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Electron-magnon scattering in dilute Pd Mn at low temperatures
Solid State Communications,
Vol. 7, pp. 1261—1265, 1969.
Pergamon Press.
Printed in Great Britain
ELECTRON—MAGNON SCATTERING IN DILUTE PdMn AT LO~NTEMPERATURES* Gwyn V~illiamsand John W. Loram School of Mathematical and Physical Sciences, University of Sussex, Brighton, England
(Received 2 June 1969 by C.W. McCombie)
The electrical resistivity of several dilute ~4Mn alloys has been measured down to O.41°K. The more notable features of the low temperature incremental resistivity A,o include (i) a sharp kink associated with the transition to the ferromagnetically ordered state, (ii) a linear decrease with decreasing temperature immediately below the transition temperature, and (iii) a limiting T 3~’2 tempera-ture dependence — as predicted on an s electron—magnon scattering model.
RECENTLY the electrical resistivity p(T) of several dilute PdFe and ~4Co alloys has been measured down to O.45°K.1,2 At temperatures below the magnetic ordering temperature T~these measurements have indicated that the incremental resistivity tip(T) (=p(T) alloy — p(T) Pd) behaves thus: (i) immediately below T~,
Fe in Pd, and 40°K for lat. % Co in Pd. In these respects Mn in Pd behaves quite differently. Its effective moment 7,8 is close to that expected 6S ~) impurity, suggesting for the ‘bare’ S-state ( that its induced polarization in the Pd matrix is small. However, the occurrence of a transition to a ferromagnetically ordered state in Pd Mn
A 1o(T) decreases linearly with decreasing ternperature, suggesting that a molecular field model provides a reasonably good description of these systems in this temperature region. (ii) At ternperatures well below T~,L~p(T)is proportional to T 3/2, a temperature dependence which has been predicted theoretically ~ on the basis of electron-magnon scattering at low temperatures in systems which are not translationally invariant,
provides clear evidence that such a polarization exists in this system, but the magnitude of the transition temperature (4°l
Fe and Co as impurities in Pd have similar properties. For example, both exhibit the giant moment phenomenon, ~ a direct6 consequence induced by of the long range spin polarization these impurities in the Pd host. Such a polar-
Dilute alloys of Mn in Pd were prepared by melting the appropriate proportions of 5N pure Pd with 3N pure Mn in a levitation furnace. Resistivity measurements were made, using the standard four probe technique, on carefully homogerüsed samples which were about 1.5 x 102 cm thick, 0.3 cm wide and 8cm long. Data on all samples were taken betWeen 0.41 and 300°K;below 4.2°Ktemperatures were stabilised and measured to within ±1 millidegree, and above 4.2°Kto better than ±1%. Finally, the
ization leads to ferromagnetic ordering, with high transition temperatures of 50°I(for lat.% ____________
*This work has been sponsored in part by the Air Force Materials Laboratory (AFSC) through the European Office of Aerospace Research (OAR), United States Air Force, under Contract F61 052—68—C—00].1.
area to length ratios of the samples were measured 1261
ELECTRON—MAGNON SCATTERING IN DILUTE PdMn
1262
Vol. 7, No. 17
Pd- 1.05 at~I.Mn ‘39 -
T(M~RAn/R((’K)
..•~
0
2
3
FIG. 1. Incremental resistivity ~\~in
5
6
7
8
~Q cm) plotted against temperature (in alloys examined.
CJ<)
for the three
Pd-1.OSot°/,Mn 1.43
140
Pd- 2.4 at,’/, Mn
~
.37
~—
T 3.42k
Pd-291a1/,Mn ~
4.81 479
-
~
-
.
[r(~xJ1~/2
FIG. 2. Incremental resistivity ~\,(in ~tci cm) plotted against T 3.2 (in ~ alloys examined. to within ±0.5%, thus enabling accurate determinations of the alloy resistivities to be deduced from the experimental data. Figure 1 shows the temperature dependence of Ap(T) below 10°K for the three alloys examined, In each alloy the transition to the ordered state is
32)
for the three
clear; this is followed by a linear decrease in ~p(T) with decreasing temperature, as observed previously for this system by Sarachik and 7 At lower temperatures however, Shaltiel. deviations from such behaviour occur. Figure 2 shows t~(T) plotted against T 3~’2, and indicates that the limiting form of the temperature dependence
Vol. 7, No. 17
ELECTRON—MAGNON SCATTERING IN DILUTE PdMn
1263
Table 1 Analysed composition*
T~(°K)
Ap(T=0)
Coeff. of linear decrease (~lcm/°K)
Coeff. of
T
— Ap(T=0) 372)Ap(T~) ~lcm
3/2
(j~lcm/°K
Pd
—
1.05 at. % Mn
3.90
+
0.02
1.3635
0.0309
0.0156
0.1015
Pd
—
2.40 at. % Mn
7.35
-~-
0.02
3.4 130
0.0308
0.0107
0.1870
Pd
—
2.91 at. % Mn
7.71
±
0.02
4.7881
0.0288
0.0090
0.1779
*
Analysis carried out by Daniel Griffiths and Co., London.
of ~p(T) Figure 2 the T 3/2 and Fig. decrease
is that predicted by Turner and Long.3 enables ~p(T=0) and the coefficient of term in the various alloys to be estimated 1, T~and the coefficient of the linear immediately below T~. These are listed
in Table 1. In the dilute limit it is expected that z~(T=0) would be proportional to the impurity concentration c. Table 1 indicates that this limit extends up to about 2.5 at. % Mn, but above this concentration, not unexpectedly, this linear relationship breaks down. Reference 3 predicts that the coefficient of the T 3~2 term should depend on concentration as c 1/2, and this appears to be obeyed must in the however alloys examined here. This agreement be regarded as fortuitous since the predicted concentration dependence relies on the use of a molecular field model for the d-band splitting (T~o c), and Table 1 indicates that this is clearly not so. The random phase or molecular field approximation does, however, enable reasonably straight-forward expressions to be derived for various parameters of the system in terms of its bulk properties. For example, assuming that the transport properties of such systems are determined by electrons in the s-band, the theory of Yosida9 yields, in the limit of strong potential scattering, the following expression for 2~{lcm
(1)
= 5.78cV V (in eV) being the deviation of the spin independent lattice potential from perfect periodicity owing to the presence of the impurity; c is the impurity concentration (at. %). The fact that equation (1) predicts incorrectly the concentration dependence of ~p(T=0) typifies the failure of the RPA, but nevertheless enables an estimate
of an ‘effective’ V to be made. This same approach also yields: ~p(T ) — Ap(T=0) = 5.78c J C
S(1+4S) 1i~cm (2) is the exchange coupling (in eV) between s-electrons of the host and the local spin (of magnitude S). This equation again predicts the concentration dependence of Ap(1~) — Ap(T= 0) incorrectly (see Table 1).
JS..lOCal
Finally, assuming that the onset of magnetic ordering is controlled by properties of the d-band, 3 Turner and Long have shown:
kT
k1cl.local 2cSN(0)
=
(3)
24K~(z/2)2/3
C
J~
is the d electron-local spin exchange integral (in eV), k is Boltzmann’s constant, and N(0) is the unenhanced density of d states of one spin orientation at the Fermi level. z is the number of d holes per atom and K~[= 1 — IN(0)I the Stoner parameter. The linear dependence of T~on c in equation (3) is again the result of using the RPA. Putting S = 5/2, N(0)K2 12/eV/atom (from the low temperature magnetic susceptibility of Pd), z = 0.36 ~‘ and K~= 0.14,12 equations (1), (2) and (3) yield values for V, Ifs-local and ‘ these are listed in Table2.
IJ~.
10~1
To summarize, the present measurements have shown that below the magnetic ordering temperature T~,the incremental resistivity Ap(T) for dilute PdMn has similar characteristics to those observed in dilute ~ Fe and ~ Co. This amounts to a linear decrease of A,o(T) with decreasing temperature immediately below TC,
1264
ELECTRON—MAGNON SCATTERING IN DILUTE ~Mn
Table 2 Alloy
relatively long range indirect ferromagnetic coupling between Mn. impurities, resulting from
V(eV) 1~s-local!(eV)IJ~
Pd— 1.05 at. % Mn 0.47 4 at. % Mn ~ Pu— L. Pd—2.91 at. % Mn 0.53
Vol. 7, No. 17
10~81 ReV)
the polarization they induce in the Pd d-band.
U.U2h
0.034 u.u~l
0.020
0.029
The second arises from direct Mn—Mn exchange .coupling, and is operative virtually only when impurities are nearest neighbours. The latter become increasingly important as the impurity concentration increases, and the work of
0.025
indicating the applicability of the molecular field model, and a limiting T 3,’2 low temperature dependence for L\p(T), as predicted on the basis of electron—niagnon scattering. The most striking difference so far revealed relates to the concentration dependence of dTC/dc. In PdFe and PdCo this quantity is an increasing function of concentration, but in PdMn it decreases with increasing concentration. In PdMri we suggest that the onset and nature of magnetic order is influenced by two factors. The first is the
Moriya ‘~ strongly suggests that direct Mn—Mn coupling will favour ant~rromagnetic alignment of these near neighbours. The direct and indirect coupling in PdMn are thus in competition (the reverse of course is true of Fe and Co in Pd) which accounts qualitatively for the observed effects. Clearly, careful magnetisation and neutron experiments on alloys of Pd containing several at. % Mn would be of considerable assistance in understanding this system.
REFERENCES 1.
WILLIAMS GWYN and LORAM J.W., J. Phys. Chem. Solids, to be published.
2.
WILLIAMS GWYN, to be published.
3.
TURNER RE., and LONG P.D., to be published.
4.
BOZORTH R.M., WOLFF P.D., DAVIS C.D., COMPTON V.B., and WERNICK J.H., Phys. Rev. 122, 1157 (1961). CLOGSTON A.M., MATTHIAS B.T., PETER M., WILLIAMS H.J., CORENZWIT E. and SHERWOOD
5.
R.C., Phys. Rev. 125, 541 (1965). 6.
LOW G.G. and HOLDEN T.M. Proc. Phys. Soc. 89, 119 (1966).
7.
SARACHIK M.P. and SHALTIEL D., J. appi. Phys. 38, 1155 (1967).
8.
CAMPBELL l.A., Proc. Phys. Soc. C, 93, 687 (1968).
9.
YOSIDA K., Phys. Rev. 107, 396 (1957).
10.
The numerical factor of 5.78 appearing in this equation is the result of using an effective mass of s-electrons, m*/m = 2.2, and 0.36s electrons per atom as quoted in Reference 11.
11.
VUILLEMIN
12.
SHIMIZU M., TAKAHASHI T. and KATSUKI A., J. Phys. Soc., Japan 18, 240 (1963).
13.
MORIYA T., Proceedings of the International School of Physics, Enrico Fermi, Course XXXVII, Academic Press — New York, 1967. This author shows that impurities with nearly half filled d shells (i.e. Mn in Pd) have a tendency to be polarised antiparallel to a neighbouring moment, while impurities with nearly filled d shells (Co in Pd) have a preference for parallel polarisation.
J.J., Phys. Rev.
144, 396 (1966).
Vol. 7, No. 17
ELECTRON—MAGNON SCATTERING IN DILUTE PdMn Die Elektrische Resistivitat verschiedener verdünnten Pd Mn Legierungen wurde gemessen bis auf 0.41°K. Die wichtigsten eigenschaften der zusátzlichen Resistivität für niedrigen Ternperaturen, tsp, sind (i) eine scharfe Diskontinuität verursacht von dem Ubergang zurn ferromagnetischen geordneten Zustand, (ii) Eine lineare Abnahme mit abnahmender Temperatur sofort unter der Ubergangstemperatur, und (iii) eine asymptotischen T 3~’2 Temperature Abhängigkeit — wie vorsagt von einem s elektron—magnon Streuungs Modell.
1265
Vol. 7, pp. 1261—1265, 1969.
Pergamon Press.
Printed in Great Britain
ELECTRON—MAGNON SCATTERING IN DILUTE PdMn AT LO~NTEMPERATURES* Gwyn V~illiamsand John W. Loram School of Mathematical and Physical Sciences, University of Sussex, Brighton, England
(Received 2 June 1969 by C.W. McCombie)
The electrical resistivity of several dilute ~4Mn alloys has been measured down to O.41°K. The more notable features of the low temperature incremental resistivity A,o include (i) a sharp kink associated with the transition to the ferromagnetically ordered state, (ii) a linear decrease with decreasing temperature immediately below the transition temperature, and (iii) a limiting T 3~’2 tempera-ture dependence — as predicted on an s electron—magnon scattering model.
RECENTLY the electrical resistivity p(T) of several dilute PdFe and ~4Co alloys has been measured down to O.45°K.1,2 At temperatures below the magnetic ordering temperature T~these measurements have indicated that the incremental resistivity tip(T) (=p(T) alloy — p(T) Pd) behaves thus: (i) immediately below T~,
Fe in Pd, and 40°K for lat. % Co in Pd. In these respects Mn in Pd behaves quite differently. Its effective moment 7,8 is close to that expected 6S ~) impurity, suggesting for the ‘bare’ S-state ( that its induced polarization in the Pd matrix is small. However, the occurrence of a transition to a ferromagnetically ordered state in Pd Mn
A 1o(T) decreases linearly with decreasing ternperature, suggesting that a molecular field model provides a reasonably good description of these systems in this temperature region. (ii) At ternperatures well below T~,L~p(T)is proportional to T 3/2, a temperature dependence which has been predicted theoretically ~ on the basis of electron-magnon scattering at low temperatures in systems which are not translationally invariant,
provides clear evidence that such a polarization exists in this system, but the magnitude of the transition temperature (4°l
Fe and Co as impurities in Pd have similar properties. For example, both exhibit the giant moment phenomenon, ~ a direct6 consequence induced by of the long range spin polarization these impurities in the Pd host. Such a polar-
Dilute alloys of Mn in Pd were prepared by melting the appropriate proportions of 5N pure Pd with 3N pure Mn in a levitation furnace. Resistivity measurements were made, using the standard four probe technique, on carefully homogerüsed samples which were about 1.5 x 102 cm thick, 0.3 cm wide and 8cm long. Data on all samples were taken betWeen 0.41 and 300°K;below 4.2°Ktemperatures were stabilised and measured to within ±1 millidegree, and above 4.2°Kto better than ±1%. Finally, the
ization leads to ferromagnetic ordering, with high transition temperatures of 50°I(for lat.% ____________
*This work has been sponsored in part by the Air Force Materials Laboratory (AFSC) through the European Office of Aerospace Research (OAR), United States Air Force, under Contract F61 052—68—C—00].1.
area to length ratios of the samples were measured 1261
ELECTRON—MAGNON SCATTERING IN DILUTE PdMn
1262
Vol. 7, No. 17
Pd- 1.05 at~I.Mn ‘39 -
T(M~RAn/R((’K)
..•~
0
2
3
FIG. 1. Incremental resistivity ~\~in
5
6
7
8
~Q cm) plotted against temperature (in alloys examined.
CJ<)
for the three
Pd-1.OSot°/,Mn 1.43
140
Pd- 2.4 at,’/, Mn
~
.37
~—
T 3.42k
Pd-291a1/,Mn ~
4.81 479
-
~
-
.
[r(~xJ1~/2
FIG. 2. Incremental resistivity ~\,(in ~tci cm) plotted against T 3.2 (in ~ alloys examined. to within ±0.5%, thus enabling accurate determinations of the alloy resistivities to be deduced from the experimental data. Figure 1 shows the temperature dependence of Ap(T) below 10°K for the three alloys examined, In each alloy the transition to the ordered state is
32)
for the three
clear; this is followed by a linear decrease in ~p(T) with decreasing temperature, as observed previously for this system by Sarachik and 7 At lower temperatures however, Shaltiel. deviations from such behaviour occur. Figure 2 shows t~(T) plotted against T 3~’2, and indicates that the limiting form of the temperature dependence
Vol. 7, No. 17
ELECTRON—MAGNON SCATTERING IN DILUTE PdMn
1263
Table 1 Analysed composition*
T~(°K)
Ap(T=0)
Coeff. of linear decrease (~lcm/°K)
Coeff. of
T
— Ap(T=0) 372)Ap(T~) ~lcm
3/2
(j~lcm/°K
Pd
—
1.05 at. % Mn
3.90
+
0.02
1.3635
0.0309
0.0156
0.1015
Pd
—
2.40 at. % Mn
7.35
-~-
0.02
3.4 130
0.0308
0.0107
0.1870
Pd
—
2.91 at. % Mn
7.71
±
0.02
4.7881
0.0288
0.0090
0.1779
*
Analysis carried out by Daniel Griffiths and Co., London.
of ~p(T) Figure 2 the T 3/2 and Fig. decrease
is that predicted by Turner and Long.3 enables ~p(T=0) and the coefficient of term in the various alloys to be estimated 1, T~and the coefficient of the linear immediately below T~. These are listed
in Table 1. In the dilute limit it is expected that z~(T=0) would be proportional to the impurity concentration c. Table 1 indicates that this limit extends up to about 2.5 at. % Mn, but above this concentration, not unexpectedly, this linear relationship breaks down. Reference 3 predicts that the coefficient of the T 3~2 term should depend on concentration as c 1/2, and this appears to be obeyed must in the however alloys examined here. This agreement be regarded as fortuitous since the predicted concentration dependence relies on the use of a molecular field model for the d-band splitting (T~o c), and Table 1 indicates that this is clearly not so. The random phase or molecular field approximation does, however, enable reasonably straight-forward expressions to be derived for various parameters of the system in terms of its bulk properties. For example, assuming that the transport properties of such systems are determined by electrons in the s-band, the theory of Yosida9 yields, in the limit of strong potential scattering, the following expression for 2~{lcm
(1)
= 5.78cV V (in eV) being the deviation of the spin independent lattice potential from perfect periodicity owing to the presence of the impurity; c is the impurity concentration (at. %). The fact that equation (1) predicts incorrectly the concentration dependence of ~p(T=0) typifies the failure of the RPA, but nevertheless enables an estimate
of an ‘effective’ V to be made. This same approach also yields: ~p(T ) — Ap(T=0) = 5.78c J C
S(1+4S) 1i~cm (2) is the exchange coupling (in eV) between s-electrons of the host and the local spin (of magnitude S). This equation again predicts the concentration dependence of Ap(1~) — Ap(T= 0) incorrectly (see Table 1).
JS..lOCal
Finally, assuming that the onset of magnetic ordering is controlled by properties of the d-band, 3 Turner and Long have shown:
kT
k1cl.local 2cSN(0)
=
(3)
24K~(z/2)2/3
C
J~
is the d electron-local spin exchange integral (in eV), k is Boltzmann’s constant, and N(0) is the unenhanced density of d states of one spin orientation at the Fermi level. z is the number of d holes per atom and K~[= 1 — IN(0)I the Stoner parameter. The linear dependence of T~on c in equation (3) is again the result of using the RPA. Putting S = 5/2, N(0)K2 12/eV/atom (from the low temperature magnetic susceptibility of Pd), z = 0.36 ~‘ and K~= 0.14,12 equations (1), (2) and (3) yield values for V, Ifs-local and ‘ these are listed in Table2.
IJ~.
10~1
To summarize, the present measurements have shown that below the magnetic ordering temperature T~,the incremental resistivity Ap(T) for dilute PdMn has similar characteristics to those observed in dilute ~ Fe and ~ Co. This amounts to a linear decrease of A,o(T) with decreasing temperature immediately below TC,
1264
ELECTRON—MAGNON SCATTERING IN DILUTE ~Mn
Table 2 Alloy
relatively long range indirect ferromagnetic coupling between Mn. impurities, resulting from
V(eV) 1~s-local!(eV)IJ~
Pd— 1.05 at. % Mn 0.47 4 at. % Mn ~ Pu— L. Pd—2.91 at. % Mn 0.53
Vol. 7, No. 17
10~81 ReV)
the polarization they induce in the Pd d-band.
U.U2h
0.034 u.u~l
0.020
0.029
The second arises from direct Mn—Mn exchange .coupling, and is operative virtually only when impurities are nearest neighbours. The latter become increasingly important as the impurity concentration increases, and the work of
0.025
indicating the applicability of the molecular field model, and a limiting T 3,’2 low temperature dependence for L\p(T), as predicted on the basis of electron—niagnon scattering. The most striking difference so far revealed relates to the concentration dependence of dTC/dc. In PdFe and PdCo this quantity is an increasing function of concentration, but in PdMn it decreases with increasing concentration. In PdMri we suggest that the onset and nature of magnetic order is influenced by two factors. The first is the
Moriya ‘~ strongly suggests that direct Mn—Mn coupling will favour ant~rromagnetic alignment of these near neighbours. The direct and indirect coupling in PdMn are thus in competition (the reverse of course is true of Fe and Co in Pd) which accounts qualitatively for the observed effects. Clearly, careful magnetisation and neutron experiments on alloys of Pd containing several at. % Mn would be of considerable assistance in understanding this system.
REFERENCES 1.
WILLIAMS GWYN and LORAM J.W., J. Phys. Chem. Solids, to be published.
2.
WILLIAMS GWYN, to be published.
3.
TURNER RE., and LONG P.D., to be published.
4.
BOZORTH R.M., WOLFF P.D., DAVIS C.D., COMPTON V.B., and WERNICK J.H., Phys. Rev. 122, 1157 (1961). CLOGSTON A.M., MATTHIAS B.T., PETER M., WILLIAMS H.J., CORENZWIT E. and SHERWOOD
5.
R.C., Phys. Rev. 125, 541 (1965). 6.
LOW G.G. and HOLDEN T.M. Proc. Phys. Soc. 89, 119 (1966).
7.
SARACHIK M.P. and SHALTIEL D., J. appi. Phys. 38, 1155 (1967).
8.
CAMPBELL l.A., Proc. Phys. Soc. C, 93, 687 (1968).
9.
YOSIDA K., Phys. Rev. 107, 396 (1957).
10.
The numerical factor of 5.78 appearing in this equation is the result of using an effective mass of s-electrons, m*/m = 2.2, and 0.36s electrons per atom as quoted in Reference 11.
11.
VUILLEMIN
12.
SHIMIZU M., TAKAHASHI T. and KATSUKI A., J. Phys. Soc., Japan 18, 240 (1963).
13.
MORIYA T., Proceedings of the International School of Physics, Enrico Fermi, Course XXXVII, Academic Press — New York, 1967. This author shows that impurities with nearly half filled d shells (i.e. Mn in Pd) have a tendency to be polarised antiparallel to a neighbouring moment, while impurities with nearly filled d shells (Co in Pd) have a preference for parallel polarisation.
J.J., Phys. Rev.
144, 396 (1966).
Vol. 7, No. 17
ELECTRON—MAGNON SCATTERING IN DILUTE PdMn Die Elektrische Resistivitat verschiedener verdünnten Pd Mn Legierungen wurde gemessen bis auf 0.41°K. Die wichtigsten eigenschaften der zusátzlichen Resistivität für niedrigen Ternperaturen, tsp, sind (i) eine scharfe Diskontinuität verursacht von dem Ubergang zurn ferromagnetischen geordneten Zustand, (ii) Eine lineare Abnahme mit abnahmender Temperatur sofort unter der Ubergangstemperatur, und (iii) eine asymptotischen T 3~’2 Temperature Abhängigkeit — wie vorsagt von einem s elektron—magnon Streuungs Modell.
1265