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Electrical resistivity measurements on the Cu2MnAl heusler alloy
1. fi,s. Ckm. &Ii& Vol. 400.w. 421-129 $'em Rc,r Lad..IpR. PktcdmGreal Brihim
ELECTRICAL RESISTIVITY MEASUREMENTS ON THE CaMnAl HEUSLER ALLOY? J. V. KUNZLER, T. A. GRANDI,W. H. SCHREINER, P. PUREUR and D. E. BRANDAO Iastitutode Ffsica, UP’RGS.Port0 Akgre. Brasil
AMmet-EIectrid rcsistivity measurementshave been performedon the Cu$fnAl Heuskr alloy in the temperahue range from 4.2 to SOiPK.An AT’ functionalitywas found for 4XK d T s MC, evidencinga BlocltGrheisea ekctron-photon scatteringmechanism.FM 270%s T s 5OtPK tbc resistivitymnybe dcacrii by the A?‘+ BP polynomial.The linear term is interpretedas dnc to the dectron-pbouonscatteringprocess wbik tbe quad&c term may be emibsd to an ek.ctronic scatteringdue to a spin disordertype relaxationprocess. The experimentalresults fail to provideevidences of s-d scatteringof tbe catduction electrons.
1.
-0u
The Heusler alloys are intermetallic compounds in the stoichiometric composition X2 YZ with the I.21 structure. The Y and 2 atoms are located alternately at the centers of the cubes formed by the X atoms. Electrical resistivity measurements have been performed on these alloys in order to study thermal decomposition[ 11, phase transitioa[21 or exchange energy[3]. Nevertheless much information might be gathered by the use of this technique on the quality of samples and the scattering mechanisms present in the electrical conduction of those metallic alloys. t-ALDErAILS
(a) Sample pnparation The Heusler alloy CuJMnAl was prepared using an electrical furnace .in vacuum atmosphere by heating the constituent elements together in an alumina crucible. Each of the metals was at least 99.9% pure. The compound was thermally treated at 750°C for 1 day. Three samples of about 1 x 2 X 15 mm were extracted by the spark erosion technique. A part of the alloy was powdered to the mesh 270 size for X-ray and magnetization measurements. The samples and powder were heattreated at 750°C for 4 hr and quenchedin cold water at a rate of 1500nin. Two of the samples and the powder were annealed at UO”C to remove stresses[4] for more than 30 hr. but after these 30 hr no improvement either in magnetization or in intensity of the superlattice lines, characteristic of the L21 structure, on an X-ray analysis, could be detected. The line intensities were in close agreement with calculated theoretical values as well as with Bradky and Rogers results[S]. A lattice parameter of s.%~~o.@J~ A was obtained. A mta~ographic analysis was also carried out both with only quenched and with annealed material. The microstructure exhibited by all samples showed single phase domains with well tWork supported in part by Con&ho National de Desenvolvimento Ciintftko e TccaoMgk~(CNPq) and Fknckdora de Estudos e Projctos (PINEP).
ddioed grain boundaries, in agreement with Green and Chin[6]. (b) Resistiairy meuslrnnrenls The resistivity measurements were performed using the standard four point d.c. method A Keithley 180 nanovoltmeter was used for the voltage measurements. The low temperature measurements were carried out in a double chamber cryostat. Temperature stabilization was better than 5 x lo-“K as monitored by standard Ge and pt calibrated resistance thermometers. In the above room temperature measurements a vacuum chamber was used and the temperature sensed by a chromei-alumel thermocouple. The temperature stabilization in this range was better than 2 x IO-‘“K. The contacts to the samples were made by pressure. The experimental errors in the absolute values of the resistivity were due, mostly, to the errors in the geomebic factors, that were about 2.2%. The precision in the ideal resistivity values, for T< lS”K, was limited by the resolution of the equipment.
Table 1 presents tbe resistive behaviour of the three measured samples at 42°K. The improvement on po due to thermal treatment of sampks A, and Al is readily seen as compared to the quenched sample A,. Nevertheless these vaIues are still high when compared with noble or transition metals. Some very small structural phase precipitations, impurities and smaIl stoichiometric deviations should be responsible for this higher po value in Cu&Al. Considering Matthiessen’s ruk as valid, we have: P(T)=Al+fi(Tf
(3.1)
where n(T) is the ideal temperature dependent resistivity. F&re 1 shows this temperahue behaviour and the data suggest the correctness of the hypothesis (3.1). In low temperatures R depends strongly on temperature and, for exampk, its absolute value in one orderof magnitude hi than for pure Ni in the same tempentture
428
J. V. KUNZIB! et al. Tabk I. Rcsistivity values, pa. at T = 4.Z’K; maximumexperimentalerror: 2.2%
I
Sample P,
I
A1
(Nkrn)
2.213
A2
A3
2.306
2.670
-1 . I
.
.
t
I . ,
.e
s
.’ I
.J’ .*’
a* .
I+
TEMPERATURE
Fig. 2.
(K)
Temperature derivative of the resistivity. ApJAT; the dashed line cow3ponds to a visual ft.
In the low temperature range T s 14°K. where the data are less precise. a least square fit to the function pr = aT”,
(3.2)
provided a value for n = 5.0-+0.4. On the other band for T > 273’K a very good fit to the polynomial (3.3)
pr=AT+BT2, . . .
,033
10
SAMPLE SAMPLE SAMPLE
50 TEMPERATURE
loo
A, A2 A3
200
could be obtained. This can be seen in Fig. 3.
50
(K)
F@. I. Ideal resistivity,n(T); the did line correspondsto a Ts law.
rmgc[7]. At 3WK the absohte value of pi compares favourab~y in order of magnitude with the majority of metals. So it seems possibk, remembering the crystalline weU-0rdere-d L2, smlcturc, to analyze the data in terms of tbe usual transport tbeorks for metals. IntheintemK!&&tempstatunrangemaybeobservedareaWkl&smoeth~inthe~functionaiity. At about lSO=‘Ka tends to illCl7WmOrerapkilywittI temperahue. This detail is better visuaked on a ApllAT curve, which is shown in Fii. 2.
I
200
I
1
300 TEMPERATURE
400
5
(K)
Fu. 3. Ideal resistivitydividedby absohttetemperature,pdT; the straight line is a least SqlUe fit to the pOtYOOmial pi(T)= l.17x10-‘+l.44xIO-‘~,/hinpfIcm,fw27YKsTs485~. The squaredlinearcorrelationcodkient of the lit. 2, is equal to 0.998.
Ekctrical nsistivity measurements on the Cu@nAl Heusler alloy &DtiXWSIoN
The fit to (3.3) allows one to suppose that the linear term is due to an electron-phonon scattering process, since BD= 330°K as obtained from low temperature specitic heat measurements[8]. Assuming that the phonon induced resistivity obeys a Bloch-GrOneisen law: paaV)=4T,
(f)‘II($),
(4.1)
which seems reasonable, since for low temperatures praT5, the value for the coefficient A in (3.3) permits an estimate for 7, which measures the intensity of ekctronphonon scattering. For T 2 &, p,& T) obeys closely the relation:
From this equation a value for q = 3.86 @ in I.rII.crn) is obtained, which is very close to the same constant in Al, e.g. Therefore it may be suggested that the nature of electron-phonon scattering is of the interband s-s type. The intermediate BT2 term for pi may be due to spin-disorder scattering. In fact, the magnetization of Cu*MnAl shows strong temperature dependent behaviour starting at about 15O”K[9]. On the other hand, preliminary measurements on the non-magnetic CunNiSn Heusler alloy do not show these strongly temperam dependent characteristics in this temperature range. These results will be published elsewhere. The BT* term in p, however, has to attenuate rapidly at low temperatures, on tbe contrary. it also should dominate the resistivity at temperatures even lower as 16“K, which is not observed. The Bloch-Griineisen law has the following assymp totic form at low temperatures (T c O.OS&):
JFCi Vd Y). No. 68
PB&? = 497.61, ($
429
(4.3)
Letting the above calculated value for r) be constant, a good fit to eqn (4.3) is only possible if 0, = 125”K, but this apparent lowering in 0, is known even for the alcaline metals [7], and is generally attributed to Umklapp process. Added to this there may also exist a magnetic resistive term which also should cause an apparent lowering in eD Thus it might be suggested that the Heusler alloy Cu&lnAl behaves resistiviely as if it had only an s-band conduction, without s-d scattering induced via phonons, but with strong spin-disorder contributions. This is in agreement with earlier models which assume localized moments in these alloys, to explain the magnetic behaviour[lO, Ill. The s-band only hypothesis is also con6rmed by tbe absence of a T2 electron-electron Baber[l2] term at low temperatures. I. Kimurs R., OhoyamaT. and Endo K.. 1. Phys. !bc. Japan 16, 1266(1961). 2. Ohoyama T., Webster P. J. and Tebbk R. S., Er. 1. Appl. plrys. 1,2 957 (1968). 3. Endo K., Tabusbi K. and Kimura R., 1. Phys. Sot. Japan 32, 285 (1972).
4.
KuruJerJ. V., Scbreiner W.. Bristoti A. and Brand6o D. E.,
1. 7’hum. Anal. 11,81 (1977). 5. Bradky A. J. aod Rodgers J. W., Ptuc. R. !Joc. MA, 340 ww. 6. Green M. L. and Chin G. Y., Mctclll.Tmnr. A61, 1118(1974). 7. Meaden G. T.. Electrical Resistance of Metals. Heywood
Books, London (1966). 8. Fenaader N. G.. W&&in L. and Myers P., 1. Phys. Chem. .wds 29. 11, 1973(1968). 9. Mkb~ltttii B., Batbk R. P., Lachcisserie E. T. and Waintal A., Solid Stale Commun. 25, 163(1978). IO. Blandin A. and CampbellI. A., Phys. Rm. Lea. 31.57 (1973). 11. Jcna P. and Geldart D. J. W.. So/id Stale Common. IS. 139
(1974). 12. Baber W. G., Pnx. R. !kx. (London) All, 383 (1937).
ELECTRICAL RESISTIVITY MEASUREMENTS ON THE CaMnAl HEUSLER ALLOY? J. V. KUNZLER, T. A. GRANDI,W. H. SCHREINER, P. PUREUR and D. E. BRANDAO Iastitutode Ffsica, UP’RGS.Port0 Akgre. Brasil
AMmet-EIectrid rcsistivity measurementshave been performedon the Cu$fnAl Heuskr alloy in the temperahue range from 4.2 to SOiPK.An AT’ functionalitywas found for 4XK d T s MC, evidencinga BlocltGrheisea ekctron-photon scatteringmechanism.FM 270%s T s 5OtPK tbc resistivitymnybe dcacrii by the A?‘+ BP polynomial.The linear term is interpretedas dnc to the dectron-pbouonscatteringprocess wbik tbe quad&c term may be emibsd to an ek.ctronic scatteringdue to a spin disordertype relaxationprocess. The experimentalresults fail to provideevidences of s-d scatteringof tbe catduction electrons.
1.
-0u
The Heusler alloys are intermetallic compounds in the stoichiometric composition X2 YZ with the I.21 structure. The Y and 2 atoms are located alternately at the centers of the cubes formed by the X atoms. Electrical resistivity measurements have been performed on these alloys in order to study thermal decomposition[ 11, phase transitioa[21 or exchange energy[3]. Nevertheless much information might be gathered by the use of this technique on the quality of samples and the scattering mechanisms present in the electrical conduction of those metallic alloys. t-ALDErAILS
(a) Sample pnparation The Heusler alloy CuJMnAl was prepared using an electrical furnace .in vacuum atmosphere by heating the constituent elements together in an alumina crucible. Each of the metals was at least 99.9% pure. The compound was thermally treated at 750°C for 1 day. Three samples of about 1 x 2 X 15 mm were extracted by the spark erosion technique. A part of the alloy was powdered to the mesh 270 size for X-ray and magnetization measurements. The samples and powder were heattreated at 750°C for 4 hr and quenchedin cold water at a rate of 1500nin. Two of the samples and the powder were annealed at UO”C to remove stresses[4] for more than 30 hr. but after these 30 hr no improvement either in magnetization or in intensity of the superlattice lines, characteristic of the L21 structure, on an X-ray analysis, could be detected. The line intensities were in close agreement with calculated theoretical values as well as with Bradky and Rogers results[S]. A lattice parameter of s.%~~o.@J~ A was obtained. A mta~ographic analysis was also carried out both with only quenched and with annealed material. The microstructure exhibited by all samples showed single phase domains with well tWork supported in part by Con&ho National de Desenvolvimento Ciintftko e TccaoMgk~(CNPq) and Fknckdora de Estudos e Projctos (PINEP).
ddioed grain boundaries, in agreement with Green and Chin[6]. (b) Resistiairy meuslrnnrenls The resistivity measurements were performed using the standard four point d.c. method A Keithley 180 nanovoltmeter was used for the voltage measurements. The low temperature measurements were carried out in a double chamber cryostat. Temperature stabilization was better than 5 x lo-“K as monitored by standard Ge and pt calibrated resistance thermometers. In the above room temperature measurements a vacuum chamber was used and the temperature sensed by a chromei-alumel thermocouple. The temperature stabilization in this range was better than 2 x IO-‘“K. The contacts to the samples were made by pressure. The experimental errors in the absolute values of the resistivity were due, mostly, to the errors in the geomebic factors, that were about 2.2%. The precision in the ideal resistivity values, for T< lS”K, was limited by the resolution of the equipment.
Table 1 presents tbe resistive behaviour of the three measured samples at 42°K. The improvement on po due to thermal treatment of sampks A, and Al is readily seen as compared to the quenched sample A,. Nevertheless these vaIues are still high when compared with noble or transition metals. Some very small structural phase precipitations, impurities and smaIl stoichiometric deviations should be responsible for this higher po value in Cu&Al. Considering Matthiessen’s ruk as valid, we have: P(T)=Al+fi(Tf
(3.1)
where n(T) is the ideal temperature dependent resistivity. F&re 1 shows this temperahue behaviour and the data suggest the correctness of the hypothesis (3.1). In low temperatures R depends strongly on temperature and, for exampk, its absolute value in one orderof magnitude hi than for pure Ni in the same tempentture
428
J. V. KUNZIB! et al. Tabk I. Rcsistivity values, pa. at T = 4.Z’K; maximumexperimentalerror: 2.2%
I
Sample P,
I
A1
(Nkrn)
2.213
A2
A3
2.306
2.670
-1 . I
.
.
t
I . ,
.e
s
.’ I
.J’ .*’
a* .
I+
TEMPERATURE
Fig. 2.
(K)
Temperature derivative of the resistivity. ApJAT; the dashed line cow3ponds to a visual ft.
In the low temperature range T s 14°K. where the data are less precise. a least square fit to the function pr = aT”,
(3.2)
provided a value for n = 5.0-+0.4. On the other band for T > 273’K a very good fit to the polynomial (3.3)
pr=AT+BT2, . . .
,033
10
SAMPLE SAMPLE SAMPLE
50 TEMPERATURE
loo
A, A2 A3
200
could be obtained. This can be seen in Fig. 3.
50
(K)
F@. I. Ideal resistivity,n(T); the did line correspondsto a Ts law.
rmgc[7]. At 3WK the absohte value of pi compares favourab~y in order of magnitude with the majority of metals. So it seems possibk, remembering the crystalline weU-0rdere-d L2, smlcturc, to analyze the data in terms of tbe usual transport tbeorks for metals. IntheintemK!&&tempstatunrangemaybeobservedareaWkl&smoeth~inthe~functionaiity. At about lSO=‘Ka tends to illCl7WmOrerapkilywittI temperahue. This detail is better visuaked on a ApllAT curve, which is shown in Fii. 2.
I
200
I
1
300 TEMPERATURE
400
5
(K)
Fu. 3. Ideal resistivitydividedby absohttetemperature,pdT; the straight line is a least SqlUe fit to the pOtYOOmial pi(T)= l.17x10-‘+l.44xIO-‘~,/hinpfIcm,fw27YKsTs485~. The squaredlinearcorrelationcodkient of the lit. 2, is equal to 0.998.
Ekctrical nsistivity measurements on the Cu@nAl Heusler alloy &DtiXWSIoN
The fit to (3.3) allows one to suppose that the linear term is due to an electron-phonon scattering process, since BD= 330°K as obtained from low temperature specitic heat measurements[8]. Assuming that the phonon induced resistivity obeys a Bloch-GrOneisen law: paaV)=4T,
(f)‘II($),
(4.1)
which seems reasonable, since for low temperatures praT5, the value for the coefficient A in (3.3) permits an estimate for 7, which measures the intensity of ekctronphonon scattering. For T 2 &, p,& T) obeys closely the relation:
From this equation a value for q = 3.86 @ in I.rII.crn) is obtained, which is very close to the same constant in Al, e.g. Therefore it may be suggested that the nature of electron-phonon scattering is of the interband s-s type. The intermediate BT2 term for pi may be due to spin-disorder scattering. In fact, the magnetization of Cu*MnAl shows strong temperature dependent behaviour starting at about 15O”K[9]. On the other hand, preliminary measurements on the non-magnetic CunNiSn Heusler alloy do not show these strongly temperam dependent characteristics in this temperature range. These results will be published elsewhere. The BT* term in p, however, has to attenuate rapidly at low temperatures, on tbe contrary. it also should dominate the resistivity at temperatures even lower as 16“K, which is not observed. The Bloch-Griineisen law has the following assymp totic form at low temperatures (T c O.OS&):
JFCi Vd Y). No. 68
PB&? = 497.61, ($
429
(4.3)
Letting the above calculated value for r) be constant, a good fit to eqn (4.3) is only possible if 0, = 125”K, but this apparent lowering in 0, is known even for the alcaline metals [7], and is generally attributed to Umklapp process. Added to this there may also exist a magnetic resistive term which also should cause an apparent lowering in eD Thus it might be suggested that the Heusler alloy Cu&lnAl behaves resistiviely as if it had only an s-band conduction, without s-d scattering induced via phonons, but with strong spin-disorder contributions. This is in agreement with earlier models which assume localized moments in these alloys, to explain the magnetic behaviour[lO, Ill. The s-band only hypothesis is also con6rmed by tbe absence of a T2 electron-electron Baber[l2] term at low temperatures. I. Kimurs R., OhoyamaT. and Endo K.. 1. Phys. !bc. Japan 16, 1266(1961). 2. Ohoyama T., Webster P. J. and Tebbk R. S., Er. 1. Appl. plrys. 1,2 957 (1968). 3. Endo K., Tabusbi K. and Kimura R., 1. Phys. Sot. Japan 32, 285 (1972).
4.
KuruJerJ. V., Scbreiner W.. Bristoti A. and Brand6o D. E.,
1. 7’hum. Anal. 11,81 (1977). 5. Bradky A. J. aod Rodgers J. W., Ptuc. R. !Joc. MA, 340 ww. 6. Green M. L. and Chin G. Y., Mctclll.Tmnr. A61, 1118(1974). 7. Meaden G. T.. Electrical Resistance of Metals. Heywood
Books, London (1966). 8. Fenaader N. G.. W&&in L. and Myers P., 1. Phys. Chem. .wds 29. 11, 1973(1968). 9. Mkb~ltttii B., Batbk R. P., Lachcisserie E. T. and Waintal A., Solid Stale Commun. 25, 163(1978). IO. Blandin A. and CampbellI. A., Phys. Rm. Lea. 31.57 (1973). 11. Jcna P. and Geldart D. J. W.. So/id Stale Common. IS. 139
(1974). 12. Baber W. G., Pnx. R. !kx. (London) All, 383 (1937).