Non-Local Voltage (NLV) Mechanisms

• Non-local voltage (NLV) is a measurement configuration that detects voltages in regions with no direct current flow, highlighting mechanisms like spin accumulation, magnon diffusion, and valley imbalance.
• Experimental setups using separated injection and detection electrodes enable precise characterization of transport channels and extraction of parameters such as diffusion lengths and spin Hall angles.
• NLV methods provide critical insights into nonlocal transport phenomena in systems ranging from magnetic insulators to superconducting hybrids and hydrodynamic electron flows.

Searching arXiv for the cited papers to ground the article in published work. Non-local voltage (NLV) denotes a voltage measured at a location through which the driving current does not directly flow. In its most common experimental realization, current is injected in one branch or terminal set, while a separate electrically isolated branch is used for voltage detection. The resulting signal is therefore not a local Ohmic drop, but a response mediated by spin accumulation, diffusing magnons, quasiparticle charge imbalance, coherent superconducting transport, valley imbalance, hydrodynamic flow, or electro-diffusive charge separation, depending on the platform (Goennenwein et al., 2015, Noh et al., 2012, Cao et al., 24 Feb 2025, Tricot et al., 2020). Across these contexts, NLV is used both as a probe of transport channels that are inaccessible in local measurements and as a diagnostic of whether the presumed mediator is genuinely non-local.

1. Measurement concept and device geometries

The defining feature of an NLV experiment is the spatial separation of injection and detection. In YIG/Pt nanostructures, the device consists of two parallel platinum strips, each $1\,\mu\mathrm{m}$ wide and $100\,\mu\mathrm{m}$ long, deposited on a $3\,\mu\mathrm{m}$-thick yttrium iron garnet film; one strip is current-biased and the voltage is measured both locally along that strip and non-locally along a second, electrically isolated strip separated by $d=200\,\mathrm{nm}$, $500\,\mathrm{nm}$, or $1\,\mu\mathrm{m}$ (Goennenwein et al., 2015). In BSTS Hall bars, current is injected between a pair of contacts at one end of the Hall bar, while the non-local voltage is measured at a pair of contacts separated from the injection point by a length $L$, outside the direct charge current path; the study analyzes contacts with $\frac{L}{w}\geq 3$, with $w=10\,\mu\mathrm{m}$ and $L_2=28\,\mu\mathrm{m}$ used for analysis (Sharma et al., 17 Sep 2025).

Comparable geometries recur in other material systems. In an Sb$100\,\mu\mathrm{m}$0Te$100\,\mu\mathrm{m}$1 topological-insulator nanowire, a direct current is applied between a non-magnetic outer lead and a ferromagnetic injector, while the non-local voltage is measured between a second ferromagnetic contact and a second outer lead; the injector and detector are separated by $100\,\mu\mathrm{m}$2 (Chen et al., 2020). In a quasi-one-dimensional aluminum structure, current is injected across one narrow wire and a wide wire, whereas the voltage is measured across the other narrow wire and the wide wire, so that the detected voltage is generated in a region through which the driving current does not directly flow (Kuznetsov et al., 29 Apr 2026). In a proximity-coupled normal-metal structure, four-terminal differential resistance is written as $100\,\mu\mathrm{m}$3, and the non-local response is measured between terminals distinct from the current path (Noh et al., 2012).

This common geometry is important but not sufficient. A plausible implication is that NLV should be treated as a measurement configuration rather than a single physical mechanism: the same wiring topology can probe magnon diffusion, spin Hall conversion, superconducting correlations, or purely charge-induced artifacts.

2. Magnonic and spin-caloritronic non-local voltage

In magnetic-insulator heterostructures, NLV is frequently a detector inverse spin Hall voltage generated by diffusing non-equilibrium magnons. In YIG/Pt nanostructures, a charge current $100\,\mu\mathrm{m}$4 in the injector Pt strip generates a transverse spin accumulation $100\,\mu\mathrm{m}$5 at the Pt/YIG interface via the spin Hall effect, this spin accumulation injects non-equilibrium spin as magnons into YIG, the magnons diffuse laterally, and a spin current is induced back into the detector Pt strip and converted by the inverse spin Hall effect into the measured $100\,\mu\mathrm{m}$6 (Goennenwein et al., 2015). The same study separates this process from spin Hall magnetoresistance (SMR): the local response is attributed to interfacial spin accumulation and torque transfer, with

$100\,\mu\mathrm{m}$7

whereas the non-local response is mediated by diffusion of nonequilibrium magnons in YIG rather than by direct charge or spin conduction (Goennenwein et al., 2015).

Angular dependence is a central discriminator. In the YIG/Pt experiment, both $100\,\mu\mathrm{m}$8 and $100\,\mu\mathrm{m}$9 show a $3\,\mu\mathrm{m}$0-modulation with magnetic-field angle for in-plane and oopj rotations, but $3\,\mu\mathrm{m}$1 includes a constant voltage offset and $3\,\mu\mathrm{m}$2 does not; $3\,\mu\mathrm{m}$3 is zero for oopt rotation, where magnon injection and transport are suppressed by symmetry (Goennenwein et al., 2015). The non-local voltage is always negative in the experimental configuration, with a signal magnitude of $3\,\mu\mathrm{m}$4 at room temperature for $3\,\mu\mathrm{m}$5, roughly $3\,\mu\mathrm{m}$6 smaller than the local SMR voltage of $3\,\mu\mathrm{m}$7; it strongly decreases with decreasing temperature and vanishes below $3\,\mu\mathrm{m}$8, while the SMR persists (Goennenwein et al., 2015). The amplitude of the non-local modulation fits the expected 1D exponential decay, and the extracted diffusion length is $3\,\mu\mathrm{m}$9 (Goennenwein et al., 2015).

Thermally driven magnon transport produces a related but distinct NLV in the non-local spin Seebeck effect. In YIG/Pt devices with two electrically isolated Pt strips, Joule heating under the injector produces a magnon chemical potential $d=200\,\mathrm{nm}$0, diffusing magnons induce a non-local inverse spin Hall voltage in the detector, and the thermal non-local signal is extracted by

$d=200\,\mathrm{nm}$1

At room temperature the non-local spin Seebeck voltage changes sign at a characteristic strip separation $d=200\,\mathrm{nm}$2; at lower temperatures, $d=200\,\mathrm{nm}$3 shows a strong temperature dependence, which suggests that both angular momentum transfer across the YIG/Pt interface and magnon transport in YIG must be taken into account (Ganzhorn et al., 2017).

In the compensated ferrimagnet GdIG, the same two-strip Pt geometry reveals a richer NLV phenomenology. The non-local voltage is very small below $d=200\,\mathrm{nm}$4, increases with temperature, vanishes at the magnetization compensation temperature $d=200\,\mathrm{nm}$5, and shows three field-dependent regimes separated by $d=200\,\mathrm{nm}$6 and $d=200\,\mathrm{nm}$7 (Ganzhorn et al., 2017). Atomistic modeling indicates that the thermal population of distinct magnon bands with opposite polarization is important for understanding the non-local voltage signal, and the unexpected field enhancement just below $d=200\,\mathrm{nm}$8 is qualitatively attributed to the balance between these modes (Ganzhorn et al., 2017). This suggests that, in ferrimagnets with multiple thermally populated magnon bands, NLV is sensitive not only to diffusion length but also to mode-resolved magnon physics.

3. Spin Hall, topological, and valley-mediated non-local voltage

In topological-insulator and strong-spin-orbit systems, NLV is used as a static probe of charge-to-spin conversion without requiring the local ferromagnetic dynamics of spin-torque ferromagnetic resonance. In molecular beam epitaxy grown BSTS thin films, the static method uses non-local voltage measurements in Hall bars with DC charge current: a charge current $d=200\,\mathrm{nm}$9 generates a transverse spin current $500\,\mathrm{nm}$0 via the spin Hall effect, the pure spin current diffuses away from the charge path, and the inverse spin Hall effect at the non-local contacts converts it back into a measured voltage (Sharma et al., 17 Sep 2025). Under a sweeping in-plane magnetic field, the non-local resistance shows a pseudo-Lorentzian Hanle line shape, fitted by

$500\,\mathrm{nm}$1

At $500\,\mathrm{nm}$2, $500\,\mathrm{nm}$3, and $500\,\mathrm{nm}$4, the extracted parameters are $500\,\mathrm{nm}$5, $500\,\mathrm{nm}$6, and $500\,\mathrm{nm}$7, with a decrease of the NLV signal at $500\,\mathrm{nm}$8 attributed to thermal effects and suppression of spin transport (Sharma et al., 17 Sep 2025).

A distinct topological realization appears in Sb$500\,\mathrm{nm}$9Te$1\,\mu\mathrm{m}$0 nanowires contacted by magnetic tunnel junction electrodes. Here, the key observation is symmetry rather than a Hanle fit: non-local voltage measurements exhibit a symmetry with respect to magnetic field applied perpendicular to the nanowire channel that is remarkably different from a channel lacking spin-momentum locking (Chen et al., 2020). In conventional non-local spin valves, simultaneous reversal of injector and detector magnetizations leaves the NLV unchanged because the relative magnetic alignment is unchanged; in the Sb$1\,\mu\mathrm{m}$1Te$1\,\mu\mathrm{m}$2 nanowire, simultaneous reversal of magnetic moments of all magnetic contacts alters the non-local voltage, and this unusual symmetry is presented as a clear signature of spin-momentum locking in the surface states (Chen et al., 2020). The surface-state Hamiltonian is written as

$1\,\mu\mathrm{m}$3

NLV also appears in the theory of nonlinear valley Hall transport, where the inverse process required for nonlocal detection is not the reciprocal of the direct process. The theory of nonlocal transport from nonlinear valley responses shows that the nonlinear inverse valley Hall effect needed to generate a nonlocal voltage signal must be valley-even, in contrast to both linear and nonlinear valley Hall effects, which are valley-odd (Cao et al., 24 Feb 2025). For the purely nonlinear case, the nonlocal voltage scales as $1\,\mu\mathrm{m}$4 and decays as $1\,\mu\mathrm{m}$5, whereas the linear case scales as $1\,\mu\mathrm{m}$6 and decays as $1\,\mu\mathrm{m}$7; under low-frequency ac driving, distinct harmonic components permit separation of linear and nonlinear responses (Cao et al., 24 Feb 2025). Combined with first-principles calculations for bilayer $1\,\mu\mathrm{m}$8-WTe$1\,\mu\mathrm{m}$9, the theory predicts $L$0 and $L$1 for $L$2, $L$3, and $L$4 (Cao et al., 24 Feb 2025). This suggests that NLV can function as a symmetry-selective probe of nonlinear valleytronics, rather than merely as a diffusion measurement.

4. Superconducting, proximity-coupled, and coherent non-local voltage

In superconducting hybrids, NLV often reflects nonlocal quasiparticle or Cooper-pair correlations rather than spin transport. In superconductor/normal-metal heterostructures, large nonlocal correlations are observed between two spatially separated normal metals, manifesting as a nonlocal voltage generated in response to a driving current, but in the proximity-coupled normal-metal configuration the mediator is a proximity-coupled normal metal rather than a direct superconducting bridge (Noh et al., 2012). The magnitude of the NLV decreases as the distance between the current path and the nonlocal probe increases, but the decay is linear rather than exponential; the nonlocal differential resistance has a finite positive value at zero bias, a peak at finite bias, and a sharp dip near $L$5 at the lowest temperatures (Noh et al., 2012). A current-separation model and quasiclassical simulations based on Usadel equations reproduce the main features at finite bias and higher temperatures, yet the sharp zero-bias dip cannot be explained by the quasiclassical theory of superconductivity (Noh et al., 2012). The paper interprets this as evidence for long-range nonlocal quasiparticle correlations that may be related to pair correlations in the proximity-coupled normal metal.

A different superconducting NLV is reported in a quasi-one-dimensional aluminum structure near the superconducting transition. Negative nonlocal direct current voltages are observed only in the interval $L$6, where the narrow wires are normal and the wide wire is superconducting, creating an N-S hybrid structure (Kuznetsov et al., 29 Apr 2026). The negative voltage arises due to a quasiparticle current flowing through the N-S interface, generating a charge-imbalance region in the superconductor that is sensed at a remote point; for $L$7, the model gives $L$8 (Kuznetsov et al., 29 Apr 2026). The peak negative NLV is

$L$9

and both the peak voltage and the critical current are suppressed by perpendicular magnetic field until they vanish near the critical field (Kuznetsov et al., 29 Apr 2026). The analysis combines a nonequilibrium Skocpol-Beasley-Tinkham charge-imbalance model with equilibrium superconducting fluctuation corrections of Aslamazov-Larkin and Maki-Thompson type (Kuznetsov et al., 29 Apr 2026).

NLV is also implicated in non-local coherent transport in three-terminal Josephson junctions under commensurate voltage bias. For a node connected to three superconductors at $\frac{L}{w}\geq 3$0, $\frac{L}{w}\geq 3$1, and $\frac{L}{w}\geq 3$2, the central non-local coherent process is the quartet process, with emergent quartet phase

$\frac{L}{w}\geq 3$3

Under symmetric commensurate bias, local Josephson harmonics are oscillatory in time and average out, while non-local quartet harmonics survive as stationary dc components (Padurariu et al., 2017). The resulting normal density of states exhibits deep and highly tunable pseudogaps, maximized at $\frac{L}{w}\geq 3$4 and absent for $\frac{L}{w}\geq 3$5, and these are proposed to be accessible by tunneling spectroscopy (Padurariu et al., 2017). In this setting, NLV is tied to phase-sensitive dc response produced only by coherent processes involving all three superconductors.

5. Macroscopic hydrodynamic and electro-diffusive non-local voltage

NLV is not restricted to mesoscopic spin or superconducting devices. In millimeter-scale strips fabricated from nominal Bi$\frac{L}{w}\geq 3$6Se$\frac{L}{w}\geq 3$7 on YBa$\frac{L}{w}\geq 3$8Cu$\frac{L}{w}\geq 3$9O$w=10\,\mu\mathrm{m}$0, the measurement geometry is compared to three resistors in series: current is injected between neighboring contacts, and voltage is measured relative to a distant contact at positions remote from the current path (Jeon et al., 9 Jul 2025). The reported NLV exceeds $w=10\,\mu\mathrm{m}$1 at only $w=10\,\mu\mathrm{m}$2 dc at a distance of $w=10\,\mu\mathrm{m}$3 from the current contact, remains above $w=10\,\mu\mathrm{m}$4 even at $w=10\,\mu\mathrm{m}$5 separation, and has an exponential decay length of $w=10\,\mu\mathrm{m}$6 at room temperature that increases to $w=10\,\mu\mathrm{m}$7 at $w=10\,\mu\mathrm{m}$8 (Jeon et al., 9 Jul 2025). The devices also display highly nonlinear current-voltage characteristics, potential peaks at current contacts, negative local resistance in vicinity geometries, and broken-parity potential distributions; the study states that only hydrodynamic electron flow simulations reproduce the observed potential peaks at current contacts and the nearly flat profile in between (Jeon et al., 9 Jul 2025). Similar observations in Bi$w=10\,\mu\mathrm{m}$9Te$L_2=28\,\mu\mathrm{m}$0/YBCO are taken to indicate generality across chemically modified topological insulators (Jeon et al., 9 Jul 2025).

An electro-diffusive analogue appears in confined electrolyte media. In a domain with fixed negative charge in an inner region and global but not local electroneutrality, analytical and numerical solutions of the Poisson-Nernst-Planck equation show that the voltage changes considerably on a spatial scale much larger than the Debye screening length (Tricot et al., 2020). The steady-state formulation uses Boltzmann distributions for mobile positive and negative ions together with the Poisson equation,

$L_2=28\,\mu\mathrm{m}$1

and in one dimension the reduced equation is

$L_2=28\,\mu\mathrm{m}$2

The resulting voltage drop is distributed over the entire domain rather than confined to a Debye layer, and the paper argues that long-range voltage drop changes are expected in neuronal microcompartments (Tricot et al., 2020). This suggests that the term non-local voltage can also describe field distributions sustained by electro-diffusion when local electroneutrality fails, even though the underlying physics is distinct from that of electronic nonlocal transport.

6. Artifacts, interpretive limits, and methodological controls

The non-local geometry is often chosen precisely to avoid spurious voltages caused by the flow of charges, yet reported non-local spin valve, Hanle spin precession, and spin Hall measurements frequently contain background signals unrelated to spins. A systematic analysis identifies seven charge-induced artifacts, grouped into signals inherent to the device structure and/or measurement setup and signals that depend on a common-mode voltage (Volmer et al., 2021). The full measured signal is written as

$L_2=28\,\mu\mathrm{m}$3

where the additional terms denote current spreading, thermoelectric voltages, input bias currents, crosstalk and interference, leakage currents, finite common-mode rejection ratio, and capacitor charging effects (Volmer et al., 2021). The study emphasizes that a common-mode voltage can create a phase-shifted, frequency-dependent signal with an amplitude several orders of magnitude larger than the actual spin signal, particularly in lock-in measurements (Volmer et al., 2021).

The proposed mitigation is a voltage-controlled current source that creates a virtual ground within the non-local detection circuit, thereby significantly diminishing all spurious voltage signals of the common-mode class in both DC and AC measurements (Volmer et al., 2021). In graphene-based non-local spin valve devices, all spurious voltage signals caused by a common-mode voltage are reported to be completely suppressed by this current source (Volmer et al., 2021). Other studies use different control logic: in YIG/Pt nanostructures, symmetry under field rotation and the absence of a signal in the oopt geometry are used to rule out local magneto-thermal voltages or charge-based leakage (Goennenwein et al., 2015); in BSTS Hall bars, reliable extraction is restricted to contact spacings with $L_2=28\,\mu\mathrm{m}$4 because closer detectors show higher background and unreliable fitting (Sharma et al., 17 Sep 2025).

Taken together, these results establish an important constraint on the interpretation of NLV. The observation of a voltage outside the direct current path does not, by itself, identify a spin, magnonic, superconducting, valley, or hydrodynamic origin. The evidentiary standard instead comes from symmetry, distance scaling, temperature dependence, field dependence, harmonic structure, and explicit suppression of charge-induced backgrounds.