Transverse Voltage Research Articles

Spin Hall effect and irreversible thermodynamics: Center-to-edge transverse current-induced voltage

We examine the Dyakonov and Perel theory of the Spin Hall effect (SHE) from the viewpoint of irreversible thermodynamics, which is more constraining than the symmetry arguments of pure phenomenology. As thermodynamic driving forces we include the thermal gradient, the gradient of the electrochemical potential (rather than the potential gradient and density gradient separately), and the ``internal'' magnetic field that is thermodynamically conjugate to the magnetization. In turn, we obtain the form of bulk transport coefficients relating the fluxes to the thermodynamic forces. Relative to Dyakonov and Perel, in addition to the new terms due to thermal gradients, the Onsager relations require three new (nonlinear) terms in the current density, and minor revisions in the current density and spin current density. For a longitudinal current along a strip, the center-to-edge transverse voltage difference, due both to the $\ensuremath{-}\ensuremath{\beta}\stackrel{P\vec}{P}\ifmmode\times\else\texttimes\fi{}\stackrel{P\vec}{E}$ term of of the number current density $\stackrel{P\vec}{q}$ and to one of the new current density terms, is calculated. An ac capacitative probe likely would not significantly disturb this effect. An appendix explicitly relates the anomalous Hall Effect to the term in the (vector) number flux that is Onsager related to the SHE term in the (tensor) spin flux.

Interplay of spin-orbit torque and thermoelectric effects in ferromagnet/normal-metal bilayers

We present harmonic transverse voltage measurements of current-induced thermoelectric and spin-orbit torque (SOT) effects in ferromagnet/normal metal bilayers, in which thermal gradients produced by Joule heating and SOT coexist and give rise to ac transverse signals with comparable symmetry and magnitude. Based on the symmetry and field-dependence of the transverse resistance, we develop a consistent method to separate thermoelectric and SOT measurements. By addressing first ferromagnet/light metal bilayers with negligible spin-orbit coupling, we show that in-plane current injection induces a vertical thermal gradient whose sign and magnitude are determined by the resistivity difference and stacking order of the magnetic and nonmagnetic layers. We then study ferromagnet/heavy metal bilayers with strong spin-orbit coupling, showing that second harmonic thermoelectric contributions to the transverse voltage may lead to a significant overestimation of the antidamping SOT. We find that thermoelectric effects are very strong in Ta(6nm)/Co(2.5nm) and negligible in Pt(6nm)/Co(2.5nm) bilayers. After including these effects in the analysis of the transverse voltage, we find that the antidamping SOTs in these bilayers, after normalization to the magnetization volume, are comparable to those found in thinner Co layers with perpendicular magnetization, whereas the field-like SOTs are about an order of magnitude smaller.

Heat-driven spin transport in a ferromagnetic metal

As a non-magnetic heavy metal is attached to a ferromagnet, a vertically flowing heat-driven spin current is converted to a transverse electric voltage, which is known as the longitudinal spin Seebeck effect (SSE). If the ferromagnet is a metal, this voltage is also accompanied by voltages from two other sources, i.e., the anomalous Nernst effect in both the ferromagnet and the proximity-induced ferromagnetic boundary layer. By properly identifying and carefully separating those different effects, we find that in this pure spin current circuit the additional spin current drawn by the heavy metal generates another significant voltage by the ferromagnetic metal itself which should be present in all relevant experiments.

Transverse Magnetoelectric Effect in Nickel Zinc Ferrite-Lead Zirconate Titanate Layered Composites

By using a elastic mechanics model the transverse magnetoelectric voltage coefficient of magnetostrictive-piezoelectric bilayer is derived according to the constitutive equations. The transverse magnetoelectric coupling of nickel zinc ferrite-lead zirconate titanate (Ni0.8Zn0.2Fe2O4–Pb (Zr,Ti)O3, NZFO-PZT) layered composites were calculated by using the corresponding material parameters of individual phases. NZFO samples have been synthesized with sol–gel technique. Layered composites NZFO-PZT and NZFO-PZT-NZFO have been fabricated by binding discs of NZFO and commercially available PZT, and the transverse magnetoelectric effect have been investigated. The peak value of transverse magnetoelectric voltage coefficient for NZFO-PZT-NZFO trilayer reaches 252.4 mV/cmOe under a bias magnetic field of about 320 Oe, which is about three times as large as that of NZFO-PZT bilayer. The interface coupling parameter of trilayer is significantly higher than that of bilayer.

Factors influencing accuracy and reproducibility of body resistance measurements by foot-to-foot impedancemeters

The electronics of a BodySignal V2 (Tefal, France) foot-to-foot impedancemeter (FFI) was modified to display the foot-to-foot resistance instead of body fat. This device was connected to electrodes of different sizes mounted on a podoscope permitting photographs of subjects feet soles and electrodes in order to calculate the contact area between feet and electrodes. The foot-to-foot resistance was found to decrease when the contact area of feet with current and voltage electrodes increased. It was also sensitive to feet displacement and a backward move of 5 cm increased the mean resistance by 37 Ω. The resistance reproducibility was tested by asking the subject to repeat measurements 10-times by stepping up and down from the podoscope. The mean SD of these tests was 0.88% of mean resistance, but it fell to 0.47% when feet position was guided and to 0.29% with transverse voltage electrodes. For good reproducibility, it is important that voltage electrodes be small and that the scale design facilitates a correct position of heels on these electrodes.

AA-stacked bilayer graphene in an applied electric field: Tunable antiferromagnetism and coexisting exciton order parameter

We study the electronic properties of AA-stacked bilayer graphene in a transverse electric field. The strong on-site Coulomb repulsion stabilizes the antiferromagnetic order in such a system. The antiferromagnetic order is suppressed by the transverse bias voltage, at least partially. The inter-plane Coulomb repulsion and non-zero voltage stabilize an exciton order parameter. The exciton order parameter coexists with the antiferromagnetism and can be as large as several tens of meV for realistic values of the bias voltage and interaction constants. The application of a transverse bias voltage can be used to control the transport properties of the bilayer.

Thermoelectric effects and magnetic anisotropy ofGa1−xMnxAsthin films

The transverse voltages generated in a ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{As}$ ferromagnetic semiconductor in planar Hall effect and transverse spin Seebeck effect configurations are systematically analyzed. The observed field dependences consist of symmetric and asymmetric contributions. The former is attributed to the planar Nernst effect in the magnetic film in the presence of an in-plane temperature gradient, while the latter is caused by the anomalous Nernst effect due to spurious out-of-plane temperature gradients with a coefficient as high as 500 $\ensuremath{\mu}V/K$. We also report on the experimental observation of the planar Hall effect measured at different temperatures. Using a Stoner-Wohlfarth model for data analysis, the anisotropy constants ${K}_{u}$ and ${K}_{c}$ of superimposed uniaxial and cubic anisotropies in the magnetic film are determined. The temperature dependence of the ${K}_{u}/{K}_{c}$ ratio reveals a gradual substitution of the cubic anisotropy dominating at low temperatures with the uniaxial anisotropy as the temperature rises. This behavior is confirmed by the simultaneous domain observation using Kerr microscopy, demonstrating different field evolutions of the domain structure at different temperatures.

Transverse voltage and chiral glass transition in [formula omitted] thin films

We report on measurements of the voltage difference between non-aligned electrical contacts placed on opposite edges of several YBa2Cu3O6+d (YBCO) thin films prepared by a chemical method. The experiments were performed while the samples were traversed by a longitudinal electrical current. Experiments are focused on the region of the superconducting transition. In many cases these transverse voltage results do not reproduce the measurements carried out with the conventional geometry, where the voltage contacts are aligned along the current orientation. An excess transverse voltage was identified in a narrow temperature range encompassing the critical temperature. The sign and detailed shape of the excess transverse voltage vary from sample to sample. The application of a magnetic field perpendicular to the film surface suppresses the effect above a certain field threshold. The shape and magnitude of the excess transverse voltage peaks are also strongly modified or suppressed in samples submitted to implantation with oxygen ions or to a slight deoxygenation process. The simplest models considering the occurrence of a transverse current flow generated by film inhomogeneities cannot explain the totality of the obtained results. We thus suggest an interpretation of the excess transverse voltage effect based on the stabilization of a chiral-glass superconducting phase in the studied YBCO films. The occurrence of this state is related to the submicron granularity that characterizes the microstructure of these films.

Mesoscopic diffusion thermopower in two-dimensional electron gases

The diffusion of energy that is locally deposited into two-dimensional electron gases by Joule heating generates transverse voltages across devices with broken symmetry. For mesoscopic structures characterized by device dimensions comparable to the energy diffusion length, the resulting thermopower strongly depends on details of the potential profile defined by electric gates. We discuss these mesoscopic features within a diffusion thermopower model and propose schemes to measure the energy diffusion length and its dependence on gate voltage.

Light-induced transverse thermoelectric effect in miscut GaAs single crystals by far-infrared laser illumination

Light-induced transverse voltage (LITV) effect was investigated in miscut GaAs (0 0 1) single crystals by a 10.6 µm continuous wave CO2 laser with low power density. Open-circuit voltage signals were observed when the sample surface was illuminated by the 10.6 µm radiation and the magnitude of the voltage increased linearly with the miscut angle as well as the laser power on the samples. The voltage sensitivity can be improved after coating a layer of graphite light absorber on the surface of the sample. Moreover, open-circuit voltage signals were also detected when the surface of the samples was heated by a thermal heater. The results suggest that the LITV in miscut GaAs single crystals mainly originates from the transverse thermoelectric effect. This work demonstrates that the miscut GaAs single crystals have potential applications for detecting optical and thermal radiations.

Dependence of oxygen content on transverse thermoelectric effect in tilted Bi2Sr2Co2Oy thin films.

The transverse thermoelectric (TE) effect has been investigated in c axis tilted Bi2Sr2Co2Oy thin films with different oxygen content. The film samples were fabricated by a chemical solution deposition method annealed under different atmospheres of O2, air, and N2, respectively. Open-circuit transverse voltage signals were observed when the surface of the films was heated by a pulsed laser as well as a continuous thermal source. With the increase of oxygen content in the films, the amplitude of the observed voltage signals increased while the response time decreased. The experimental results can be explained by a mechanism involving the transverse TE effect as well as the transport theory of TE materials.

Magnetic scanning gate microscopy of graphene Hall devices (invited)

We have performed sensitivity mapping of graphene Hall devices with the width of 0.6–15 μm operating in the diffusive regime under non-uniform, local magnetic and electric fields induced by a scanning metallic magnetic probe. The transverse voltage was recorded, while tuning the magnitude and orientation of the bias current, the probe-sample distance, and orientation of the probe magnetization. A strong two-fold symmetry pattern has been observed, as a consequence of capacitive coupling between the probe and the sample. The effect is particularly pronounced in small devices (<1 μm), where the dominating electric field contribution significantly lowers the effective area of the magnetic sensor. We show that implementation of the Kelvin probe feedback loop in the standard scanning gate microscopy setup drastically reduces parasitic electric field effects and improves magnetic sensitivity.

Separation of longitudinal spin Seebeck effect from anomalous Nernst effect: Determination of origin of transverse thermoelectric voltage in metal/insulator junctions

The longitudinal spin Seebeck effect (LSSE) and the anomalous Nernst effect (ANE) are investigated in various metal/insulator junction systems and a clear separation of the LSSE from the ANE induced by static magnetic proximity is demonstrated. This separation is realized by comparing transverse thermoelectric voltage in in-plane magnetized (IM) and perpendicularly magnetized (PM) configurations, where the LSSE appears only in the IM configuration while the ANE appears both in the IM and PM configurations. We show that, in Pt/Y${}_{3}$Fe${}_{5}$O${}_{12}$ samples, the LSSE voltage in the IM configuration is three orders of magnitude greater than the proximity-ANE contamination estimated from the data in the PM configuration. This quantitative voltage comparison between the IM and PM configurations is corroborated by systematic voltage measurements in Ni${}_{81}$Fe${}_{19}$/Gd${}_{3}$Ga${}_{5}$O${}_{12}$, Pt/Gd${}_{3}$Ga${}_{5}$O${}_{12}$, Au/Y${}_{3}$Fe${}_{5}$O${}_{12}$, and Au/Gd${}_{3}$Ga${}_{5}$O${}_{12}$ samples and by our phenomenological model calculation. The LSSE measurements in high magnetic field regions further confirm that the observed voltage in the Pt/Y${}_{3}$Fe${}_{5}$O${}_{12}$ and Au/Y${}_{3}$Fe${}_{5}$O${}_{12}$ samples is of magnon origin. We apply this voltage comparison method also to a Ni${}_{81}$Fe${}_{19}$/Y${}_{3}$Fe${}_{5}$O${}_{12}$ sample and show that both the LSSE and ANE exist in this sample.

Hybrid spin noise spectroscopy and the spin Hall effect

Here we suggest a hybrid spin noise spectroscopy technique, which is sensitive to the spin Hall effect. Our main idea is to study correlations between transverse voltage fluctuations and spin polarization fluctuations, which appear as a result of spin-charge coupling that is fundamental for the spin Hall effect. It is shown that, while the standard spin-spin correlation function is not sensitive to the spin Hall effect, spin-transverse voltage and transverse voltage--transverse voltage correlation functions provide the missing sensitivity, which is linear and quadratic in the spin Hall coefficient, respectively. We anticipate that the proposed method could find applications in studies of spin-charge coupling in semiconductors and other materials.

Transverse Spin Seebeck Effect versus Anomalous and Planar Nernst Effects in Permalloy Thin Films

Transverse magnetothermoelectric effects are studied in Permalloy thin films grown on MgO and GaAs substrates and compared to those grown on suspended SiN(x) membranes. The transverse voltage along platinum strips patterned on top of the Permalloy films is measured versus the external magnetic field as a function of the angle and temperature gradients. After the identification of the contribution of the planar and anomalous Nernst effects, we find an upper limit for the transverse spin Seebeck effect, which is several orders of magnitude smaller than previously reported.

Features of the direct magnetoelectric effect in two-layer Tb0.12Dy0.2Fe0.68-PbZr0.53Ti0.47O3 composites

The transverse magnetoelectric effect in two-layer Tb0.12Dy0.2Fe0.68-PbZr0.53Ti0.47O3 composites with Tb0.12Dy0.2Fe0.68 ferromagnetic layers of various thicknesses are studied over the temperature range of 77 to 423 K at resonant frequencies of the bending oscillations. It is established that for all of the studied composites, the transverse magnetoelectric voltage constant passes at 253 K through a peak whose nature is associated with features of the magnetic constituent of the composites.

3-D Mapping of Sensitivity of Graphene Hall Devices to Local Magnetic and Electrical Fields

We report the response of sub-micron epitaxial graphene Hall devices to localized and inhomogeneous magnetic field produced by an MFM tip. We analyze the magneto-transport properties of epitaxial graphene and report the independent contribution of magnetic and electric fields in the measured transverse voltage maps with respect to the lateral and vertical position of the tip. A finite element model has also been developed to support the experimental results.

Large transverse thermoelectric voltage effect in incline-oriented SrTi1−xNbxO3 films with cubic structure

SrTi1−xNbxO3 films with cubic structure were grown on LaAlO3 single crystal substrates by pulsed laser deposition, in which the inclination angle of the (001) plane orientation was in strict accordance with 10° against the film surface. The maximal peak value of transverse thermoelectric voltage of up to 6.88 V was obtained for the sample with the optimum thickness around 500 nm. The large voltage signals indicate SrTi1−xNbxO3 films have considerable anisotropy of the Seebeck coefficient ΔS which reaches to ∼25 μV/K. The results demonstrate cubic structure materials also can be used to develop large transverse thermoelectric voltage effect.

Spin rectification enabled by anomalous Hall effect

We report the observation of a transverse dc voltage which appears when a radio frequency (rf) current flows along the longitudinal direction of a ferromagnetic Hall device. This effect is fully explained through the spin rectification enabled by the anomalous Hall effect, which is nonlinear coupling between the dynamic magnetization and the rf current. The observed resonant feature and angular dependent line shape are related to the magnetization precession driven by a rf magnetic field. This suggests a method for detection of spin dynamic and rf magnetic field vector.

The Enhancement of Laser-Induced Transverse Voltage in Tilted Bi2Sr2Co2Oy Thin Films with a Graphite Light Absorption Layer

Laser-induced transverse voltage effect is investigated in c-axis tilted Bi2Sr2Co2Oy thin films coated with a graphite layer by using three different laser sources with wavelength ranging from ultraviolet to near-infrared. Due to the transverse thermoelectric effect, voltage signals are detected when the film surface is irradiated by these three lasers and the voltage sensitivity is enhanced as a result of the increasing light absorption at the graphite layer. This work demonstrates that the graphite can be used as an effective absorption layer for fabrication of light detectors based on the photo-thermo-electric conversion.