in heavy fermion study. 1. Because of the competition between interionic RKKY [5] regime and the Kondo e!ect we expect the Kondo e!ect to show itself where J is at a minimum (as ij a function of x). J is a function of separation of the ij magnetic ions DR !R D which itself can be calculated i j as a function of the lattice parameters and through them as a function of x(c.e.c) [6], z2F(2k DR !R D) & i j J J ij E & where 1 F(w)" (w cos w!sin w) with w"2k DR !R D. & i j u4 Gd has 5 and Gd has 6 nearest-neighbors [5]. I II DR !R D has been calculated for these nearest-neighi j bor ion pairs (Table 1). Using the above relations we considered the di!erent ion pairs, and calculated the x(c.e.c) corresponding to the minimum J for each ij pair (Table 2). For di!erent ion pairs the minimum J occurs at di!erent x. The only pair constitutes from ij two Gd II ions (R !R ) shows a minimum for G$II 5 J at x"0.46 (Fig. 2 shows the variation of J with ij ij x for R !R and the minimum is seen at G$II 5 x"0.46).Thereby we expect the Kondo e!ect at around x"0.46, which was con"rmed by our experimental work (Fig. 1). 2. One of the parameters which can show a measure of electron localization is the e!ective mass. Based on the above calculations and experimental result we were led to calculate the electron e!ective mass for Gd Au Al (x"0.4). 2 0.4 0.6
!This ion pair gave the minimum in J corresponding ij x "0.46 (Fig. 2). .*/ "Nearest-neighbor.
Table 2 The values of x for the nearest-neighbor ion pairs .*/ Type of Gd ions
R !R j i
x .*/
II-I II-II II-I II-I II-II II-I I-II I-II I-I I-II I-II
R !R G$II 1 R !R G$II 2 R !R G$II 3 R !R G$II 4 R !R G$II 5 R !R G$II 6 R !R G$I 1 R !R G$I 2 R !R G$I 3 R !R G$I 4 R !R G$I 5
0.55 1.57 0.90 0.37 0.46! 1.27 2.76 0.37 0.5 1.42 1.27
!The acceptable value for x
.*/
.
Fig. 2. Variation of J with x. ij
Our experimental result (Fig. 1) shows the observed Kondo temperature for Gd Au Al to be around 2 0.4 0.6 50 K. From the observed Kondo temperature (¹ ) J(0)s, K the exchange integral between the conduction electrons
180
A. Yazdani, R. Khorassani / Physica B 281&282 (2000) 178}180
and the localized 4f orbital electrons, can be calculated by
A
B
E 1 ¹ " & exp " k K g(E )J(0) & where J(0) can also be calculated by 2<2 J(0)" . E !E & 4& By varying mH in the above relations until the two J(0)s are equal we were able to calculate the e!ective mass. For mH"29m }35m the J(0)s for the two relations coincided. 0 0
References [1] R.M. Martin, Phys. Rev. Lett. 48 (1982) 362. [2] T. Brugger et al., Phys. Rev. Lett. 71 (1993) 248. [3] Yazdani, J.St. Gardner, Phys. Stat. Sol. B 208 (1998) 465. [4] J.K. Yakinthos, P.F. Ikonomou, T.A. Topolos, J. Magn. Magn. Mater. 8 (1978) 308. [5] T. Kasuya, Theor. Phys. 115 (1978) 45. [6] A. Yazdani, A. Ramazani, J. Sci. Iran 9 (3) (1998) 273.