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Muon spin relaxation study of exchange coupling in dilute Ag Mn alloys
Journal of Magnetism and Magnetic Materials 54-57 (1986) 1103-1104
1103
MUON SPIN RELAXATION STUDY OF EXCHANGE COUPLING R.H. HEFFNER,
IN DILUTE AgMn ALLOYS
D . W . C O O K E , R.L. H U T S O N , M.E. S C H I L L A C I
Los Alamos National Laboratory. Los Alamo& N M 87545, USA
S.A. D O D D S , G . A . G I S T Rice University, Houston, TX 77251. USA
a n d D.E. M a c L A U G H L I N University of California. Riverside, CA 92521, USA
We have observed for the first time a conduction-electron-mediatedcomponent of the interaction between muons and local moments in a dilute magnetic alloys, AgMn. Comparison of the amplitude of this component and neutron quasielastic linewidth data yields some disagreement with a covalent-mixing exchange model.
We have used m u o n spin relaxation (~tSR) to examine some single-ion properties of Mn local moments in Ag. We find that the coupling between muons and M n moments is partially mediated by conduction-electron spin-density oscillations (SDO), so that we can determine the exchange constant average JSDO appropriate to SDO coupling. Our value for JSDO, 2.8 eV, is larger but more reliable than values found from N M R [1] or ESR [2]. This constitutes the first observation of SDO by ~xSR, and the first unambiguous determination of JSDO for A gMn. We compare our result to the exchange constant JK appropriate to Korringa relaxation of Mn impurities by conduction-electron scattering, as obtained from neutron scattering data [3], and obtain evidence against attributing exchange entirely to covalent mixing in A gMn. Aga_cMn c samples with c = 0.003, 0.016 and 0.030 were prepared by arc-melting the weighed constituents, followed by 10 h anneal at 800°C and a quench. Concentrations were verified by ac susceptibility measurements of the spin-glass freezing temperature Tg and by determination of the residual resistance. Agreement with previous measurements [4] was good. One of the samples was also analyzed by atomic absorption spectroscopy, and found to have the nominal concentration. M u o n spin relaxation data were obtained in a conventional ~SR spectrometer at the Clinton P. Anderson Meson Physics Facility (LAMPF), using transverse external fields [5]. In order to avoid complications due to spin-glass effects, all data were obtained at temperatures above 3Tg(c). Muon relaxation in a transverse field H is dominated by inhomogeneous broadening due to Mn spin polarization, as discussed previously [6]. A detailed calculation [7] yields an exponential relaxation function, and we have fitted our data accordingly. The inhomogeneous linewidth 1/T~ is proportional to c and to the M n spin
polarization (Sz). In the high-temperature limit the M n polarization follows a Curie law [8], so one expects 1/T~ o: cH/T. Experimentally, the constants of proportionality are (0.270 + 0.007), (0.276 + 0.016) and (0.267 + 0.013) Fts- I Oe -1 K for c = 0.003, 0.016 and 0.030, respectively. We note that these values are essentially constant over a decade of variation of c. The constant of proportionality can be calculated in the dilute limit [7], assuming a m u o n - M n coupling of the form A ~ / = [BsD o cos(ZkFri+ep)+Bdip(1 --3 cos20i)]
× (S:)/ri 3,
(1)
where A0~ is the muon frequency shift due to a M n ion at (ri, Or), and ~ is the phase of the SDO coupling. The coefficients BSDo and Bdi p a r e the amplitudes of the indirect SDO coupling and the direct dipolar coupling, respectively. For BSDo = 0, one obtains
(1/T2* )dip = 5.065y~n ( Peff~B) 2cH/3kBT,
(2)
where ~,, is the muon gyromagnetic ratio and n is the host-site n u m b e r density. The numerical factor arises from averaging over muon and impurity positions. The form of eq. (2), which contains the effective Mn magnetic moment Peff~B, facilitates comparison with magnetization measurements. Although not all of our samples would be considered dilute, numerical calculations [9] confirm that eq. (2) is adequate for c ~< 0.07. Magnetization measurements on the c = 0.016 sample [10] yield Pelf = 5.53, in agreement with previous high-temperature results [8]. Using this value in eq. (2), we obtain a value of 0.160 ~s - 1 0 e -1 K for the constant of proportionality in the purely dipolar case, which is substantially smaller than the observed constant. An excess linewidth due to a non-random distri-
0 3 0 4 - 8 8 5 3 / 8 6 / $ 0 3 . 5 0 © Elsevier Science P u b l i s h e r s B.V.
1104
R.H. Heffner et al. / Exchange coupling in dilute A ggMn alloys
bution of muon stopping sites is unlikely, in view of (1) the observed linear concentration dependence of 1/T~, and (2) the good agreement with purely dipolar coupling obtained for muon linewidths in A gEr [11]. Neither of these results would be obtained if muon sites were not randomly distributed. Therefore, it is reasonable to attribute the excess broadening in A gMn to the SDO mechanism, which is expected to be stronger for a 3d ion than for a rare earth. The case of mixed coupling, where both BsD o and Bdip are non-zero, has also been treated by Walstedt and Walker [7]. Using their numerical results, and the observed ratio (l/T~')exp/(1/T2*)dip ~ 1.7, we find BsD O ].8Bdi p. (A similar procedure for C uMn, using the parameters of ref. [1], yields a negligible SDO contribution to the muon linewidth.) Walstedt and Walker [1] have summarized the formalism needed to relate 1/7"2" (and the local moment spin-flip time ~'K discussed below) to exchange scattering of conduction electrons by a local moment. They assume a wave-factor-dependent exchange parameter J ( k , k') which includes both atomic and covalent-mixing contributions. Their calculation also includes the effects of potential scattering at the impurity site and enhancement of the conduction electron susceptibility. In the case of Ag, conduction-band enhancement is negligible [12] and we may use free-electron model parameters [13]. We then have K~J~ BSD° -- 8~nt~B I gsD°['
(3)
where ] JsDo ] is an appropriate average of J ( k , k') over the Fermi surface and K~ is the muon Knight shift in the pure host [1]. Using the experimentally derived values of BSDo, and K~ = 94 p p m [14], we obtain ] JSDO] = (2.8 4-_0.3) eV. Values of [JsDoI in A gMn obtained by N M R [1] and ESR [2] are considerably smaller than this, but the N M R experiments may have been affected by metallurgical problems [1] and interpretation of the ESR data may have been affected by failure to break the bottleneck fully [3]. The present determination of JSDO is free of these problems. We now consider the Mn local-moment Korringa relaxation time ~'K, related to the exchange constant average JK
for spin-flip conduction-electron scattering by (1-KT)
'=('u/h)knp(EF)2j
2.
(4)
where p ( E F ) is the density of states per spin at the Fermi surface. F r o m quasielastic neutron scattering experiments Murani [3] has obtained a Korringa product ('rKT) ! = (5.7 4- 0.5) X 10 9 S 1 K 1 which yields ]JK [ = 0.85 eV [3]. One may ask if the exchange constant averages JsDo (~SR) and JK (neutron scattering) are consistent with a reasonable set of exchange parameters. If the covalent mixing contribution to J ( k , k') is assumed to be completely dominant then I JsDo/JK I = ~ - [1], which is less than the measured ratio of 3.3 _ 0.6. This may indicate that direct exchange contributions are also important, but a proper evaluation of the additional terms requires the potential-scattering phase shifts [1], which are not reliably known. Alternatively, recent photoemission results [15] suggest that the Schrieffer-Wolf transformation, which underlies our analysis, may be inadequate to describe the strong mixing in A gMn. This work was performed under the auspices of the US Department of Energy, and was also supported by the US National Science Foundation. Grants D M R 79-09223 and D M R 81-15543. [1] R.E. Walstedt and L.R. Walker, Phys. Rev. B 11 (1975) 3280. [2] D. Davidov et al., Phys. Rev. B 11 (1975) 3546. [3] A.P. Murani, J. Magn. Magn. Mat. 25 (1981) 68. [4] P.J. Ford and J.A. Mydosh, Phys. Rev. B 14 (1981) 2057. V. Cannella and J.A. Mydosh, AIP Conf. Proc. 18 (1974) 651. [5] E, Karlsson, Phys. Rep. 82 (1982) 271. [6] R.H. Heffner et al., J. Appl. Phys. 53 (1982) 2174. [7] R.E. Walstedt and L.R. Walker, Phys. Rev. B 9 (1974) 4857. [8] A.K. Majumdar et al., Solid State Commun. 45 (1983) 907. [9] R.H. Heffner et al., J. Appl. Phys, 55 (1984) 1703. [10] We are grateful for magnetization measurements by L.J. Azevedo, Sandia National Laboratory. [11] J.A. Brown et al., Phys. Rev. Lett. 47 (1981) 261: similar results have been obtained for AgEr (unpublished). [12] D.C. Vier et al., Phys. Rev. B 29 (1984) 88. [13] D.L. Martin, Phys. Rev. 170 (1968) 650. [14] A. Schenck, Helv. Phys. Acta 54 (1981) 471. [15] D. van der Marel et al., Phys. Rev. Lett. 53 (1984) 206.
1103
MUON SPIN RELAXATION STUDY OF EXCHANGE COUPLING R.H. HEFFNER,
IN DILUTE AgMn ALLOYS
D . W . C O O K E , R.L. H U T S O N , M.E. S C H I L L A C I
Los Alamos National Laboratory. Los Alamo& N M 87545, USA
S.A. D O D D S , G . A . G I S T Rice University, Houston, TX 77251. USA
a n d D.E. M a c L A U G H L I N University of California. Riverside, CA 92521, USA
We have observed for the first time a conduction-electron-mediatedcomponent of the interaction between muons and local moments in a dilute magnetic alloys, AgMn. Comparison of the amplitude of this component and neutron quasielastic linewidth data yields some disagreement with a covalent-mixing exchange model.
We have used m u o n spin relaxation (~tSR) to examine some single-ion properties of Mn local moments in Ag. We find that the coupling between muons and M n moments is partially mediated by conduction-electron spin-density oscillations (SDO), so that we can determine the exchange constant average JSDO appropriate to SDO coupling. Our value for JSDO, 2.8 eV, is larger but more reliable than values found from N M R [1] or ESR [2]. This constitutes the first observation of SDO by ~xSR, and the first unambiguous determination of JSDO for A gMn. We compare our result to the exchange constant JK appropriate to Korringa relaxation of Mn impurities by conduction-electron scattering, as obtained from neutron scattering data [3], and obtain evidence against attributing exchange entirely to covalent mixing in A gMn. Aga_cMn c samples with c = 0.003, 0.016 and 0.030 were prepared by arc-melting the weighed constituents, followed by 10 h anneal at 800°C and a quench. Concentrations were verified by ac susceptibility measurements of the spin-glass freezing temperature Tg and by determination of the residual resistance. Agreement with previous measurements [4] was good. One of the samples was also analyzed by atomic absorption spectroscopy, and found to have the nominal concentration. M u o n spin relaxation data were obtained in a conventional ~SR spectrometer at the Clinton P. Anderson Meson Physics Facility (LAMPF), using transverse external fields [5]. In order to avoid complications due to spin-glass effects, all data were obtained at temperatures above 3Tg(c). Muon relaxation in a transverse field H is dominated by inhomogeneous broadening due to Mn spin polarization, as discussed previously [6]. A detailed calculation [7] yields an exponential relaxation function, and we have fitted our data accordingly. The inhomogeneous linewidth 1/T~ is proportional to c and to the M n spin
polarization (Sz). In the high-temperature limit the M n polarization follows a Curie law [8], so one expects 1/T~ o: cH/T. Experimentally, the constants of proportionality are (0.270 + 0.007), (0.276 + 0.016) and (0.267 + 0.013) Fts- I Oe -1 K for c = 0.003, 0.016 and 0.030, respectively. We note that these values are essentially constant over a decade of variation of c. The constant of proportionality can be calculated in the dilute limit [7], assuming a m u o n - M n coupling of the form A ~ / = [BsD o cos(ZkFri+ep)+Bdip(1 --3 cos20i)]
× (S:)/ri 3,
(1)
where A0~ is the muon frequency shift due to a M n ion at (ri, Or), and ~ is the phase of the SDO coupling. The coefficients BSDo and Bdi p a r e the amplitudes of the indirect SDO coupling and the direct dipolar coupling, respectively. For BSDo = 0, one obtains
(1/T2* )dip = 5.065y~n ( Peff~B) 2cH/3kBT,
(2)
where ~,, is the muon gyromagnetic ratio and n is the host-site n u m b e r density. The numerical factor arises from averaging over muon and impurity positions. The form of eq. (2), which contains the effective Mn magnetic moment Peff~B, facilitates comparison with magnetization measurements. Although not all of our samples would be considered dilute, numerical calculations [9] confirm that eq. (2) is adequate for c ~< 0.07. Magnetization measurements on the c = 0.016 sample [10] yield Pelf = 5.53, in agreement with previous high-temperature results [8]. Using this value in eq. (2), we obtain a value of 0.160 ~s - 1 0 e -1 K for the constant of proportionality in the purely dipolar case, which is substantially smaller than the observed constant. An excess linewidth due to a non-random distri-
0 3 0 4 - 8 8 5 3 / 8 6 / $ 0 3 . 5 0 © Elsevier Science P u b l i s h e r s B.V.
1104
R.H. Heffner et al. / Exchange coupling in dilute A ggMn alloys
bution of muon stopping sites is unlikely, in view of (1) the observed linear concentration dependence of 1/T~, and (2) the good agreement with purely dipolar coupling obtained for muon linewidths in A gEr [11]. Neither of these results would be obtained if muon sites were not randomly distributed. Therefore, it is reasonable to attribute the excess broadening in A gMn to the SDO mechanism, which is expected to be stronger for a 3d ion than for a rare earth. The case of mixed coupling, where both BsD o and Bdip are non-zero, has also been treated by Walstedt and Walker [7]. Using their numerical results, and the observed ratio (l/T~')exp/(1/T2*)dip ~ 1.7, we find BsD O ].8Bdi p. (A similar procedure for C uMn, using the parameters of ref. [1], yields a negligible SDO contribution to the muon linewidth.) Walstedt and Walker [1] have summarized the formalism needed to relate 1/7"2" (and the local moment spin-flip time ~'K discussed below) to exchange scattering of conduction electrons by a local moment. They assume a wave-factor-dependent exchange parameter J ( k , k') which includes both atomic and covalent-mixing contributions. Their calculation also includes the effects of potential scattering at the impurity site and enhancement of the conduction electron susceptibility. In the case of Ag, conduction-band enhancement is negligible [12] and we may use free-electron model parameters [13]. We then have K~J~ BSD° -- 8~nt~B I gsD°['
(3)
where ] JsDo ] is an appropriate average of J ( k , k') over the Fermi surface and K~ is the muon Knight shift in the pure host [1]. Using the experimentally derived values of BSDo, and K~ = 94 p p m [14], we obtain ] JSDO] = (2.8 4-_0.3) eV. Values of [JsDoI in A gMn obtained by N M R [1] and ESR [2] are considerably smaller than this, but the N M R experiments may have been affected by metallurgical problems [1] and interpretation of the ESR data may have been affected by failure to break the bottleneck fully [3]. The present determination of JSDO is free of these problems. We now consider the Mn local-moment Korringa relaxation time ~'K, related to the exchange constant average JK
for spin-flip conduction-electron scattering by (1-KT)
'=('u/h)knp(EF)2j
2.
(4)
where p ( E F ) is the density of states per spin at the Fermi surface. F r o m quasielastic neutron scattering experiments Murani [3] has obtained a Korringa product ('rKT) ! = (5.7 4- 0.5) X 10 9 S 1 K 1 which yields ]JK [ = 0.85 eV [3]. One may ask if the exchange constant averages JsDo (~SR) and JK (neutron scattering) are consistent with a reasonable set of exchange parameters. If the covalent mixing contribution to J ( k , k') is assumed to be completely dominant then I JsDo/JK I = ~ - [1], which is less than the measured ratio of 3.3 _ 0.6. This may indicate that direct exchange contributions are also important, but a proper evaluation of the additional terms requires the potential-scattering phase shifts [1], which are not reliably known. Alternatively, recent photoemission results [15] suggest that the Schrieffer-Wolf transformation, which underlies our analysis, may be inadequate to describe the strong mixing in A gMn. This work was performed under the auspices of the US Department of Energy, and was also supported by the US National Science Foundation. Grants D M R 79-09223 and D M R 81-15543. [1] R.E. Walstedt and L.R. Walker, Phys. Rev. B 11 (1975) 3280. [2] D. Davidov et al., Phys. Rev. B 11 (1975) 3546. [3] A.P. Murani, J. Magn. Magn. Mat. 25 (1981) 68. [4] P.J. Ford and J.A. Mydosh, Phys. Rev. B 14 (1981) 2057. V. Cannella and J.A. Mydosh, AIP Conf. Proc. 18 (1974) 651. [5] E, Karlsson, Phys. Rep. 82 (1982) 271. [6] R.H. Heffner et al., J. Appl. Phys. 53 (1982) 2174. [7] R.E. Walstedt and L.R. Walker, Phys. Rev. B 9 (1974) 4857. [8] A.K. Majumdar et al., Solid State Commun. 45 (1983) 907. [9] R.H. Heffner et al., J. Appl. Phys, 55 (1984) 1703. [10] We are grateful for magnetization measurements by L.J. Azevedo, Sandia National Laboratory. [11] J.A. Brown et al., Phys. Rev. Lett. 47 (1981) 261: similar results have been obtained for AgEr (unpublished). [12] D.C. Vier et al., Phys. Rev. B 29 (1984) 88. [13] D.L. Martin, Phys. Rev. 170 (1968) 650. [14] A. Schenck, Helv. Phys. Acta 54 (1981) 471. [15] D. van der Marel et al., Phys. Rev. Lett. 53 (1984) 206.