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Hyperfine interactions in europium chalcogenides
Journal of Magnetism and Magnetic Materials 31-34 (1983) 427-428 HYPERFINE K. U E N O
INTERACTIONS
*, A. Y A N A S E
427
IN EUROPIUM
CHALCOGENIDES
** a n d T. K A S U Y A
Department of Physics, Tohoku University, Sendai Japan
The hyperfine interaction in europium chalcogenides is discussed theoretically. The f-s transfer mechanism explains the nearest neighbour transferred hyperfine interaction. Moreover the p-s and p - f transfer mechanisms explain the next nearest neighbour transferred hyperfine interaction. The estimated values and chalcogen dependences of these are in good agreement with the experiments.
The series of the divalent europium chalcogenides EuX is considered to be a good representation of the simple Heisenberg magnets. The exchange interaction between two localized 4f spins S~, and Sj at lattice points R~ and R j of Eu 2+ is expressed in terms of an exchange constant J q , and is of the form /-/ox = - 2S, jS, Sj.
Xx .x
AijliSj.
= U-
(l)
0304-8853/83/0000-0000/$03.00
"',
,
,
' - -'
X.
r
'-'--'-----~ "-x-
~
2
®
/, 0.~ . . . .
Z5
(3)
* Present address: Fuji Electric Corporate Research and Development Ltd. 2-2-1 Nagasaka, Yokosuka 240-01, Japan. ** Present address: Integrated Arts of Science, University of Osaka Prefecture, Sakai 591, Japan.
2i
4
(2)
When i is different from j , the field is called the transferred hyperfine field (THF). The values of J/j can be determined in a variety of experiments [1] and the values of Aij are determined in the nuclear magnetic resonance in the various magnetic phases of EuX or Eu I _~SrxX [2,3]. The experimental values of the T H F and the exchange constants are shown in fig. 1. The chalcogen dependences of the nearest neighbour (nn) exchange J! and the T H F H, are similar to each other with positive values, even though it is not clear for H t in EuTe within experimental accuracy. The next nearest neighbour (nnn) exchange Jz and the T H F H z are negative with similar chalcogen dependence except for J2 in EuO. The absolute values of H i in EuS, EuSe and EuTe are much smaller than those of H z, while [Jd has similar magnitude to ]Jz[ in the~e compounds. The mechanism of the exchange interaction is discussed precisely by Kasuya [4]. We consider, in this paper, similar mechanisms for THF. The main mechanism for -/1 is the transfer of a 4f electron to a crystal 5d state [4]. On the other hand, the
"-.{~.
Ci,
When 4f spins have a mean value (Sy), the hyperfine field acting on I i is given by
H, = . 4 ~ j ( s j > / g ~ .
"" "~x
3
Nuclear spins I~ of Eu 2+ have the hyperfine interaction with 4f spins. Hhf =
4
Eu-X
S,l,,Se4~ , e.f, 30 d i s t a n c e in ~,
Fig. 1. Experimental values of the transferred hyperfine fields and the exchange constants in Eu chalcogenides are shown as functions of lattice constants. main mechanism for H~ is the transfer of a 4f electron to a crystal 6s state, because the hyperfine interaction in 6s states is much larger than that in 5d states. The perturbation process of the second order in the transfer energy and the first order in the hyperfine interaction in 6s state gives
k~,. C~'( k' l' )e-ik'R'< fm'l l/lkl' ) 2A6. 2s,
(4)
in which C6,(k, v) is the 6s component of the conduction band state k, ~, with energy E ( k , 1,), ( f m e l V [ k v ) the transfer matrix between a 4f (me = - 3 ..... 3) and the conduction band state and A6, the hyperfine interaction of an atomic 6s state. When the position R./is nn, Aj_ l may be written as
I( fs,~)12A,,
A, (&- e,)22s ,,
(5)
Here (fso) is the transfer integral of Slater Koster, E, the mean energy of the 6s component of conduction bands and Er the 4f energy level. If we use the following values for EuO (fso) = 0.1 eV, E, - E t = 4 eV and Ar, =
© 1983 N o r t h - H o l l a n d
428
K. Ueno et al. / Hyperfine interactions in E u X
0.425 cm -1 [4], we haveA I = 1.21 x 10 -4 cm - l , which corresponds to H 1 = 3.8 kOe, and is in reasonable agreement with the experimental value. The values of (fso) in the EuX are determined by the 4f-6s overlaps between nn E u - E u and decrease exponentially with increasing lattice constants as discussed for Jl in ref. [4]. The small values of H 1 in EuS, EuSe and EuTe are explained in this way. The above mechanism also contributes to H 2 and J2. Using the band structure of EuX [5] and eq. (3), we obtain the ratio of H 2 / H 1 and Jz/Jl in this mechanism as follows.
H z / H 1 = 0.25, J2/J~ = 0.36.
(6)
Because the bottom of the 5d bands is lower than the bottom of the 6s band, the ratio is larger in the exchange constants than in THF. Since the value of Jl is large in EuO, this mechanism gives a large positive contribution to J2. This is the reason why EuO has positive J2. Subtraction this value from the observed value leaves a very small negative value which is rather consistent with that expected from the following mechanism. On the other hand, this contribution to H 2 in EuO is small and is not so important. As the main mechanism for -/2, the second order RKKY type perturbation processes of the p - d interband transition using the d - f exchange, are important [4], in which d-character is mixed in the p-band through the p - d mixing mechanism. The similar processes for T H F gives the following results.
A~ ~ =
JaA6sl(pso )l z
IE,- epl'
(7) '
and Apf = _
A6sl(pso ) ( p f o )] 2 3
(8)
The process for eq. (7) is that a p-band electron jumps up to a 6s conduction band state through the 6s hyperfine interaction and comes back through s-f exchange interaction Jsf to the n n n site, in which the 6s character mixes to the p-band through the s - p mixing process. In the process for eq. (8) the last process is replaced by that in which a n n n 4f electron jumps into the p-hole through p - f mixing and the excited electron fills this 4f-hole. Using ( p s o ) = 3.3 eV, ( p r o ) = 0.5 eV, E S - Eo = 10.7 eV, E s - E f = 8.0 eV, A 6 s = 0.425 c m - ~ and J s f = 0.025 eV, we obtain the contributions of eqs. (7) and (8) to H 2 as - 0 . 9 kOe and - 2 . 7 kOe, respectively, for EuSe. The total value of - 3.6 kOe agrees well with the experimental value of EuSe. All the transfer integrals which appear in eqs. (7) and (8) are those concerning p-bands. Therefore they become gradually larger with increasing atomic number of chalcogens. This explains the chalcogen dependence of H 2 in fig. 1. In conclusion, similar mechanisms could satisfactorily explain both of exchange and transferred hyperfine interaction in Eu-chalcogenides. Through this process, the validity for the values of various effective one-particle transfer matrix elements, estimated from the band calculation, are confirmed.
References [1] L. Passell, O.W. Dietrich and J. Als-Nielsen, Phys. Rev. BI4 (1976) 4897. [2] T. Hihara, K. Kojirna and T. Kamigaichi, J. Phys. Soc. Japan 50 (1981) 1499. [3] H. Lutgemeier, Ch. Sauer and W. Ainn, Proc. 1980 MRS Ann. Meeting in Berlin. [4] T. Kasuya, IBM J. Res. Dev. 14 (t970) 214. [5] S.J. Cho, Phys. Rev. BI (1970) 4585.
INTERACTIONS
*, A. Y A N A S E
427
IN EUROPIUM
CHALCOGENIDES
** a n d T. K A S U Y A
Department of Physics, Tohoku University, Sendai Japan
The hyperfine interaction in europium chalcogenides is discussed theoretically. The f-s transfer mechanism explains the nearest neighbour transferred hyperfine interaction. Moreover the p-s and p - f transfer mechanisms explain the next nearest neighbour transferred hyperfine interaction. The estimated values and chalcogen dependences of these are in good agreement with the experiments.
The series of the divalent europium chalcogenides EuX is considered to be a good representation of the simple Heisenberg magnets. The exchange interaction between two localized 4f spins S~, and Sj at lattice points R~ and R j of Eu 2+ is expressed in terms of an exchange constant J q , and is of the form /-/ox = - 2S, jS, Sj.
Xx .x
AijliSj.
= U-
(l)
0304-8853/83/0000-0000/$03.00
"',
,
,
' - -'
X.
r
'-'--'-----~ "-x-
~
2
®
/, 0.~ . . . .
Z5
(3)
* Present address: Fuji Electric Corporate Research and Development Ltd. 2-2-1 Nagasaka, Yokosuka 240-01, Japan. ** Present address: Integrated Arts of Science, University of Osaka Prefecture, Sakai 591, Japan.
2i
4
(2)
When i is different from j , the field is called the transferred hyperfine field (THF). The values of J/j can be determined in a variety of experiments [1] and the values of Aij are determined in the nuclear magnetic resonance in the various magnetic phases of EuX or Eu I _~SrxX [2,3]. The experimental values of the T H F and the exchange constants are shown in fig. 1. The chalcogen dependences of the nearest neighbour (nn) exchange J! and the T H F H, are similar to each other with positive values, even though it is not clear for H t in EuTe within experimental accuracy. The next nearest neighbour (nnn) exchange Jz and the T H F H z are negative with similar chalcogen dependence except for J2 in EuO. The absolute values of H i in EuS, EuSe and EuTe are much smaller than those of H z, while [Jd has similar magnitude to ]Jz[ in the~e compounds. The mechanism of the exchange interaction is discussed precisely by Kasuya [4]. We consider, in this paper, similar mechanisms for THF. The main mechanism for -/1 is the transfer of a 4f electron to a crystal 5d state [4]. On the other hand, the
"-.{~.
Ci,
When 4f spins have a mean value (Sy), the hyperfine field acting on I i is given by
H, = . 4 ~ j ( s j > / g ~ .
"" "~x
3
Nuclear spins I~ of Eu 2+ have the hyperfine interaction with 4f spins. Hhf =
4
Eu-X
S,l,,Se4~ , e.f, 30 d i s t a n c e in ~,
Fig. 1. Experimental values of the transferred hyperfine fields and the exchange constants in Eu chalcogenides are shown as functions of lattice constants. main mechanism for H~ is the transfer of a 4f electron to a crystal 6s state, because the hyperfine interaction in 6s states is much larger than that in 5d states. The perturbation process of the second order in the transfer energy and the first order in the hyperfine interaction in 6s state gives
k~,. C~'( k' l' )e-ik'R'< fm'l l/lkl' ) 2A6. 2s,
(4)
in which C6,(k, v) is the 6s component of the conduction band state k, ~, with energy E ( k , 1,), ( f m e l V [ k v ) the transfer matrix between a 4f (me = - 3 ..... 3) and the conduction band state and A6, the hyperfine interaction of an atomic 6s state. When the position R./is nn, Aj_ l may be written as
I( fs,~)12A,,
A, (&- e,)22s ,,
(5)
Here (fso) is the transfer integral of Slater Koster, E, the mean energy of the 6s component of conduction bands and Er the 4f energy level. If we use the following values for EuO (fso) = 0.1 eV, E, - E t = 4 eV and Ar, =
© 1983 N o r t h - H o l l a n d
428
K. Ueno et al. / Hyperfine interactions in E u X
0.425 cm -1 [4], we haveA I = 1.21 x 10 -4 cm - l , which corresponds to H 1 = 3.8 kOe, and is in reasonable agreement with the experimental value. The values of (fso) in the EuX are determined by the 4f-6s overlaps between nn E u - E u and decrease exponentially with increasing lattice constants as discussed for Jl in ref. [4]. The small values of H 1 in EuS, EuSe and EuTe are explained in this way. The above mechanism also contributes to H 2 and J2. Using the band structure of EuX [5] and eq. (3), we obtain the ratio of H 2 / H 1 and Jz/Jl in this mechanism as follows.
H z / H 1 = 0.25, J2/J~ = 0.36.
(6)
Because the bottom of the 5d bands is lower than the bottom of the 6s band, the ratio is larger in the exchange constants than in THF. Since the value of Jl is large in EuO, this mechanism gives a large positive contribution to J2. This is the reason why EuO has positive J2. Subtraction this value from the observed value leaves a very small negative value which is rather consistent with that expected from the following mechanism. On the other hand, this contribution to H 2 in EuO is small and is not so important. As the main mechanism for -/2, the second order RKKY type perturbation processes of the p - d interband transition using the d - f exchange, are important [4], in which d-character is mixed in the p-band through the p - d mixing mechanism. The similar processes for T H F gives the following results.
A~ ~ =
JaA6sl(pso )l z
IE,- epl'
(7) '
and Apf = _
A6sl(pso ) ( p f o )] 2 3
(8)
The process for eq. (7) is that a p-band electron jumps up to a 6s conduction band state through the 6s hyperfine interaction and comes back through s-f exchange interaction Jsf to the n n n site, in which the 6s character mixes to the p-band through the s - p mixing process. In the process for eq. (8) the last process is replaced by that in which a n n n 4f electron jumps into the p-hole through p - f mixing and the excited electron fills this 4f-hole. Using ( p s o ) = 3.3 eV, ( p r o ) = 0.5 eV, E S - Eo = 10.7 eV, E s - E f = 8.0 eV, A 6 s = 0.425 c m - ~ and J s f = 0.025 eV, we obtain the contributions of eqs. (7) and (8) to H 2 as - 0 . 9 kOe and - 2 . 7 kOe, respectively, for EuSe. The total value of - 3.6 kOe agrees well with the experimental value of EuSe. All the transfer integrals which appear in eqs. (7) and (8) are those concerning p-bands. Therefore they become gradually larger with increasing atomic number of chalcogens. This explains the chalcogen dependence of H 2 in fig. 1. In conclusion, similar mechanisms could satisfactorily explain both of exchange and transferred hyperfine interaction in Eu-chalcogenides. Through this process, the validity for the values of various effective one-particle transfer matrix elements, estimated from the band calculation, are confirmed.
References [1] L. Passell, O.W. Dietrich and J. Als-Nielsen, Phys. Rev. BI4 (1976) 4897. [2] T. Hihara, K. Kojirna and T. Kamigaichi, J. Phys. Soc. Japan 50 (1981) 1499. [3] H. Lutgemeier, Ch. Sauer and W. Ainn, Proc. 1980 MRS Ann. Meeting in Berlin. [4] T. Kasuya, IBM J. Res. Dev. 14 (t970) 214. [5] S.J. Cho, Phys. Rev. BI (1970) 4585.