3B2v7:51c ED:chanakshi=br GML4:3:1 MAGMA : 8450 Prod:Type:com pp:123ðcol:fig::NILÞ PAGN: thilakam SCAN: bindu ARTICLE IN PRESS 1 3 Journal of Magnetism and Magnetic Materials ] (]]]]) ]]]­]]] 5 7 Low-frequency response in the magnetic susceptibility of 9 antiferromagnetically coupled Fe/Cr multilayers 11 F.G. Alieva,*, J.L. Martinezb, V.V. Moshchalkovc, Y.Bruynseraedec, 13 A.P. Levanuyka, R.Villara a 15 Dept. de Fisica Materia Condensada, Instituto de Ciencia de Materiales ``Nicolas Cabrera'', Universidad Autonoma de Madrid, C-III, 28049, Madrid, Spain b 17 ICMM-CSIC, Cantoblanco, 28049, Madrid Spain c Laboratorium voor Vaste-Stoffysica en Magnetisme, K.U.Leuven, Belgium 19 21 Abstract 23 The magnetic field and temperature dependence of the low-frequency ( f o104 HzÞ in- and out-of-phase magnetic response of antiferromagnetically coupled Fe/Cr(1 0 0) shows that at T > 100 K both the real ðw0Þ and imaginary ðw00Þ 25 parts of the susceptibility exhibit hysteretic dependence on the magnetic field with maxima of w00ðHÞ at HE725 Oe.At T ¼ 2 K the losses exhibit an unusual strong frequency dependence describable within a single relaxation time scheme. 27 The corresponding relaxation time proves to be strongly field-dependent which could be related to some quantum tunneling processes at low temperatures. r 2001 Published by Elsevier Science B.V. 29 Keywords: Multilayers; Susceptibility-AC; Domain wall dynamics; Relaxation 31 33 57 35 A great deal of the known dynamical properties of The magnetic field dependence of the real and 59 antiferromagnetically coupled MML is related to the imaginary (in logarithmic scale) contributions of the 37 high-frequency (GHz ) range.The only data on the low- magnetic susceptibility in [Fe(30 (A /Cr(13 (A ) 61 10 MML frequency response of MML we were able to find are measured at 300, 20 and 5 K is shown in Fig.1a and b. 39 those of Ref.[1] where the real ðw0Þ and the imaginary At high temperatures (T > 100 K), independently of the 63 ðw00Þ parts of the magnetic susceptibility of a superlattice applied ACDF (2­8 Oe) , both w0ðHÞ and w00ðHÞ show 41 Fe/Cr(2 1 1) were measured at a frequency f ¼ 103 Hz hysteretic dependence on the magnetic field with the 65 and at a non-specified temperature.The epitaxial maxima of the losses at HC7ð20230Þ Oe.Lowering the 43 ½Fe=Cr 67 n (n=10) multilayer is deposited in a MBE temperature from 300 K to about 10 K, the losses system on MgO(0 0 1) substrates held at a temperature somewhat decrease.At lower temperatures the losses 45 of 501C.Details of sample preparation and character- (in finite small field) begin to increase.If the ACDF does 69 ization have been published before [2].We measured not exceed some critical value (p4 Oe), the hysteretic 47 both the real w0 and the imaginary w00 parts of the dependence of the losses on the magnetic field gradually 71 magnetic susceptibility defined as MðoÞ=HðoÞ (here disappears below approximately 50K.One more re- 49 HðoÞ is an 73 51 75 53 UNCORRECTED PROOF AC driving field (ACDF) and MðoÞ is the markable feature is an appearance at lower temperatures corresponding magnetic response) by using Physical (To7 K) of a minimum in the magnetic losses at H ¼ 0 (at frequencies 3 Hzof o167 Hz) and Magnetic (see Fig.1b). (77 Hzof o9876 Hz) Property Measurement Systems We studied the frequency dependence of w00 at T ¼2 (Quantum Design). and 10 K (Fig.2). At higher temperatures, the out-of- 77 phase susceptibility is too small to study its frequency 55 *Tel.: +34-13-974756; fax: +34-91- 3974744. dependence.The main surprise is that it exhibits a 79 E-mail address: farkhad.aliev@uam.es (F.G. Aliev). well-pronounced frequency dependence at T ¼ 2 K 0304-8853/01/$ - see front matter r 2001 Published by Elsevier Science B.V. PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 0 8 8 7 - 3 MAGMA : 8450 ARTICLE IN PRESS 2 F.G. Aliev et al. / Journal of Magnetism and Magnetic Materials ] (]]]]) ]]]­]]] 1 1x10-6 e)e) 57 2x10-8 2x10-8 (a) 1x10-7 u/Ou/O 2K 1x10-7 2K 3 mm 300K fit fit ((TT==22K K)) 59 e) (ee) (e 1x10-8 10K 1x10-8 10K 5 50 O50 O e) 61 ( ( 20K 00 u/O 5x10-7 00 55000 000 10000 10000 7 m e)e) f ( f (H Hzz)) 63 ´(e 9876 H 9876 Hzz u/Ou/O 9 mm 65 5x10-8 5x10-8 5K 3211 3211 (e (e 11 987 987 67 0 (b) 300K 13 20K 69 5K e) 15 321 321 u/O 71 10-8 m 33 00 17 (e 73 -5 -500 00 5500 H ( H (O Oe) e) 19 75 10-9 Fig.2. Imaginary contributions to the magnetic susceptibility -50 0 50 21 of ½Feð30 (A=Crð13 (AÞ H (Oe) 10 multilayer measured at five different 77 frequencies with ACDF=4O e at 2 K.For clarity, the curves 23 Fig.1. Real (part a) and imaginary (part b) contributions to w``ðHÞ obtained for 987, 3211 and 9876 Hz are shifted upwards 79 the magnetic susceptibility of ½Feð30 (A=Crð13 (AÞ correspondingly on 1:5 10 8; 3 10 8 and 5 10 8 emu/Oe. 10 multilayer The inset shows the frequency dependence of the dissipation 25 measured at 987 Hz with ACDF=4 Oe and at different 81 temperatures between 300 K and 5 K. at small non-zero magnetic field (H ¼ 50 Oe) at temperature T ¼ 2 and 10 K.The bold solid line represents fit described in 27 the main text. 83 29 (H ¼ 50 Oe) and this dependence may be reasonably 85 fitted by the single relaxation time formula w00 ¼ 31 w0ot=1 þ ðotÞ2 with tC2:5 10 4 s (see inset in first approaches the maximum (and w00 increases) and 87 Fig.2).Let us recall that one expects that the response then moves away from the maximum (and w00 decreases). 33 of domain structures is characterized by a broad The same happens with the point corresponding to 89 distribution of the relaxation times with w00 almost f ¼ 9876 Hz but, of course, it passes the maximum later, 35 independent of frequency.This seems to be the case for at a smaller field.We see that the model of a single 91 higher temperatures: the frequency dependence of w00 at relaxation time allows to explain the dependence w00ðHÞ 37 T ¼ 10 K is nearly absent with a much broader as well. 93 maximum shifted to higher frequencies.Note that in The observed temperature evolution of the dependen- 39 the studied frequency range the real part of the cies w0ðHÞ and w00ðHÞ might in part be due to evolut- 95 susceptibility is within 20% independent on f when ion of the domain structure which remains basically 41 frequency is changed between 3 and 9876 Hz. unknown for low temperatures.However, the changes 97 Fig.2 shows w00ðHÞ measured at five different are too drastic to be accounted for by 43 frequencies between 3 and 9876 Hz.One sees a non- an evolution of the domain structure alone.It is 99 trivial behavior of w00 at low fields: a well defined tempting to relate the decrease of the relaxation 45 minimum in w00ðHÞ at H ¼ 0 for f ¼ 321 and 987 Hz, a time to tunneling processes which provoke a ``chain'' 101 more narrow minimum flanked by two symmetric or a ``shock wave'' of other processes leading to a 47 maxima for f ¼ 3211 Hz and a similar behavior but less rapid relaxation.An enlightening discussion of such 103 pronounced and with an even narrower minimum for a possibility was given in Ref.[3].But, of course, one 49 f ¼ 9876 105 51 107 53 UNCORRECTED PROOF Hz.All these curves can be qualitatively has first to understand why the distribution of explained if one supposes that the above relaxation time the relaxation times becomes so narrow at low decreases as H diminishes and tðH ¼ 0Þ is less than temperatures. tðH ¼ 50 OeÞ by about an order of magnitude.Indeed, In conclusion, we have shown that the out-of- as t decreases the maximum of the curve in the inset of phase low-frequency magnetic response in antiferro- 109 Fig.2 shifts to the right. One sees that the points magnetically coupled Fe/Cr multilayers is strongly 55 corresponding to f ¼ 321 Hz, 987 Hz move away from dependent on temperature, magnetic field and, at 111 the maximum.The point corresponding to f ¼ 3211 Hz very low temperatures, on frequency.Magnetic losses MAGMA : 8450 ARTICLE IN PRESS F.G. Aliev et al. / Journal of Magnetism and Magnetic Materials ] (]]]]) ]]]­]]] 3 1 at a non-zero (and fairly low) magnetic field magnetization in antiferromagnetically coupled multi- first decrease but then increase with lowering of layers. 17 3 the temperature.At temperatures below 7 K and for the AC drive frequencies f B1022103 Hz we observed a Authors thank A.Chubukov, A.Buzdin and F. 19 5 dip in the magnetic field dependence of losses for fields Guinea for fruitful discussions.The work has been Hoð10215Þ Oe.At T ¼ 2 K and H ¼ 50 Oe the supported by Spanish MCYT (BFM2000-0016). 21 7 frequency dependence of the losses can be satisfactorily described within a single relaxation time scheme. References 23 9 The dependence of w00 on the magnetic field can be interpreted as the field dependence of the relaxat- [1] S. Rakhmanova, D.L. Mills, E.E. Fullerton, Phys. Rev. 25 11 ion time which increases by an order of magnitude B 57 (1998) 476. at the field changes from H ¼ 50 Oe to zero. [2] R.Schad, et al., Appl.Phys.Lett.64 (1994) 3500. 27 13 We believe that these data suggest an important role [3] P.C.E. Stamp, E.M. Chudnovskii, B. Barbara, Int. J .Mod. of quantum tunneling in the temporal evolution of Phys.6 (1992) 1355. 29 15 UNCORRECTED PROOF