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Dynamics of the diluted Ising antiferromagnet Fe0.42Zn0.58F2 at strong fields
Journal of Magnetism and Magnetic Materials 226}230 (2001) 1309}1311
Dynamics of the diluted Ising antiferromagnet Fe Zn F at strong "elds A. Rosales-Rivera , J.M. Ferreira, F.C. Montenegro * Departamento de Fisica, Universidad Nacional de Colombia, A.A. 127, Manizales, Colombia Departamento de Fisica, Universidade Federal de Pernambuco. 50670-901, Recife, PE, Brazil
Abstract The random-"eld Ising model (RFIM) system Fe Zn F is studied by magnetization and AC susceptibility measurements, under "nite DC applied "elds (H). For weak random "elds (corresponding to H(20 KOe), the phase transition (PT) at ¹ (H) is accompanied by the critical slowing down inherent to the random "eld problem. For higher H, the PT is destroyed and a glassy dynamics dominates the magnetic behavior. 2001 Elsevier Science B.V. All rights reserved. Keywords: Spin glasses; Random magnets; Dynamic properties
The diluted antiferromagnet (DAF) Fe Zn F unV \V der a uniform magnetic "eld (H) applied parallel to the easy direction is probably the most studied experimental realization of the random-"eld Ising model (RFIM) in d"3 (For recent reviews of the RFIM problem, see for instance, Refs. [1,2]). For concentrations above the percolation threshold (x "0.24), the condensed phase of this ,compound exhibits long-range order (LRO) for H"0. When a weak H is applied collinear with the uniaxial direction, LRO is still present, but the critical behavior at T (H) exhibits a crossover from random exchange Ising model (REIM) to RFIM, provided ¹ (H) is reached from below in a protocol, where the sample is zero-"eld cooled (ZFC) below ¹ before the application , of H. Under strong dilution (x 0.25), Fe Zn F presV \V ents spin-glass characteristics [3,4]. The application of intense "elds (corresponding to the strong random "eld regime) renders LRO unstable and induces a glassy phase in the upper part of the (H,T) phase diagram [5}8].
* Corresponding author. Tel.: #55-81-271-8450; fax: #5581-271-0359. E-mail address: [email protected] (F.C. Montenegro).
The phase boundaries and dynamics of the RFIM system Fe Zn F are studied here by magnetization and AC susceptibility techniques, in a SQUID MPMS-5 (Quantum design), in the "eld range 0)H)5 T, for temperatures 5)T)30 K. Fig. 1 compares d(M/H)/dT versus T and the real part of the AC susceptibility, versus T, in the zero-"eld cooling (ZFC) and "eld-cooling (FC) procedures. At low H, a small ZFC}FC hysteresis is observed in d(M/H)/dT below an equilibrium temperature T (H). This hysteresis corresponds to an excess in the FC magnetization, which relaxes towards the ZFC ground state just below T (H). In this weak RFIM regime, d(M/H)/dT shows a sharp and symmetric ZFC peak at the critical temperature T (H). The peak shifts to lower temperatures as H increases, following the expected REIM to RFIM crossover scaling T !T (H)&H , , with 1.4 (see Fig. 2). The ZFC shows a maximum, rounded by the extreme critical slowing down, which coincides in temperature with the ZFC d(M/H)/dT peak. exhibits negligible ZFC}FC hysteresis and no ob servable shift in the peak temperature occurs as a function of f. Our results in the weak RFIM regime are in agreement with those previously observed in Fe Zn F by King et. al. [9], con"rming the low frequency nature of the critical #uctuations in RFIM
0304-8853/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 0 8 3 7 - 4
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A. Rosales-Rivera et al. / Journal of Magnetism and Magnetic Materials 226}230 (2001) 1309}1311
Fig. 1. (a) d(M/H)/dT versus T and (b) versus T (measured at f"1 Hz) for several H. Filled symbols are ZFC data and open symbols are FC. The amplitude of the AC "eld is h "4 Oe.
systems. For H'20 kOe, the ZFC d(M/H)/dT peaks show a visible rounding, which increase as &H. The ZFC}FC hysteresis extends to lower temperatures and the ZFC magnetization becomes time dependent, re#ecting the instability of the AF LRO. In this strong RFIM regime, the ZFC peak splits into a small low-T peak at ¹"¹ (H) and a second broad maximum at ¹"¹ (H), with ¹ (H)(¹ (H). A pronounced ZFC}FC hysteresis is found, close to and below T . At low frequencies ( f&1 Hz), the second peak at T (H) coincides quite well with T (H), as obtained from the ZFC}FC irreversibility of the magnetization, in the time scale of the experiments. At higher frequencies, however, the narrow low-T peak at T (H) disappears and the broad peaking at T (H) becomes the only feature in the versus T curves. These latter characteristics re#ect the glassy dynamics, which occur at the strong RFIM regime [10]. The critical, T (H), and equilibrium, T (H), bound aries, measured from the magnetization data, are mapped in the dynamic phase diagram of Fig. 2. We include, for comparison, the location of the temperatures T (H) and T (H) obtained from the ZFC data at frequencies f"1 and 100 Hz. In the weak RFIM regime, both T (H) and T (H) follow the expected REIM}RFIM crossover scaling. The extrapolation of T (H) to HP0 gives the NeH el temperature ¹ "27.85$0.15 K. The second ZFC , broad peak at T (H), perceived only for H'20 kOe, coincides quite well at low frequencies with the equilibrium temperature T (H), de"ned in terms of the
Fig. 2. Dynamic phase diagram of Fe Zn F . T (H) and T (H), boundaries (open symbols), were obtained from magnet ization data. T (H) and T (H) ("lled symbols) were obtained from the ZFC measurements, at frequencies f"1 and 100 Hz. The solid and dashed lines are "ts using REIM-RFIM crossover scaling for T (H) and T (H), respectively, using "1.42. T (H) and T (H) are plotted linearly versus H in the inset, after a mean-"eld correction is made to each.
ZFC}FC irreversibility of the magnetization. In the strong RFIM regime, however, T (H) follows a convex de Almeida}Thouless line ('2), which shifts to lower temperatures as f decreases, as observed in spin glasses. In fact, ¹ (H)"¹ (H) only when 1/f coincides with the time scale of the `DCa magnetization measurements (1}100 s, typically). The frequency dependence of the position of the low-T peak at T (H) is restricted to the strong random "eld regime. The presented results reconcile earlier concepts associated with the weak RFIM problem with recent experimental data in Fe Zn F . The extreme rounding of V \V ZFC d(TM)/dT peaks found[11,12] at high H, and the existence of two ZFC peaks [13] for x&0.50, are not in the scope of the Imry}Ma [14] arguments, valid only for the weak RFIM problem. These features, instead, are associated to the e!ects of a random-"eld induced glassy dynamics in samples of Fe Zn F . V \V This work was supported by CAPES, CNPq and FINEP (Brazilian agencies). One of us (A.R.R) acknowledges the support of the FundacioH n para la PromocioH n de la InvestigacioH n y la TecnologmH a, Banco de la RepuH blica (Colombian Agency). References [1] D.P. Belanger, A.P. Young, J. Magn. Magn. Mater. 100 (1991) 272.
A. Rosales-Rivera et al. / Journal of Magnetism and Magnetic Materials 226}230 (2001) 1309}1311 [2] D.P. Belanger, in: A.P. Young (Ed.), Spin Glasses and Random Fields, World Scienti"c, Singapore, 1997. [3] F.C. Montenegro, M.D. Coutinho-Filho, S.M. Rezende, Europhys. Lett. 8 (1989) 273. [4] E.P. Raposo, M.D. Coutinho-Filho, F.C. Montenegro, Europhys. Lett. 29 (1995) 507. [5] F.C. Montenegro, U.A. Leita o, M.D. Coutinho-Filho, S.M. Rezende, J. Appl. Phys 67 (1990) 5243. [6] F.C. Montenegro, A.R. King, V. Jaccarino, S.-J. Han, D.P. Belanger, Phys. Rev. B 44 (1991) 2155. [7] F.C. Montenegro, K.A. Lima, M.S. Torikachvili, A.H. Lacerda, J. Magn . Magn Mater. 177}181 (1998) 145.
1311
[8] F.C. Montenegro, K.A. Lima, M.S. Torikachvili, A.H. Lacerda, Ibid. Mater. Sci. Forum 302}303 (1999) 371. [9] A.R. King, J.A. Mydosh, V. Jaccarino, Phys. Rev. Lett. 56 (1986) 2525. [10] A. Rosales-Rivera, J.M. Ferreira, F.C Montenegro, unpublished. [11] R.J. Birgeneau, Q. Feng, Q.J. Harris, J.P. Hill, A.P. Ramirez, T.R. Thurston, Phys. Rev. Lett. 75 (1995) 1198. [12] R.J. Birgeneau, J. Magn. Magn. Mater. 177}181 (1998) 1. [13] Ch. Binek, S. Kuttler, W. Kleemann, Phys. Rev. Lett. 75 (1995) 2412. [14] Y. Imry, S.K. Ma, Phys. Rev. Lett. 35 (1975) 1399.
Dynamics of the diluted Ising antiferromagnet Fe Zn F at strong "elds A. Rosales-Rivera , J.M. Ferreira, F.C. Montenegro * Departamento de Fisica, Universidad Nacional de Colombia, A.A. 127, Manizales, Colombia Departamento de Fisica, Universidade Federal de Pernambuco. 50670-901, Recife, PE, Brazil
Abstract The random-"eld Ising model (RFIM) system Fe Zn F is studied by magnetization and AC susceptibility measurements, under "nite DC applied "elds (H). For weak random "elds (corresponding to H(20 KOe), the phase transition (PT) at ¹ (H) is accompanied by the critical slowing down inherent to the random "eld problem. For higher H, the PT is destroyed and a glassy dynamics dominates the magnetic behavior. 2001 Elsevier Science B.V. All rights reserved. Keywords: Spin glasses; Random magnets; Dynamic properties
The diluted antiferromagnet (DAF) Fe Zn F unV \V der a uniform magnetic "eld (H) applied parallel to the easy direction is probably the most studied experimental realization of the random-"eld Ising model (RFIM) in d"3 (For recent reviews of the RFIM problem, see for instance, Refs. [1,2]). For concentrations above the percolation threshold (x "0.24), the condensed phase of this ,compound exhibits long-range order (LRO) for H"0. When a weak H is applied collinear with the uniaxial direction, LRO is still present, but the critical behavior at T (H) exhibits a crossover from random exchange Ising model (REIM) to RFIM, provided ¹ (H) is reached from below in a protocol, where the sample is zero-"eld cooled (ZFC) below ¹ before the application , of H. Under strong dilution (x 0.25), Fe Zn F presV \V ents spin-glass characteristics [3,4]. The application of intense "elds (corresponding to the strong random "eld regime) renders LRO unstable and induces a glassy phase in the upper part of the (H,T) phase diagram [5}8].
* Corresponding author. Tel.: #55-81-271-8450; fax: #5581-271-0359. E-mail address: [email protected] (F.C. Montenegro).
The phase boundaries and dynamics of the RFIM system Fe Zn F are studied here by magnetization and AC susceptibility techniques, in a SQUID MPMS-5 (Quantum design), in the "eld range 0)H)5 T, for temperatures 5)T)30 K. Fig. 1 compares d(M/H)/dT versus T and the real part of the AC susceptibility, versus T, in the zero-"eld cooling (ZFC) and "eld-cooling (FC) procedures. At low H, a small ZFC}FC hysteresis is observed in d(M/H)/dT below an equilibrium temperature T (H). This hysteresis corresponds to an excess in the FC magnetization, which relaxes towards the ZFC ground state just below T (H). In this weak RFIM regime, d(M/H)/dT shows a sharp and symmetric ZFC peak at the critical temperature T (H). The peak shifts to lower temperatures as H increases, following the expected REIM to RFIM crossover scaling T !T (H)&H , , with 1.4 (see Fig. 2). The ZFC shows a maximum, rounded by the extreme critical slowing down, which coincides in temperature with the ZFC d(M/H)/dT peak. exhibits negligible ZFC}FC hysteresis and no ob servable shift in the peak temperature occurs as a function of f. Our results in the weak RFIM regime are in agreement with those previously observed in Fe Zn F by King et. al. [9], con"rming the low frequency nature of the critical #uctuations in RFIM
0304-8853/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 0 8 3 7 - 4
1310
A. Rosales-Rivera et al. / Journal of Magnetism and Magnetic Materials 226}230 (2001) 1309}1311
Fig. 1. (a) d(M/H)/dT versus T and (b) versus T (measured at f"1 Hz) for several H. Filled symbols are ZFC data and open symbols are FC. The amplitude of the AC "eld is h "4 Oe.
systems. For H'20 kOe, the ZFC d(M/H)/dT peaks show a visible rounding, which increase as &H. The ZFC}FC hysteresis extends to lower temperatures and the ZFC magnetization becomes time dependent, re#ecting the instability of the AF LRO. In this strong RFIM regime, the ZFC peak splits into a small low-T peak at ¹"¹ (H) and a second broad maximum at ¹"¹ (H), with ¹ (H)(¹ (H). A pronounced ZFC}FC hysteresis is found, close to and below T . At low frequencies ( f&1 Hz), the second peak at T (H) coincides quite well with T (H), as obtained from the ZFC}FC irreversibility of the magnetization, in the time scale of the experiments. At higher frequencies, however, the narrow low-T peak at T (H) disappears and the broad peaking at T (H) becomes the only feature in the versus T curves. These latter characteristics re#ect the glassy dynamics, which occur at the strong RFIM regime [10]. The critical, T (H), and equilibrium, T (H), bound aries, measured from the magnetization data, are mapped in the dynamic phase diagram of Fig. 2. We include, for comparison, the location of the temperatures T (H) and T (H) obtained from the ZFC data at frequencies f"1 and 100 Hz. In the weak RFIM regime, both T (H) and T (H) follow the expected REIM}RFIM crossover scaling. The extrapolation of T (H) to HP0 gives the NeH el temperature ¹ "27.85$0.15 K. The second ZFC , broad peak at T (H), perceived only for H'20 kOe, coincides quite well at low frequencies with the equilibrium temperature T (H), de"ned in terms of the
Fig. 2. Dynamic phase diagram of Fe Zn F . T (H) and T (H), boundaries (open symbols), were obtained from magnet ization data. T (H) and T (H) ("lled symbols) were obtained from the ZFC measurements, at frequencies f"1 and 100 Hz. The solid and dashed lines are "ts using REIM-RFIM crossover scaling for T (H) and T (H), respectively, using "1.42. T (H) and T (H) are plotted linearly versus H in the inset, after a mean-"eld correction is made to each.
ZFC}FC irreversibility of the magnetization. In the strong RFIM regime, however, T (H) follows a convex de Almeida}Thouless line ('2), which shifts to lower temperatures as f decreases, as observed in spin glasses. In fact, ¹ (H)"¹ (H) only when 1/f coincides with the time scale of the `DCa magnetization measurements (1}100 s, typically). The frequency dependence of the position of the low-T peak at T (H) is restricted to the strong random "eld regime. The presented results reconcile earlier concepts associated with the weak RFIM problem with recent experimental data in Fe Zn F . The extreme rounding of V \V ZFC d(TM)/dT peaks found[11,12] at high H, and the existence of two ZFC peaks [13] for x&0.50, are not in the scope of the Imry}Ma [14] arguments, valid only for the weak RFIM problem. These features, instead, are associated to the e!ects of a random-"eld induced glassy dynamics in samples of Fe Zn F . V \V This work was supported by CAPES, CNPq and FINEP (Brazilian agencies). One of us (A.R.R) acknowledges the support of the FundacioH n para la PromocioH n de la InvestigacioH n y la TecnologmH a, Banco de la RepuH blica (Colombian Agency). References [1] D.P. Belanger, A.P. Young, J. Magn. Magn. Mater. 100 (1991) 272.
A. Rosales-Rivera et al. / Journal of Magnetism and Magnetic Materials 226}230 (2001) 1309}1311 [2] D.P. Belanger, in: A.P. Young (Ed.), Spin Glasses and Random Fields, World Scienti"c, Singapore, 1997. [3] F.C. Montenegro, M.D. Coutinho-Filho, S.M. Rezende, Europhys. Lett. 8 (1989) 273. [4] E.P. Raposo, M.D. Coutinho-Filho, F.C. Montenegro, Europhys. Lett. 29 (1995) 507. [5] F.C. Montenegro, U.A. Leita o, M.D. Coutinho-Filho, S.M. Rezende, J. Appl. Phys 67 (1990) 5243. [6] F.C. Montenegro, A.R. King, V. Jaccarino, S.-J. Han, D.P. Belanger, Phys. Rev. B 44 (1991) 2155. [7] F.C. Montenegro, K.A. Lima, M.S. Torikachvili, A.H. Lacerda, J. Magn . Magn Mater. 177}181 (1998) 145.
1311
[8] F.C. Montenegro, K.A. Lima, M.S. Torikachvili, A.H. Lacerda, Ibid. Mater. Sci. Forum 302}303 (1999) 371. [9] A.R. King, J.A. Mydosh, V. Jaccarino, Phys. Rev. Lett. 56 (1986) 2525. [10] A. Rosales-Rivera, J.M. Ferreira, F.C Montenegro, unpublished. [11] R.J. Birgeneau, Q. Feng, Q.J. Harris, J.P. Hill, A.P. Ramirez, T.R. Thurston, Phys. Rev. Lett. 75 (1995) 1198. [12] R.J. Birgeneau, J. Magn. Magn. Mater. 177}181 (1998) 1. [13] Ch. Binek, S. Kuttler, W. Kleemann, Phys. Rev. Lett. 75 (1995) 2412. [14] Y. Imry, S.K. Ma, Phys. Rev. Lett. 35 (1975) 1399.