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Nonlinear conduction and anomalous susceptibility of sliding electronic crystals: Charge and spin density waves
Synthetic Metals86 (1997) 2223-2224
ELSEVIER
Nonlinear
conduction
and anomalous susceptibility of sliding electronic Charge and Spin Density Waves.
S. BrazovskiilY’ and A. Larkin2**. ‘ESRF - ILL, BP 156 X, Grenoble, Cedex 9, Fkance; 2 Univ. of Minnesota, Dept. of Phys., Minneapolis, MN 55455, ’ On leave fmm the Landau Institute, Moscow, Russia.
crystals:
USA;
Abstract Metastable plastic deformations of sliding electronic crystals determine their low frequency dielectric susceptibility s(T, w), long time relaxation and nonlinear I - V characteristics. We present a theory of plastic deformations due to the pinning induced dislocation loops which originate the local met&able state. Within the same model we describe the two remarkable features which became commonly observed in Charge and Spin Density Waves (DW). There are both the anomalous peak of s(T, w = const) and the characteristic I - V curve with second threshold field in sliding regime. Namely the features of E(T) result from a competition of the local relaxation with the collective pinning effected by freezing of the Coulomb screening. The upper critical field in I - V curves is reached when the shortest life time configurations are accessed by the fast moving DW. Key~o&s: Conductivity, Susceptibiliv, Charge density waves; Spin density waves
1.
Introduction.
Sliding
versus
Pinning.
The Charge Density Waves formation was the very first effect faced at the beginning of the Synthetic Metals epoch. Later the Spin Density Waves appeared as the counterparts of the organic superconductivity. The unique features of the Density W&es (DWs) are related to their special property of the collective sliding. With the longest story of experimental and theoretical studies the DWs are still mysterious and provocative. The current trends are common for a variety of Electronic Crystals, see [l] and for the vortex lattices in superconductors. We have proposed [2, 3, 41 a theory of MPDs due to the pinning-induced solitons or dislocation loops to describe uniquely the two bright experimental features of DWS: The anomalous peak of s(T, w = const) [5, 6, 7, 8, 91; The I-V curve with a second threshold field &2 in sliding regime [lo, 111. The Main Ingredients are the following: The DW superstructure N cos[&+ cp]; the DW phase deformations bq(r’, t) N electric polarization, the DW velocity v = + N electric current, the pinning force Fpin acting against the applied field E and the DW elastic strain; & M Fpin as a function of &+Yor v; MPDs as an origin of Fr;,,; Bisolitons or Dislocation Loops as visualizations of the MPDs; Crossover between two types of pinning, their additivity to Frin. and to E-‘; Activation of the MPDs by displacements and their relaxation rate 7-l with respect to v or w( the MPDs contributes to Fpin only at wr >> 1 or vr >> 1). The theoretical bibliography can be found in [3, 41. o379-6779/97/$17.000 1997 Else&r Science S.A. Au figtas t-m&
PII SO379-6779(%)048126
The two types of pinning are usually distinguished. COLLECTIVE or WEAK pinning comes from the elastic interference of many impurities. It originates the first threshold field Ei to initiate the sliding similarly to conventional rest- and dry frictions. Its characteristic features are: Small critical field for the friction at rest Ei o( l/s; Large response E, correlation volumes and barriers Vb between MS; Huge relaxation times r N exp[Vb/T]. The collective pinning is dramatically affected by the anomalous T dependence of the DW elasticity - the effect of long range Coulomb interactions is the incompressibility of the ECs which is gradually lifted by a thermally activated normal screening; it leads to the low T release of the collective pinning. LOCAL or STRONG pinning comes from rare metsstable centers which provide finite barriers, hence the reachable relaxation times 7. Being released at low w or v, it becomes the main source of dispersion, relaxation and dissipation. Just these effects are addressed in our studies. 2.
The peak.
origin
of the
low
T low
w susceptibility
Sliding DWs are principally characterized by their giant dielectric susceptibility E N lo6 - log and by a low threshold field Et which develops below the transition temperature. Bemarkably, a new sharp maximum of E(w,T) has been observed in several DW materials at low T and for very low frequencies w [5, 6, 7, 8, 91. With w decreasing from 104Hz to 10°Hz, the maximum height is growing rapidly while its
2224
S. Brazovskii, A. Lmkin /Synthetic Metals 86 {I 997) 2223-2224
position T,,,=(w) is shifting towards low T. Remarkably the uprising parts T > T,,,= of all plots E(W = const,T) seem to follow the same master curve E(T) and differ only by the cutoff Tmz(w) below which E drops sharply. The explanation for anomaly in E has been suggested [3] as a combined effect of the collective and the local pinning. The different types of pinning compete to contribute to c-l so that the lowest E dominates and near T,,,,, the pinning force is minimal. Namely at the higher T slope the T dependence arises from the dispersionless - infinite barriers for collective MSs - collective pinning affected by statically screened Coulomb interactions. At the lower T slope the dispersion of E and the peak position T,,(w) come from the relaxation of local MPDs. With increasing T the local states approach the thermal equilibrium, in average F,,i,, + 0 hence E(T,w) grows with increasing T until the collective pinning force becomes important. Within the local pinning regime at relatively low w or high T only those long living states contribute which are due to rear occasions of large impurity potentials V - T In l/w. which provides a direct access Then l/~l~~ N PbTln(l/w) to the distribution of barriers p!,(K)!
3.
The I - V characteristics of sliding DWs the origin of the upper threshold field &z.
changes to & = &2 - const [h(v~/v)]~/~ at intermediate v. At low v, & - VT with an activated behavior of the MS relaxation time 7 which emulates the normal conductivity. Finally at lowest v we find E N vQ , a - T with a diverging differential resistance. 4.
Conclusions
We have suggested a unified picture of pinned CDW or SDW which describes altogether the susceptibility anomaly, long time relaxation and nonlinear I - V characteristics. The peak of e(T) results from a competition of the local metastable plasticity with the collective pinning effected by freezing out of the Coulomb screening. In V - I curves the upper threshold field &2 is reached when the metastable plastic deformations with shortest life time are accessed by the fast moving DW. In a sense the fast sliding DW works as a ‘Linear Accelerator’ to test short living resonances. Acknowledgments. The authors acknowledge the hospitality of the French institutes ILL’, ESRF’ and CRTBTlV2 in Grenoble, LPS at U-PSud’ in Orsay; the ITP at UCSB in USA - the Grant NSFITPPHYS 94/07194. The authors are grateful to J.Brill, M.Itkis, P.Monceau and F.Nad for discussions.
and
Another surprise from the low T studies was the observation of the two distinct threshold fields for the onset of the DW sliding, see [lo, 111and references therein. 1. Above the first threshold El - 10m3f 1 V/cm the DW starts to slide collectively while incoherently yet. 2. Above the second threshold &z - 1 t lo2 V/cm the DW starts to slide coherently, the I - V curve may become very steep. In our interpretation f1 can be only the rest friction due to the collective pinning. Contrary &z is the high velocity limit of the dry friction force via the energy dissipation by a moving DW. Above &2 the power gained from external field & is sufficient to create necessary MPDs to overcome local pinning. Namely the energy 2E, is absorbed by creation of the diverging soliton pair which emerges after each DW period passing over an impurity. For the impurities concentration n; per chain we find &z = ni2E./2r corresponding to infinite v. At finite large v this limiting voltage is approached as ,!Z= &2 - con&/v7 which
References [l] Proceedings of the “International Workshop on Electronic Crystals”, June 1993,ed.byS.Brazovskii,P.Monceau, J.Physique, France,Colloque, Septemberl993. [2] A. I. Larkin, Sov. Phys. JETP 105 (1994) 1793. [3] A. Larkin and S. Brazovskii, Sol. State Commun., (1995) 275. [4] S. Brazovskii, Proceedings of the NATO ASI, Plenum Press 1996,to be publ.; S. Brazovskii and A. Larkin, preprint. [5] Jie Yang, N. P. Ong, Phys.Reu. B44(1991) 1991. [6] 4. G. Kriza, Y. Kim, A. Beleznay, G. Mihaly Solid Stote Commun., 79 (1991) 811. [7] F.Ya. Nad, P. Monceau, Solid State Comm. 87 (1993) 13; and in [l], p.343. [8] K. BiljakoviC,J. C. Lasjaunias, P. Monceau, in [l], p.335. [9] J. C. Lasjaunias, K. BiljakoviC, F.Ya. Nad, P. Monceau, K. Bechgaard, Phys.Reu.Lett. 72(1994) 1283. [lo] G.Mihaly, T.Chen, T.W.Kim, G.Griiner, Phys.Rev. B38(1988) 3602. [ll] M. Itkis, F.Ya. Nad, P. Monceau, J.Phys.:Condensedmatter 2( 1990)8327.
ELSEVIER
Nonlinear
conduction
and anomalous susceptibility of sliding electronic Charge and Spin Density Waves.
S. BrazovskiilY’ and A. Larkin2**. ‘ESRF - ILL, BP 156 X, Grenoble, Cedex 9, Fkance; 2 Univ. of Minnesota, Dept. of Phys., Minneapolis, MN 55455, ’ On leave fmm the Landau Institute, Moscow, Russia.
crystals:
USA;
Abstract Metastable plastic deformations of sliding electronic crystals determine their low frequency dielectric susceptibility s(T, w), long time relaxation and nonlinear I - V characteristics. We present a theory of plastic deformations due to the pinning induced dislocation loops which originate the local met&able state. Within the same model we describe the two remarkable features which became commonly observed in Charge and Spin Density Waves (DW). There are both the anomalous peak of s(T, w = const) and the characteristic I - V curve with second threshold field in sliding regime. Namely the features of E(T) result from a competition of the local relaxation with the collective pinning effected by freezing of the Coulomb screening. The upper critical field in I - V curves is reached when the shortest life time configurations are accessed by the fast moving DW. Key~o&s: Conductivity, Susceptibiliv, Charge density waves; Spin density waves
1.
Introduction.
Sliding
versus
Pinning.
The Charge Density Waves formation was the very first effect faced at the beginning of the Synthetic Metals epoch. Later the Spin Density Waves appeared as the counterparts of the organic superconductivity. The unique features of the Density W&es (DWs) are related to their special property of the collective sliding. With the longest story of experimental and theoretical studies the DWs are still mysterious and provocative. The current trends are common for a variety of Electronic Crystals, see [l] and for the vortex lattices in superconductors. We have proposed [2, 3, 41 a theory of MPDs due to the pinning-induced solitons or dislocation loops to describe uniquely the two bright experimental features of DWS: The anomalous peak of s(T, w = const) [5, 6, 7, 8, 91; The I-V curve with a second threshold field &2 in sliding regime [lo, 111. The Main Ingredients are the following: The DW superstructure N cos[&+ cp]; the DW phase deformations bq(r’, t) N electric polarization, the DW velocity v = + N electric current, the pinning force Fpin acting against the applied field E and the DW elastic strain; & M Fpin as a function of &+Yor v; MPDs as an origin of Fr;,,; Bisolitons or Dislocation Loops as visualizations of the MPDs; Crossover between two types of pinning, their additivity to Frin. and to E-‘; Activation of the MPDs by displacements and their relaxation rate 7-l with respect to v or w( the MPDs contributes to Fpin only at wr >> 1 or vr >> 1). The theoretical bibliography can be found in [3, 41. o379-6779/97/$17.000 1997 Else&r Science S.A. Au figtas t-m&
PII SO379-6779(%)048126
The two types of pinning are usually distinguished. COLLECTIVE or WEAK pinning comes from the elastic interference of many impurities. It originates the first threshold field Ei to initiate the sliding similarly to conventional rest- and dry frictions. Its characteristic features are: Small critical field for the friction at rest Ei o( l/s; Large response E, correlation volumes and barriers Vb between MS; Huge relaxation times r N exp[Vb/T]. The collective pinning is dramatically affected by the anomalous T dependence of the DW elasticity - the effect of long range Coulomb interactions is the incompressibility of the ECs which is gradually lifted by a thermally activated normal screening; it leads to the low T release of the collective pinning. LOCAL or STRONG pinning comes from rare metsstable centers which provide finite barriers, hence the reachable relaxation times 7. Being released at low w or v, it becomes the main source of dispersion, relaxation and dissipation. Just these effects are addressed in our studies. 2.
The peak.
origin
of the
low
T low
w susceptibility
Sliding DWs are principally characterized by their giant dielectric susceptibility E N lo6 - log and by a low threshold field Et which develops below the transition temperature. Bemarkably, a new sharp maximum of E(w,T) has been observed in several DW materials at low T and for very low frequencies w [5, 6, 7, 8, 91. With w decreasing from 104Hz to 10°Hz, the maximum height is growing rapidly while its
2224
S. Brazovskii, A. Lmkin /Synthetic Metals 86 {I 997) 2223-2224
position T,,,=(w) is shifting towards low T. Remarkably the uprising parts T > T,,,= of all plots E(W = const,T) seem to follow the same master curve E(T) and differ only by the cutoff Tmz(w) below which E drops sharply. The explanation for anomaly in E has been suggested [3] as a combined effect of the collective and the local pinning. The different types of pinning compete to contribute to c-l so that the lowest E dominates and near T,,,,, the pinning force is minimal. Namely at the higher T slope the T dependence arises from the dispersionless - infinite barriers for collective MSs - collective pinning affected by statically screened Coulomb interactions. At the lower T slope the dispersion of E and the peak position T,,(w) come from the relaxation of local MPDs. With increasing T the local states approach the thermal equilibrium, in average F,,i,, + 0 hence E(T,w) grows with increasing T until the collective pinning force becomes important. Within the local pinning regime at relatively low w or high T only those long living states contribute which are due to rear occasions of large impurity potentials V - T In l/w. which provides a direct access Then l/~l~~ N PbTln(l/w) to the distribution of barriers p!,(K)!
3.
The I - V characteristics of sliding DWs the origin of the upper threshold field &z.
changes to & = &2 - const [h(v~/v)]~/~ at intermediate v. At low v, & - VT with an activated behavior of the MS relaxation time 7 which emulates the normal conductivity. Finally at lowest v we find E N vQ , a - T with a diverging differential resistance. 4.
Conclusions
We have suggested a unified picture of pinned CDW or SDW which describes altogether the susceptibility anomaly, long time relaxation and nonlinear I - V characteristics. The peak of e(T) results from a competition of the local metastable plasticity with the collective pinning effected by freezing out of the Coulomb screening. In V - I curves the upper threshold field &2 is reached when the metastable plastic deformations with shortest life time are accessed by the fast moving DW. In a sense the fast sliding DW works as a ‘Linear Accelerator’ to test short living resonances. Acknowledgments. The authors acknowledge the hospitality of the French institutes ILL’, ESRF’ and CRTBTlV2 in Grenoble, LPS at U-PSud’ in Orsay; the ITP at UCSB in USA - the Grant NSFITPPHYS 94/07194. The authors are grateful to J.Brill, M.Itkis, P.Monceau and F.Nad for discussions.
and
Another surprise from the low T studies was the observation of the two distinct threshold fields for the onset of the DW sliding, see [lo, 111and references therein. 1. Above the first threshold El - 10m3f 1 V/cm the DW starts to slide collectively while incoherently yet. 2. Above the second threshold &z - 1 t lo2 V/cm the DW starts to slide coherently, the I - V curve may become very steep. In our interpretation f1 can be only the rest friction due to the collective pinning. Contrary &z is the high velocity limit of the dry friction force via the energy dissipation by a moving DW. Above &2 the power gained from external field & is sufficient to create necessary MPDs to overcome local pinning. Namely the energy 2E, is absorbed by creation of the diverging soliton pair which emerges after each DW period passing over an impurity. For the impurities concentration n; per chain we find &z = ni2E./2r corresponding to infinite v. At finite large v this limiting voltage is approached as ,!Z= &2 - con&/v7 which
References [l] Proceedings of the “International Workshop on Electronic Crystals”, June 1993,ed.byS.Brazovskii,P.Monceau, J.Physique, France,Colloque, Septemberl993. [2] A. I. Larkin, Sov. Phys. JETP 105 (1994) 1793. [3] A. Larkin and S. Brazovskii, Sol. State Commun., (1995) 275. [4] S. Brazovskii, Proceedings of the NATO ASI, Plenum Press 1996,to be publ.; S. Brazovskii and A. Larkin, preprint. [5] Jie Yang, N. P. Ong, Phys.Reu. B44(1991) 1991. [6] 4. G. Kriza, Y. Kim, A. Beleznay, G. Mihaly Solid Stote Commun., 79 (1991) 811. [7] F.Ya. Nad, P. Monceau, Solid State Comm. 87 (1993) 13; and in [l], p.343. [8] K. BiljakoviC,J. C. Lasjaunias, P. Monceau, in [l], p.335. [9] J. C. Lasjaunias, K. BiljakoviC, F.Ya. Nad, P. Monceau, K. Bechgaard, Phys.Reu.Lett. 72(1994) 1283. [lo] G.Mihaly, T.Chen, T.W.Kim, G.Griiner, Phys.Rev. B38(1988) 3602. [ll] M. Itkis, F.Ya. Nad, P. Monceau, J.Phys.:Condensedmatter 2( 1990)8327.