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Localized magnetic moments on very dilute Fe impurities in copper
Solid State Communications
Vol. 2, pp. 209-212,1964.
PergamonPress,
Inc. Printedin
the United States.
LOCALIZED MAGNETIC MOMENTS ON VERY DILUTE Fe IMPURITIES IN COPPER* R. D. Taylor, Los
T. A. Kitchens,
Alamos Scientific
Laboratory, (Received
D. E. Nagle, W. A. Steyert University
Los
of California,
and W. E. UillettB Alamos,
New Mexico
15 June 1964 by E. Burstein)
The magnetic behavior of very dilute Fe impurities in Cu has been studied as a function of temperature between 1. lo and 310’K in applied ma etic fields up to 61 kOe by means of the Miissbauer hyperfine spectra of Fe % . The temperature dependence of the negative internal field is explained in terms of a localized moment on Fe which is coupled to the host lattice. y of the MBssbauer spec:a?; ~f!~~~~~$q impurities in several host lattices, we have discovered some cases of a large internal field anomaly at the impurity nucleus. 2 For copper at 4oK the hype fine splitting of the 14.4 keV y ray from the Fs 57 impurity corresponds to an effective field, &ff, which is only 56 per cent of the applied field, H; at 3000K H,ff is found to correspond approximately to H, as e_wecte$ T_he results may be represented by Heff = H + Hi is an internal field, yhich ig the Ease of copper can be defined by H,ff = H - a H. The parameter a is independent of H, but is dependent on the temperature. A separate circular olarization experiment showed that for Fe %7 in Cu Heff is parallel to H.
exchange
the auspices of University of
pressure
about the holder.
The 14.4 keV Y rays were analyzed with a room temperature absorber containing Fe57, together with a conventional velocity spectrum analyzer. I, 3 Our most precise results were obtained using a narrow, single-line absorber consisting of Fe57 enriched K4Fe(CN)6- 3H20. Generally the hyperfine spectrum was well resolved in the magnetic fields applied so that Heff was easily deduced from the observed splitting. In the cases where the spectrum was not resolved Iieff was deduced from the line broadening. Three copper sources were used: 2mC Co57 in commercial grade Cu, 15 mC Co57 in 99.895 per cent Cu foil, and 0.3 mC of special high purity Co57 (C0~~/Ca57 < 1) diffused 0.001 in.into 99.999 per cent Cu. Thus the concentration of magnetic impurities was varied by several orders of magnitude, the lowest being about 40 ppm, yet at 4oK the three resulting values of the parameter Q are the sam within experimental error. At 300°K and 4OK a was found to be 0.02 f 0.02 and 0.44 f 0.02 respectively, independent of H over the range 10 to 61.2 kOe, the maximum field used. Extensive measurements of I$ff as a function of T at 30.8 and 61.2 kOe showed that Hi is not simply a function of H/T, hence the system does not behave like a system of independent large localized moments, which gave rife to the paramagnetic behavior of Fe in Pd. In
The method we employed was to diffuse a small amount of Co57 into the ost material and study the Mijssbauer spectrum Q of the 14.4 keV Y ray emitted from the Fe57 nuclei as a function of H and T. The field could be varied from 0 to 61 kOe and the temperature of the source from 1. lo to 3100K. The magnet was a l/2 in. I.D. Nb-Zr superconducting solenoid operating in liquid He; the sample was held in the center of the solenoid y a copper holder containing a heat switch, a a heater, and thermometers. The temperature of the source could be determined by a vapor-pressure thermometer, a carbon resistance thermometer, and a thermocouple, and the temperature was regulated by the heater, the heat switch, and by varying the of Physics,
gas
Atomic Energy
209
Commission.
210
Vol. 2, No. 7
LOCALIZED MAGNETIC MOMENTS
T(OK) 100
200
1, Hr30.8 .
Hx61.2
,
kOe
300
-0.4
kOe -0.3
(J/J+I)(T/2s) FIG. 1 Calculated curves of SHi/‘uHHsat versus (T/25) (J/J + 1). The experimental data are scaled to provide the best fit to the calculated curves. zero external field the copper sources showed no spontaneous hyperfine splitting or broadening at any temperature. The combined line width observed for the Cu source (H = 0) and thin Fe57 absorber was 0.23 mm/set, which is within 5 per cent of the natural line width, after correction for finite thickness of the absorber. With the ferrocyanide absorber the corresponding line width observed was 0.29 mm/set at all temperatures. Furthermore, at 61.2 kOe and temperatures above 80oK the hyperfine spectra were sufficiently well resolved using the ferrocyanide absorber to obtain a line width from the outer pair of peaks. A width of 0.29 mm/set was obtained indicating all Fe impurities are magnetically equivalent sites. The results can be explained by a localized moment at the Fe site which is coupled to the host lattice. A lucid treatyent of the local-moment problem by Anderson indicates that this moment is due to a local 3-d state admixed with 4-s states of the conduction electrons. A Hartree-Fock self-consistent approach then
provides the requirements for a local moment on a model having one electron or hole in the 3-d shell. Anderson ShOWSthat for an iron group impurity in Cu a local moment is present or absent depending on the position of the Fermi surface, and on the density of states of the free electron. Cu is on the border line between the magnetic and nonmagnetic states. On the basis of our experimental data we can say that Fe in Cu has a magnetic moment, and on the basis of a simplified model, we can estimate the magnitude of this moment and its interaction with the surrounding host atoms. The interaction between the moment and the host has been discussed by Housley and Dash. 6 A very simple model of the interaction follows; however a more rigorous and complete discussion of the nature,d the impurity-host coupling will be given. The internal field is given by Hi=Hsat&/J w_SlereJ is the Fe atomic spin quantum number, the overall time average of the spin vector and Hsat the saturation value of the internal
LOCALIZED MAGNETIC MOMENTS
Vol. 2, No. 7
field. ‘9 * J is assumed to be coupled with a strengtr j to a randoplly moving host electronic field, S(t); let z = jS(t)/k, k being the Boltzmann constant. Assuming the host electronic field variation is slow compared to the thermal relaxation time the thermal average
211
(s) (J + 1)/J = 33.5oK and H,,+ = -350 J/ J + 1; H,gt is always expressed in kOe and CIin Bohr magnetons. The hyperfine field of the iron-group metals is thought to be primarily due to polarization of the core electrons by the polarized 3-d electrons;g on this picture Hsat m -125 cl. 10 From the relation H,,t LI= -350 J/J + 1 we conclude u - 1.7(5/J + 1)1/2 and Hsat 5 -210(5/J +1)1/2. Experimentally it appears from Fig. 1 that J 2 2 and therefore under the above assumptions, u = 1.55 f 0.15 and Hsat’ -190 & 20. Interestingly g = u/J < 0.7, a result consistent with Anderson’s one 3-d hole model5 where the eigenstate, $, of the Hamiltonian is an admixture of 3-d spin-up states, 3-d spindown states, and 4-s conduction electron states. This model has two energy levels, thus J = l/2; furthermore, u is less than one because of the admixture; hence, 0 z u/J 2 2. Confidence in the validity of the above assumptions is provided by the observation that if u = 1,7(5/J + l)l/2 and s(J + l)/(J) = 33.5oK susceptibility measure ments of 0.005 per cent Fe in Cu are explained over the entire range of temperatures from 4OK to room temperature. l1 Experiments are now underway with dilute Fe in Au, Rh, and other metals.
+(t)>/J
= rclii + k;] EBJ(\uii + k&‘kT)‘j I (uH+ ks(‘j 1 where cris the Fe electronic moment azd BJ(x) is the Brillouin function._ Averaging over the random positions of S(t) (i.e. over a longer period of time assumsd to be great compared to the fluctuations in S(t) but small compared to the lifetime of the excited nucle_ar levels) yields an Hi which is proportional to H for uH 2 ks, a condition well satisfied for the present data. Figure 1 shows the results of this averaging calculation expressed in terms of the dimensionless variables SHi/QHH,,t and (J/J + 1) (T/2s) where s is assumed to be independent of H and T. The experimental data of a versus T, scaled to give the best fit, are also shown in Fig. 1. We see from the scaling that (J/J + 1) (t/2S) = T/67 and SHi/‘UHHsat = 1.425 C. Thus References 1.
CRAIG P. P., NAGLE D. E., 12 (1962).
2.
TAYLOR R. D., STEYERT W. A. and NAGLE D. E., Proceedings of the Third International Conference on the Massbauer Effect, Cornell University, September 1963. Rev. Mod. -. 36, 406 (1964). See also BLUM N, FREEMAN A. J. and GRODZINS L., s p, 406. -
3.
FRAUENFELDER
4.
DASH J. G. and SIEGWARTH J.,
5.
ANDERSON P. W., Phys. 1030 (1961).
6.
HOUSLEY R. M. and DASH J. G., Proceedings of the Third International Conference on the MBssbauer Effect, Cornell University, September 1963. Rev. Mod. Phys. E, 409 (1964).
7.
HOUSLEY R. M. and DASH J. G., Phys.
8.
FREEMAN A. J.,
9.
WATSON R. E. and FREEMAN A. J., Phys. Rev. 123, 2027 (1961). We have neglected the This contribution is hard to predict contribution of the polarized 4s electrons to m. due to competing effects which tend to polarize them parallel and aati-parallel to the 3-d In any event it is expected to be smaller than the core polarization effect. moment.
10.
STEYERT W.A. and TAYLOR R.D.,
H., The Mijssbauer
Phys.
Effect.
W. A. Benjamin,
Rev. Sci. Instr.
Rev. 124, 41 (1961).
2, -
Phys.
Inc.,
New York
9, =
(1962).
1276 (1963).
See also WOLFF P. A.,
Rev. Letters
Rev. Letters
Phys.
Rev. 124, =
to be published.
Rev. 130, 889 (1963).
Preliminary measurements for dilute Fe in Au show that this assumed coefficient can be significantly lower than 125. For Fe in Au the low value of s(J + 1)/J = 3.7oK permits a 60 kOe
212
LOCALIZED MAGNETIC MOMENTS
Vol. 2, No. 7
field to almost saturate g>/J, and hence H,,t can be measured directly to be -173 kOe. Thus, with uHs,t(J + 1)/J measured, we can calculate u(J + U/J to be 3.8 Bohr mignetons, and hence H6at = -45.5 u(J + 1)/J. 11.
HEDGCOCK F. T., Phys. Rev. 104, 1564 (1956). 57 Mit HiIfe des Miissbauer-Hyperfeinspektrums von Fe wurden die magnetischen Eigenschaften sehr verdunnter Fe Uisungen im Cu bei Temperaturen zwischen 1. 1°K und 310°K und bei angelegten Magnetfeldern his zu einer Stike von 61 kilogauss untersucht. Die Temperaturabtingigkeit des negativen inneren Feldes kann dadurch erklkt werden dass ein lokalisiertes Moment im Fe mit dem Wirtsgitter verkoppelt 1st.
Vol. 2, pp. 209-212,1964.
PergamonPress,
Inc. Printedin
the United States.
LOCALIZED MAGNETIC MOMENTS ON VERY DILUTE Fe IMPURITIES IN COPPER* R. D. Taylor, Los
T. A. Kitchens,
Alamos Scientific
Laboratory, (Received
D. E. Nagle, W. A. Steyert University
Los
of California,
and W. E. UillettB Alamos,
New Mexico
15 June 1964 by E. Burstein)
The magnetic behavior of very dilute Fe impurities in Cu has been studied as a function of temperature between 1. lo and 310’K in applied ma etic fields up to 61 kOe by means of the Miissbauer hyperfine spectra of Fe % . The temperature dependence of the negative internal field is explained in terms of a localized moment on Fe which is coupled to the host lattice. y of the MBssbauer spec:a?; ~f!~~~~~$q impurities in several host lattices, we have discovered some cases of a large internal field anomaly at the impurity nucleus. 2 For copper at 4oK the hype fine splitting of the 14.4 keV y ray from the Fs 57 impurity corresponds to an effective field, &ff, which is only 56 per cent of the applied field, H; at 3000K H,ff is found to correspond approximately to H, as e_wecte$ T_he results may be represented by Heff = H + Hi is an internal field, yhich ig the Ease of copper can be defined by H,ff = H - a H. The parameter a is independent of H, but is dependent on the temperature. A separate circular olarization experiment showed that for Fe %7 in Cu Heff is parallel to H.
exchange
the auspices of University of
pressure
about the holder.
The 14.4 keV Y rays were analyzed with a room temperature absorber containing Fe57, together with a conventional velocity spectrum analyzer. I, 3 Our most precise results were obtained using a narrow, single-line absorber consisting of Fe57 enriched K4Fe(CN)6- 3H20. Generally the hyperfine spectrum was well resolved in the magnetic fields applied so that Heff was easily deduced from the observed splitting. In the cases where the spectrum was not resolved Iieff was deduced from the line broadening. Three copper sources were used: 2mC Co57 in commercial grade Cu, 15 mC Co57 in 99.895 per cent Cu foil, and 0.3 mC of special high purity Co57 (C0~~/Ca57 < 1) diffused 0.001 in.into 99.999 per cent Cu. Thus the concentration of magnetic impurities was varied by several orders of magnitude, the lowest being about 40 ppm, yet at 4oK the three resulting values of the parameter Q are the sam within experimental error. At 300°K and 4OK a was found to be 0.02 f 0.02 and 0.44 f 0.02 respectively, independent of H over the range 10 to 61.2 kOe, the maximum field used. Extensive measurements of I$ff as a function of T at 30.8 and 61.2 kOe showed that Hi is not simply a function of H/T, hence the system does not behave like a system of independent large localized moments, which gave rife to the paramagnetic behavior of Fe in Pd. In
The method we employed was to diffuse a small amount of Co57 into the ost material and study the Mijssbauer spectrum Q of the 14.4 keV Y ray emitted from the Fe57 nuclei as a function of H and T. The field could be varied from 0 to 61 kOe and the temperature of the source from 1. lo to 3100K. The magnet was a l/2 in. I.D. Nb-Zr superconducting solenoid operating in liquid He; the sample was held in the center of the solenoid y a copper holder containing a heat switch, a a heater, and thermometers. The temperature of the source could be determined by a vapor-pressure thermometer, a carbon resistance thermometer, and a thermocouple, and the temperature was regulated by the heater, the heat switch, and by varying the of Physics,
gas
Atomic Energy
209
Commission.
210
Vol. 2, No. 7
LOCALIZED MAGNETIC MOMENTS
T(OK) 100
200
1, Hr30.8 .
Hx61.2
,
kOe
300
-0.4
kOe -0.3
(J/J+I)(T/2s) FIG. 1 Calculated curves of SHi/‘uHHsat versus (T/25) (J/J + 1). The experimental data are scaled to provide the best fit to the calculated curves. zero external field the copper sources showed no spontaneous hyperfine splitting or broadening at any temperature. The combined line width observed for the Cu source (H = 0) and thin Fe57 absorber was 0.23 mm/set, which is within 5 per cent of the natural line width, after correction for finite thickness of the absorber. With the ferrocyanide absorber the corresponding line width observed was 0.29 mm/set at all temperatures. Furthermore, at 61.2 kOe and temperatures above 80oK the hyperfine spectra were sufficiently well resolved using the ferrocyanide absorber to obtain a line width from the outer pair of peaks. A width of 0.29 mm/set was obtained indicating all Fe impurities are magnetically equivalent sites. The results can be explained by a localized moment at the Fe site which is coupled to the host lattice. A lucid treatyent of the local-moment problem by Anderson indicates that this moment is due to a local 3-d state admixed with 4-s states of the conduction electrons. A Hartree-Fock self-consistent approach then
provides the requirements for a local moment on a model having one electron or hole in the 3-d shell. Anderson ShOWSthat for an iron group impurity in Cu a local moment is present or absent depending on the position of the Fermi surface, and on the density of states of the free electron. Cu is on the border line between the magnetic and nonmagnetic states. On the basis of our experimental data we can say that Fe in Cu has a magnetic moment, and on the basis of a simplified model, we can estimate the magnitude of this moment and its interaction with the surrounding host atoms. The interaction between the moment and the host has been discussed by Housley and Dash. 6 A very simple model of the interaction follows; however a more rigorous and complete discussion of the nature,d the impurity-host coupling will be given. The internal field is given by Hi=Hsat&/J w_SlereJ is the Fe atomic spin quantum number,
LOCALIZED MAGNETIC MOMENTS
Vol. 2, No. 7
field. ‘9 * J is assumed to be coupled with a strengtr j to a randoplly moving host electronic field, S(t); let z = jS(t)/k, k being the Boltzmann constant. Assuming the host electronic field variation is slow compared to the thermal relaxation time the thermal average
211
(s) (J + 1)/J = 33.5oK and H,,+ = -350 J/ J + 1; H,gt is always expressed in kOe and CIin Bohr magnetons. The hyperfine field of the iron-group metals is thought to be primarily due to polarization of the core electrons by the polarized 3-d electrons;g on this picture Hsat m -125 cl. 10 From the relation H,,t LI= -350 J/J + 1 we conclude u - 1.7(5/J + 1)1/2 and Hsat 5 -210(5/J +1)1/2. Experimentally it appears from Fig. 1 that J 2 2 and therefore under the above assumptions, u = 1.55 f 0.15 and Hsat’ -190 & 20. Interestingly g = u/J < 0.7, a result consistent with Anderson’s one 3-d hole model5 where the eigenstate, $, of the Hamiltonian is an admixture of 3-d spin-up states, 3-d spindown states, and 4-s conduction electron states. This model has two energy levels, thus J = l/2; furthermore, u is less than one because of the admixture; hence, 0 z u/J 2 2. Confidence in the validity of the above assumptions is provided by the observation that if u = 1,7(5/J + l)l/2 and s(J + l)/(J) = 33.5oK susceptibility measure ments of 0.005 per cent Fe in Cu are explained over the entire range of temperatures from 4OK to room temperature. l1 Experiments are now underway with dilute Fe in Au, Rh, and other metals.
+(t)>/J
= rclii + k;] EBJ(\uii + k&‘kT)‘j I (uH+ ks(‘j 1 where cris the Fe electronic moment azd BJ(x) is the Brillouin function._ Averaging
CRAIG P. P., NAGLE D. E., 12 (1962).
2.
TAYLOR R. D., STEYERT W. A. and NAGLE D. E., Proceedings of the Third International Conference on the Massbauer Effect, Cornell University, September 1963. Rev. Mod. -. 36, 406 (1964). See also BLUM N, FREEMAN A. J. and GRODZINS L., s p, 406. -
3.
FRAUENFELDER
4.
DASH J. G. and SIEGWARTH J.,
5.
ANDERSON P. W., Phys. 1030 (1961).
6.
HOUSLEY R. M. and DASH J. G., Proceedings of the Third International Conference on the MBssbauer Effect, Cornell University, September 1963. Rev. Mod. Phys. E, 409 (1964).
7.
HOUSLEY R. M. and DASH J. G., Phys.
8.
FREEMAN A. J.,
9.
WATSON R. E. and FREEMAN A. J., Phys. Rev. 123, 2027 (1961). We have neglected the This contribution is hard to predict contribution of the polarized 4s electrons to m. due to competing effects which tend to polarize them parallel and aati-parallel to the 3-d In any event it is expected to be smaller than the core polarization effect. moment.
10.
STEYERT W.A. and TAYLOR R.D.,
H., The Mijssbauer
Phys.
Effect.
W. A. Benjamin,
Rev. Sci. Instr.
Rev. 124, 41 (1961).
2, -
Phys.
Inc.,
New York
9, =
(1962).
1276 (1963).
See also WOLFF P. A.,
Rev. Letters
Rev. Letters
Phys.
Rev. 124, =
to be published.
Rev. 130, 889 (1963).
Preliminary measurements for dilute Fe in Au show that this assumed coefficient can be significantly lower than 125. For Fe in Au the low value of s(J + 1)/J = 3.7oK permits a 60 kOe
212
LOCALIZED MAGNETIC MOMENTS
Vol. 2, No. 7
field to almost saturate g>/J, and hence H,,t can be measured directly to be -173 kOe. Thus, with uHs,t(J + 1)/J measured, we can calculate u(J + U/J to be 3.8 Bohr mignetons, and hence H6at = -45.5 u(J + 1)/J. 11.
HEDGCOCK F. T., Phys. Rev. 104, 1564 (1956). 57 Mit HiIfe des Miissbauer-Hyperfeinspektrums von Fe wurden die magnetischen Eigenschaften sehr verdunnter Fe Uisungen im Cu bei Temperaturen zwischen 1. 1°K und 310°K und bei angelegten Magnetfeldern his zu einer Stike von 61 kilogauss untersucht. Die Temperaturabtingigkeit des negativen inneren Feldes kann dadurch erklkt werden dass ein lokalisiertes Moment im Fe mit dem Wirtsgitter verkoppelt 1st.