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Dynamical properties of amorphous Fe90−xCoxZr10 (x = 10, 40) alloys
PHYSICA ELSEVIER
Physica B 213&214 (1995) 532 534
Dynamical properties of amorphous (x = 10, 40) alloys
Fe9o
-
xCoxZr o
Z.C. Lu a'*, Z.Q. Li b, J.Z. Li b, J. Kang b, C.T. Ye b, B.G. Shen ¢, Z. Xianyu ~ "Department q/Physics, Northeastern Universi~,, Shenyang 110006, China h China Institute of Atomic Energy', Beijing 102413, China " lnstitute o f Physics, China Academy q f Science, Beo'ing 100080. China
Abstract Inelastic neutron-scattering experiments on amorphous Fego xCoxZrlo(X = 10 and 40) alloys have been performed. Generalized phonon densities of states (PDOS) were deduced from the measured time-of-flight spectra at room temperature. The results show that in the energy region below 17 meV, the generalized PDOS of the amorphous FesoCo~oZrl 0 Invar alloy is obviously softer than that of the amorphous FesoCo40Zr~o non-Invar alloy. It is suggested that the softening of the low-energy PDOS in Invar alloys could be attributed to an enhancement of the electron-phonon interaction.
1. Introduction The Invar problem has attracted continuous interest for about a century because of its fundamental importance in understanding the ferromagnetism of transition metals. Invar alloys are characterized by an anomalously small thermal expansion coefficient below the Curie temperature. Besides, Invar alloys show other unusual physical properties: the observed decrease of magnetization with increasing temperature at low temperature is more than twice as fast as can be accounted for using the spin-wave spectra obtained by neutron scattering [1, 2]. In a very elaborate analysis, Ishikawa proposed the existence of some hidden excitation which must be responsible for the additional decrease of magnetization [3]. Recently, Kim pointed out that the hidden excitation can be a phonon by considering the electron phonon interaction (EPI) in a ferromagnet [4]. In this paper, we try to
* Corresponding author.
obtain some information about the behavior of the phonons in Invar alloys by inelastic neutron-scattering experiments on amorphous Fego-xCoxZrlo(X = 10 and 40) alloys and identify that phonons play an important role in the Invar effect [5].
2. Experiments Amorphous Fe9o_~Co~Zr~o(X = 10 and 40) alloys about 1.5 mm wide and 20-30 lam thick were prepared by the melt-spinning technique in an argon atmosphere. The amorphism of the ribbons was checked by X-ray diffraction. The thermal-expansion curves were measured by a differential transformer method. The thermomagnetization curves in an external field of 12 kOe were measured with an extracting sample magnetometer. The accuracy of the magnetic moment measurements is 3 × 10 4 emu. Inelastic neutron-scattering (INS) experiments were performed at room temperature on the timeof-flight (TOF) spectrometer at the Heavy-Water Research Reactor (HWRR) of the China Institute of
0921-4526/95/$09.50 C 1995 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 5 ) 0 0 2 0 2 - 2
533
Z.C. Lu et al. ,Ph.vsica B 213&214 (1995) 532 534
Atomic Energy in Beijing. An incident neutron energy of 18.2 meV was used for neutron-energy-gain scattering. Nine detector boxes, each with six 3He counters, were arranged over scattering angles between 30 and 90 ~. The samples of about 10 g were placed in a thin AI container. The measured double differential cross sections were corrected for background scattering (empty container) and 3He detector calibration. For the present multicomponent samples, the generalized phonon densities of states (PDOS), G(ho)), are deduced from measured TOF spectra by weighting the vibrations of the ith atom with the ratio a~/M~(cr~: bound scattering cross-section, Me atomic mass). The multiphonon contributions to the calculated G(he)) were corrected in a self-consistent manner. It should be noted that since the present INS was performed in the large-angle range, the magnetic scattering which results from spin waves in the small-angle range is excluded.
Fe ./
5 4
\
F e s o C ~
0
-I
I
I
200
100
I
I
I
300 400 500 T(K) curves
Fig. 1. Thermal-expansion l:e~) .,Co~Zr~oalloys.
I
600
700 800
for
amorphous
3. Results and discussion
200 Fig. 1 shows thermal expansion curves. It can be seen that the amorphous Fe8oColoZrlo alloy exhibits a negative thermal expansion coefficient below the Curie temperature To, indicating a distinct Invar characteristic, while the amorphous FesoCo4oZrlo alloy (T~ = 810 K) shows no Invar effect. Fig. 2 shows the temperature dependence of the magnetization. As seen from Fig. 2, the decrease in magnetization of the amorphous FesoColoZr~o alloy, with increasing temperature is much faster than that of the amorphous FesoCo4oZr:o alloy, indicating another lnvar characteristic of the amorphous FesoCO~0Zr~o alloy. The G(h~o) spectra measured at room temperature below T~ are shown in Fig. 3. Due to the finite resolution of the spectrometer, the data below 5 meV were not accessible in this study, and were extrapolated to zero frequency assuming a quadratic Debye spectrum for purposes of area-normalization. It is noticeable that in the energy region below about 17 meV, the G(ho)) spectrum of the amorphous FesoColoZrlo alloy is obviously softer than that of the amorphous FesoCo4oZrlo alloy. In order to understand the true cause of the softening, we first take account of the effect of the mass of the replaced element on the G(he)) spectra. It is well known that the vibrational frequency of a heavy atom is smaller than that of a light atom. Therefore, the replacement of iron by cobalt should make the low-energy PDOS softer. Actually, the opposite tendency was observed, which excluded a possible cause of the observed softening. In addition, for amorphous alloys, the continuous variation of concentration would not cause the structure transformation which usually occurs for most crystalline Invar alloys
Fe~Co~Zr,o ~ q J
"~ 150 \
.... -....::....:..:.::::..:::.::...-.------
..................................... .....
,,,
,., "'" "~oo.~
,.~,,,,o%...,
/v 100
F%oCotoZr~o
0
200
! 00
300
T (K) Fig. 2. Magnetization versus temperature curves for amorphous Feo0 .~CoxZrloalloys.
0.05
.___ Fe~C%0Zq0 ~ Fe~Co4~Zrlo
../~,~ /~,
0.04
o.o'I./ . . . . O l d l ~ "-
0
L
I
lO
L
i
~
20
i
30
.
40
,
50
E(meV)
Fig. 3. Generalized phonon densities of states for amorphous l=eg0 ,Co~Zrl0 alloys.
534
ZC Lu et al./Physica B 213&214 (1995) 532-534
and complicates the softening phenomenon. Thus, it may be concluded that the softening of the low-energy phonons in the amorphous FesoColoZrl 0 Invar alloy is closely related to the Invar effect. This result provides the first observation of distinct concentration-dependent softening of the low-energy phonons in alloys. Since the low-energy phonons predominantly affect the thermodynamical properties at low temperature, the additional low-energy states in Invar alloys indicate a large phonon contribution to low-temperature specific heat, which is in good agreement with the actual measurements of the specific heat for the amorphous Fe9oZrlo and Co9oZrlo alloys [6]. The origin of this dynamical anomaly may be discussed in terms of the electron-phonon interaction (EPI) [7]. The renormalized phonon frequency toq given by the Hamiltonian with EPI term, Hop, is given as 2 = O~q
~-'~q
e - gq2 ~;(q,
This work was supported by the National Science Foundation of China.
(1)
where f~q is the bare phonon frequency given by the Hamiltonian without Hep , Z~ is the charge susceptibility and gq is the electron-phonon coupling constant and depends upon the electron density of states N(Ef) at the Fermi energy Ef [8]; gq ~ N ( E f ) ( I 2 ) ,
neto-volume effect [9] and the temperature dependence of magnetization [10], and shown that a phonon carries a negative magnetization ( ~ 0.1#B) for an itinerant electron ferromagnet [4]. Based on our experimental results, we agree with Kim's view and believe that the enhancement of the EPI has two possible effects on the behavior of phonons in Invar alloys: (i) increase in the magnitude of the phonon-assisted magnetization (ii) increase in the thermal excitation of the low-energy phonons. Both effects result in an additional decrease of magnetization with increasing temperature in Invar alloys, which is consistent with experimental fact. We hope that out experimental results will encourage further theoretical studies on the EPI in Invar alloys.
(2)
where (12) is the matrix element averaged over the Fermi surface. According to Eq. (2), if the N(Ef) of the Invar alloy is larger than that of the non-Invar alloy, which has been found experimentally in the crystalline Fe Ni alloy [8], the 9q is enhanced. As a result, the enhancement of the EPI in Invar alloys results in the phonon softening according to Eq. (1). Therefore, present results show experimentally the existence of the enhanced EPI in the Invar alloy. Recently, Kim has emphasized the importance role of the EPI in understanding the mag-
References
[1] M. Kohgi, Y. lshikawa and N. Wakabayashi, Solid State Commun. 18 (1976) 509. [2] Y. Ishikawa, K. Yamada, K. Tajima and K. Fukamichi, J. Phys. Soc. Japan 50 (1981) 1958. 1-3] Y. lshikawa, S. Onodera and K. Tajima, J. Magn. Magn. Mater. 10 (1979) 183. [4] D.J. Kim, J. Magn. Magn. Mater. 125 (1993) L257. 1-5] D.J. Kim, J. Magn. Magn. Mater. 74 (1988) 255. [6] Y. Obi, L.C. Vlarg, R. Motsay and D.G. Onn, J. Appl. Phys. 53 (1982) 2304. [7] D. Pines, in: Elementary Excitations in Solids (Benjamin, New York, 1964). [8] D.G. Pettifor, J. Phys. F 7 (1977) 1009. [9] D.J. Kim, Phys. Rev. B 39 (1989) 6844. [10] S. Fukumoto, S. Ukon and D.J. Kim, J. Magn. Magn. Mater. 90 (1990) 743.
Physica B 213&214 (1995) 532 534
Dynamical properties of amorphous (x = 10, 40) alloys
Fe9o
-
xCoxZr o
Z.C. Lu a'*, Z.Q. Li b, J.Z. Li b, J. Kang b, C.T. Ye b, B.G. Shen ¢, Z. Xianyu ~ "Department q/Physics, Northeastern Universi~,, Shenyang 110006, China h China Institute of Atomic Energy', Beijing 102413, China " lnstitute o f Physics, China Academy q f Science, Beo'ing 100080. China
Abstract Inelastic neutron-scattering experiments on amorphous Fego xCoxZrlo(X = 10 and 40) alloys have been performed. Generalized phonon densities of states (PDOS) were deduced from the measured time-of-flight spectra at room temperature. The results show that in the energy region below 17 meV, the generalized PDOS of the amorphous FesoCo~oZrl 0 Invar alloy is obviously softer than that of the amorphous FesoCo40Zr~o non-Invar alloy. It is suggested that the softening of the low-energy PDOS in Invar alloys could be attributed to an enhancement of the electron-phonon interaction.
1. Introduction The Invar problem has attracted continuous interest for about a century because of its fundamental importance in understanding the ferromagnetism of transition metals. Invar alloys are characterized by an anomalously small thermal expansion coefficient below the Curie temperature. Besides, Invar alloys show other unusual physical properties: the observed decrease of magnetization with increasing temperature at low temperature is more than twice as fast as can be accounted for using the spin-wave spectra obtained by neutron scattering [1, 2]. In a very elaborate analysis, Ishikawa proposed the existence of some hidden excitation which must be responsible for the additional decrease of magnetization [3]. Recently, Kim pointed out that the hidden excitation can be a phonon by considering the electron phonon interaction (EPI) in a ferromagnet [4]. In this paper, we try to
* Corresponding author.
obtain some information about the behavior of the phonons in Invar alloys by inelastic neutron-scattering experiments on amorphous Fego-xCoxZrlo(X = 10 and 40) alloys and identify that phonons play an important role in the Invar effect [5].
2. Experiments Amorphous Fe9o_~Co~Zr~o(X = 10 and 40) alloys about 1.5 mm wide and 20-30 lam thick were prepared by the melt-spinning technique in an argon atmosphere. The amorphism of the ribbons was checked by X-ray diffraction. The thermal-expansion curves were measured by a differential transformer method. The thermomagnetization curves in an external field of 12 kOe were measured with an extracting sample magnetometer. The accuracy of the magnetic moment measurements is 3 × 10 4 emu. Inelastic neutron-scattering (INS) experiments were performed at room temperature on the timeof-flight (TOF) spectrometer at the Heavy-Water Research Reactor (HWRR) of the China Institute of
0921-4526/95/$09.50 C 1995 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 5 ) 0 0 2 0 2 - 2
533
Z.C. Lu et al. ,Ph.vsica B 213&214 (1995) 532 534
Atomic Energy in Beijing. An incident neutron energy of 18.2 meV was used for neutron-energy-gain scattering. Nine detector boxes, each with six 3He counters, were arranged over scattering angles between 30 and 90 ~. The samples of about 10 g were placed in a thin AI container. The measured double differential cross sections were corrected for background scattering (empty container) and 3He detector calibration. For the present multicomponent samples, the generalized phonon densities of states (PDOS), G(ho)), are deduced from measured TOF spectra by weighting the vibrations of the ith atom with the ratio a~/M~(cr~: bound scattering cross-section, Me atomic mass). The multiphonon contributions to the calculated G(he)) were corrected in a self-consistent manner. It should be noted that since the present INS was performed in the large-angle range, the magnetic scattering which results from spin waves in the small-angle range is excluded.
Fe ./
5 4
\
F e s o C ~
0
-I
I
I
200
100
I
I
I
300 400 500 T(K) curves
Fig. 1. Thermal-expansion l:e~) .,Co~Zr~oalloys.
I
600
700 800
for
amorphous
3. Results and discussion
200 Fig. 1 shows thermal expansion curves. It can be seen that the amorphous Fe8oColoZrlo alloy exhibits a negative thermal expansion coefficient below the Curie temperature To, indicating a distinct Invar characteristic, while the amorphous FesoCo4oZrlo alloy (T~ = 810 K) shows no Invar effect. Fig. 2 shows the temperature dependence of the magnetization. As seen from Fig. 2, the decrease in magnetization of the amorphous FesoColoZr~o alloy, with increasing temperature is much faster than that of the amorphous FesoCo4oZr:o alloy, indicating another lnvar characteristic of the amorphous FesoCO~0Zr~o alloy. The G(h~o) spectra measured at room temperature below T~ are shown in Fig. 3. Due to the finite resolution of the spectrometer, the data below 5 meV were not accessible in this study, and were extrapolated to zero frequency assuming a quadratic Debye spectrum for purposes of area-normalization. It is noticeable that in the energy region below about 17 meV, the G(ho)) spectrum of the amorphous FesoColoZrlo alloy is obviously softer than that of the amorphous FesoCo4oZrlo alloy. In order to understand the true cause of the softening, we first take account of the effect of the mass of the replaced element on the G(he)) spectra. It is well known that the vibrational frequency of a heavy atom is smaller than that of a light atom. Therefore, the replacement of iron by cobalt should make the low-energy PDOS softer. Actually, the opposite tendency was observed, which excluded a possible cause of the observed softening. In addition, for amorphous alloys, the continuous variation of concentration would not cause the structure transformation which usually occurs for most crystalline Invar alloys
Fe~Co~Zr,o ~ q J
"~ 150 \
.... -....::....:..:.::::..:::.::...-.------
..................................... .....
,,,
,., "'" "~oo.~
,.~,,,,o%...,
/v 100
F%oCotoZr~o
0
200
! 00
300
T (K) Fig. 2. Magnetization versus temperature curves for amorphous Feo0 .~CoxZrloalloys.
0.05
.___ Fe~C%0Zq0 ~ Fe~Co4~Zrlo
../~,~ /~,
0.04
o.o'I./ . . . . O l d l ~ "-
0
L
I
lO
L
i
~
20
i
30
.
40
,
50
E(meV)
Fig. 3. Generalized phonon densities of states for amorphous l=eg0 ,Co~Zrl0 alloys.
534
ZC Lu et al./Physica B 213&214 (1995) 532-534
and complicates the softening phenomenon. Thus, it may be concluded that the softening of the low-energy phonons in the amorphous FesoColoZrl 0 Invar alloy is closely related to the Invar effect. This result provides the first observation of distinct concentration-dependent softening of the low-energy phonons in alloys. Since the low-energy phonons predominantly affect the thermodynamical properties at low temperature, the additional low-energy states in Invar alloys indicate a large phonon contribution to low-temperature specific heat, which is in good agreement with the actual measurements of the specific heat for the amorphous Fe9oZrlo and Co9oZrlo alloys [6]. The origin of this dynamical anomaly may be discussed in terms of the electron-phonon interaction (EPI) [7]. The renormalized phonon frequency toq given by the Hamiltonian with EPI term, Hop, is given as 2 = O~q
~-'~q
e - gq2 ~;(q,
This work was supported by the National Science Foundation of China.
(1)
where f~q is the bare phonon frequency given by the Hamiltonian without Hep , Z~ is the charge susceptibility and gq is the electron-phonon coupling constant and depends upon the electron density of states N(Ef) at the Fermi energy Ef [8]; gq ~ N ( E f ) ( I 2 ) ,
neto-volume effect [9] and the temperature dependence of magnetization [10], and shown that a phonon carries a negative magnetization ( ~ 0.1#B) for an itinerant electron ferromagnet [4]. Based on our experimental results, we agree with Kim's view and believe that the enhancement of the EPI has two possible effects on the behavior of phonons in Invar alloys: (i) increase in the magnitude of the phonon-assisted magnetization (ii) increase in the thermal excitation of the low-energy phonons. Both effects result in an additional decrease of magnetization with increasing temperature in Invar alloys, which is consistent with experimental fact. We hope that out experimental results will encourage further theoretical studies on the EPI in Invar alloys.
(2)
where (12) is the matrix element averaged over the Fermi surface. According to Eq. (2), if the N(Ef) of the Invar alloy is larger than that of the non-Invar alloy, which has been found experimentally in the crystalline Fe Ni alloy [8], the 9q is enhanced. As a result, the enhancement of the EPI in Invar alloys results in the phonon softening according to Eq. (1). Therefore, present results show experimentally the existence of the enhanced EPI in the Invar alloy. Recently, Kim has emphasized the importance role of the EPI in understanding the mag-
References
[1] M. Kohgi, Y. lshikawa and N. Wakabayashi, Solid State Commun. 18 (1976) 509. [2] Y. Ishikawa, K. Yamada, K. Tajima and K. Fukamichi, J. Phys. Soc. Japan 50 (1981) 1958. 1-3] Y. lshikawa, S. Onodera and K. Tajima, J. Magn. Magn. Mater. 10 (1979) 183. [4] D.J. Kim, J. Magn. Magn. Mater. 125 (1993) L257. 1-5] D.J. Kim, J. Magn. Magn. Mater. 74 (1988) 255. [6] Y. Obi, L.C. Vlarg, R. Motsay and D.G. Onn, J. Appl. Phys. 53 (1982) 2304. [7] D. Pines, in: Elementary Excitations in Solids (Benjamin, New York, 1964). [8] D.G. Pettifor, J. Phys. F 7 (1977) 1009. [9] D.J. Kim, Phys. Rev. B 39 (1989) 6844. [10] S. Fukumoto, S. Ukon and D.J. Kim, J. Magn. Magn. Mater. 90 (1990) 743.