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Probing spin dynamics by conductance fluctuations and noise in mesoscopic spin-glass
Physica B 249—251 (1998) 500—503
Probing spin dynamics by conductance fluctuations and noise in mesoscopic spin-glass J. Jaroszyn´ski!,*, T. Dietl!, J. Wro´bel!, G. Karczewski!, T. Wojtowicz!, G. Grabecki!, M. Sawicki!, E. Papis", E. Kamin´ska", A. Piotrowska" ! Institute of Physics, Polish Academy of Sciences, Al. Lotniko& w 32/46, PL-02668 Warszawa, Poland " Institute of Electron Technology, Al. Lotniko& w 32/46, PL- 02668 Warszawa, Poland
Abstract Millikelvin magnetoconductance studies performed in mesoscopic spin-glass n`-Cd Mn Te wires reveal strong 1~x x effects of Mn spins upon universal conductance fluctuations. In particular, scattering potential of the frozen spins leads to magnetic and thermal irreversibilities of the fluctuation patterns. Slowly fluctuating spins, on the other hand, are an efficient source of conductance noise providing a real-time probe of spin dynamics. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: Universal conductance fluctuations; Spin-glasses; Diluted magnetic semiconductors
Despite many years of considerable experimental and theoretical effort, a satisfactory understanding of the magnetic order in spin glasses is still lacking. Since theoretical suggestions [1] that the sensitivity of quantum interference of scattered waves to the instantaneous configuration of the localized spins in mesoscopic systems might serve as an important tool for testing models of spin glasses, considerable efforts have been devoted to fabrication and studies of metallic nanostructures doped with magnetic impurities. In particular, Weissman and coworkers [2], by employing high current density, detected 1/f conductance noise in both macroscopic films and mesoscopic wires of Cu Mn . Despite this initial 1~x x progress, the picture emerging from the subsequent studies of mesoscopic metallic spin-glass systems is * Corresponding author. Tel.: #48 22 8433113; fax: #48 22 8430926; e-mail: [email protected].
rather confusing. The absence of both 1/f noise and irreversibilities in the studied nanostructures is assigned to either too small total concentration of the spins for the phase transition to show up [3] or to an enhancement of spin freezing in nanostructured wires [4]. We have performed detailed experimental studies of universal conductance fluctuations (UCF) and noise in wires of diluted magnetic semiconductor (DMS) n`-Cd Mn Te. Similar measure1~x x ments were carried out for wires [5,6] and films [6] of n`-CdTe. In the studied range of Mn concentrations 0.01)x)0.2, the short-range antiferromagnetic spin—spin interactions lead to the spin-glass transition at 0.01)¹ )2.5 K [7], respectively. ' Because of a large difference between the relevant length scales, the studied wires are mesoscopic from the point of view of the electronic properties but macroscopic as far as the magnetic subsystem is
0921-4526/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 1 7 3 - 2
J. Jaroszyn& ski et al. / Physica B 249—251 (1998) 500—503
concerned. This important feature, together with the absence of the competing Kondo effect (due to the ferromagnetic character of the s—d exchange interaction) [8], make DMS particularly suitable for the meaningful examination of spin effects, in both the paramagnetic and spin-glass phases, by means of a coherent transport. Iodine-doped Cd Mn Te films with x up to 0.2, thickness of 1~x x 0.3 lm, and electron concentrations around 1018 cm~3 are grown by MBE onto (0 0 1) oriented SI-GaAs epiready substrates with 3 lm CdTe undoped buffer layers. It has been confirmed [9] that the electrical activity of the iodine impurities [10], in stark contrast to the indium donors [11], varies little with the Mn concentration x for x)0.3. Accordingly, the highest electron concentration that is obtained by iodine doping reaches — in the case of Cd Mn Te by four orders of magnitude greater 0.8 0.2 values than those which could be reached with indium donors. Mesoscopic samples are patterned by means of electron-beam lithography followed by wet etching into six-probe bridges with arm dimensions 4 lm]0.3 lm, as shown in the inset to Fig. 1b. Ohmic contacts were formed by alloying indium. Magnetoconductance measurements were performed in a dilution refrigerator down to 30 mK and in magnetic fields up to 9 T. Low AC currents down to 100 pA (i.e. the current density by six orders of magnitude smaller than that in the previous experiments [12]) were employed for the resistance and its noise measurements in a dilution
501
refrigerator, carefully protected against electromagnetic noise. Fig. 1 presents the conductance G of the n`Cd Mn Te wire as a function of the magnetic 0.93 0.07 field B and time t at selected temperatures ¹. Both aperiodic conductance fluctuations and the noise are readily observed over wide temperature and field ranges under our experimental conditions. A strong decrease in correlation field B of the # UCFs on lowering temperature is clearly visible in Fig. 1a. As shown previously [5], this effect results from the spin splitting-induced redistribution of the electrons between the spin subbands, and the associated changes in the length of the interfering waves of the carriers at the Fermi level, a dominant mechanism of the UCF generation in magnetic materials with a large and temperature-dependent effective Lande´ factor. The conductance noise seen in Fig. 1b exhibits 1/f spectral characteristics at ¹(¹ , so that at ' sufficiently low frequencies it dominates over other noise sources. For the same reason, in the presence of the noise UCF “fingerprints” are no longer perfectly reproducible, especially at temperatures well below ¹ . We observe large irreproducibilities dur' ing cycling between high fields $B at a constant . temperature ¹(¹ . As shown in Fig. 2, the effect ' is clearly visible for n`-Cd Mn Te wire for 0.80 0.20 B "8 T and at ¹"50 mK, a factor of 50 lower . than ¹ , at which the Zeeman energy gk B is five ' B . times greater than k ¹ , in agreement with the B '
Fig. 1. Conductance of the Cd Mn Te wire with n"5]1018 cm~3 as a function of the magnetic field (a) and time (b) at selected 0.93 0.07 temperatures from 30 mK (top curve) to 900 mK (bottom curve) measured at I"0.5 nA.
502
J. Jaroszyn& ski et al. / Physica B 249—251 (1998) 500—503
Fig. 2. Magnetoconductance patterns of two subsequent sweeps from !8 to 8 T and back, taken on n`-Cd Mn Te 1~x x wire. Traces are shifted vertically for clarity. The bottom curve shows difference between these traces.
recent predictions of the Monte-Carlo simulations [13]. This precludes, in particular, a meaningful examination of the Onsager—Bu¨ttiker symmetry relations [14]. It is also found that differences between the UCF patterns corresponding to subsequent sweeps appear primarily in the region of low magnetic fields. Thus, such data provide direct information on the field range, over which some spin configurations remain frozen during the time of the field sweep. Another example of a strong influence of the spin-glass freezing upon the phenomena of quantum transport are documented in Fig. 3, which presents rms (*G) of both the fluctuations and the noise for the wires of spin-glass n`-Cd Mn Te, 1~x x x"0.07, and 0.2. For comparison, results of UCF measurements on similar wires of diamagnetic n`CdTe and paramagnetic n`-Cd Mn Te are 0.99 0.01 also displayed. An increase of rms (*G) is observed when lowering the temperature across the bulk values of ¹ , as determined by the magnetic studies ' of Cd Mn Te [7]. In contrast to the amplitude 1~x x of UCF, *G , which varies weakly with Mn conUCF centration, the noise amplitude *G increases /0*4% strongly with x. Actually, as shown in Fig. 3, there exist field values for x"0.2 at which *G be/0*4% comes greater than *G . UCF It is still an open question whether the spin-glass phase is more accurately described in terms of spin droplet excitations [15] or by hierarchical dynam-
Fig. 3. Amplitude *G in Cd Mn Te wires with x"0 (*), UCF 1~x x 0.01 (+), 0.07 (h) and 0.2 (L) and of the noise *G for x"0.07 /0*4% (j) and 0.2 (v) as a function of the temperature. The spin-glass freezing temperature ¹ "0.3 K for Cd Mn Te wire, is ' 0.93 0.07 shown by arrows; ¹ "2.5 K for Cd Mn Te. ' 0.8 0.2
ics [16]. Statistical analysis of the conductance noise makes it possible to discriminate between these two models. A work in this direction is under way. We thank Jacek Kossut for critical reading of the manuscript and Polish KBN for financial support under Grant No. 2-P03B-6411.
References [1] B.L. Altshuler, B.Z. Spivak, Pisma Zh. Eksp. Teor. Fiz. 42 (1985) 363 [JETP Lett. 42 (1986) 477]; S. Feng et al., Phys. Rev. B 36 (1987) 5624. [2] M.B. Weissman, N.E. Israeloff, G.B. Alers, J. Magn. Magn. Mater. 114 (1992) 87; M.B. Weissman, Rev. Mod. Phys. 65 (1993) 829. [3] A. Benoit et al., Superlattices Microstruct. 11 (1992) 313; C. Van Haesendonck et al., in: M.A. Reed, W.P. Kirk (Eds.), Nanostructures Physics and Fabrication, Academic Press, Boston, 1989, p. 467. [4] P.G.N. de Vegvar, L.P. Le´vy, Phys. Rev. Lett. 68 (1992) 3485. [5] J. Jaroszyn´ski et al., Phys. Rev. Lett. 75 (1995) 3170. [6] J. Jaroszyn´ski et al., Thin Solid Films 306 (1997), in press. [7] M.A. Novak et al., J. Appl. Phys. 57 (1985) 3418. [8] For a review on DMS, see, e.g., T. Dietl, in: T.S. Moss, (eds.), Handbook on Semiconductors, vol. 3b, North-Holland, Amsterdam, 1994, p. 1251; J.K. Furdyna, J. Appl. Phys. 64, (1988) R29.
J. Jaroszyn& ski et al. / Physica B 249—251 (1998) 500—503 [9] G. Karczewski et al., Acta Phys. Polon., in press. [10] F. Fischer et al., J. Crystal Growth 141 (1994) 93. [11] G. Karczewski et al., Thin Solid Films 267 (1995) 79. [12] N.E. Israeloff et al, Phys. Rev. Lett. 63 (1989) 794; N.E. Israeloff, G.B. Alers, M.B. Weissman, Phys. Rev. B 44 (1991) 12613.
503
[13] M. Cieplak, B.R. Bu"ka, T. Dietl, Phys. Rev. B 44 (1991) 12337; M. Cieplak, B.R. Bu"ka, T. Dietl, ibid. 51 (1995) 8939. [14] S. Hershfield, Phys. Rev. B 44 (1991) 3320. [15] D.S. Fisher, D.A. Huse, Phys. Rev. B 38 (1988) 373; ibid. 38 (1988) 386. [16] G. Parisi, Phys. Rev. Lett. 43 (1979) 1754.
Probing spin dynamics by conductance fluctuations and noise in mesoscopic spin-glass J. Jaroszyn´ski!,*, T. Dietl!, J. Wro´bel!, G. Karczewski!, T. Wojtowicz!, G. Grabecki!, M. Sawicki!, E. Papis", E. Kamin´ska", A. Piotrowska" ! Institute of Physics, Polish Academy of Sciences, Al. Lotniko& w 32/46, PL-02668 Warszawa, Poland " Institute of Electron Technology, Al. Lotniko& w 32/46, PL- 02668 Warszawa, Poland
Abstract Millikelvin magnetoconductance studies performed in mesoscopic spin-glass n`-Cd Mn Te wires reveal strong 1~x x effects of Mn spins upon universal conductance fluctuations. In particular, scattering potential of the frozen spins leads to magnetic and thermal irreversibilities of the fluctuation patterns. Slowly fluctuating spins, on the other hand, are an efficient source of conductance noise providing a real-time probe of spin dynamics. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: Universal conductance fluctuations; Spin-glasses; Diluted magnetic semiconductors
Despite many years of considerable experimental and theoretical effort, a satisfactory understanding of the magnetic order in spin glasses is still lacking. Since theoretical suggestions [1] that the sensitivity of quantum interference of scattered waves to the instantaneous configuration of the localized spins in mesoscopic systems might serve as an important tool for testing models of spin glasses, considerable efforts have been devoted to fabrication and studies of metallic nanostructures doped with magnetic impurities. In particular, Weissman and coworkers [2], by employing high current density, detected 1/f conductance noise in both macroscopic films and mesoscopic wires of Cu Mn . Despite this initial 1~x x progress, the picture emerging from the subsequent studies of mesoscopic metallic spin-glass systems is * Corresponding author. Tel.: #48 22 8433113; fax: #48 22 8430926; e-mail: [email protected].
rather confusing. The absence of both 1/f noise and irreversibilities in the studied nanostructures is assigned to either too small total concentration of the spins for the phase transition to show up [3] or to an enhancement of spin freezing in nanostructured wires [4]. We have performed detailed experimental studies of universal conductance fluctuations (UCF) and noise in wires of diluted magnetic semiconductor (DMS) n`-Cd Mn Te. Similar measure1~x x ments were carried out for wires [5,6] and films [6] of n`-CdTe. In the studied range of Mn concentrations 0.01)x)0.2, the short-range antiferromagnetic spin—spin interactions lead to the spin-glass transition at 0.01)¹ )2.5 K [7], respectively. ' Because of a large difference between the relevant length scales, the studied wires are mesoscopic from the point of view of the electronic properties but macroscopic as far as the magnetic subsystem is
0921-4526/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 1 7 3 - 2
J. Jaroszyn& ski et al. / Physica B 249—251 (1998) 500—503
concerned. This important feature, together with the absence of the competing Kondo effect (due to the ferromagnetic character of the s—d exchange interaction) [8], make DMS particularly suitable for the meaningful examination of spin effects, in both the paramagnetic and spin-glass phases, by means of a coherent transport. Iodine-doped Cd Mn Te films with x up to 0.2, thickness of 1~x x 0.3 lm, and electron concentrations around 1018 cm~3 are grown by MBE onto (0 0 1) oriented SI-GaAs epiready substrates with 3 lm CdTe undoped buffer layers. It has been confirmed [9] that the electrical activity of the iodine impurities [10], in stark contrast to the indium donors [11], varies little with the Mn concentration x for x)0.3. Accordingly, the highest electron concentration that is obtained by iodine doping reaches — in the case of Cd Mn Te by four orders of magnitude greater 0.8 0.2 values than those which could be reached with indium donors. Mesoscopic samples are patterned by means of electron-beam lithography followed by wet etching into six-probe bridges with arm dimensions 4 lm]0.3 lm, as shown in the inset to Fig. 1b. Ohmic contacts were formed by alloying indium. Magnetoconductance measurements were performed in a dilution refrigerator down to 30 mK and in magnetic fields up to 9 T. Low AC currents down to 100 pA (i.e. the current density by six orders of magnitude smaller than that in the previous experiments [12]) were employed for the resistance and its noise measurements in a dilution
501
refrigerator, carefully protected against electromagnetic noise. Fig. 1 presents the conductance G of the n`Cd Mn Te wire as a function of the magnetic 0.93 0.07 field B and time t at selected temperatures ¹. Both aperiodic conductance fluctuations and the noise are readily observed over wide temperature and field ranges under our experimental conditions. A strong decrease in correlation field B of the # UCFs on lowering temperature is clearly visible in Fig. 1a. As shown previously [5], this effect results from the spin splitting-induced redistribution of the electrons between the spin subbands, and the associated changes in the length of the interfering waves of the carriers at the Fermi level, a dominant mechanism of the UCF generation in magnetic materials with a large and temperature-dependent effective Lande´ factor. The conductance noise seen in Fig. 1b exhibits 1/f spectral characteristics at ¹(¹ , so that at ' sufficiently low frequencies it dominates over other noise sources. For the same reason, in the presence of the noise UCF “fingerprints” are no longer perfectly reproducible, especially at temperatures well below ¹ . We observe large irreproducibilities dur' ing cycling between high fields $B at a constant . temperature ¹(¹ . As shown in Fig. 2, the effect ' is clearly visible for n`-Cd Mn Te wire for 0.80 0.20 B "8 T and at ¹"50 mK, a factor of 50 lower . than ¹ , at which the Zeeman energy gk B is five ' B . times greater than k ¹ , in agreement with the B '
Fig. 1. Conductance of the Cd Mn Te wire with n"5]1018 cm~3 as a function of the magnetic field (a) and time (b) at selected 0.93 0.07 temperatures from 30 mK (top curve) to 900 mK (bottom curve) measured at I"0.5 nA.
502
J. Jaroszyn& ski et al. / Physica B 249—251 (1998) 500—503
Fig. 2. Magnetoconductance patterns of two subsequent sweeps from !8 to 8 T and back, taken on n`-Cd Mn Te 1~x x wire. Traces are shifted vertically for clarity. The bottom curve shows difference between these traces.
recent predictions of the Monte-Carlo simulations [13]. This precludes, in particular, a meaningful examination of the Onsager—Bu¨ttiker symmetry relations [14]. It is also found that differences between the UCF patterns corresponding to subsequent sweeps appear primarily in the region of low magnetic fields. Thus, such data provide direct information on the field range, over which some spin configurations remain frozen during the time of the field sweep. Another example of a strong influence of the spin-glass freezing upon the phenomena of quantum transport are documented in Fig. 3, which presents rms (*G) of both the fluctuations and the noise for the wires of spin-glass n`-Cd Mn Te, 1~x x x"0.07, and 0.2. For comparison, results of UCF measurements on similar wires of diamagnetic n`CdTe and paramagnetic n`-Cd Mn Te are 0.99 0.01 also displayed. An increase of rms (*G) is observed when lowering the temperature across the bulk values of ¹ , as determined by the magnetic studies ' of Cd Mn Te [7]. In contrast to the amplitude 1~x x of UCF, *G , which varies weakly with Mn conUCF centration, the noise amplitude *G increases /0*4% strongly with x. Actually, as shown in Fig. 3, there exist field values for x"0.2 at which *G be/0*4% comes greater than *G . UCF It is still an open question whether the spin-glass phase is more accurately described in terms of spin droplet excitations [15] or by hierarchical dynam-
Fig. 3. Amplitude *G in Cd Mn Te wires with x"0 (*), UCF 1~x x 0.01 (+), 0.07 (h) and 0.2 (L) and of the noise *G for x"0.07 /0*4% (j) and 0.2 (v) as a function of the temperature. The spin-glass freezing temperature ¹ "0.3 K for Cd Mn Te wire, is ' 0.93 0.07 shown by arrows; ¹ "2.5 K for Cd Mn Te. ' 0.8 0.2
ics [16]. Statistical analysis of the conductance noise makes it possible to discriminate between these two models. A work in this direction is under way. We thank Jacek Kossut for critical reading of the manuscript and Polish KBN for financial support under Grant No. 2-P03B-6411.
References [1] B.L. Altshuler, B.Z. Spivak, Pisma Zh. Eksp. Teor. Fiz. 42 (1985) 363 [JETP Lett. 42 (1986) 477]; S. Feng et al., Phys. Rev. B 36 (1987) 5624. [2] M.B. Weissman, N.E. Israeloff, G.B. Alers, J. Magn. Magn. Mater. 114 (1992) 87; M.B. Weissman, Rev. Mod. Phys. 65 (1993) 829. [3] A. Benoit et al., Superlattices Microstruct. 11 (1992) 313; C. Van Haesendonck et al., in: M.A. Reed, W.P. Kirk (Eds.), Nanostructures Physics and Fabrication, Academic Press, Boston, 1989, p. 467. [4] P.G.N. de Vegvar, L.P. Le´vy, Phys. Rev. Lett. 68 (1992) 3485. [5] J. Jaroszyn´ski et al., Phys. Rev. Lett. 75 (1995) 3170. [6] J. Jaroszyn´ski et al., Thin Solid Films 306 (1997), in press. [7] M.A. Novak et al., J. Appl. Phys. 57 (1985) 3418. [8] For a review on DMS, see, e.g., T. Dietl, in: T.S. Moss, (eds.), Handbook on Semiconductors, vol. 3b, North-Holland, Amsterdam, 1994, p. 1251; J.K. Furdyna, J. Appl. Phys. 64, (1988) R29.
J. Jaroszyn& ski et al. / Physica B 249—251 (1998) 500—503 [9] G. Karczewski et al., Acta Phys. Polon., in press. [10] F. Fischer et al., J. Crystal Growth 141 (1994) 93. [11] G. Karczewski et al., Thin Solid Films 267 (1995) 79. [12] N.E. Israeloff et al, Phys. Rev. Lett. 63 (1989) 794; N.E. Israeloff, G.B. Alers, M.B. Weissman, Phys. Rev. B 44 (1991) 12613.
503
[13] M. Cieplak, B.R. Bu"ka, T. Dietl, Phys. Rev. B 44 (1991) 12337; M. Cieplak, B.R. Bu"ka, T. Dietl, ibid. 51 (1995) 8939. [14] S. Hershfield, Phys. Rev. B 44 (1991) 3320. [15] D.S. Fisher, D.A. Huse, Phys. Rev. B 38 (1988) 373; ibid. 38 (1988) 386. [16] G. Parisi, Phys. Rev. Lett. 43 (1979) 1754.