Browsing by Subject "Magnetism"

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Archaeomagnetism as a Geochronological Tool: Dating a Levantine Iron Age Conflagration
(2018-06) Stillinger, Michele D.
Meaningful interpretation of past human culture requires an accurate chronology that can be correlated with our modern calendar. The timing of seminal events during the Levantine Iron Age (~ 1200 to 600 BCE) is hotly debated because conventional dating methods are fraught with subjective interpretations and analytical inaccuracies. This research uses archaeomagnetism, a subfield of paleomagnetism, as an alternative geochronological dating technique. Utilizing traditional archaeomagnetic materials (e.g. pottery) and testing new geologically based materials (ancient bread ovens called tabuns), a new Near East Archaeomagnetic Dating Curve (NEAC) was constructed to date four occupational deposits and a large conflagration at the Iron Age village of Khirbet Summeily, Israel. The results indicate that the destruction was likely associated with the 925 BCE Egyptian military campaign of Sheshonq I (22nd Dynasty). In addition, a new high in geomagnetic field intensity was measured that confirms the recently identified 8th Century BCE intensity spike for the region. This research provides new data that will enable geophysical researchers to improve models of geomagnetic field variability and core processes for the first three millennia BCE.
Characterization of Spin Hall and Magneto-ionic Devices for Logic, Memory and Neuromorphic Applications
(2021-07) Sahu, Protyush
This thesis is divided into two parts. In the first part, my research is focused on spin-to-charge conversion in amorphous Gd (40%)-alloyed Bismuth Selenide (60%) (BSG) thin films. The spin Hall effect has emerged as a key proponent for spintronic devices. Such devices typically consist of a bilayer structure made from a spin Hall channel and a ferromagnet. Polycrystalline Bi2Se3 was discovered to have a large spin Hall effect. Spin Hall angle and spin Hall efficiency (SCE) have been key parameters for comparing spin Hall channels. However, the output voltage becomes an essential requirement for spin logic devices, which also depends on resistivity. Gd (40%) alloyed Bi2Se3, grown by sputtering, can fill these gaps for spin logic devices. The material is amorphous, ensuring good scalability. Resistivity as a function of temperature showed strong signs of 3D variable range hopping with a characteristic Mott temperature of 9.7 x 105 K and a room temperature resistivity of 60,000 µOhm.cm. With 5nm in-plane CoFeB, the spin pumping results show good symmetric peaks for different excitation frequencies. The spin to charge conversion efficiency (~ Jc/Js) increased with decreasing thickness of BSG. Second harmonic measurements were performed to characterize thermal effects. The spin-orbit torque was negligible due to the dominance of thermal effects and current shunting through the ferromagnet. Anomalous Nernst effect was found to be the dominant thermal effect. However, it couldn’t explain our spin pumping results due to the lack of BSG thickness dependence and the dominance of the first harmonic voltage. The spin pumping was concluded to originate from the inverse spin Hall effect in BSG layer. My research focuses on irreversible magneto-ionic devices for one-time-programmable memory and neuromorphic applications in the second part of the thesis. Magneto-ionic devices rely on ionic movement through a gate dielectric to manipulate the magnetic properties of a magnetic material. We use Co20Fe60B20 perpendicular magnetic anisotropy (PMA) thin films. CoFeB/MgO interfacial PMA is a consequence of orbital overlapping between Oxygen and transition metal atoms. We further engineer the device to enable field-free magnetization switching. We use an exchange bias field from an adjacent ferromagnet ([Co(0.3nm)/Pd(0.7nm)]3) separated by a non-magnetic layer (Ta), forming a [Co(0.3nm)/Pd(0.7nm)]3/Ta/CoFeB/MgO structure. Pd (111) was used as the seed layer for [Co(0.3nm)/Pd(0.7nm)]3. The final stack is given by: Substrate/Ta(5nm)/Pd(10nm)/[Co(0.3nm)/Pd(0.7nm)]3/Ta(1nm)/CoFeB(1.3nm)/MgO(2nm). XRD and HRTEM were used to characterize the film, which showed distinct layers with some interdiffusion and a polycrystalline Pd(111). This stack is then topped with an ionic gate made from 100nm sputtered SiOx. AHE minor curves showed that the two ferromagnets have weak antiferromagnetic coupling. Application of negative gate voltage decreases the coercivity of CoFeB from ~34 Oe to 16 Oe, signaling a lowered PMA. The exchange bias field magnitude increases from ~ 25 Oe to ~ 45 Oe, due to the decrease in thickness of CoFeB. Major loop measurements show no change in [Co(0.3nm)/Pd(0.7nm)]3 layer with gate voltage. Oxygen ions from SiOx move towards the interface of MgO/CoFeB interface under negative gate voltage. This creates an overoxidation of the interface and destroys the interfacial PMA of CoFeB. This makes the CoFeB layer go from a bi-stable to a monostable state, resulting in a pathway for a field-free magnetization switch.
Complexity at cobaltite interfaces: the interplay between strain, stoichiometry, magnetism and transport
(2014-12) Bose, Shameek
Thin films and heterostructures of the perovskite cobaltites are of great interest, not only from the point of view of fundamental physics and materials science, but also for technological applications such as solid oxide fuel cells and gas membranes. Their properties are, however, severely deteriorated from the bulk, being dominated by the presence of interfacial "dead layers". Working with the prototypical SrTiO3 (001)/La1-xSrxCoO3 (LSCO) system, our group recently discovered that this degradation in the magnetism and electronic transport at the interface is caused by nanoscopic magneto-electronic phase separation. This was shown to occur primarily due to accumulation of oxygen vacancies near the interface, driven by the interplay between the strain state and the ordering of oxygen vacancies. In the present work we show how this understanding allows for engineering of the interfacial magnetic and electronic transport properties via manipulation of this oxygen vacancy superstructure. We first demonstrate a synthesis technique that utilizes a unique high pressure oxygen plasma to sputter LSCO thin films over a wide doping range 0.05  x  0.80. Then, using reciprocal space mapping and transmission electron microscopy, we demonstrate the ability to control, via the vacancy ordering, the critical strain relaxation thickness by changing the sign of the strain (from tensile on SrTiO3 to compressive on LaAlO3) and crystallographic orientation ((001) vs. (110)). We then provide cross sectional electron energy loss spectroscopy data to show that this strain and orientation control preserves both oxygen and hole carrier concentration at the LaAlO3(001)/LSCO and SrTiO3(110)/LSCO interfaces, strikingly different to the severely depleted SrTiO3(001)/LSCO interface. SQUID magnetometry, polarized neutron reflectometry (PNR) and magneto-transport confirm the concomitant mitigation of the interfacial degradation for LSCO films grown on LaAlO3(001) and SrTiO3(110), as compared to films grown on SrTiO3 (001). Finally, we use scanning tunneling microscopy to provide direct real space images of the magneto-electronic phase separation in ultrathin LSCO on SrTiO3(001). Our work thus demonstrates the ability to utilize oxygen vacancy ordering as a tunable control parameter to tailor interfacial electronic and magnetic properties, with profound implications for the myriad other systems that exhibit unique properties due to such ordering.
Design, synthesis, and characterization of transition metal compounds using binucleating and bifunctional ligands: strategies for the multi-electron reduction of small molecules
(2014-01) Zall, Christopher Michael
The work described in this thesis focuses on two strategies to promote multi-electron redox within simple inorganic systems. The first involves electronic coupling between two mid-to-late first-row transition metals in the form of strong metal-metal bonds. The second involves tethering a redox-active cofactor to a mononuclear transition metal site via a bifunctional ligand platform. In Chapter 1, the background and theory relevant to achieving multi-electron reactivity using bimetallic complexes are discussed, with a particular focus on the electronic coupling between first-row transition metals. In Chapter 2, the electronic structure reinvestigation of two "trigonal lantern" bimetallic complexes is discussed. These complexes, Fe2(DPhF)3 and Co2(DPhF)3, (DPhF = N,N'-diphenylformamidinate) contain remarkably short metal-metal distances of 2.23 Å and 2.38 Å, respectively, while also possessing large magnetic moments indicative of strong, ferromagnetic coupling between the two metal centers. The electronic structures of these molecules have been studied by a variety of physical and theoretical methods. The molecules have energetically well-isolated high-spin electronic configurations of S = 7/2 and S = 5/2, respectively, and fully delocalized M(1.5)M(1.5) oxidation states. The strong metal-metal bonding, electronic delocalization, and high-spin states are shown to be interrelated, resulting from the distribution of electrons in a molecular orbital manifold that has very small orbital energy differences, engendered by the weak-field ligands and trigonal coordination geometry. In Chapter 3, the synthesis and characterization of new bimetallic complexes a new, chelating tris(amidinato)amine are discussed. This ligand provides a similar ligand environment to the original "trigonal lanterns" but also contains a single axial donor that differentiates the two metal sites. The homobimetallic dicobalt complex of this ligand, Co2LPh, has been synthesized and possesses an even shorter Co-Co distance, at 2.29 Å, than Co2(DPhF)3. In addition, a heterobimetallic iron-cobalt complex, FeCoLPh, has also been prepared that contains the shortest known Fe-Co distance, at 2.18 Å. The positions of the iron and cobalt atoms in this complex were assigned by anomalous dispersion methods; these reveal that the compound is essentially a single species, rather than a mixture of heterobimetallic isomers, and that the cobalt selectively occupies the tetracoordinate "bottom" site, bound to the axial nitrogen donor while the iron occupies the tricoordinate "top" site. Both Co2LPh and FeCoLPh possess high-spin electronic configurations and strong metal-metal bonds. While the asymmetric ligand environment creates a distinct polarization of the molecular orbitals and oxidation states, the metal-metal bonding is largely unaffected and is qualitatively similar to that observed in Fe2(DPhF)3 and Co2(DPhF)3. In Chapter 4, the design and coordination chemistry of a bifunctional ligand system containing a reversible organic hydride donor group is presented. This ligand tethers a redox-active phenanthridinium group to a phosphine donor in order to facilitate bifunctional reactivity, in which the hydride donor and an appended metal center react cooperatively to activate and reduce substrates. Palladium dichloride complexes containing two such ligands have been prepared: these can be cleanly interconverted between hydride-"loaded" and -"unloaded" forms by reaction with hydride acceptors and donors. In addition, lower-coordinate palladium complexes have been studied that can react with dihydrogen (H2) and show intriguing exchange of the hydrides between positions at the metal and ligand.
Emergent 1/f noise in systems of oscillating nanomagnetic dots
(2016-08) Costanzi, Barry
The observation of noise signals with a $\frac{1}{f}$ power spectral density dependence on frequency \emph{f} is both ubiquitous in quantitative measurements across fields, and not entirely well understood. So-called ``$\frac{1}{f}$" spectra have been observed in systems spanning the realm of physics, and in other disciplines as well. Van der Ziel's model of $\frac{1}{f}$ noise as a composite of Lorentizian noise signals is the most widely accepted explanation for $\frac{1}{f}$, but experiments have for the most part only implicitly confirmed the result thus far. In this thesis, an explicit bottom-up approach to the Van der Ziel model is presented by combining random telegraph noise signals in square magnetic dots. Square dots made of the iron-nickel alloy Permalloy were fabricated to be 250 nm on a side and $\sim$ 10 nm thick. The configurational anisotropy of the dots is small enough to reduce energy barriers between adjacent magnetic states to approximately thermal energies through the application of an external field, causing two-state thermal hopping of the magnetization. This magnetization was measured through the anisotropic magnetoresistance of the dots. The random telegraph signals generate Lorentizan spectra when transformed to the frequency domain, and are shown to combine to form $\frac{1}{f}$ spectra when multiple dots are measured in series. The energy landscape of the dots is determined through easy-axis coercivity measurements, and the distribution of energy barriers predicts a range of applied fields where individual noise signals should combine to produce $\frac{1}{f}$ noise by the Van der Ziel model. Experiment shows good agreement with the predicted range of these ``noise fields" for two different series of samples with different coercivity distributions. Measurements of both individual dots and aggregate multi-dot signals show that the number of individual oscillating dots necessary to produce an aggregate $\frac{1}{f}$ signal is lower than might be expected, with $\frac{1}{f}$ observed in collections of fewer than ten oscillating dots, and in some cases as few as two. Additionally, while the statistics over multiple samples agree with the Van der Ziel model, individual collections of dots exhibiting $\frac{1}{f}$ noise can either vary signifcantly from the ideal Van der Ziel distribution, or defy the distribution description altogether when the number of dots becomes too few. This suggests that the Van der Ziel model is a sufficient but not necessary condition for observing $\frac{1}{f}$ noise in a collection of Lorentizan oscillators, and that the actual requirements to generate $\frac{1}{f}$ noise are much looser than Van der Ziel's. In systems with any type of distribution of Lorentizan signals, $\frac{1}{f}$ noise is likely due to combination of those signals. This result is relevant other systems exhibiting magnetic noise, as well as non-magnetic systems displaying both RTN and $\frac{1}{f}$ noise.
High Charge-to-Spin and Spin-to-Charge Conversion Enhanced by Quantum Confinement Effect in Sputtered Topological Insulator Thin Films
(2019-01) DC, Mahendra
The spin-orbit torque (SOT) arising from materials with large spin-orbit coupling promises a path for ultra-low power and fast magnetic-based storage and computational devices. The SOT switching of magnetization can be used in the SOT-memory and computational devices whereas the spin-to-charge conversion can be utilized for reading of magnetization state in computational devices. Recent reports on topological insulators show high SOT but the industry compatible growth process is still lacking. Furthermore, SOT switching of perpendicular magnetization from topological insulators is demonstrated but still with large current density and large external field. We investigated the SOT from magnetron-sputtered bismuth selenide thin films in BixSe(1-x)/Co20Fe60B20 heterostructures by using dc planar Hall and spin-torque ferromagnetic resonance (ST-FMR) methods. Remarkably, the spin torque efficiency ( ) was determined to be as large as 18.62 ± 0.13 and 8.67 ± 1.08, using the dc planar Hall and ST-FMR methods, respectively. Moreover, switching of perpendicular CoFeB multilayers using SOT from the BixSe(1-x) has been observed at room temperature (RT) with low critical magnetization switching current density ( ) 4.3 × 105 A/cm2. Quantum transport simulations using realistic sp3 tight binding model suggests that the high SOT in sputtered BixSe(1-x) is due to a quantum confinement effect, whose charge-to-spin conversion efficiency enhances with reduced size and dimensionality. The demonstrated , ease of growth of the films on a silicon substrate, and successful growth and switching of perpendicular CoFeB multilayers on BixSe(1-x) film provide an avenue for the use of bismuth selenide thin films as a spin-density generator in SOT-based memory and logic devices. In addition to charge-to-spin conversion, we also performed spin-to-charge conversion by sputtered bismuth selenide thin films. For the spin-to-charge conversion experiment, we prepared Sub/Si/SiO2/Bi43Se57/Co20Fe60B20 heterostructures with in-plane magnetization. High spin-to-charge conversion voltage signals have been observed at room temperature. The spin-pumping voltage decreases with an increase in the size of the grains. The figure-of-merit of spin-to-charge conversion inverse Edelstein effect length ( ) is estimated to be as large as 0.32 nm. The large is due to the spin-momentum locking and is further enhanced by quantum confinement in the nano sized grains of the sputtered bismuth selenide films. We also investigated the effect on spin-pumping voltage due to the insertion of layers MgO and Ag. The MgO insertion layer has almost completely suppressed the spin-pumping voltage whereas Ag insertion layer has enhanced the spin-pumping voltage as large as 40%. The suppression of spin-pumping voltage due to the insertion of insulating layer indicates that the thermal effects are negligible in the spin-pumping signal. The enhancement of spin-to-charge conversion voltage by insertion Ag layer is due to the Rashba-Edelstein effect. Moreover, the conducting ferromagnetic layer can influence both SOT and spin-to-charge conversion voltage. We investigated spin-to-charge conversion in sputtered Y3Fe5O12(YIG)/BS bi-layers at room temperature. The spin current is pumped to the BS layer by the precession of magnetization at ferromagnetic resonance in the YIG layer. is estimated to be as large as (0.11 ± 0.03) nm in YIG/BS (4 nm). Moreover, also shows a dependence on the bismuth selenide film thickness in YIG/BS structure, which is consistent with the spin-to-charge conversion in conducting ferromagnet and also in case of charge-to-spin conversion.
The Investigation Of New Magnetic Materials And Their Phenomena Using Ultrafast Fresnel Transmission Electron Microscopy
(2017-02) Schliep, Karl
State-of-the-art technology drives scientific progress, pushing the boundaries of our current understanding of fundamental processes and mechanisms. Our continual scientific advancement is hindered only by what we can observe and experimentally verify; thus, it is reasonable to assert that instrument development and improvement is the cornerstone for technological and intellectual growth. For example, the invention of transmission electron microscopy (TEM) allowed us to observe nanoscale phenomena for the first time in the 1930s and even now it is invaluable in the development of smaller, faster electronics. As we uncover more about the fundamentals of nanoscale phenomena, we have realized that images alone reveal only a snapshot of the story; to continue progressing we need a way to observe the entire scene unfold (e.g. how defects affect the flow of current across a transistor or how thermal energy propagates in nanoscale systems like graphene). Recently, by combining the spatial resolution of a TEM with the temporal resolution of ultrafast lasers, ultrafast electron microscopy  or microscope  (UEM) has allowed us to simultaneously observe transient nanoscale phenomena at ultrafast timescales. Ultrafast characterization techniques allow for the investigation of a new realm of previously unseen phenomenon inherent to the transient electronic, magnetic, and structural properties of materials. However, despite the progress made in ultrafast techniques, capturing the nanoscale spatial sub-ns temporal mechanisms and phenomenon at play in magnetic materials (especially during the operation of magnetic devices) has only recently become possible using UEM. With only a handful of instruments available, magnetic characterization using UEM is far from commonplace and any advances made are sparsely reported, and further, specific to the individual instrument. In this dissertation, I outline the development of novel magnetic materials and the establishment of a UEM lab at the University of Minnesota and how I explored the application of it toward the investigation of magnetic materials. In my discussion of UEM, I have made a concerted effort to highlight the unique challenges faced when getting a UEM lab running so that new researchers may circumvent these challenges. Of note in my graduate studies, I assisted in the development of three different magnetic material systems, strained Fe nanoparticles for permanent magnetic applications, FePd for applications in spintronic devices, and a rare-earth transition-metal (RE-TM) alloy that exhibits new magneto-optic phenomena. In studying the morphological and magnetic effects of lasers on these RE-TM alloys using the in situ laser irradiation capabilities of UEM along with standard TEM techniques and computational modeling, I uncovered a possible limitation in their utility for memory applications. Furthermore, with the aid of particle tracing software, I was able to optimize our UEM system for magnetic imaging and demonstrate the resolution of ultrafast demagnetization using UEM.
Magnetic and physical characteristics of magnetite associated with deformation and exsolution.
(2011-10) Till, Jessica Lynn
This thesis contains a collection of laboratory-based studies designed to characterize the magnetic properties and physical aspects of magnetite that result from deformation or high temperature growth. In Chapter 2, a detailed rock magnetic characterization of rocks containing nanoscale magnetite exsolved from volcanic glass identifies the location of domain-state thresholds through distinct transitions in remanence and susceptibility properties. This unique material is an excellent candidate for standard material to be used in studies of magnetite granulometry. In Chapter 3, theoretical timescales for the growth of sub-microscopic magnetite needles during exsolution from plagioclase are calculated using results of diffusion experiments. Measured diffusivities are modeled to calculate the amount of diffusion-limited growth possible under different conditions of nucleation temperature and cooling rate. In Chapters 4 and 5, the development and evolution of magnetic fabrics are investigated through deformation experiments on synthetic rock-analogues at high temperatures and ductile conditions. Stress-induced changes in rock magnetic properties after deformation are significant. Examination of deformation-induced remagnetization demonstrates that a primary remanence can survive conditions equivalent to moderate metamorphism in certain cases and that petrofabric can play an important role in determining the remanence stability. High-temperature deformation experiments result in a pattern of anisotropy development that indicates plastic deformation of magnetic grains, which is distinct from anisotropy development resulting from different magnetite strain responses. Experimental data are combined with theoretical magnetic anisotropy models and used to estimate effective magnetite strains and strain partitioning from magnetic fabric data in deformed samples. Finally, observations of strong shape-preferred orientation and deformation-induced microstructures in magnetite grains from high-temperature shear experiments indicate plastic deformation of magnetite. Microstructural observations place constraints on the rheological behavior of magnetite and the conditions in which dislocation creep is dominant. These observations prompt a re-examination of the previously established magnetite flow laws which are modified and used to construct new deformation mechanism maps.
Magnetic domain wall dynamics in patterned nanowires
(2015-08) Galkiewicz, Andrew
This thesis describes the dynamics of magnetic domain walls in two very different ferromagnetic systems. In one system, the magnetization prefers to lie in the plane of the film, which leads to relatively large and complex domain wall structures. In the other system, in which the magnetization is oriented out of the film plane, the domain walls are much smaller and simpler but are more susceptible to the influence of interface effects. In both cases, the dynamics of the domain walls are strongly influenced by the presence of defects, e.g. the inevitable edge and surface roughness of a patterned nanowire. In this dissertation, I explore the resonance dynamics of isolated and coupled transverse domain walls. I show that an intrinsic domain wall mode arises as a result of the pinning effects of the wire edge roughness, by comparing experimental results with micromagnetic simulations. Because of the strong pinning effects, the dynamics of coupled transverse domain walls are also influenced by the edge roughness, leading to the presence of two distinct modes. Using a simple onedimensional model, the domain wall separation dependence of the two resonant frequencies is explained. As edge roughness is unavoidable, I argue that stochastic pinning effects will be present in other DW resonance experiments. I also explore the propagation of a domain wall through a wire, driven under the influence of magnetic fields and electrical currents. The velocity of the domain wall is shown to follow a model where the domain wall moves via a succession of thermally-activated jumps between pinning sites in the wire. A current-to-field equivalence is established, and the nature of this equivalence is explored through the application of static magnetic fields in the plane of the film. These fields influence the internal structure of the domain wall and thus the torques generated by the current. From the symmetry of these torques, it is revealed that the application of a current leads to a spin-Hall effect in an adjacent non-magnetic layer in the film structure, which influences the domain wall dynamics. A nontrivial suppression of the current-to-field efficiency is observed under large in-plane fields, which is potentially linked to how the domain wall moves through a defect landscape.
Magnetic vortex dynamics: non-linear dynamics, pinning mechanisms, and dimensionality crossover.
(2012-01) Chen, Te-Yu
The dynamics of a magnetic vortex, which is the simplest realization of a domain structure, are influenced profoundly by non-linear effects at both large and small amplitudes. For example, a strongly driven magnetic vortex is unstable with respect to internal deformation, leading to reversal of its core magnetization. At small amplitudes, a second class of non-linear phenomena are associated with pinning of the vortex core. The pinning of magnetic vortices is closely related to the pinning of domain walls in ferromagnetic films. For both cases, however, the absence of an appropriate characterization tool has limited the ability to correlate the physical and magnetic microstructures of ferromagnetic films with specific pinning mechanisms. Given this range of phenomena, there is also an acute need for a global picture of vortex dynamics over a wide range of excitation amplitudes and frequencies. In this dissertation, I show a global phase diagram of vortex dynamics in permalloy (Ni80Fe20) disks by probing the response spectrum over four orders of magnitude in excitation power. A clear boundary separates pinned and unpinned dynamics in a phase space of amplitude and frequency. I also discuss a highly quantitative analysis of the pinning potential for defects, and how it can be used to trace the dynamics of a single vortex from deep in the pinning regime to the onset of core reversal. Regarding the pinning mechanism, I show that the pinning of a magnetic vortex is strongly correlated with surface roughness, and I make a quantitative comparison of the pinning energy and spatial range in films of various thickness. The results demonstrate that thickness fluctuations on the lateral length scale of the vortex core diameter, i.e., an effective roughness at a specific length scale, provide the dominant pinning mechanism. I argue that this mechanism will be important in virtually any soft ferromagnetic film. Finally, I show the dynamics of a magnetic vortex cross over from two-dimensional (2D) to three-dimensional (3D) with increasing disk thickness. A 2D mode of the vortex dynamics is the lowest frequency excitation below the crossover region, above which a 3D mode becomes the lowest frequency excitation.
Magnetism in correlated electron systems
(2019-08) Ye, Mengxing
This dissertation covers several aspects of magnetism in correlated electron systems. The rapid progress in understanding the origins and consequences of emergent quantum phenomena in correlated electron systems is pushed by the advances in theoretical developments, quantum material realizations and experiment probes. Magnetism has been found to be a driving force in many examples. We start with analysis of frustrated magnetic systems with localized spins. We first show the phase diagram of the triangular lattice Heisenberg $J_1$-$J_2$ model in a magnetic field, which exhibit a cascade of field induced magnetic phase transitions. We next critically examine the quantized thermal Hall measurement in Kitaev material and emphasize the importance the spin-lattice coupling in the observation of the quantization. We then study the spin-density-wave state in a compensated metal on a triangular lattice in the weak coupling limit, which develops the same ordering pattern as in the localized spin picture. While the system is not sensitive to the frustration as in a localized spin system, the magnetic field triggers a time-reversal-invariant bond order, unique in a compensated metal. Finally, we study the pseudogap physics, which describes the anomalies in the electronic properties of the system in transition between a Mott insulator with magnetic order and a normal metal by varying certain external parameter, such as temperature or the doping level away from half-filling. We analyze within the magnetic precursor scenario, and show that a coplanar magnetic order, which can be realized in the Hubbard model on a triangular lattice, introduces a knob that controls the strength of the pseudogap behavior. We find a transition between normal Fermi liquid like behavior and pseudogap behavior by varying the value of the knob.
Neutron Scattering, Muon Spin Rotation/Relaxation, and Charge Transport Study of the Electron-Doped Cuprate Superconductors
(2017-05) LI, Yangmu
Exploring and understanding the exotic properties, phases, phase transitions exhibited by quantum materials are central research thrusts in contemporary condensed matter physics and materials science. One class of quantum materials that has attracted much attention during the past three decades is the family of copper-oxide (cuprate) high-transition-temperature superconductors. This family not only manifests superconductivity, a technologically useful macroscopic quantum state, but offers great opportunities for us to understand and control quantum phase transitions in the presence of strong electron-electron correlations. Investigating the competing, coexisting, and intertwined orders exhibited by the cuprate materials challenges us to consider new theoretical descriptions. This Thesis focuses on a specific type of cuprate superconductor, namely the electron-doped cuprate materials. The phases exhibited by these materials (antiferromagnetism, superconductivity, and charge order) depend on the degree of chemical substitution and oxygen reduction. Because these chemical manipulations induce simultaneous modifications to multiple parameters (e.g., chemical potential, band structure, local disorder, etc.), the electron-doped cuprate materials exhibit a rich and complex phase diagram that remains to be fully understood. The results presented in this Thesis provide crucial links between the normal and superconducting states and between the electron- and hole-doped parts of the phase diagram. High-quality single crystals of the archetypal electron-doped cuprate superconductor Nd2-xCexCuO4+d (NCCO) are synthesized using the state-of-the-art traveling-solvent floating-zone technique, and characterized by various in-house techniques, including Laue X-ray diffraction, magnetization (using a superconducting quantum interference device), scanning electron microscopy, and energy dispersive X-ray spectroscopy. The magnetic properties (Neel temperature, staggered magnetization, instantaneous spin-spin correlation length, magnetic volume fraction, and spin fluctuation timescales) and the electronic properties (Fermi surface topology, electrical resistivity, Hall constant, magnetoresistivity, upper critical field, superconducting volume fraction, and superfluid density) are studied with neutron scattering, muon spin rotation/relaxation (MuSR), and high-magnetic-field transport measurements at national laboratories in the United States and Canada. Published data for NCCO and other electron-doped cuprates are reanalyzed and compared with the new results obtained for NCCO. Simulations are performed for the instantaneous spin-spin correlation length and magnetoresistivity. A revised phase diagram of the electron-doped cuprates is constructed in the multi-dimensional parameter space of temperature, chemical substitution, and oxygen reduction. Three distinct phases are observed as a function of chemical substitution and oxygen reduction: (1) a long-range antiferromagnetic phase, where the Fermi surface consists of small electron pockets; (2) a bulk superconducting phase, where the Fermi surface consists of small electron and hole pockets; (3) a phase at high doping levels with a large hole Fermi surface. A disorder-smeared, first-order phase transition with microscopic phase separation is identified between the long-range antiferromagnetic and bulk superconducting phases. Specifically, this phase transition is observed to be volume-wise, and distinct spin fluctuation timescales are found for each phase. The magnetoresistivity measurements presented in this Thesis together with previous charge transport studies show two-band (electron and hole) contributions to the normal-state transport properties in electron-doped cuprate samples with bulk superconductivity. In addition, the two-band features are observed in the characteristic properties of the superconductor, including the upper critical field and the superfluid density. Universal scaling is demonstrated between the superconducting transition temperature and the hole superfluid density for both electron- and hole-doped cuprates, which clearly points to hole-related superconductivity in the nominally electron-doped cuprates. This scaling extends the famous Uemura scaling established for the hole-doped cuprates. The analysis of the superfluid density of the electron-doped cuprates follows that of prior theoretical work. Furthermore, new and published data for the ab-plane resistivity, Hall coefficient, cotangent of the Hall angle, and c-axis resistivity for the electron- and hole-doped cuprates are analyzed. The ab-plane resistivity of the electron- and hole-doped cuprates and the c-axis resistivity of the electron-doped cuprates features an upturn at low temperature/doping and a quadratic temperature-dependent contribution. Universal scaling between coefficients that characterize the low-temperature upturn is obtained for both electron- and hole-doped cuprates, indicative of a single underlying origin of the resistivity upturns, regardless of the nominal dopant type. The ab-plane transport scattering rate exhibits a quadratic (Fermi-liquid) temperature dependence, and is nearly independent of doping, compound and carrier type (electrons versus holes).
The origin of magnetic noise in nanoscale square dots
(2014-05) Endean, Daniel E.
Magnetic fluctuations, also referred to as magnetic noise, in very small (sub-micron) magnetic systems are important both in studying the fundamental physics of statistical mechanics and in technology. Thermal fluctuations of the magnetization define the ultimate limit of magnetic storage densities and sensing technologies but may be useful in some biomedical applications. At high frequencies (>100 kHz), fluctuations of the magnetization about the internal field are the dominant form of magnetic noise. At lower frequencies, 1/f and random telegraph noise have been observed in many magnetic systems. Yet these noise sources are challenging to reproduce due to their origin in defects and, thus, identification of the physical mechanism which produces them is difficult. Further progress in studying magnetic noise requires a model system where the fluctuations are reproducible and the physical origin is known. In this thesis, random telegraph noise is identified in square magnetic dots and shown to originate from a configurational anisotropy associated with the square dot geometry. The square dots were fabricated from thin (10 nm) Permalloy films with side lengths ranging from 200 nm to 1000 nm, and the magnetization was measured via the anisotropic magnetoresistance. It is first shown, through measurements unaffected by the noise in these samples, that the square dot geometry exhibits a preference for the magnetization to align parallel to an edge of the square. A model of this four-fold configurational anisotropy explains the behavior of the magnetization and provides two methods to characterize the strength of the anisotropy.It is then shown that when a field is applied along the dot diagonal, the configurational anisotropy barrier in this direction is lowered, which allows thermal switching of the magnetization between low-energy magnetic states. The telegraph state lifetimes are quantified and shown to vary with applied field magnitude, field direction, and temperature as expected. The switching rate obeys an Arrhenius law and the energy barriers measured in the noise data agree well with those measurements independent from the noise. In addition, micromagnetic simulations of the Landau-Lifshitz-Gilbert equation reproduce the observed behavior and confirm the explanation of the magnetic noise in these samples.
Probing Spin Glass Energy Landscapes with 1/f Noise
(2021-01) Harrison, David
The spin-glass transition is a dynamical phase transition, similar in nature to that of structural glasses and other systems. Upon quenching from above the transition temperature Tg to a measurement temperature T < Tg, experiments and simulations have unveiled an underlying length scale, the spin-glass correlation length, that grows very slowly with time. The time-dependent growth correlation length is key to the observed dynamics and to the understanding of the underlying energy barrier distribution. Analysis of our measurements provides the first explicit determination of the evolution of the spin-glass energy barrier distribution as a function of film thickness and temperature. By fabricating samples of multiple thicknesses, and allowing the correlation length to grow to the sample thickness on experimental timescales, it becomes possible to extract information about the length dependence of the energy barriers. We have made measurements of the 1/f noise in the resistance of spin-glass films of five thicknesses. These results are consistent with the limited earlier thin film measurements, despite the use of a different cooling protocol. A recent analysis, based on simulations of mesoscale samples with a number of spins comparable to those under experimental study, provided an explanation for the barrier growth in the earlier measurements, but suggested that our cooling protocol would have produced very different dynamics, consistent with activation over a single, temperature-independent barrier distribution, which we do not observe. This suggests that either the growth of in-plane correlations are playing a role, or that the explanation for the barrier growth in the earlier measurements applies to our measurements in spite of our cooling protocol.
Protocol Dependence of Spatially Inhomogeneous Magnetic Systems
(2024-05) Freedberg, Jennifer
The work presented in this dissertation studies the effects of measurement protocol on magnetic systems. There are two broad classes of metallic systems which will be described -- ferromagnets and spin glasses. The research presented demonstrates a clear protocol dependence for both for nonequilibrium dynamical magnetic materials such as spin glass and metallic ferromagnetic systems. Thus, for experimental reproducibility, it is necessary for one to specify the protocol used to prepare and take measurements. In a single crystal of CuMn 7.92 at.%, the out-of-equilibrium dynamics of aging, rejuvenation, and memory are explored. By using a double-waiting time protocol and quenching to the measuring temperatures, the underlying dynamics of the memory effect are able to be observed with no finite cooling rate effects. After quantifying the memory loss seen in glassy systems, previously proposed explanations were experimentally tested and a quantitative model developed. We find that coincident growth of spin glass correlations reduces the amount of memory retained, and that there is an additional length scale present whose ratio with size of the original correlated regions controls the severity of the memory loss. The effects of a finite cooling rate in spin glasses are then investigated as the temperature is swept continuously. We quantitatively find competing effects of aging and rejuvenation. This implies that the growth rates of glassy order between protocols utilizing quenches cannot naively be compared to protocols which use a finite rate of cooling. Additionally, we determine that the slower growth observed in the finite cooling rate protocols is due to rejuvenation, rather than cumulative aging. In four metallic ferromagnets, four paths to a net-zero magnetzation state are explored. This was done by demagnetizing samples using four different methods and then conducting the same measurements afterwards. The results indicated that the path to zero magnetization changes the behavior of the system, and thus the preparation of the initial state affected subsequent measurements.
Quantification of magnetic components in sediments with applications in paleoenvironmental studies.
(2011-12) Lascu, Ioan
The present dissertation is a collection of papers investigating the magnetic properties of sediments. The main aim of the work presented here is to study the magnetic characteristics of sedimentary deposits by using a methodology that efficiently quantifies the contributions of various ferrimagnetic components in sediments, and to exemplify how this model can be used to make inferences about past climatic and environmental variability. Magnetic minerals in sediments have long been used as indicators of variability in the factors controlling sediment deposition, and sediment-magnetic properties can be interpreted in terms of the processes controlling the fluxes of various magnetic components. Ferrimagnetic minerals, such as magnetite, are strong magnetically, and tend to dominate the signal from bulk measurements. Two sedimentary ferrimagnetic components that play a major role in shaping the magnetic record with time: a detrital component and a biogenic component. The detrital component of magnetic assemblages probably accounts for the greater proportion of the magnetic signal in many records, and therefore has been the focus of most environmental magnetism studies. The processes that control detrital records are mostly tied to local hydrology, climate, and vegetation cover. However, there is strong evidence that many magnetic assemblages are dominated by autochthonous magnetic particles, which in most cases are produced as a result of direct biologic control. Knowing the contribution of each of these components to the total mass of ferrimagnetic material becomes important when making inferences about past climatic or environmental conditions. The theoretical mixing model devised here using the characteristics of detrital and biogenic end members was tested on lake sediments from Minnesota. The analysis incorporates both spatial and temporal effects on magnetic record. We have investigated the history of sediment flux to Deming Lake, Minnesota, for the past 1000 years. Our results reveal several episodes of reduced precipitation, during which less sediment is mobilized from the catchment by overland flow and runoff. The most prominent episode occurred at the end of the Little Ice Age, indicating that this time period was not only cold but might have been drier than previously thought. The spatial control on sediment-magnetic properties was established via a survey of the magnetic properties of surface sediments from several Minnesota lakes. The magnetic properties are controlled by the competing fluxes of detrital and biogenic particles, according to location in the basin, while the position of the oxic-anoxic interface controls whether biogenic magnetite is formed in the sediment or in the water column, with implications in the preservation of intact versus collapsed bacterial chains. The thesis concludes with an incursion into the magnetic properties of chemical sediments from caves, or speleothems. The magnetic recordings preserved in calcite speleothems hold enormous potential for paleomagnetic and paleoenvironmental reconstructions. Speleothems lock in magnetization instantly, are not affected by post-depositional effects, and can be dated with high precision. The natural remanence in speleothems is carried mainly by magnetite, and the main remanence acquisition mechanism is depositional, through physical alignment of detrital magnetic grains parallel to the Earth's magnetic field. Future speleothem magnetism studies should benefit from increasingly sensitive magnetometers, operating at high spatial resolution, that are able to resolve short-term geomagnetic variability, and characterize events such as geomagnetic excursions at an unprecedented scale.
Saturation magnetization of iron sixteen nitrogen two, a 40- year mystery
(2012-03) Ji, Nian
While the material α”-Fe16N2 and its interesting magnetic behavior were discovered decades ago, there is still no unified answer to the question on whether this phase has a giant saturation magnetization (Ms). There are three important “missing pieces” that emerge upon examination of the magnetization and discussing the magnetism of this system 1) There is lack of direct measure of the saturation magnetization on Fe16N2. Conventional magnetometer-based (VSM or SQUID) methods can only measure the total magnetic moment of the samples. The evaluation of the Ms value involves the challenging estimation of the thin film sample volume and the subtle assessment of magnetic contributions from underlayers, substrates or possible impurity phases, resulting in unpredictable errors. 2) There is no convincing theory/model to rationalize the existence of giant Ms. The conventional band theory based first-principles calculations only predicts an Ms value similar to that of pure Fe. 3) There is lack of experiments to explore the underlying physics of the magnetism in Fe16N2 from an electronic state viewpoint l. The previous investigations only focus on the saturation magnetization measurement. Fundamental physics experiments using advanced tools such as polarized neutron and synchrotron x-rays were seldom reported, which may provide unique and independent information on understanding the magnetism in this material system. On the purpose of addressing these three issues mentioned above. We first picked up a unique facing-target sputtering approach to synthesize Fe16N2 epitaxial thin films. A detailed structure and chemical analysis confirmed the crystallinity and epitaxial quality of fabricated Fe16N2 films. In terms of magnetic characterization, in addition to systematically study the saturation magnetization of the prepared films using a vibrating sample magnetometer (VSM) based method., for the first time,we have discovered the partial localization behavior of 3d electrons in Fe16N2 thin film samples by using polarized synchrotron x-rays. Furthermore, we have used polarized neutron reflectometry (PNR) to directly measure the saturation magnetization in absolute unit, which confirms the presence of giant saturation magnetization. The observed saturation magnetization of Fe16N2 phase is up to 2500 emu/cm3, which is significantly larger than that of the currently known limit (Fe65Co35 with saturation magnetization of 1900 emu/cm3) To understand the origin of the giant magnetization, we proposed a “cluster + atom” model, which pointeded out a possible scenario to develop this unusual magnetism in this Fe-N system. Synchrotron x-ray experiments also provided supporting evidences of the charge transfer from the itinerant iron atom to the Fe6N cluster, which is consistent with the proposed model. We further discussed the perpendicular anisotropy and the relatively large spin polarization ratio of these Fe16N2 films, which will be very useful for future magnetoresistive devices with perpendicular anisotropy and low damping constant.
Time- and phase-resolved spectroscopy of three-magnon scattering
(2023-06) Hamill, Alex
In ferromagnets, scattering processes between magnon modes have been an active platform for the investigation of nonlinear wave interactions and chaotic dynamics for over six decades. Despite this rich history, questions remain regarding the nature of these interactions. In this regard, three-magnon scattering of the ferromagnetic resonance (FMR) mode is of particular appeal: the threshold FMR magnon population at which scattering occurs is distinctly low, enabling its investigation over a wide range of excitation powers. This particular scattering process requires the availability of magnon modes at half of the frequency of the FMR mode. This requirement is readily fulfilled in magnetic films of micrometer thickness, as the associated dipolar interactions lead to a dip in their magnon dispersion. Existing studies of three-magnon scattering have largely focused on its influence on the magnon populations and on the steady-state behavior. A comprehensive understanding of its transient behavior (i.e. how it evolves in time as it approaches steady state) is missing. Similarly, little is known about the influence of three-magnon scattering on the magnons' phases. This is largely the case for other magnon scattering processes as well. There is also a lack of a formal understanding of the relationship between the forward and backward three-magnon scattering processes, i.e. between splitting and confluence. These gaps are, in part, owing to the fact that there is a lack of a comprehensive time- and phase-resolved experimental investigation of the three-magnon scattering process. Magnon scattering processes are most commonly investigated through diode-based techniques, which are relatively insensitive and lack phase resolution. They are also most commonly investigated through Brillouin light scattering spectroscopy; this technique is typically employed for large excitation powers, and its phase-sensitive implementations have not been applied to three-magnon scattering. Motivated by the above, I have assembled a time- and phase-resolved homodyning spectrometer that is operable over six orders of magnitude in microwave power. This spectrometer demonstrates a time resolution of 2 ns, and its sensitivity enables measurement of the transient behavior down to an excitation power of 10 microwatts. Upon measuring the resonance peak of the FMR mode, I observed satellite peaks near that of the FMR resonance. Such satellite peaks are observed in the literature as well. I found that they originate from the excitation of magnon modes with finite in-plane wavevectors, due to the inhomogeneity of the microwave field throughout the sample. To address this inhomogeneity, I created a microstrip waveguide with a signal line width of approximately 3.4 mm, such that it is appreciably wider than the 2 mm-wide sample. This ensures a highly uniform microwave field and, therefore, the highly isolated excitation of the FMR mode. Isolating the excitation of the FMR mode in this manner enables a clear interpretation of the measured transient behavior, and contributes toward the strong agreement observed between my experiment and my semianalytical model. With the above developments, I have investigated the transient behavior of the FMR mode during this scattering process over five orders of magnitude in power. In addition to my observing the expected transient behavior, in which the scattering monotonically suppresses the FMR magnon population to its threshold value, I find a second nonlinear in which the FMR magnon population exhibits transient oscillations about its threshold value. I find that both these oscillations and the timescale of the initial transient peak are highly dependent on the excitation power. At high powers, I find a third nonlinear regime in which the scattering generates 180-degree phase shifts of the FMR magnons. Moreover, I find that both these phase shifts and the transient oscillations reappear upon removing the microwave excitation (i.e. after turn-off). To supplement the experiment, and to understand my findings, I have derived a simplified semianalytical model of this scattering process based on the Landau-Lifshitz-Gilbert equation. Upon linearizing my model, I found that the oscillatory regime corresponds to a transition of the nonlinear regime's fixed point from a stable node to a stable spiral. I also extracted the predicted scaling of the oscillation frequency with the microwave field amplitude. Upon extracting the associated scaling of the experimental data, I found it to be in quantitative agreement with the predicted scaling over several orders of magnitude in power. To investigate the 180-degree phase shifts observed in the experiment, I generalized my model to allow for phase dynamics by omitting the standard assumption of harmonic time dependence. Numerically solving this generalized model, I found that it predicts these 180-degree phase shifts. In order to derive the equations of motion of the magnon populations, one begins with the generalized model and assumes harmonic time dependence. Remarkably, when accounting for the 180-degree phase shift in this harmonic approximation, I found that the phase shifts correspond to reversals in the scattering direction: in the magnon populations' equations of motion, the phase shift switches the sign of the scattering terms such that the scattering is now driving the FMR mode instead of damping it. These reversals explain the observed transient oscillations after turn-off: even without the excitation field, the FMR population may still oscillate via reversals between the forward and backward scattering process. These experimental and theoretical developments further the state of the art of the investigation of magnon scattering processes. The findings of my investigation provide a more comprehensive understanding of the transient behavior of this scattering process, and reveal the nontrivial interplay between three-magnon scattering and the magnons' phases.
Transport and Magnetism in Bulk and Thin Film Strontium Titanate
(2015-10) Ambwani, Palak
SrTiO3 is a wide band-gap perovskite oxide semiconductor that is widely investigated in the bulk form, due to its remarkable electronic properties. These properties arise from its quantum paraelectric nature which enables unique features, such as, a high-mobility low-density metallic state, quantum transport in an unusual limit, and the most dilute superconducting state thus reported. Recent advances in deposition of oxide thin films and heterostructures have further led to some remarkable observations, such as, the strain-enhancement of mobility in doped thin films of SrTiO3, and the presence of 2D electron gases at interfaces and in delta-doped layers. The presence of magnetic moments and their possible ordering, and the simultaneous observation of quantum oscillations and superconductivity, have been reported in these 2D electron gases. While magnetism has been observed in heterostructures of SrTiO3, there have been limited reports on magnetism in bulk SrTiO3. The first part of this thesis (Chapter 3) discusses how circularly polarized light can induce an extremely long-lived magnetic moment in slightly oxygen-deficient but otherwise nominally pure SrTiO3-δ bulk crystals. These magnetic signals, which are induced at zero applied magnetic field and at low temperatures below ~ 18 K, can be controlled in both magnitude and sign by means of the circular polarization and wavelength of sub-bandgap illumination (400-500 nm), and point to the existence of optically polarizable "V" _"O" -related complexes in the forbidden gap of SrTiO3-δ, rather than collective or long-range magnetic order. The methods used to detect optically induced magnetization are also discussed (Appendix A). The phenomenal progress reported in thin films and heterostructures of SrTiO3 has been possible only by precise control of stoichiometry and defect density in SrTiO3 using techniques such as oxide/LASER MBE or high-temperature PLD. The next part of the thesis (Chapter 4) demonstrates that high pressure oxygen RF sputtering from a ceramic target is similarly capable of growth of high-quality, precisely stoichiometric thin films of SrTiO3. By employing homoepitaxy on SrTiO3(001) substrates, it is shown that optimization of deposition temperature (above 750 C), oxygen pressure (above 2.5 mBar) and deposition rate (below 1.5 Å/min) leads to films that are indistinguishable from the substrate via grazing incidence and wide-angle X-ray scattering. The importance of pre-annealing of substrates in oxygen above 900 C and polishing the target prior to deposition, to obtain bulk-like lattice parameters and eliminate interfacial scattering contrast, is reiterated. Detailed transport measurements were also performed on reduced films grown on LaAlO3(001) and LSAT(001) substrates. The films were found to be semiconducting with mobilities at least an order lower than bulk. Detection and quantification of trace impurities was carried out using PIXE, and the possible causes of low mobility and semiconducting transport characteristics are discussed. Despite the rapid recent progress in thin film deposition techniques, controlled dopant incorporation and attainment of high mobility in thin films of SrTiO3 remain problematic. The last part of the thesis (Chapter 5) discusses the use of analytical scanning transmission electron microscopy to study the local atomic and electronic structure of Nb-doped SrTiO3 both in ideally substitutionally-doped bulk single crystals, and epitaxial thin films. The films are deposited under conditions that would yield highly stoichiometric undoped SrTiO3, as discussed in the previous chapter, but are nevertheless insulating. The Nb incorporation in such films was found to be highly inhomogeneous on nanoscopic length-scales, with large quantities of what is deduced to be interstitial Nb. Electron energy loss spectroscopy reveals changes in the electronic density of states in Nb-doped SrTiO3 films compared to undoped SrTiO3, but without a clear shift in the Fermi edge, that is seen in bulk single crystal Nb-doped SrTiO3. Analysis of atomic-resolution annular dark-field images leads to the conclusion that the interstitial Nb is in the Nb0 state, confirming that it is electrically inactive. It is argued that this approach will enable future work establishing the vitally needed relationships between synthesis/processing conditions and electronic properties of Nb-doped SrTiO3 thin films.
Two-level noise and stochastic resonance in individual permalloy nanoscale magnets
(2015-08) Youngblood, Bern
We present the results of a study on stochastic resonance in individual magnetic random telegraph oscillators. We have fabricated sub-micron magnetic samples, which have multiple stable magnetic states. We are able to observe random telegraph switching between magnetic states and tune the energetics by varying the temperature and applied external field. If a small AC field is applied to the system, it will modulate the energy well depth for the two states and the system shows stochastic resonance near the matching condition 2f[A] = ?[D], where ?[D] is the drive frequency and f is the characteristic frequency of magnetic transitions. We fit our measured data for the resonance amplitude and phase of the particle as a function of temperature to a linear-response model and obtain good agreement. At low temperatures we observe a peak in the phase lag of the returned signal, which is consistent with linear-response theories. At higher temperatures, our fitted model parameters suggest that the particle has an energy surface that is not sinusoidal. This contradicts our initial approximation for the energy surface, but it is consistent with a model for magnetic energy that takes into account the magnetization dynamics near the conditions for random telegraph switching. Our work is the first clear observation of stochastic resonance in a single superparamagnetic particle where the energetics are modulated by an applied field. In addition, our work is the first physical system where stochastic resonance has been characterized with sufficient detail to allow for comparison to linear-response models.

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