The discovery of superconductivity in the quantum critical Kondo-lattice system YbRh2Si2 at an extremely low temperature of 2 mK has inspired efforts to perform high-resolution electrical resistivity measurements down to this temperature range in highly conductive materials. Here we show that control over the sample geometry by microstructuring using focused-ion-beam techniques allows to reach ultra-low temperatures and increase signal-to-noise ratios (SNRs) tenfold, without adverse effects to sample quality. In five experiments we show four-terminal sensing resistance and magnetoresistance measurements which exhibit sharp phase transitions at the Néel temperature, and Shubnikov–de-Haas (SdH) oscillations between 13 T and 18 T where we identified a new SdH frequency of 0.39 kT. The increased SNR allowed resistance fluctuation (noise) spectroscopy that would not be possible for bulk crystals, and confirmed intrinsic 1/f-type fluctuations. Under controlled strain, two thin microstructured samples exhibited a large increase of TN from 67 mK up to 188 mK while still showing clear signatures of the phase transition and SdH oscillations. Superconducting quantum interference device-based thermal noise spectroscopy measurements in a nuclear demagnetization refrigerator down to 0.95 mK, show a sharp superconducting transition at Tc = 1.2 mK. These experiments demonstrate microstructuring as a powerful tool to investigate the resistance and the noise spectrum of highly conductive correlated metals over wide temperature ranges.
Microstructuring YbRh2Si2 for resistance and noise measurements down to ultra-low temperatures, New J. Phys. 24, 123033 (2022)
We present a combined study of thermal expansion and resistance fluctuation spectroscopy measurements exploring the static and dynamic aspects of the charge-glass formation in the quasi-two-dimensional organic conductors θ−(BEDT-TTF)2MM′(SCN)4 with M = Cs and M′ = Co,Zn. In these materials, the emergence of a novel charge-glass state so far has been interpreted in purely electronic terms by considering the strong frustration of the Coulomb interactions on a triangular lattice. Contrary to this view, we provide comprehensive evidence for the involvement of a structural glasslike transition at Tg∼90−100K. This glassy transition can be assigned to the freezing of structural conformations of the ethylene endgroups in the donor molecule with an activation energy of Ea≈0.32eV, and the concomitant slowing down of the charge-carrier dynamics is well described by a model of nonexponential kinetics. These findings disclose an important aspect of the phase diagram and calls for revisiting the present views of the glassy dynamics in the whole family of θ−(BEDT-TTF)2MM′(SCN)4. Our results suggest that the entanglement of slow structural and charge-cluster dynamics due to the intimate coupling of lattice and electronic degrees of freedom determine the charge-glass formation under geometric frustration.
Involvement of structural dynamics in charge-glass formation in strongly frustrated molecular metals, Phys. Rev. B 105, L041114 (2022)
Role of Oxygen Defects in Conductive-Filament Formation in Y2O3-Based Analog RRAM Devices as Revealed by Fluctuation Spectroscopy, Phys. Rev. Applied 14, 034029 (2020)
We investigate the low-frequency charge-carrier dynamics of a molecular dimer-Mott insulator β′−(BEDT−TTF)2ICl2, where the freezing of charge fluctuations on the dimers gives rise to electronic ferroelectricity. We show that conductance fluctuation (noise) spectroscopy allows one to probe changes in the dielectric properties at elevated temperatures, where samples are even still in the conductive regime. Our results explain the formation of electric polarization states leading to glassy and relaxor-type ferroelectric behavior that is frequently observed in these systems. The onset of distinct two-level fluctuations and changes of the underlying 1/f-type noise indicate the formation of nanoscale polar regions, the dynamics of which depends on the applied electric fields. Conductance noise spectroscopy therefore is a suitable tool for investigating the onset of electric-polarization dynamics in molecular and other, inorganic charge-driven ferroelectrics.
Formation of nanoscale polarized clusters as precursors of electronic ferroelectricity probed by conductance noise spectroscopy, Phys. Rev. B 102, 100103(R) (2020)
Inelastic neutron scattering measurements on the molecular dimer-Mott insulator κ−(BEDT−TTF)2Cu[N(CN)2]Cl reveal a phonon anomaly in a wide temperature range. Starting from Tins∼50–60 K where the charge gap opens, the low-lying optical phonon modes become overdamped upon cooling towards the antiferromagnetic ordering temperature TN=27 K, where also a ferroelectric ordering at TFE≈TN occurs. Conversely, the phonon damping becomes small again when spins and charges are ordered below TN, while no change of the lattice symmetry is observed across TN in neutron diffraction measurements. We assign the phonon anomalies to structural fluctuations coupled to charge and spin degrees of freedom in the BEDT-TTF molecules.
Lattice Dynamics Coupled to Charge and Spin Degrees of Freedom in the Molecular Dimer-Mott Insulator κ−(BEDT−TTF)2Cu[N(CN)2]Cl, Phys. Rev. Lett. 123, 027601 (2019)
Fluctuation spectroscopy measurements of quasi-two-dimensional organic charge-transfer salts (BEDT-TTF)2X are reviewed. In the past decade, the method has served as a new approach for studying the low-frequency dynamics of strongly correlated charge carriers in these materials. We review some basic aspects of electronic fluctuations in solids, and give an overview of selected problems where the analysis of 1/f-type fluctuations and the corresponding slow dynamics provide a better understanding of the underlying physics. These examples are related to (1) an inhomogeneous current distribution due to phase separation and/or a percolative transition; (2) slow dynamics due to a glassy freezing either of structural degrees of freedom coupling to the electronic properties or (3) of the electrons themselves, e.g., when residing on a highly-frustrated crystal lattice, where slow and heterogeneous dynamics are key experimental properties for the vitrification process of a supercooled charge-liquid. Another example is (4), the near divergence and critical slowing down of charge carrier fluctuations at the finite-temperature critical endpoint of the Mott metal-insulator transition. Here also indications for a glassy freezing and temporal and spatial correlated dynamics are found. Mapping out the region of ergodicity breaking and understanding the influence of disorder on the temporal and spatial correlated fluctuations will be an important realm of future studies, as well as the fluctuation properties deep in the Mott or charge-ordered insulating states providing a connection to relaxor or ordered ferroelectric states studied by dielectric spectroscopy.
Low-frequency dynamics of strongly correlated electrons in (BEDT-TTF)2X studied by fluctuation spectroscopy, Crystals 8, 166 (2018)
By the fabrication of periodically arranged nanomagnetic systems it is possible to engineer novel physical properties by realizing artificial lattice geometries that are not accessible via natural crystallization or chemical synthesis. This has been accomplished with great success in two dimensions in the fields of artificial spin ice and magnetic logic devices, to name just two. Although first proposals have been made to advance into three dimensions (3D), established nanofabrication pathways based on electron beam lithography have not been adapted to obtain free-form 3D nanostructures. Here we demonstrate the direct-write fabrication of freestanding ferromagnetic 3D nano-architectures. By employing micro-Hall sensing, we have determined the magnetic stray field generated by our free-form structures in an externally applied magnetic field and we have performed micromagnetic and macro-spin simulations to deduce the spatial magnetization profiles in the structures and analyze their switching behavior. Furthermore we show that the magnetic 3D elements can be combined with other 3D elements of different chemical composition and intrinsic material properties.
We combined scanning tunneling microscopy and locally resolved magnetic stray field measurements on the ferromagnetic semimetal EuB6, which exhibits a complex ferromagnetic order and a colossal magnetoresistance effect. In a zero magnetic field, scanning tunneling spectroscopy visualizes the existence of local inhomogeneities in the electronic density of states, which we interpret as the localization of charge carriers due to the formation of magnetic polarons. Micro-Hall magnetometry measurements of the total stray field emanating from the end of a rectangular-shaped platelike sample reveals evidence for magnetic clusters also in finite magnetic fields. In contrast, the signal detected below the faces of the magnetized sample measures a local stray field indicating the formation of pronounced magnetic inhomogeneities consistent with large clusters of percolated magnetic polarons.
Evidence for ferromagnetic clusters in the colossal-magnetoresistance material EuB6, Phys. Rev. Lett. 120, 257201 (2018)
We have studied the low-frequency dynamics of the charge carriers in different organic chargetransfer salts κ-(BEDT-TTF)2X with polymeric anions X by using resistance noise spectroscopy. Our aim is to investigate the structural, glass-like transition caused by the conformational degrees of freedom of the BEDT-TTF molecules’ terminal ethylene groups. Although of fundamental importance for studies of the electronic ground-state properties, the phenomenology of the glassy dynamics has been minimally investigated and its origin is not understood. Our systematic studies of fluctuation spectroscopy of various different compounds reveal a universal, pronounced maximum in the resistance noise power spectral density related to the glass transition. The energy scale of this process can be identified with the activation energy of the glass-like ethylene endgroup structural dynamics as determined from thermodynamic andNMRmeasurements. For the first time for this class of ‘plastic crystals’,we report a typical glassy property of the relaxation time, namely a Vogel–Fulcher–Tammann law, and are able to determine the degree of fragility of the glassy system. Supporting ab initio calculations provide an explanation for the origin and phenomenology of the glassy dynamics in different systems in terms of a simple two-level model, where the relevant energy scales are determined by the coupling of the ethylene endgroups to the anions.
Origin of the glass-like dynamics in molecular metals κ-(BED-TTF)2X: implications from fluctuation spectroscopy and ab initio calculations, New. J. Phys. 17, 083057 (2015) (open access)
Lorentzian spectra indicating two-level fluctuations in the vicinity of the glass-like structural ordering of the BEDT-TTF molecules' terminal ethylene groups.
We present measurements of the thermal dynamics of a Co-based single building block of an artificial square spin ice fabricated by focused electron-beam-induced deposition (FEBID). We employ micro-Hall magnetometry, an ultra-sensitive tool to study the stray field emanating from magnetic nanostructures, as a new technique to access the dynamical properties during the magnetization reversal of the spin-ice nanocluster. The obtained hysteresis loop exhibits distinct steps, displaying a reduction of their "coercive field" with increasing temperature. Therefore, thermally unstable states could be repetitively prepared by relatively simple temperature and field protocols allowing one to investigate the statistics of their switching behavior within experimentally accessible timescales. For a selected switching event, we find a strong reduction of the so-prepared states' "survival time" with increasing temperature and magnetic field. Besides the possibility to control the lifetime of selected switching events at will, we find evidence for a more complex behavior caused by the special spin ice arrangement of the macrospins, i.e., that the magnetic reversal statistically follows distinct “paths” most likely driven by thermal perturbation.
Nanocluster building blocks of artificial square spin ice: Stray-field studies of thermal dynamics, J. Appl. Phys. 117, 17C746 (2015)
Magnetic stray-field studies of a single Cobalt nanoelement as a component of the building blocks of artificial square spinice, J. Magn. Magn. Mat. (published online, 20 August 2015)
We compare the results of an individual building block (nanocluster) of interacting elements in artificial square spin ice with the switching of a single nanoisland. By analyzing the survival function of the repeatedly prepared state in a given temperature range, we find thermally activated switching dynamics. A detailed analysis of the hysteresis loop reveals a metastable microstate preceding the overall magnetization reversal of the single nanoelement, also found in micromagnetic simulations. Such internal degrees of freedom may need to be considered, when analyzing the thermal dynamics of larger spin ice configurations on different lattice types.
We report on the dramatic slowing down of the charge carrier dynamics in a quasi-two-dimensional organic conductor, which can be reversibly tuned through the Mott metal-insulator transition (MIT). At the finite-temperature critical end point, we observe a divergent increase of the resistance fluctuations accompanied by a drastic shift of spectral weight to low frequencies, demonstrating the critical slowing down of the order parameter (doublon density) fluctuations. The slow dynamics is accompanied by non-Gaussian fluctuations, indicative of correlated charge carrier dynamics. A possible explanation is a glassy freezing of the electronic system as a precursor of the Mott MIT.
Critical Slowing Down of the Charge Carrier Dynamics at the Mott Metal-Insulator Transition, Phys. Rev. Lett. 114, 216403 (2015)
So-called second noise spectra provide evidence for non-Gaussian fluctuations at the second-order critical endpoint of the first-order Mott metal-insulator transition. A possible explanation is glassy dynamics of the correlated electrons, where our results indicate a picture, where the system wanders collectively between metastable states related by a kinetic hierarchy.
The coupling of magnetic and electronic degrees of freedom to the crystal lattice in the ferromagnetic semimetal EuB6, which exhibits a complex ferromagnetic order and a colossal magnetoresistance effect, is studied by high-resolution thermal expansion and magnetostriction experiments. EuB6 may be viewed as a model system, where pure magnetism-tuned transport and the response of the crystal lattice can be studied in a comparatively simple environment, i.e., not influenced by strong crystal-electric field effects and Jahn-Teller distortions.We find a very large lattice response, quantified by (i) the magnetic Grüneisen parameter, (ii) the spontaneous strain when entering the ferromagnetic region, and (iii) the magnetostriction in the paramagnetic temperature regime. Our analysis reveals that a significant part of the lattice effects originates in the magnetically driven delocalization of charge carriers, consistent with the scenario of percolating magnetic polarons. A strong effect of the formation and dynamics of local magnetic clusters on the lattice parameters is suggested to be a general feature of colossal magnetoresistance materials.
Lattice Strain Accompanying the Colossal Magnetoresistance Effect in EuB6, Phys. Rev. Lett. 113, 067202 (2014)
Magnetically driven electronic phase separation in the semimetallic ferromagnet EuB6, Phys. Rev. B 86, 184425 (2012)
Combined measurements of fluctuation spectroscopy and weak nonlinear transport of the semimetallic ferromagnet EuB6 reveal unambiguous evidence for magnetically driven electronic phase separation consistent with the picture of percolation of magnetic polarons (MP), which form highly conducting magnetically ordered clusters in a paramagnetic and “poorly conducting” background. These different parts of the conducting network are probed separately by the noise spectroscopy/nonlinear transport and the conventional linear resistivity. We suggest a comprehensive and “universal” scenario for theMPpercolation, which occurs at a critical magnetization either induced by ferromagnetic order at zero field or externally appliedmagnetic fields in the paramagnetic region.
Multiferroics, showing simultaneous ordering of electrical and magnetic degrees of freedom, are remarkable materials as seen from both the academic and technological points of view. A prominent mechanism of multiferroicity is the spin-driven ferroelectricity, often found in frustrated antiferromagnets with helical spin order. There, as for conventional ferroelectrics, the electrical dipoles arise from an off-centre displacement of ions. However, recently a different mechanism, namely purely electronic ferroelectricity, where charge order breaks inversion symmetry, has attracted considerable interest. Here we provide evidence for ferroelectricity, accompanied by antiferromagnetic spin order, in a two-dimensional organic chargetransfer salt, thus representing a new class of multiferroics. We propose a charge-order-driven mechanism leading to electronic ferroelectricity in this material. Quite unexpectedly for electronic ferroelectrics, dipolar and spin order arise nearly simultaneously. This can be ascribed to the loss of spin frustration induced by the ferroelectric ordering. Hence, here the spin order is driven by the ferroelectricity, in marked contrast to the spin-driven ferroelectricity in helical magnets.
Multiferroicity in an organic charge-transfer salt that is suggestive of electric-dipoledriven magnetism, Nature Materials 11, 755 (2012)
Multiferroicity in the Mott insulating charge transfer salt κ-(BEDT-TTF)2Cu[N(CN)]2Cl, IEEE Trans. Magn. 50, 2700107 (2014)
The proposed multiferroic state of the organic charge-transfer salt k-(ET)2Cu[N(CN)2]Cl has been studied by dc conductivity, magnetic susceptibility and measurements of the dielectric constant in various differently prepared single crystals. In the majority of crystals, we confirm the existence of an order-disorder-type ferroelectric state, which coincides with
antiferromagnetic order. This phenomenology rules out scenarios which consider an inhomogeneous, short-range ordered ferroelectric state. Measurements of the dielectric constant and the magnetic susceptibility on the same crystals reveal that both transitions lie very close to each other or even collapse, indicating that both types of order are intimately coupled to each other. We address issues of the frequency dependence of the dielectric constant epsilon' and the dielectric loss epsilon'' and discuss sample-to-sample variations.
Prof. Dr. Jens Müller
Physik, Campus Riedberg
Raum _ _.326
60438 Frankfurt am Main
T +49 69 798 47274
F +49 69 798 47277
E Jens Müller
Physik, Campus Riedberg
Raum _ 0.321
60438 Frankfurt am Main
T +49 69 798 47242
F +49 69 798 47250
E Birgit Scherff