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Suppression of spin fluctuations by magnetic field in Ni3Al as evidenced from magnetoresistivity
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 272–276 (2004) 493–494
Suppression of spin fluctuations by magnetic field in Ni3 Al as evidenced from magnetoresistivity B. Annie D’ Santhoshinia, S.N. Kaula,b,* a
School of Physics, University of Hyderabad, Central University P.O., Hyderabad 500 046, Andhra Pradesh, India b CITIMAC, University of Cantabria, 39005 Santander, Spain
Abstract The suppression of spin waves and spin fluctuations with magnetic field in Ni3 Al has been, for the first time, quantified through the field dependence of their contributions to resistivity and magnetoresistivity. r 2003 Elsevier B.V. All rights reserved. PACS: 75.30.m; 75.10.Lp Keywords: Electrical resistivity; Magnetoresistivity; Spin waves; Spin fluctuations; Itinerant magnetism
According to the spin fluctuation theory [1], the spin waves (SW) and non-propagating spin fluctuations (SF) in weak itinerant-electron (WI) ferromagnets manifest themselves in the contributions to the electrical resistivity ðrÞ that vary with temperature as rSW ðTÞBT 2 at lowtemperatures and rSF ðTÞBT 5=3 at temperatures close to TC (Curie point). Based on this prediction, we propose to study the suppression of SW and SF by external magnetic field ðHÞ in WI ferromagnet Ni3 Al by monitoring the reduction in the coefficients of the T 2 [2,3] and T 5=3 terms in the expression for rðTÞ with increasing H: To implement this strategy, high-resolution rðTÞ; and longitudinal magnetoresistivity (in Hp8 TÞ; Drjj =r ½rjj ðH; TÞ rðH ¼ 0; TÞ=rðH ¼ 0; TÞ; measurements were performed from 2.5 to 300 K on the ‘annealed’ (AN) and ‘quenched’ (QN) Ni3 Al polycrystalline samples, as well as on a Ni3 Al single crystal (SC). The electric current (typically 100 mA) and magnetic field are directed along the length in the case of AN and QN samples, and along the cylindrical axis (which is also the easy direction of magnetization [1 1 1]) in SC. The relevant details about the samples used in this study are furnished elsewhere [4].
*Corresponding author. Tel.: +91-040-23012455; fax: +91-040-23010227. E-mail address: [email protected] (S.N. Kaul).
Fig. 1 depicts the typical Drjj =r versus T plots at fixed values of H: Drjj =r is negative and goes through a peak at TCTC : This peak becomes more and more pronounced as H increases so much so that the peak height, ðDrjj =rÞp ; reaches values as high as 7:2%; 11:0% and 15:4% at H ¼ 8 T for the samples QN, AN and SC. While negative magnetoresistivity [MR] is a consequence of the suppression of thermally excited spin waves and spin fluctuations by magnetic field ðHÞ; the peak in MR at TCTC reflects the fact that at such temperatures, spin fluctuations have maximum amplitude and are thus most sensitive to H: Fig. 2 demonstrates that the field dependence of ðDrjj =rÞp is adequately described by the empirical relation ðDrjj =rÞp ¼ A½1 cH n with AE0 and the exponent n ¼ 0:50ð5Þ; 0:50ð5Þ and 0.88(2) for the samples QN, AN and SC. While no temperature shift in the peak position with H is discernible for the AN and SC samples, the peak in Drjj =r shifts to higher temperatures with increasing H in the sample QN. Since the quenched sample has more site disorder [4] than the other two samples, site disorder limits ðDrjj =rÞp to a lower value and makes the peak position field-dependent. The prediction of the SF theory [1] that SW/SF and SF contributions to rð0; TÞ manifest themselves as rSW=SF BT 2 and rSF BT 5=3 at low temperatures and at TtTC ; respectively, is borne out by our data in that the expressions rðH; TÞ ¼ rðH; 0Þ½1 þ A2 ðHÞT 2 and
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.485
ARTICLE IN PRESS 494
B. Annie D’ Santhoshini, S.N. Kaul / Journal of Magnetism and Magnetic Materials 272–276 (2004) 493–494
Fig. 3.
pffiffiffiffiffi H dependence of the coefficients A2 and A5=3 :
Fig. 1. Drjj =r vs. T plots at constant field values.
essentially govern the thermal demagnetisation in the ranges Tt0:25 TC and 0:4 TC tTtTC ; permits monitoring of the suppression of SW and SF by H through the field dependence of the coefficients A2 and A5=3 : That both thesepffiffiffiffi coefficients depend on field as AðHÞ ¼ ffi Að0Þ½1 Z H ; where AðHÞ A2 ðHÞ or A5=3 ðHÞ; is clearly evident from the data presented in Fig. 3. In this figure, previously reported [3] A2 ðHÞ data are included for comparison. None of the existing theories [1,2] addresses the issue of the field dependence of the coefficient A5=3 : Contrasted with the observed field dependence of the coefficient A2 ; the theory due to Ueda [2] predicts that A2 ðHÞ = A2 ð0Þ½1 Z0 H 2 at low fields. We thank Department of Science and Technology, New Delhi, for supporting this work under the grant Do No. SP/S2/M-21/97.
Fig. 2. Field dependence of ðDrjj =rÞp :
rðH; TÞ ¼ r0 ðH; 0Þ½1 þ A5=3 ðHÞT 5=3 with H ¼ 0 or a0; closely reproduce the ‘zero-field’ resistivity, rð0; TÞ and ‘in-field’ resistivity, rðH; TÞ; in the temperature ranges 2:5 KpTt10 K and 0:75tðT=TC Þt0:98; respectively. The bulk magnetisation result [5] that SW and SF
References [1] [2] [3] [4]
K. Ueda, T. Moriya, J. Phys. Soc. Jpn. 39 (1975) 605. K. Ueda, Solid State Commun. 19 (1976) 965. M. Yoshizawa, et al., J. Phys. Soc. Jpn. 61 (1992) 3313. Anita Semwal, S.N. Kaul, J. Phys.: Condens. Matter 14 (2002) 5829. [5] Anita Semwal, S.N. Kaul, Phys. Rev. B 60 (1999) 12799.
Journal of Magnetism and Magnetic Materials 272–276 (2004) 493–494
Suppression of spin fluctuations by magnetic field in Ni3 Al as evidenced from magnetoresistivity B. Annie D’ Santhoshinia, S.N. Kaula,b,* a
School of Physics, University of Hyderabad, Central University P.O., Hyderabad 500 046, Andhra Pradesh, India b CITIMAC, University of Cantabria, 39005 Santander, Spain
Abstract The suppression of spin waves and spin fluctuations with magnetic field in Ni3 Al has been, for the first time, quantified through the field dependence of their contributions to resistivity and magnetoresistivity. r 2003 Elsevier B.V. All rights reserved. PACS: 75.30.m; 75.10.Lp Keywords: Electrical resistivity; Magnetoresistivity; Spin waves; Spin fluctuations; Itinerant magnetism
According to the spin fluctuation theory [1], the spin waves (SW) and non-propagating spin fluctuations (SF) in weak itinerant-electron (WI) ferromagnets manifest themselves in the contributions to the electrical resistivity ðrÞ that vary with temperature as rSW ðTÞBT 2 at lowtemperatures and rSF ðTÞBT 5=3 at temperatures close to TC (Curie point). Based on this prediction, we propose to study the suppression of SW and SF by external magnetic field ðHÞ in WI ferromagnet Ni3 Al by monitoring the reduction in the coefficients of the T 2 [2,3] and T 5=3 terms in the expression for rðTÞ with increasing H: To implement this strategy, high-resolution rðTÞ; and longitudinal magnetoresistivity (in Hp8 TÞ; Drjj =r ½rjj ðH; TÞ rðH ¼ 0; TÞ=rðH ¼ 0; TÞ; measurements were performed from 2.5 to 300 K on the ‘annealed’ (AN) and ‘quenched’ (QN) Ni3 Al polycrystalline samples, as well as on a Ni3 Al single crystal (SC). The electric current (typically 100 mA) and magnetic field are directed along the length in the case of AN and QN samples, and along the cylindrical axis (which is also the easy direction of magnetization [1 1 1]) in SC. The relevant details about the samples used in this study are furnished elsewhere [4].
*Corresponding author. Tel.: +91-040-23012455; fax: +91-040-23010227. E-mail address: [email protected] (S.N. Kaul).
Fig. 1 depicts the typical Drjj =r versus T plots at fixed values of H: Drjj =r is negative and goes through a peak at TCTC : This peak becomes more and more pronounced as H increases so much so that the peak height, ðDrjj =rÞp ; reaches values as high as 7:2%; 11:0% and 15:4% at H ¼ 8 T for the samples QN, AN and SC. While negative magnetoresistivity [MR] is a consequence of the suppression of thermally excited spin waves and spin fluctuations by magnetic field ðHÞ; the peak in MR at TCTC reflects the fact that at such temperatures, spin fluctuations have maximum amplitude and are thus most sensitive to H: Fig. 2 demonstrates that the field dependence of ðDrjj =rÞp is adequately described by the empirical relation ðDrjj =rÞp ¼ A½1 cH n with AE0 and the exponent n ¼ 0:50ð5Þ; 0:50ð5Þ and 0.88(2) for the samples QN, AN and SC. While no temperature shift in the peak position with H is discernible for the AN and SC samples, the peak in Drjj =r shifts to higher temperatures with increasing H in the sample QN. Since the quenched sample has more site disorder [4] than the other two samples, site disorder limits ðDrjj =rÞp to a lower value and makes the peak position field-dependent. The prediction of the SF theory [1] that SW/SF and SF contributions to rð0; TÞ manifest themselves as rSW=SF BT 2 and rSF BT 5=3 at low temperatures and at TtTC ; respectively, is borne out by our data in that the expressions rðH; TÞ ¼ rðH; 0Þ½1 þ A2 ðHÞT 2 and
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.485
ARTICLE IN PRESS 494
B. Annie D’ Santhoshini, S.N. Kaul / Journal of Magnetism and Magnetic Materials 272–276 (2004) 493–494
Fig. 3.
pffiffiffiffiffi H dependence of the coefficients A2 and A5=3 :
Fig. 1. Drjj =r vs. T plots at constant field values.
essentially govern the thermal demagnetisation in the ranges Tt0:25 TC and 0:4 TC tTtTC ; permits monitoring of the suppression of SW and SF by H through the field dependence of the coefficients A2 and A5=3 : That both thesepffiffiffiffi coefficients depend on field as AðHÞ ¼ ffi Að0Þ½1 Z H ; where AðHÞ A2 ðHÞ or A5=3 ðHÞ; is clearly evident from the data presented in Fig. 3. In this figure, previously reported [3] A2 ðHÞ data are included for comparison. None of the existing theories [1,2] addresses the issue of the field dependence of the coefficient A5=3 : Contrasted with the observed field dependence of the coefficient A2 ; the theory due to Ueda [2] predicts that A2 ðHÞ = A2 ð0Þ½1 Z0 H 2 at low fields. We thank Department of Science and Technology, New Delhi, for supporting this work under the grant Do No. SP/S2/M-21/97.
Fig. 2. Field dependence of ðDrjj =rÞp :
rðH; TÞ ¼ r0 ðH; 0Þ½1 þ A5=3 ðHÞT 5=3 with H ¼ 0 or a0; closely reproduce the ‘zero-field’ resistivity, rð0; TÞ and ‘in-field’ resistivity, rðH; TÞ; in the temperature ranges 2:5 KpTt10 K and 0:75tðT=TC Þt0:98; respectively. The bulk magnetisation result [5] that SW and SF
References [1] [2] [3] [4]
K. Ueda, T. Moriya, J. Phys. Soc. Jpn. 39 (1975) 605. K. Ueda, Solid State Commun. 19 (1976) 965. M. Yoshizawa, et al., J. Phys. Soc. Jpn. 61 (1992) 3313. Anita Semwal, S.N. Kaul, J. Phys.: Condens. Matter 14 (2002) 5829. [5] Anita Semwal, S.N. Kaul, Phys. Rev. B 60 (1999) 12799.