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The Kondo effect in low temperature deposited Cu(Fe) films
Solid State Communications, Vol. 16, pp. 367—369, 1975.
Pergamon Press.
Printed in Great Britain
ThE KONDO EFFECT IN LOW TEMPERATURE DEPOSITED Cu(Fe) FILMS* P.J. Silverman and C.V. Bnscoe Physics Department, University of North Carolina, Chapel Hill, North Carolina 27514, U.S.A. (Received 16 October 1974 by A.G. Chynoweth)
Highly disordered Cu(Fe) films were preparedby condensing a dilute Cu(Fe) alloy onto a lHe temperature substrate. The Kondo temperature Tk was computed by fitting the data to the Applebaum—Kondo resistivity formula. The computed Tk was found to be the same as that ofbulk, crystalline Cu(Fe).
SEVERAL studies have been made of the Kondo (resistivity minimum) effect in Cu(Fe) films deposited below room temperature.13 Compared to bulk Cu(Fe) such films are highly disordered, however, Knorr, Lim, and Leslie have found that the resistivity minimum occurs at the same temperature (Tm) as in bulk Cu(Fe).1 Rather than taking the characteristic temperature of the Kondo effect in Cu(Fe) to be Tm Loram, Whali and Ford4 have defined a characteristic temperature Tk by fitting their data to the Appelbaum— Kondo resistivity formula.5 Summers, Lipham, and Roberts have shown that large changes in Tk (—100 K) may occur even when the change in Tm is very small (—‘ 1 K).6 Since T~ is much more sensitive to changes in the Kondo phenomenon than Tm we have determined Tk for a number of Cu(Fe) films which were condensed on lHe temperature substrates in order to see if the structural disorder resulting from the “quench” condensation produced changes in T~. At low temperatures the resistivity of a Cu(Fe) film can be assumed to be the sum of three terms —
+ Pphonon + Pdefect where P~mis the Kondo resistivity, Pphonon is the resistivity due to phonon scattering, and Pdetect ~ the resistivity due to scattering from defects in the Cu —
It is customary to take the characteristic ternperature of a Kondo system TK to be either the temperature at which the resistivity minimum occurs or the temperature where the resistivity has increased from its value at Tm half way to its value at T = 0 K. While convenient, such a choice for TK may not be representative of the Kondo phenomenon since Tm is to some degree dependant on phonon and defect scattering in the host lattice. An alternate method for determining a characteristic temperature was suggested by Loram, Whall and Ford4 who fit their data to the Appelbaum—Kondo resistivity formula5 /T T \2 ~ = c A B in —i-) (2) \TK TKJ —
___________
*
lattice. In the films used in this study P defect was temperature independent below 16K. The Kondo resistivity minimum is produced by the fact that p phono~decreases as the temperature is lowered while ~ increases. The temperature at which the resistivity minimum occurs is thus determined by the effect of two processes: spin scattering, characterized by the Kondo temperature Tk and phonon scattering characterized by the Debye temperature. Two materials with the same T~might have resistivity minima occurring at different temperatures simply because they have different Debye temperatures.
This work was supported by the Materials Research Center, U.N.C. under Grant Number GH.33632 from the National Science Foundation,
—-
where c is the Fe concentration; A and B are constants; and T~is a characteristic temperature. The T~determined in this fashion is roughly twice the usually 367
368
THE KONDO EFFECT IN Cu(Fe) FILMS
accepted Kondo temperature TK for Cu(Fe). However, this is of no importance in the present work where only changes in T~are of interest. The most important feature of this method is that it permits the determination of a characteristic temperature that is unaffected (a) by phonon scattering which is negligible in the temperature range where T~was determined, and (b) by the presence (or absence) of large amounts of scattering from lattice defects.
266
Vol. 16, No.4
-
Cu(~FAIIO74~
•~
~ 265
-
264
-
0.1 ATOMIC % Fe
232
~‘-l6K Anneal
-
~-70K Anneal
-
0
~23l-
The Cu(Fe) samples were prepared by melting measured quantities of Cu and Fe in a covered graphite crucible, heated by an external heater, in a vacuum furnace. The Cu(Fe) ingots were cut into pellets and then etched in HNO3 to remove surface contamination. The Cu(Fe) alloys thus prepared were “flash” evaporated from a W boat onto a Z.cut natural quartz substrate held at 6.5 K in a lHe cryostat.evaporator. The deposition of the films took place in <5 sec. The films were 300 A thick as measured by the Toiansky method.SeveralpureCufilmswerepreparedinthe same way as the alloy films. These films showed no low temperature resistance anomaly but otherwise behaved the same as the alloy films, thus demonstrating a negligible concentration of magnetic impurities in the Cu from which the alloys were made and that the low temperature resistance anomalies observed in Cu(Fe) films deposited at —6.5 K were due to the presence of magnetic impurities and not to the disordered structure of the films,
Table 1. TK ofquench condensed Cu(Fe) films Sample No.
At.% Fe
Anneal temperature
T~
12473 31174 4874 11074 11074 11074 Summers, Lipham, and Roberts (Bulk alloy not disordered)6
0.038 0.047 0.047 0.1 0.1 0.1
15.5 K 19.5K 18.5 K 16.0 K 70K 270 K
59 ±4K 65±4K 64 ±4K 64 ±4K 59 ±4K 68 ±4K
0.0112
—
62
±2K
-
230
90
-
89
-
-
-
270K Anneal
188
87
-
I 2
111111 3 45
10
1111
100
TEMPERATURE (K)
FIG. 1. Resistance vs temperature curve of a Cu + —0.1 at.% Fe film deposited at —7K after annealing at ‘-16K, —70K, and 270 K. were made. After annealing T~was determined from the resistance vs temperature curve of the films by fitting the data in the temperature range 8 K ~ T ~ 16 K to the Appelbaum—Kondo resistivity formula [equation (2)]. The T~of quench condensed Cu(Fe) films was found to be the same as that of bulk, crystalline Cu(Fe), futhermore, Tk are wasgiven not changed by annealing the films. The results in Table 1. The T~of a bulk, crystalline Cu(Fe) sample 6contaming 112 p.p.m. Fe is given for cor~iparison. The structure of Cu films quench condensed onto lHe temperature substrates has been studied by Feldtkeller,7 who found that the films were composed of —25 A ciystallites. The residual resistivity of Feldtkeller’s films was p~ 25 p~7cm,which in a free electron approximation corresponds to a mean free path 1— 20 A. This suggests that the residual resistivity is due to scattering at grain boundaries. In the present study Po was found to be 15—20j.i&2cm, corresponding to a crystallite size of 25—3 5 A. Korn2 and MOnch and Sander8 have also found the residual resistivity of low temperature condensed Cu films to “—
Since the film structure was not stable the films were annealed at 16 K before any measurements
I
20 30 50
Vol. 16, No.4
THE KONDO EFFECT IN Cu(Fe) FILMS
be —15—20 p12cm. One notable exception is the value Po 50041cm reported by Hauser, eta!.3 which corresponds to an effective 1—’ 1 A, a value smaller than the effective mean free path in such .materials as amorphous Bi and Ga.9 Feldtkeller was able to produce residual resistivities 500 p12cm only by incorporating 9 per cent SiO into quench condensed Cu films.7 This suggests that the disordered Cu(Fe) films produced by Hauser, et a!. may have contained a substantial percentage of impurities and provides a possible explanation for the change in TK they observed.3
369
films prepared in the present study were composed of small crystallites. Assuming the Fe was distributed randomly, a rough estimate reveals that for a 2.5 A nearest neighbor distance in the Cu lattice and 25 A crystallites —50 per cent of the Fe atoms will lie on grain boundaries, even for a crystallite size of 50 A 25 per cent of the Fe wifi lie on grain boundaries. Thus, many of the Fe atoms will be in positions in which the Cu lattice is distorted and should be in an envbomnent different from that of bulk, crystalline Cu. ‘~
The annealing behavior of quench condensed films provides further information on their structure, Mönch and Sander8 determined from measurements of the stored energy release upon annealing that the ifims are composed of “highly disordered material between small crystallites.” Annealing behavior identical to that found by MOnch and Sander was ob. served in the present study.
Since the present measurements show that T~is the same in quench condensed Cu(Fe) films as in bulk, crystalline Cu(Fe) we believe that T~in Cu(Fe) is only wealdy dependant on long range order in the Cu lattice and the details of the environment of the Fe atoms. Simultaneous measurements of the electrical resistivity and microstructure of quench condensed Cu(Fe) films would be a useful method of furthering this study.
In view of the preceding discussion it seems justified to assume that the quench condensed Cu(Fe)
Acknowledgement We would like to thank Dr. L.D. Roberts for many helpful conversations during the preparation of this paper. —
REFERENCES 1.
KNORR K., LIM C.S. and LESLIE J.D., Solid State Commun. 10, 637 (1972).
2.
KORN D.,Z. Phys. 238, 275 (1970).
3.
HAUSER J.J., HAMANN D.R. and KAMMLOTT G.W., Phys. Rev. B3, 2211(1971).
4. 5.
LORAM J.W., WHALL T.E. and FORD P.J.,Phys. Rev. B2, 857 (1970). APPELBAUM J.A. and KONDO J.,Phys. Rev. Lett. 19,906 (1967).
6.
SUMMERS G.P., LIPHAM J.G. and ROBERTS L.D.,Phys. Rev. B8, 2106 (1973).
7. 8.
FELDTKELLER E., Z. Phys. 157,65 (1959). MONCH W. and SANDER W., Z. Phys. 157, 149 (1959).
9.
SHIER J. and GINSBERG D.,Phys. Rev. 147, 384 (1966).
Pergamon Press.
Printed in Great Britain
ThE KONDO EFFECT IN LOW TEMPERATURE DEPOSITED Cu(Fe) FILMS* P.J. Silverman and C.V. Bnscoe Physics Department, University of North Carolina, Chapel Hill, North Carolina 27514, U.S.A. (Received 16 October 1974 by A.G. Chynoweth)
Highly disordered Cu(Fe) films were preparedby condensing a dilute Cu(Fe) alloy onto a lHe temperature substrate. The Kondo temperature Tk was computed by fitting the data to the Applebaum—Kondo resistivity formula. The computed Tk was found to be the same as that ofbulk, crystalline Cu(Fe).
SEVERAL studies have been made of the Kondo (resistivity minimum) effect in Cu(Fe) films deposited below room temperature.13 Compared to bulk Cu(Fe) such films are highly disordered, however, Knorr, Lim, and Leslie have found that the resistivity minimum occurs at the same temperature (Tm) as in bulk Cu(Fe).1 Rather than taking the characteristic temperature of the Kondo effect in Cu(Fe) to be Tm Loram, Whali and Ford4 have defined a characteristic temperature Tk by fitting their data to the Appelbaum— Kondo resistivity formula.5 Summers, Lipham, and Roberts have shown that large changes in Tk (—100 K) may occur even when the change in Tm is very small (—‘ 1 K).6 Since T~ is much more sensitive to changes in the Kondo phenomenon than Tm we have determined Tk for a number of Cu(Fe) films which were condensed on lHe temperature substrates in order to see if the structural disorder resulting from the “quench” condensation produced changes in T~. At low temperatures the resistivity of a Cu(Fe) film can be assumed to be the sum of three terms —
+ Pphonon + Pdefect where P~mis the Kondo resistivity, Pphonon is the resistivity due to phonon scattering, and Pdetect ~ the resistivity due to scattering from defects in the Cu —
It is customary to take the characteristic ternperature of a Kondo system TK to be either the temperature at which the resistivity minimum occurs or the temperature where the resistivity has increased from its value at Tm half way to its value at T = 0 K. While convenient, such a choice for TK may not be representative of the Kondo phenomenon since Tm is to some degree dependant on phonon and defect scattering in the host lattice. An alternate method for determining a characteristic temperature was suggested by Loram, Whall and Ford4 who fit their data to the Appelbaum—Kondo resistivity formula5 /T T \2 ~ = c A B in —i-) (2) \TK TKJ —
___________
*
lattice. In the films used in this study P defect was temperature independent below 16K. The Kondo resistivity minimum is produced by the fact that p phono~decreases as the temperature is lowered while ~ increases. The temperature at which the resistivity minimum occurs is thus determined by the effect of two processes: spin scattering, characterized by the Kondo temperature Tk and phonon scattering characterized by the Debye temperature. Two materials with the same T~might have resistivity minima occurring at different temperatures simply because they have different Debye temperatures.
This work was supported by the Materials Research Center, U.N.C. under Grant Number GH.33632 from the National Science Foundation,
—-
where c is the Fe concentration; A and B are constants; and T~is a characteristic temperature. The T~determined in this fashion is roughly twice the usually 367
368
THE KONDO EFFECT IN Cu(Fe) FILMS
accepted Kondo temperature TK for Cu(Fe). However, this is of no importance in the present work where only changes in T~are of interest. The most important feature of this method is that it permits the determination of a characteristic temperature that is unaffected (a) by phonon scattering which is negligible in the temperature range where T~was determined, and (b) by the presence (or absence) of large amounts of scattering from lattice defects.
266
Vol. 16, No.4
-
Cu(~FAIIO74~
•~
~ 265
-
264
-
0.1 ATOMIC % Fe
232
~‘-l6K Anneal
-
~-70K Anneal
-
0
~23l-
The Cu(Fe) samples were prepared by melting measured quantities of Cu and Fe in a covered graphite crucible, heated by an external heater, in a vacuum furnace. The Cu(Fe) ingots were cut into pellets and then etched in HNO3 to remove surface contamination. The Cu(Fe) alloys thus prepared were “flash” evaporated from a W boat onto a Z.cut natural quartz substrate held at 6.5 K in a lHe cryostat.evaporator. The deposition of the films took place in <5 sec. The films were 300 A thick as measured by the Toiansky method.SeveralpureCufilmswerepreparedinthe same way as the alloy films. These films showed no low temperature resistance anomaly but otherwise behaved the same as the alloy films, thus demonstrating a negligible concentration of magnetic impurities in the Cu from which the alloys were made and that the low temperature resistance anomalies observed in Cu(Fe) films deposited at —6.5 K were due to the presence of magnetic impurities and not to the disordered structure of the films,
Table 1. TK ofquench condensed Cu(Fe) films Sample No.
At.% Fe
Anneal temperature
T~
12473 31174 4874 11074 11074 11074 Summers, Lipham, and Roberts (Bulk alloy not disordered)6
0.038 0.047 0.047 0.1 0.1 0.1
15.5 K 19.5K 18.5 K 16.0 K 70K 270 K
59 ±4K 65±4K 64 ±4K 64 ±4K 59 ±4K 68 ±4K
0.0112
—
62
±2K
-
230
90
-
89
-
-
-
270K Anneal
188
87
-
I 2
111111 3 45
10
1111
100
TEMPERATURE (K)
FIG. 1. Resistance vs temperature curve of a Cu + —0.1 at.% Fe film deposited at —7K after annealing at ‘-16K, —70K, and 270 K. were made. After annealing T~was determined from the resistance vs temperature curve of the films by fitting the data in the temperature range 8 K ~ T ~ 16 K to the Appelbaum—Kondo resistivity formula [equation (2)]. The T~of quench condensed Cu(Fe) films was found to be the same as that of bulk, crystalline Cu(Fe), futhermore, Tk are wasgiven not changed by annealing the films. The results in Table 1. The T~of a bulk, crystalline Cu(Fe) sample 6contaming 112 p.p.m. Fe is given for cor~iparison. The structure of Cu films quench condensed onto lHe temperature substrates has been studied by Feldtkeller,7 who found that the films were composed of —25 A ciystallites. The residual resistivity of Feldtkeller’s films was p~ 25 p~7cm,which in a free electron approximation corresponds to a mean free path 1— 20 A. This suggests that the residual resistivity is due to scattering at grain boundaries. In the present study Po was found to be 15—20j.i&2cm, corresponding to a crystallite size of 25—3 5 A. Korn2 and MOnch and Sander8 have also found the residual resistivity of low temperature condensed Cu films to “—
Since the film structure was not stable the films were annealed at 16 K before any measurements
I
20 30 50
Vol. 16, No.4
THE KONDO EFFECT IN Cu(Fe) FILMS
be —15—20 p12cm. One notable exception is the value Po 50041cm reported by Hauser, eta!.3 which corresponds to an effective 1—’ 1 A, a value smaller than the effective mean free path in such .materials as amorphous Bi and Ga.9 Feldtkeller was able to produce residual resistivities 500 p12cm only by incorporating 9 per cent SiO into quench condensed Cu films.7 This suggests that the disordered Cu(Fe) films produced by Hauser, et a!. may have contained a substantial percentage of impurities and provides a possible explanation for the change in TK they observed.3
369
films prepared in the present study were composed of small crystallites. Assuming the Fe was distributed randomly, a rough estimate reveals that for a 2.5 A nearest neighbor distance in the Cu lattice and 25 A crystallites —50 per cent of the Fe atoms will lie on grain boundaries, even for a crystallite size of 50 A 25 per cent of the Fe wifi lie on grain boundaries. Thus, many of the Fe atoms will be in positions in which the Cu lattice is distorted and should be in an envbomnent different from that of bulk, crystalline Cu. ‘~
The annealing behavior of quench condensed films provides further information on their structure, Mönch and Sander8 determined from measurements of the stored energy release upon annealing that the ifims are composed of “highly disordered material between small crystallites.” Annealing behavior identical to that found by MOnch and Sander was ob. served in the present study.
Since the present measurements show that T~is the same in quench condensed Cu(Fe) films as in bulk, crystalline Cu(Fe) we believe that T~in Cu(Fe) is only wealdy dependant on long range order in the Cu lattice and the details of the environment of the Fe atoms. Simultaneous measurements of the electrical resistivity and microstructure of quench condensed Cu(Fe) films would be a useful method of furthering this study.
In view of the preceding discussion it seems justified to assume that the quench condensed Cu(Fe)
Acknowledgement We would like to thank Dr. L.D. Roberts for many helpful conversations during the preparation of this paper. —
REFERENCES 1.
KNORR K., LIM C.S. and LESLIE J.D., Solid State Commun. 10, 637 (1972).
2.
KORN D.,Z. Phys. 238, 275 (1970).
3.
HAUSER J.J., HAMANN D.R. and KAMMLOTT G.W., Phys. Rev. B3, 2211(1971).
4. 5.
LORAM J.W., WHALL T.E. and FORD P.J.,Phys. Rev. B2, 857 (1970). APPELBAUM J.A. and KONDO J.,Phys. Rev. Lett. 19,906 (1967).
6.
SUMMERS G.P., LIPHAM J.G. and ROBERTS L.D.,Phys. Rev. B8, 2106 (1973).
7. 8.
FELDTKELLER E., Z. Phys. 157,65 (1959). MONCH W. and SANDER W., Z. Phys. 157, 149 (1959).
9.
SHIER J. and GINSBERG D.,Phys. Rev. 147, 384 (1966).