A. Goltsev | University of Aveiro (original) (raw)
Papers by A. Goltsev
Physical Review Letters, 2012
We reveal the nature of the avalanche collapse of the giant viable component in multiplex network... more We reveal the nature of the avalanche collapse of the giant viable component in multiplex networks under perturbations such as random damage. Specifically, we identify latent critical clusters associated with the avalanches of random damage. Divergence of their mean size signals the approach to the hybrid phase transition from one side, while there are no critical precursors on the other side. We find that this discontinuous transition occurs in scale-free multiplex networks whenever the mean degree of at least one of the interdependent networks does not diverge.
Handbook of Optimization in Complex Networks, 2012
Many real-world complex systems are represented not by single networks but rather by sets of inte... more Many real-world complex systems are represented not by single networks but rather by sets of interdependent networks. In these specific networks, vertices in each network mutually depend on vertices in other networks. In the simplest representative case, interdependent networks are equivalent to the so-called multiplex networks containing vertices of one sort but several kinds of edges. Connectivity properties of these networks and their robustness against damage differ sharply from ordinary networks. Connected components in ordinary networks are naturally generalized to viable clusters in multiplex networks whose vertices are connected by paths passing over each individual sort of their edges. We examine the robustness of the giant viable cluster to random damage. We show that random damage to these systems can lead to the avalanche collapse of the viable cluster, and that this collapse is a hybrid phase transition combining a discontinuity and the critical singularity. For this transition we identify latent critical clusters associated with the avalanches triggered by a removal of single vertices. Divergence of their mean size signals the approach to the hybrid phase transition from one side, while there are no critical precursors on the other side. We find that this discontinuous transition occurs in scale-free multiplex networks whenever the mean degree of at least one of the interdependent networks does not diverge.
Lecture Notes in Physics, 2004
We review a general approach that describes the spectra of eigenvalues for random graphs with a l... more We review a general approach that describes the spectra of eigenvalues for random graphs with a local tree-like structure. The exact equations to the spectra of networks with a local tree-like structure, are presented. The tail of the density of eigenvalues r</font >( l</font >)\rho \left( \lambda \right) at large | l</font >|\left| \lambda \right| is related to the behavior of the vertex degree distribution for large value of degree. In particular, as P( k) ~ </font >k-</font >g</font > P\left( k\right) \sim k^{-\gamma }, r</font >( l</font >) ~ </font >| l</font >| 1-</font >2g</font >\rho \left( \lambda \right) \sim \left| \lambda \right| ^{1-2\gamma }. Under an effective medium approximation we propose a simple approximation, calculate spectra of various graphs analytically. We also analyse the spectra of various complex networks and discuss the role of vertices of low degree. We show that spectra of locally tree-like random graphs gives a good description of the spectral properties of real-life networks like the Internet.
Physical Review E, 2005
We study pair correlations in cooperative systems placed on complex networks. We show that usuall... more We study pair correlations in cooperative systems placed on complex networks. We show that usually in these systems, the correlations between two interacting objects (e.g., spins), separated by a distance ℓ, decay, on average, faster than 1/(ℓz ℓ). Here z ℓ is the mean number of the ℓth nearest neighbors of a vertex in a network. This behavior, in particular, leads to a dramatic weakening of correlations between second and more distant neighbors on networks with fat-tailed degree distributions, which have a divergent number z2 in the infinite network limit. In this case, only the pair correlations between the nearest neighbors are observable. We obtain the pair correlation function of the Ising model on a complex network and also derive our results in the framework of a phenomenological approach.
Physical Review E, 2011
We introduce the heterogeneous-k-core, which generalizes the k-core, and contrast it with bootstr... more We introduce the heterogeneous-k-core, which generalizes the k-core, and contrast it with bootstrap percolation. Vertices have a threshold ki which may be different at each vertex. If a vertex has less than ki neighbors it is pruned from the network. The heterogeneous-k-core is the sub-graph remaining after no further vertices can be pruned. If the thresholds ki are 1 with probability f or k ≥ 3 with probability (1 − f), the process forms one branch of an activation-pruning process which demonstrates hysteresis. The other branch is formed by ordinary bootstrap percolation. We show that there are two types of transitions in this heterogeneous-k-core process: the giant heterogeneousk-core may appear with a continuous transition and there may be a second, discontinuous, hybrid transition. We compare critical phenomena, critical clusters and avalanches at the heterogeneous-kcore and bootstrap percolation transitions. We also show that network structure has a crucial effect on these processes, with the giant heterogeneous-k-core appearing immediately at a finite value for any f > 0 when the degree distribution tends to a power law P (q) ∼ q −γ with γ < 3.
Physica C: Superconductivity, 2003
Recently an anomalous acoustoelectrical (AE) effect produced by surface acoustic waves (SAW) in t... more Recently an anomalous acoustoelectrical (AE) effect produced by surface acoustic waves (SAW) in thin La 0:67 Ca 0:33 MnO 3 films deposited on a piezoelectric LiNbO 3 substrate was discovered [Phys. Rev. Lett. 87 (2001) 146602]. The SAW, launched along the distinct crystallographic axis (þz) of the structure, induces a dc current I AE in the film, which in the ordinary AE effect would be odd with respect to the SAW wave vector q. However, in the investigated case I AE contains, along with the ordinary odd component, an anomalous one, which is even in q. The anomalous effect dominates near the metal-insulator transition, while the ordinary effect prevails at high and low temperatures. The anomalous effect appears to depend on strong modulation of the film conductivity resulting from the elastic deformations carried by the SAW. We have investigated the influence of an in-plane magnetic field H on the magnitude of I AE , and found an increase of about 50% when H was parallel to q. The increase was limited to the anomalous component of I AE. We speculate that this may be caused by magnetic field induced changes in the conductivity dependence on pressure. The ordinary AE current was left essentially unchanged. Apparently the boost given to this component by the increase of conductivity in a magnetic field is compensated by the corresponding SAW attenuation decrease. We have also conducted I AE measurements with the SAW split into two components of equal amplitude, propagating in the film in opposite directions. As a result, we have obtained cancellation of the ordinary I AE component and augmentation of the anomalous one, i.e. we have confirmed our understanding of the AE effects.
Nature, 2002
Ferroelectromagnets are an interesting group of compounds that complement purely (anti-)ferroelec... more Ferroelectromagnets are an interesting group of compounds that complement purely (anti-)ferroelectric or (anti-)ferromagnetic materials--they display simultaneous electric and magnetic order. With this coexistence they supplement materials in which magnetization can be induced by an electric field and electrical polarization by a magnetic field, a property which is termed the magnetoelectric effect. Aside from its fundamental importance, the mutual control of electric and magnetic properties is of significant interest for applications in magnetic storage media and 'spintronics'. The coupled electric and magnetic ordering in ferroelectromagnets is accompanied by the formation of domains and domain walls. However, such a cross-correlation between magnetic and electric domains has so far not been observed. Here we report spatial maps of coupled antiferromagnetic and ferroelectric domains in YMnO3, obtained by imaging with optical second harmonic generation. The coupling originates from an interaction between magnetic and electric domain walls, which leads to a configuration that is dominated by the ferroelectromagnetic product of the order parameters.
Journal of Magnetism and Magnetic Materials, 2002
ABSTRACT We report on acoustic and acoustoelectric (AE) studies of La0.67Ca0.33MnO3 (LCMO) films ... more ABSTRACT We report on acoustic and acoustoelectric (AE) studies of La0.67Ca0.33MnO3 (LCMO) films deposited on a LiNbO3 substrate. Surface acoustic wave (SAW) attenuation in the LCMO films has been measured at different sound frequencies in the wide temperature range. Our measurements confirm the hole-like conductivity in La0.67Ca0.33MnO3 films and reveal an anomalous (even in the SAW wave vector) contribution to the AE effect, which coexists with the ordinary (odd) effect. The anomalous AE effect is shown to be due to a strong modulation of the film conductivity produced by elastic deformations carried by the SAW.
Journal of Magnetism and Magnetic Materials, 2005
A variety of bulk as well as local magnetoelectric effects are observed in RMnO 3 compounds with ... more A variety of bulk as well as local magnetoelectric effects are observed in RMnO 3 compounds with R ¼ Sc; Y; In; Ho; Er; Tm; Yb; Lu due to the coexistence of ferroelectric and multiple magnetic ordering. On the one hand, 'gigantic' magnetoelectric bulk effects, where magnetic phase control is exerted by applied electric or magnetic fields, are revealed. On the other hand, interaction of domain walls leads to a coupling of ferroelectric and antiferromagnetic domains, and a contribution to the linear magnetoelectric effect that is induced in the antiferromagnetic domain walls is identified. The effects are observed by linear and nonlinear magnetooptical techniques and explained microscopically by the interplay of magnetic exchange, wall magnetization, and ferroelectric distortion.
Physical Review Letters, 2003
The structure of antiferromagnetic (AFM) domain walls and their interaction with lattice strain a... more The structure of antiferromagnetic (AFM) domain walls and their interaction with lattice strain are derived taking the multiple-order-parameter compound YMnO 3 as a model example. Contrary to the conviction that AFM domain walls are energetically unfavorable, their interaction with lattice strain lowers the total energy of the system and leads to a piezomagnetic clamping of the electric and magnetic order parameters in good agreement with the available experimental data.
Physical Review E, 2013
We study the role of scale-free structure and noise in collective dynamics of neuronal networks. ... more We study the role of scale-free structure and noise in collective dynamics of neuronal networks. For this purpose, we simulate and study analytically a cortical circuit model with stochastic neurons. We compare collective neuronal activity of networks with different topologies: classical random graphs and scale-free networks. We show that, in scale-free networks with divergent second moment of degree distribution, an influence of noise on neuronal activity is strongly enhanced in comparison with networks with a finite second moment. A very small noise level can stimulate spontaneous activity of a finite fraction of neurons and sustained network oscillations. We demonstrate tolerance of collective dynamics of the scale-free networks to random damage in a broad range of the number of randomly removed excitatory and inhibitory neurons. A random removal of neurons leads to gradual decrease of frequency of network oscillations similar to the slowing-down of the alpha rhythm in Alzheimer's disease. However, the networks are vulnerable to targeted attacks. A removal of a few excitatory or inhibitory hubs can impair sustained network oscillations.
Nature, 2002
Ferroelectromagnets are an interesting group of compounds that complement purely (anti-) ferroele... more Ferroelectromagnets are an interesting group of compounds that complement purely (anti-) ferroelectric or (anti-) ferromagnetic materials -they display simultaneous electric and magnetic order1-3.
Journal of Magnetism and Magnetic Materials, 2004
Journal of Magnetism and Magnetic Materials, 2005
Physical Review Letters, 2003
Physical Review B, 1999
ABSTRACT We have carried out ultrasonic investigations of (TMTSF)2PF6 in the spin-density-wave (S... more ABSTRACT We have carried out ultrasonic investigations of (TMTSF)2PF6 in the spin-density-wave (SDW) ground state. Some features for the elastic behavior of the SDW state are found. One of the acoustic modes shows a jump in the sound velocity at the critical temperature of the SDW transition (TSDW≈12K) and a relaxation peak in the attenuation of sound just below TSDW. From this peak we have estimated the characteristic relaxation time of the spin fluctuations along the b axis to be t0=2×10-11s. The sound velocity of another acoustic mode changes with temperature as the square of the order parameter. Besides a maximum just below TSDW the attenuation of this mode has an exponential behavior at low temperatures and yields an energy gap value equal to 2Δ(0)≈96K, which is much larger than the BCS value 2Δ(0)≈43K. In addition there is an acoustic mode which displays a slow decrease of the sound velocity in the SDW state. We have also studied the influence of a magnetic field applied along the c* axis on the acoustic properties of (TMTSF)2PF6: TSDW increases in the magnetic field. We discuss our experimental results in the frame of theoretical considerations which are based on the assumption that phonons influence the exchange interaction between the spins of the conducting electrons and thus couple to the SDW (magnetoelastic coupling). In our model, the temperature behavior of the sound velocity and the attenuation of sound is related to the real and imaginary parts of the dynamical spin susceptibility. This model allows us to classify the temperature behavior of different acoustic modes and to explain the observed anomalies in the sound velocity and the attenuation of sound in the SDW ground state.
Synthetic Metals, 1999
ABSTRACT Acoustic measurements of (TMTSF)2PF6 have been performed in the temperature range 2 K &a... more ABSTRACT Acoustic measurements of (TMTSF)2PF6 have been performed in the temperature range 2 K < T < 40 K. The behavior of the sound velocity and attenuation observed at the transition to the SDW ground state 12 K depends on the particular mode propagating in the crystal: Mode I shows a jump of the sound velocity at tsdw; for mode II the velocity increases with decreasing temperature as the square of the order parameter; a third type exhibits only a kink in the temperature dependence of the sound velocity at tsdw. We apply various models and discuss the coupling of the SDW to the lattice.
Physical Review Letters, 2001
We have studied acoustoelectric (AE) effect produced by surface acoustic waves (SAW) in a monolit... more We have studied acoustoelectric (AE) effect produced by surface acoustic waves (SAW) in a monolithic layered structure, composed of piezodielectric LiNbO 3 substrate and La 0.67 Ca 0.33 MnO 3 film. The experiments unexpectedly revealed in the longitudinal AE effect an anomalous contribution, invariant upon reversal of SAW propagation, which coexists with the ordinary (odd in wave vector) effect. The anomalous effect dominates near the metal-insulator transition, while the ordinary effect prevails at high and low temperatures. We show that the anomalous effect is caused by strong modulation of the film conductivity produced by the SAW elastic deformations. PACS numbers: 72.50.+b, 77.65.Dq, 75.30.Vn Typeset using REVT E X 1
Physical Review B, 2005
A magnetic Bragg reflection corresponding to the wave vector k 13 = ͑2 / a͒ ͓ 1 2 , 1 2 , 1 2 ͔ o... more A magnetic Bragg reflection corresponding to the wave vector k 13 = ͑2 / a͒ ͓ 1 2 , 1 2 , 1 2 ͔ of the antiferroquadrupolar ordering in CeB 6 is found without external magnetic field below the Néel temperature T N Ϸ 2.4 K. Its intensity is two orders of magnitude weaker than those due to the basic magnetic structure. The peak has a width of the other Bragg reflections below T N , but widens abruptly at T = T N with the simultaneous increase of intensity. The correlation length of the antiferromagnetic fluctuations just above T N is of the order of 10 Å. The peak intensity decreases to zero at T Ϸ 7 K with no visible anomaly at the antiferroquadrupolarordering temperature T Q Ϸ 3.3 K. The features of the magnetic peak ͑ 1 2 , 1 2 , 1 2 ͒ are typical for the itinerant magnetism. Interacting multipole moments may also give a contribution to this peak.
Physical Review Letters, 2012
We reveal the nature of the avalanche collapse of the giant viable component in multiplex network... more We reveal the nature of the avalanche collapse of the giant viable component in multiplex networks under perturbations such as random damage. Specifically, we identify latent critical clusters associated with the avalanches of random damage. Divergence of their mean size signals the approach to the hybrid phase transition from one side, while there are no critical precursors on the other side. We find that this discontinuous transition occurs in scale-free multiplex networks whenever the mean degree of at least one of the interdependent networks does not diverge.
Handbook of Optimization in Complex Networks, 2012
Many real-world complex systems are represented not by single networks but rather by sets of inte... more Many real-world complex systems are represented not by single networks but rather by sets of interdependent networks. In these specific networks, vertices in each network mutually depend on vertices in other networks. In the simplest representative case, interdependent networks are equivalent to the so-called multiplex networks containing vertices of one sort but several kinds of edges. Connectivity properties of these networks and their robustness against damage differ sharply from ordinary networks. Connected components in ordinary networks are naturally generalized to viable clusters in multiplex networks whose vertices are connected by paths passing over each individual sort of their edges. We examine the robustness of the giant viable cluster to random damage. We show that random damage to these systems can lead to the avalanche collapse of the viable cluster, and that this collapse is a hybrid phase transition combining a discontinuity and the critical singularity. For this transition we identify latent critical clusters associated with the avalanches triggered by a removal of single vertices. Divergence of their mean size signals the approach to the hybrid phase transition from one side, while there are no critical precursors on the other side. We find that this discontinuous transition occurs in scale-free multiplex networks whenever the mean degree of at least one of the interdependent networks does not diverge.
Lecture Notes in Physics, 2004
We review a general approach that describes the spectra of eigenvalues for random graphs with a l... more We review a general approach that describes the spectra of eigenvalues for random graphs with a local tree-like structure. The exact equations to the spectra of networks with a local tree-like structure, are presented. The tail of the density of eigenvalues r</font >( l</font >)\rho \left( \lambda \right) at large | l</font >|\left| \lambda \right| is related to the behavior of the vertex degree distribution for large value of degree. In particular, as P( k) ~ </font >k-</font >g</font > P\left( k\right) \sim k^{-\gamma }, r</font >( l</font >) ~ </font >| l</font >| 1-</font >2g</font >\rho \left( \lambda \right) \sim \left| \lambda \right| ^{1-2\gamma }. Under an effective medium approximation we propose a simple approximation, calculate spectra of various graphs analytically. We also analyse the spectra of various complex networks and discuss the role of vertices of low degree. We show that spectra of locally tree-like random graphs gives a good description of the spectral properties of real-life networks like the Internet.
Physical Review E, 2005
We study pair correlations in cooperative systems placed on complex networks. We show that usuall... more We study pair correlations in cooperative systems placed on complex networks. We show that usually in these systems, the correlations between two interacting objects (e.g., spins), separated by a distance ℓ, decay, on average, faster than 1/(ℓz ℓ). Here z ℓ is the mean number of the ℓth nearest neighbors of a vertex in a network. This behavior, in particular, leads to a dramatic weakening of correlations between second and more distant neighbors on networks with fat-tailed degree distributions, which have a divergent number z2 in the infinite network limit. In this case, only the pair correlations between the nearest neighbors are observable. We obtain the pair correlation function of the Ising model on a complex network and also derive our results in the framework of a phenomenological approach.
Physical Review E, 2011
We introduce the heterogeneous-k-core, which generalizes the k-core, and contrast it with bootstr... more We introduce the heterogeneous-k-core, which generalizes the k-core, and contrast it with bootstrap percolation. Vertices have a threshold ki which may be different at each vertex. If a vertex has less than ki neighbors it is pruned from the network. The heterogeneous-k-core is the sub-graph remaining after no further vertices can be pruned. If the thresholds ki are 1 with probability f or k ≥ 3 with probability (1 − f), the process forms one branch of an activation-pruning process which demonstrates hysteresis. The other branch is formed by ordinary bootstrap percolation. We show that there are two types of transitions in this heterogeneous-k-core process: the giant heterogeneousk-core may appear with a continuous transition and there may be a second, discontinuous, hybrid transition. We compare critical phenomena, critical clusters and avalanches at the heterogeneous-kcore and bootstrap percolation transitions. We also show that network structure has a crucial effect on these processes, with the giant heterogeneous-k-core appearing immediately at a finite value for any f > 0 when the degree distribution tends to a power law P (q) ∼ q −γ with γ < 3.
Physica C: Superconductivity, 2003
Recently an anomalous acoustoelectrical (AE) effect produced by surface acoustic waves (SAW) in t... more Recently an anomalous acoustoelectrical (AE) effect produced by surface acoustic waves (SAW) in thin La 0:67 Ca 0:33 MnO 3 films deposited on a piezoelectric LiNbO 3 substrate was discovered [Phys. Rev. Lett. 87 (2001) 146602]. The SAW, launched along the distinct crystallographic axis (þz) of the structure, induces a dc current I AE in the film, which in the ordinary AE effect would be odd with respect to the SAW wave vector q. However, in the investigated case I AE contains, along with the ordinary odd component, an anomalous one, which is even in q. The anomalous effect dominates near the metal-insulator transition, while the ordinary effect prevails at high and low temperatures. The anomalous effect appears to depend on strong modulation of the film conductivity resulting from the elastic deformations carried by the SAW. We have investigated the influence of an in-plane magnetic field H on the magnitude of I AE , and found an increase of about 50% when H was parallel to q. The increase was limited to the anomalous component of I AE. We speculate that this may be caused by magnetic field induced changes in the conductivity dependence on pressure. The ordinary AE current was left essentially unchanged. Apparently the boost given to this component by the increase of conductivity in a magnetic field is compensated by the corresponding SAW attenuation decrease. We have also conducted I AE measurements with the SAW split into two components of equal amplitude, propagating in the film in opposite directions. As a result, we have obtained cancellation of the ordinary I AE component and augmentation of the anomalous one, i.e. we have confirmed our understanding of the AE effects.
Nature, 2002
Ferroelectromagnets are an interesting group of compounds that complement purely (anti-)ferroelec... more Ferroelectromagnets are an interesting group of compounds that complement purely (anti-)ferroelectric or (anti-)ferromagnetic materials--they display simultaneous electric and magnetic order. With this coexistence they supplement materials in which magnetization can be induced by an electric field and electrical polarization by a magnetic field, a property which is termed the magnetoelectric effect. Aside from its fundamental importance, the mutual control of electric and magnetic properties is of significant interest for applications in magnetic storage media and 'spintronics'. The coupled electric and magnetic ordering in ferroelectromagnets is accompanied by the formation of domains and domain walls. However, such a cross-correlation between magnetic and electric domains has so far not been observed. Here we report spatial maps of coupled antiferromagnetic and ferroelectric domains in YMnO3, obtained by imaging with optical second harmonic generation. The coupling originates from an interaction between magnetic and electric domain walls, which leads to a configuration that is dominated by the ferroelectromagnetic product of the order parameters.
Journal of Magnetism and Magnetic Materials, 2002
ABSTRACT We report on acoustic and acoustoelectric (AE) studies of La0.67Ca0.33MnO3 (LCMO) films ... more ABSTRACT We report on acoustic and acoustoelectric (AE) studies of La0.67Ca0.33MnO3 (LCMO) films deposited on a LiNbO3 substrate. Surface acoustic wave (SAW) attenuation in the LCMO films has been measured at different sound frequencies in the wide temperature range. Our measurements confirm the hole-like conductivity in La0.67Ca0.33MnO3 films and reveal an anomalous (even in the SAW wave vector) contribution to the AE effect, which coexists with the ordinary (odd) effect. The anomalous AE effect is shown to be due to a strong modulation of the film conductivity produced by elastic deformations carried by the SAW.
Journal of Magnetism and Magnetic Materials, 2005
A variety of bulk as well as local magnetoelectric effects are observed in RMnO 3 compounds with ... more A variety of bulk as well as local magnetoelectric effects are observed in RMnO 3 compounds with R ¼ Sc; Y; In; Ho; Er; Tm; Yb; Lu due to the coexistence of ferroelectric and multiple magnetic ordering. On the one hand, 'gigantic' magnetoelectric bulk effects, where magnetic phase control is exerted by applied electric or magnetic fields, are revealed. On the other hand, interaction of domain walls leads to a coupling of ferroelectric and antiferromagnetic domains, and a contribution to the linear magnetoelectric effect that is induced in the antiferromagnetic domain walls is identified. The effects are observed by linear and nonlinear magnetooptical techniques and explained microscopically by the interplay of magnetic exchange, wall magnetization, and ferroelectric distortion.
Physical Review Letters, 2003
The structure of antiferromagnetic (AFM) domain walls and their interaction with lattice strain a... more The structure of antiferromagnetic (AFM) domain walls and their interaction with lattice strain are derived taking the multiple-order-parameter compound YMnO 3 as a model example. Contrary to the conviction that AFM domain walls are energetically unfavorable, their interaction with lattice strain lowers the total energy of the system and leads to a piezomagnetic clamping of the electric and magnetic order parameters in good agreement with the available experimental data.
Physical Review E, 2013
We study the role of scale-free structure and noise in collective dynamics of neuronal networks. ... more We study the role of scale-free structure and noise in collective dynamics of neuronal networks. For this purpose, we simulate and study analytically a cortical circuit model with stochastic neurons. We compare collective neuronal activity of networks with different topologies: classical random graphs and scale-free networks. We show that, in scale-free networks with divergent second moment of degree distribution, an influence of noise on neuronal activity is strongly enhanced in comparison with networks with a finite second moment. A very small noise level can stimulate spontaneous activity of a finite fraction of neurons and sustained network oscillations. We demonstrate tolerance of collective dynamics of the scale-free networks to random damage in a broad range of the number of randomly removed excitatory and inhibitory neurons. A random removal of neurons leads to gradual decrease of frequency of network oscillations similar to the slowing-down of the alpha rhythm in Alzheimer's disease. However, the networks are vulnerable to targeted attacks. A removal of a few excitatory or inhibitory hubs can impair sustained network oscillations.
Nature, 2002
Ferroelectromagnets are an interesting group of compounds that complement purely (anti-) ferroele... more Ferroelectromagnets are an interesting group of compounds that complement purely (anti-) ferroelectric or (anti-) ferromagnetic materials -they display simultaneous electric and magnetic order1-3.
Journal of Magnetism and Magnetic Materials, 2004
Journal of Magnetism and Magnetic Materials, 2005
Physical Review Letters, 2003
Physical Review B, 1999
ABSTRACT We have carried out ultrasonic investigations of (TMTSF)2PF6 in the spin-density-wave (S... more ABSTRACT We have carried out ultrasonic investigations of (TMTSF)2PF6 in the spin-density-wave (SDW) ground state. Some features for the elastic behavior of the SDW state are found. One of the acoustic modes shows a jump in the sound velocity at the critical temperature of the SDW transition (TSDW≈12K) and a relaxation peak in the attenuation of sound just below TSDW. From this peak we have estimated the characteristic relaxation time of the spin fluctuations along the b axis to be t0=2×10-11s. The sound velocity of another acoustic mode changes with temperature as the square of the order parameter. Besides a maximum just below TSDW the attenuation of this mode has an exponential behavior at low temperatures and yields an energy gap value equal to 2Δ(0)≈96K, which is much larger than the BCS value 2Δ(0)≈43K. In addition there is an acoustic mode which displays a slow decrease of the sound velocity in the SDW state. We have also studied the influence of a magnetic field applied along the c* axis on the acoustic properties of (TMTSF)2PF6: TSDW increases in the magnetic field. We discuss our experimental results in the frame of theoretical considerations which are based on the assumption that phonons influence the exchange interaction between the spins of the conducting electrons and thus couple to the SDW (magnetoelastic coupling). In our model, the temperature behavior of the sound velocity and the attenuation of sound is related to the real and imaginary parts of the dynamical spin susceptibility. This model allows us to classify the temperature behavior of different acoustic modes and to explain the observed anomalies in the sound velocity and the attenuation of sound in the SDW ground state.
Synthetic Metals, 1999
ABSTRACT Acoustic measurements of (TMTSF)2PF6 have been performed in the temperature range 2 K &a... more ABSTRACT Acoustic measurements of (TMTSF)2PF6 have been performed in the temperature range 2 K < T < 40 K. The behavior of the sound velocity and attenuation observed at the transition to the SDW ground state 12 K depends on the particular mode propagating in the crystal: Mode I shows a jump of the sound velocity at tsdw; for mode II the velocity increases with decreasing temperature as the square of the order parameter; a third type exhibits only a kink in the temperature dependence of the sound velocity at tsdw. We apply various models and discuss the coupling of the SDW to the lattice.
Physical Review Letters, 2001
We have studied acoustoelectric (AE) effect produced by surface acoustic waves (SAW) in a monolit... more We have studied acoustoelectric (AE) effect produced by surface acoustic waves (SAW) in a monolithic layered structure, composed of piezodielectric LiNbO 3 substrate and La 0.67 Ca 0.33 MnO 3 film. The experiments unexpectedly revealed in the longitudinal AE effect an anomalous contribution, invariant upon reversal of SAW propagation, which coexists with the ordinary (odd in wave vector) effect. The anomalous effect dominates near the metal-insulator transition, while the ordinary effect prevails at high and low temperatures. We show that the anomalous effect is caused by strong modulation of the film conductivity produced by the SAW elastic deformations. PACS numbers: 72.50.+b, 77.65.Dq, 75.30.Vn Typeset using REVT E X 1
Physical Review B, 2005
A magnetic Bragg reflection corresponding to the wave vector k 13 = ͑2 / a͒ ͓ 1 2 , 1 2 , 1 2 ͔ o... more A magnetic Bragg reflection corresponding to the wave vector k 13 = ͑2 / a͒ ͓ 1 2 , 1 2 , 1 2 ͔ of the antiferroquadrupolar ordering in CeB 6 is found without external magnetic field below the Néel temperature T N Ϸ 2.4 K. Its intensity is two orders of magnitude weaker than those due to the basic magnetic structure. The peak has a width of the other Bragg reflections below T N , but widens abruptly at T = T N with the simultaneous increase of intensity. The correlation length of the antiferromagnetic fluctuations just above T N is of the order of 10 Å. The peak intensity decreases to zero at T Ϸ 7 K with no visible anomaly at the antiferroquadrupolarordering temperature T Q Ϸ 3.3 K. The features of the magnetic peak ͑ 1 2 , 1 2 , 1 2 ͒ are typical for the itinerant magnetism. Interacting multipole moments may also give a contribution to this peak.