- Email: [email protected]
Random-field destructed first-order phase transition in FeCl2:Mg
Journal of Magnetism and Magnetic Materials 140-144 (1995) 1551-1552
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ELSEVIER
Random-field destructed first-order phase transition in FeC12:Mg J. Kushauer *, W. Kleemann Angewandte Physik, Gerhard-Mercator-Universitiit Duisburg, 47048 Duisburg, Germany Abstract
Smearing of the first-order metamagnetic phase transition in Fe x Mgl -xCl2, 0.7 < x < 1, is observed at low temperatures, T ~ 0.2TN, in Faraday optical measurements. Local random fields either due to dilution and an applied field or due to a quenched antiferromagnetic (AF) domain state (DS) give rise to a crossover from first- to second-order behavior at the AF-paramagnetic (PM) field-induced transition. In agreement with model calculations the A F - P M transition field H~ is considerably enhanced when starting from a DS, which is stable even against field reversal provided that [ H I < Hc.
Rounding at the first-order phase transition (FOPT) in a random-field Ising model (RFIM) system has been predicted in a pioneering paper by Imry and Wortis [1]. Recently [2], this idea revived in the discussion of the dynamics of disorder-driven FOPTs. A critical value of disorder, Re, is predicted, at which the phase transition first becomes continuous. In this paper we report on rounding observed at the metamagnetic FOPT in antiferromagnetic (AF) solid solutions FexMgl_xC12, 0.7 < x < 1, which we believe to be due to randomness in the sense of the above theory [2]. As is well-known [3], FexMg 1_xC12 with x < 1 represents a diluted antiferromagnet in an external field H (DAFF for short), the order parameter of which is subject to random fields (RFs) as a consequence of both random dilution and H [4]. We argue that in this case the critical disorder R c [2] corresponds to critical coordinates of [xc, Hc(x~)] at which the FOPT becomes second-order. The avalanche-like paramagnetic (PM) domains become subcritical with non-divergent correlation lengths, ~ < ~, as x > x~. Even more drastic rounding of the FOPT is observed, if at fixed dilution - the sample is transformed into a metastable AF domain state (DS) by field-cooling (FC) under H ~ 0 [5] prior to driving it PM by increasing H to above He. In addition we demonstrate the extraordinary stability of the DS, once established, against severe changes of H, e.g. between + H and - H . The inset (a) of Fig. 1 shows the Faraday micrograph of the first PM domain (black) emerging from the A F background (white) in pure FeCI 2 at T = 10 K when reaching an applied field H a = 843 k A / m . In contrast, the inset (b) of Fig. 1 shows a typical domain structure of the diluted
* Corresponding author. Fax: +49-203-379 3163; email: [email protected],de.
system Feo.9Mgo.lCl 2 [6] at T = 2.8 K, H a = 780 k A / m . Both domain structures recorded after zero-field cooling (ZFC) are stabilized by demagnetization fields within the A F - P M mixed region, H d < H a < H c2. The black PM domain shown in Fig. 1, inset (a), represents the largest possible avalanche of the new phase in the pure system. Introducing RFs by diamagnetic dilution and H a ~ 0, the 0.02
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H/H c Fig. 1. 0/0ma x vs. H / H e measured in FexMg 1_xC12 with x = 1 (1), 0.8 (2) and 0.7 (3) at T = 4.06, 2.8 and 2.06 K, respectively, after ZFC, and with x = 0 . 8 at T = 2 . 8 K (4) after FC with Ha=557 kA/m and subsequent cycling through H r = - 5 5 7 kA/m (cf. Fig. 2, inset (a)). The inset shows AF (white) and PM (black, grey) domains at T = 10 K, H a = 841 kA/m, x = 1 (a) and T = 2.8 K, H a = 671 kA/m, x = 0.9 [6] (b).
0304-8853/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0 3 0 4 - 8 8 5 3 ( 9 4 ) 0 0 9 0 7 - 4
J. Kushauer, W. Kleemann /Journal of Magnetism and Magnetic Materials 140-144 (1995) 1551-1552
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-Hr [kA/m] Fig. 2. A0(H a = 0) vs. -- H r obtained on Feo.sMg0.2C12 after FC with Ha = 557 kA/m to T = 2.8 K and subsequent cycling through H r < 0. Insets (a) and (b) show 0 vs. H a after ZFC (curves l(a), (b)), FC with H a = 557 kA/m, from H a = 557 k A / m to H r = - 5 5 7 (2(a)) and - 1178 kA/m (2(b)), and from H r to H a > Hc2 > 557 kA/m, 3(a) and (b). Arrows in (a) and (b) denote to the directions of field change.
excess magnetization, represented by A 0, when compared with the ZFC value in curves l(a) or l(b) [3,5]. Obviously the 'small cycle' (a), - H e 1 < H a
nucleation of the PM phase obviously takes place on various length scales. This is visible in Fig. 1, inset (b), where the 'infinite' avalanche is replaced by PM domains of smaller size. Penetrating bubble domains (black) reach average diameters of 5 - 1 0 ~xm, whereas non-penetrating domains at or below the sample surfaces (grey) are smaller, some of them even failing short of the resolution limit of the Faraday microscope. The size distribution of the PM nucleation causes smearing of the onset of the FOPT at H e. In Fig. 1 the normalized Faraday rotation 0 / / 0 m a x , being proportional to the normalized magnetization, is plotted versus H / H e for different dilutions x = 1, 0.8 and 0.7. 0m~x denotes the Faraday rotation at saturation, H a > He2. H / H e, is the relative internal field after correction for demagnetization, where H e = He(x). The curves 1, 2 and 3 refer to the same relative temperature, T I T N = 0.17, where T = 4.06, 2.8 and 2.07 K, respectively. Increased smearing at increasing disorder is clearly observed similarly as predicted for the reversal of ferromagnetic magnetization under quenched disorder [2]. In contrast to that situation, however, in the present DAFF case H is responsible for both the RFs and the FOPT. The insets (a) and (b) of Fig. 2, henceforth referred to as (a) and (b), show various isothermal magnetization curves, 0 vs. H a, of Feo.sMgo.2C12 at To = 2.8 K. The ' virgin' curves l(a) and l(b) correspond to curve 2 of Fig. 1 and start from AF long-range order (LRO) at H a = 0. Completely different magnetization curves are obtained after FC from T = 40 K to To with H a = 557 k A / m and cycling H a from 557 through - 5 5 7 k A / m (curve 2(a)) or - 1 1 7 4 (curve 2(b)) back to beyond 557 k A / m (curves 3(a) and 3(b), respectively). They start with appreciable
"
N, n and n w are the numbers of the AF domains, magnetic ions and wall spins, respectively. Assuming non-magnetic walls nw -~ 0, small AF domains n ~ 2N, and, typically, x = 0.8, we find HDS_PM = 2HAF_PM. The D S - P M transition is characterized by local spin-flips on submicroscopical length scales. That is why newly formed PM domains are not resolved by light microscopy. In parallel, the magnetization curve appears strongly smeared (Fig. 1, curve 4) thus indicating super-critical disorder
R > R c. In conclusion, we have shown that both RFs and RF induced DSs may drive the metamagnetic transition of FexMgl_xCI2, 0 . 7 _ < x < 1, from first to second order. Furthermore, the reversal of the RF induced remanent magnetization has been studied. Acknowledgements: Thanks are due to D. Bertrand for providing a sample. This work was supported by DFG through SFB 166. References [1] Y. Imry and M. Wortis, Phys. Rev. B 19 (1979) 3580. [2] J.P. Sethna, K. Dahmen, S. Kartha, J.A. Kmmhansl, B.W. Roberts and J.D. Shore, Phys. Rev. Lett. 70 (1993) 3347. [3] U.A. Leita6 and W. Kleemann, Phys. Rev. B 35 (1987) 8696. [4] S. Fishman and A. Aharony, J. Phys. C 12 (1979) L 729. [5] For a review see: W. Kleemann, Int. J. Mod. Phys. B 7 (1993) 2469. [6] J. Mattsson, J. Kushauer, D. Bertrand, J. Ferr6 and W. Kleemann, J. Magn. Magn. Mater. 130 (1994) 216. [7] J. Kushauer, W. Kleemann, J. Mattsson and P. Nordblad, Phys. Rev. B 49 (1994) 6346.
-..m
Journal Of magnetism
~
and m~orlals
magnetic
,~
ELSEVIER
Random-field destructed first-order phase transition in FeC12:Mg J. Kushauer *, W. Kleemann Angewandte Physik, Gerhard-Mercator-Universitiit Duisburg, 47048 Duisburg, Germany Abstract
Smearing of the first-order metamagnetic phase transition in Fe x Mgl -xCl2, 0.7 < x < 1, is observed at low temperatures, T ~ 0.2TN, in Faraday optical measurements. Local random fields either due to dilution and an applied field or due to a quenched antiferromagnetic (AF) domain state (DS) give rise to a crossover from first- to second-order behavior at the AF-paramagnetic (PM) field-induced transition. In agreement with model calculations the A F - P M transition field H~ is considerably enhanced when starting from a DS, which is stable even against field reversal provided that [ H I < Hc.
Rounding at the first-order phase transition (FOPT) in a random-field Ising model (RFIM) system has been predicted in a pioneering paper by Imry and Wortis [1]. Recently [2], this idea revived in the discussion of the dynamics of disorder-driven FOPTs. A critical value of disorder, Re, is predicted, at which the phase transition first becomes continuous. In this paper we report on rounding observed at the metamagnetic FOPT in antiferromagnetic (AF) solid solutions FexMgl_xC12, 0.7 < x < 1, which we believe to be due to randomness in the sense of the above theory [2]. As is well-known [3], FexMg 1_xC12 with x < 1 represents a diluted antiferromagnet in an external field H (DAFF for short), the order parameter of which is subject to random fields (RFs) as a consequence of both random dilution and H [4]. We argue that in this case the critical disorder R c [2] corresponds to critical coordinates of [xc, Hc(x~)] at which the FOPT becomes second-order. The avalanche-like paramagnetic (PM) domains become subcritical with non-divergent correlation lengths, ~ < ~, as x > x~. Even more drastic rounding of the FOPT is observed, if at fixed dilution - the sample is transformed into a metastable AF domain state (DS) by field-cooling (FC) under H ~ 0 [5] prior to driving it PM by increasing H to above He. In addition we demonstrate the extraordinary stability of the DS, once established, against severe changes of H, e.g. between + H and - H . The inset (a) of Fig. 1 shows the Faraday micrograph of the first PM domain (black) emerging from the A F background (white) in pure FeCI 2 at T = 10 K when reaching an applied field H a = 843 k A / m . In contrast, the inset (b) of Fig. 1 shows a typical domain structure of the diluted
* Corresponding author. Fax: +49-203-379 3163; email: [email protected],de.
system Feo.9Mgo.lCl 2 [6] at T = 2.8 K, H a = 780 k A / m . Both domain structures recorded after zero-field cooling (ZFC) are stabilized by demagnetization fields within the A F - P M mixed region, H d < H a < H c2. The black PM domain shown in Fig. 1, inset (a), represents the largest possible avalanche of the new phase in the pure system. Introducing RFs by diamagnetic dilution and H a ~ 0, the 0.02
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H/H c Fig. 1. 0/0ma x vs. H / H e measured in FexMg 1_xC12 with x = 1 (1), 0.8 (2) and 0.7 (3) at T = 4.06, 2.8 and 2.06 K, respectively, after ZFC, and with x = 0 . 8 at T = 2 . 8 K (4) after FC with Ha=557 kA/m and subsequent cycling through H r = - 5 5 7 kA/m (cf. Fig. 2, inset (a)). The inset shows AF (white) and PM (black, grey) domains at T = 10 K, H a = 841 kA/m, x = 1 (a) and T = 2.8 K, H a = 671 kA/m, x = 0.9 [6] (b).
0304-8853/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0 3 0 4 - 8 8 5 3 ( 9 4 ) 0 0 9 0 7 - 4
J. Kushauer, W. Kleemann /Journal of Magnetism and Magnetic Materials 140-144 (1995) 1551-1552
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-Hr [kA/m] Fig. 2. A0(H a = 0) vs. -- H r obtained on Feo.sMg0.2C12 after FC with Ha = 557 kA/m to T = 2.8 K and subsequent cycling through H r < 0. Insets (a) and (b) show 0 vs. H a after ZFC (curves l(a), (b)), FC with H a = 557 kA/m, from H a = 557 k A / m to H r = - 5 5 7 (2(a)) and - 1178 kA/m (2(b)), and from H r to H a > Hc2 > 557 kA/m, 3(a) and (b). Arrows in (a) and (b) denote to the directions of field change.
excess magnetization, represented by A 0, when compared with the ZFC value in curves l(a) or l(b) [3,5]. Obviously the 'small cycle' (a), - H e 1 < H a
nucleation of the PM phase obviously takes place on various length scales. This is visible in Fig. 1, inset (b), where the 'infinite' avalanche is replaced by PM domains of smaller size. Penetrating bubble domains (black) reach average diameters of 5 - 1 0 ~xm, whereas non-penetrating domains at or below the sample surfaces (grey) are smaller, some of them even failing short of the resolution limit of the Faraday microscope. The size distribution of the PM nucleation causes smearing of the onset of the FOPT at H e. In Fig. 1 the normalized Faraday rotation 0 / / 0 m a x , being proportional to the normalized magnetization, is plotted versus H / H e for different dilutions x = 1, 0.8 and 0.7. 0m~x denotes the Faraday rotation at saturation, H a > He2. H / H e, is the relative internal field after correction for demagnetization, where H e = He(x). The curves 1, 2 and 3 refer to the same relative temperature, T I T N = 0.17, where T = 4.06, 2.8 and 2.07 K, respectively. Increased smearing at increasing disorder is clearly observed similarly as predicted for the reversal of ferromagnetic magnetization under quenched disorder [2]. In contrast to that situation, however, in the present DAFF case H is responsible for both the RFs and the FOPT. The insets (a) and (b) of Fig. 2, henceforth referred to as (a) and (b), show various isothermal magnetization curves, 0 vs. H a, of Feo.sMgo.2C12 at To = 2.8 K. The ' virgin' curves l(a) and l(b) correspond to curve 2 of Fig. 1 and start from AF long-range order (LRO) at H a = 0. Completely different magnetization curves are obtained after FC from T = 40 K to To with H a = 557 k A / m and cycling H a from 557 through - 5 5 7 k A / m (curve 2(a)) or - 1 1 7 4 (curve 2(b)) back to beyond 557 k A / m (curves 3(a) and 3(b), respectively). They start with appreciable
"
N, n and n w are the numbers of the AF domains, magnetic ions and wall spins, respectively. Assuming non-magnetic walls nw -~ 0, small AF domains n ~ 2N, and, typically, x = 0.8, we find HDS_PM = 2HAF_PM. The D S - P M transition is characterized by local spin-flips on submicroscopical length scales. That is why newly formed PM domains are not resolved by light microscopy. In parallel, the magnetization curve appears strongly smeared (Fig. 1, curve 4) thus indicating super-critical disorder
R > R c. In conclusion, we have shown that both RFs and RF induced DSs may drive the metamagnetic transition of FexMgl_xCI2, 0 . 7 _ < x < 1, from first to second order. Furthermore, the reversal of the RF induced remanent magnetization has been studied. Acknowledgements: Thanks are due to D. Bertrand for providing a sample. This work was supported by DFG through SFB 166. References [1] Y. Imry and M. Wortis, Phys. Rev. B 19 (1979) 3580. [2] J.P. Sethna, K. Dahmen, S. Kartha, J.A. Kmmhansl, B.W. Roberts and J.D. Shore, Phys. Rev. Lett. 70 (1993) 3347. [3] U.A. Leita6 and W. Kleemann, Phys. Rev. B 35 (1987) 8696. [4] S. Fishman and A. Aharony, J. Phys. C 12 (1979) L 729. [5] For a review see: W. Kleemann, Int. J. Mod. Phys. B 7 (1993) 2469. [6] J. Mattsson, J. Kushauer, D. Bertrand, J. Ferr6 and W. Kleemann, J. Magn. Magn. Mater. 130 (1994) 216. [7] J. Kushauer, W. Kleemann, J. Mattsson and P. Nordblad, Phys. Rev. B 49 (1994) 6346.