Hall-Memresistance in Spintronic Memory

• Hall-memresistance is a family of memory effects where a Hall voltage couples to an internal state variable (e.g., magnetic flux or Néel vector) to encode past excitation history.
• The phenomenon is realized through diverse architectures such as feedback spin valves, mixed-symmetry Hall devices, and quantum anomalous Hall systems, each demonstrating unique hysteretic responses.
• Theoretical frameworks expand traditional memristor models with heterogeneous terms, highlighting the role of Hall responses in dynamic feedback, stability analysis, and nonvolatile memory applications.

Searching arXiv for the cited Hall-memresistance and related papers to ground the article in recent literature. arXiv search: "^^^^^^^^6hall memresistance6^^^^^^^^" Querying arXiv search tool for Hall-memresistance-related papers. {"^^^^^^^^6query6 OR ^^^^^^^^6all:\6 memresistance6^^^^^^^^\" OR ti:\6^^^^^^^^"Antiferromagnetic Hall-Memristors\"^^^^^^^^6 OR ti:\6^^^^^^^^"A Feedback Spin-Valve Memristive System\"","max_results":^^^^6query6hall memresistance6^^^^,"sort_by":"relevance"} Searching arXiv for exact titles and topic keywords. Using arXiv search to retrieve the primary sources by title. Hall-memresistance denotes a class of history-dependent transport phenomena in which a Hall voltage, a Hall-derived longitudinal voltage, or a Hall-type resistance level is coupled to an internal state variable and therefore encodes memory. In the literature considered here, that state variable is variously the magnetic flux in a feedback giant-magnetoresistive spin valve, the perpendicular magnetization of engineered Hall bars, the quantized Hall state of a quantum anomalous Hall device, trap occupation in a topological field-effect memristor, or the Néel vector in an antiferromagnet. The unifying feature is architectural rather than microscopic: the Hall channel either updates the internal state, reads it out, or does both, so the measured response depends on prior excitation &&&^^^^6hall memresistance6^^^^&&&); (&&&^^^^6query6^^^^&&&); (&&&^^^^6all:\6^^^^&&&); (&&&^^^^6 OR all:\6^^^^&&&)].

^^^^6query6^^^^. Conceptual scope and formal definitions

The earliest explicit theoretical formulation in this set is a generalized memristive system built from controlled spin polarizations in a giant-magnetoresistive material and a feedback loop based on the classical Hall Effect. That work already departs from the strict homogeneous memristor picture by allowing a pinched hysteretic loop whose self-crossing knot is not located at the origin, and by showing that passive memory systems not subject to Ohm’s Law can display such non-origin-crossing dynamics (&&&^^^^6 OR ti:\6^^^^&&&).

Within that formalism, a homogeneous memristive system has

PRESERVED_PLACEHOLDER_^^^^6hall memresistance6^^^^

so every PRESERVED_PLACEHOLDER_^^^^6query6^^^^–PRESERVED_PLACEHOLDER_^^^^6all:\6^^^^ loop must cross the origin. The broadened heterogeneous form is

PRESERVED_PLACEHOLDER_^^^^6 OR all:\6^^^^

where the nonzero PRESERVED_PLACEHOLDER_^^^^6 OR ti:\6^^^^ permits off-origin pinched loops. The same work further enlarges the framework to compound memory electronic systems,

PRESERVED_PLACEHOLDER_^^^^6 OR ti:\6^^^^

for situations in which resistive, capacitive, and inductive memory effects are tightly combined (&&&^^^^6 OR ti:\6^^^^&&&).

Later uses of the term are more device-specific. In mixed-symmetry Hall devices, Hall-memresistance appears as a longitudinal readout voltage whose odd-in-field component tracks magnetization because the Hall coefficient is engineered to vary along the current path. In antiferromagnetic Hall-memristors, it is defined directly as a transverse Hall resistance that depends on the history of the applied electric field via a slowly varying Néel vector. In quantum anomalous Hall memory, the stored bit is the sign of a quantized Hall resistance level. This suggests that Hall-memresistance is best understood as a family of memory-resistance effects mediated by Hall physics rather than as a single constitutive law.

^^^^6all:\6^^^^. Feedback spin-valve origin and generalized memristive dynamics

The feedback spin-valve realization is built from a CPP-stack giant-magnetoresistive spin valve consisting of two ferromagnetic layers separated by a thin nonmagnetic spacer. When the two magnetizations are parallel the resistance is low, $R_{\uparrow\uparrow}$; when antiparallel it is high, $R_{\uparrow\downarrow}$. The memristive behavior is created by driving the GMR stack with a current $i(t)$, using the classical Hall voltage generated in the same conductor to drive a feedback coil, and letting the resulting magnetic flux $\phi_m$ bias the ferromagnetic layers and hence modify the instantaneous GMR resistance PRESERVED_PLACEHOLDER_^^^^6query6hall memresistance6^^^^ (&&&^^^^6 OR ti:\6^^^^&&&).

The empirical GMR law is

PRESERVED_PLACEHOLDER_^^^^6query6query6^^^^

with PRESERVED_PLACEHOLDER_^^^^6query6all:\6^^^^ a normalization flux. The Hall electromotive force is

PRESERVED_PLACEHOLDER_^^^^6query6 OR all:\6^^^^

using PRESERVED_PLACEHOLDER_^^^^6query6 OR ti:\6^^^^. Together with the coil relation PRESERVED_PLACEHOLDER_^^^^6query6 OR ti:\6^^^^, the dynamics reduce to

PRESERVED_PLACEHOLDER_^^^^6query66^^^^

PRESERVED_PLACEHOLDER_^^^^6query6^^^^7

The quadratic term PRESERVED_PLACEHOLDER_^^^^6query6^^^^8 is the heterogeneous contribution that breaks strict PRESERVED_PLACEHOLDER_^^^^6query6^^^^9 homogeneity (&&&^^^^6 OR ti:\6^^^^&&&).

Under a sinusoidal drive PRESERVED_PLACEHOLDER_^^^^6all:\6hall memresistance6^^^^, numerical simulation gives a pinched hysteresis loop in the PRESERVED_PLACEHOLDER_^^^^6all:\6query6^^^^–PRESERVED_PLACEHOLDER_^^^^6all:\6all:\6^^^^ plane, but the self-crossing knot lies off the origin. Physically, even when PRESERVED_PLACEHOLDER_^^^^6all:\6 OR all:\6^^^^, the flux PRESERVED_PLACEHOLDER_^^^^6all:\6 OR ti:\6^^^^ need not vanish, so

PRESERVED_PLACEHOLDER_^^^^6all:\6 OR ti:\6^^^^

can be satisfied by nonzero PRESERVED_PLACEHOLDER_^^^^6all:\66^^^^. In the limit PRESERVED_PLACEHOLDER_^^^^6all:\6^^^^7, corresponding to large inductance, the PRESERVED_PLACEHOLDER_^^^^6all:\6^^^^8-dynamics decouple and the system recovers a homogeneous memristor PRESERVED_PLACEHOLDER_^^^^6all:\6^^^^9 with PRESERVED_PLACEHOLDER_^^^^6 OR all:\6hall memresistance6^^^^, so the pinch point returns to the origin. If the feedback-inductance term dominates, the hysteresis collapses into a single loop with no self-crossing (&&&^^^^6 OR ti:\6^^^^&&&).

The same analysis provides a sufficient stability condition using a Floquet-exponent estimate. Writing PRESERVED_PLACEHOLDER_^^^^6 OR all:\6query6^^^^ around a limit cycle and bounding the periodic coefficient with the fact that PRESERVED_PLACEHOLDER_^^^^6 OR all:\6all:\6^^^^ is bounded by PRESERVED_PLACEHOLDER_^^^^6 OR all:\6 OR all:\6^^^^, the exponent satisfies

PRESERVED_PLACEHOLDER_^^^^6 OR all:\6 OR ti:\6^^^^

so asymptotic stability is ensured if

PRESERVED_PLACEHOLDER_^^^^6 OR all:\6 OR ti:\6^^^^

The significance of this result is conceptual as much as dynamical: it establishes that non-origin pinching is compatible with passive memory behavior when the constitutive law is heterogeneous rather than homogeneous.

^^^^6 OR all:\6^^^^. Mixed-symmetry Hall devices and magnetization memory

A distinct Hall-memresistance concept was developed in conducting films with a Hall coefficient that varies along the current trajectory. In such directionally inhomogeneous media, a longitudinal voltage acquires an antisymmetric, odd-in-field component. The underlying mechanism is not a violation of Onsager reciprocity, but the superposition of Ohmic and Hall voltages in a medium whose Hall response is spatially nonuniform (&&&^^^^6query6^^^^&&&).

Two CoPRESERVED_PLACEHOLDER_^^^^6 OR all:\66^^^^PdPRESERVED_PLACEHOLDER_^^^^6 OR all:\6^^^^7 implementations were fabricated. The three-terminal Hall bar uses a single ferromagnetic stripe in which contacts “a” and “c” source the current and a third contact “b” lies downstream on the same edge as “a”. The partitioned FM–NM Hall bar divides a contiguous bar into a ferromagnetic segment with large extraordinary Hall coefficient PRESERVED_PLACEHOLDER_^^^^6 OR all:\6^^^^8 and a thick, low-resistance normal-metal segment with negligible ordinary Hall response. In both cases the effective Hall coefficient profile is discontinuous along PRESERVED_PLACEHOLDER_^^^^6 OR all:\6^^^^9, with a finite Hall response in the FM section and zero response either at the reference contact or in the NM section (&&&^^^^6query6^^^^&&&).

In the circuit model, the local Hall voltages at two cross-sections are

PRESERVED_PLACEHOLDER_^^^^6 OR ti:\6hall memresistance6^^^^

and the edge voltages become

PRESERVED_PLACEHOLDER_^^^^6 OR ti:\6query6^^^^

In the ideal three-terminal or FM–NM geometries, one cross-section has zero Hall coefficient or zero local magnetization, so the odd component is maximal:

PRESERVED_PLACEHOLDER_^^^^6 OR ti:\6all:\6^^^^

The measured longitudinal voltage in the three-terminal device can therefore be written as

PRESERVED_PLACEHOLDER_^^^^6 OR ti:\6 OR all:\6^^^^

so reversing PRESERVED_PLACEHOLDER_^^^^6 OR ti:\6 OR ti:\6^^^^ shifts the readout by PRESERVED_PLACEHOLDER_^^^^6 OR ti:\6 OR ti:\6^^^^ (&&&^^^^6query6^^^^&&&).

The memory mechanism relies on perpendicular anisotropy and square hysteresis loops in the ferromagnetic sections. Magnetization is reversed by sweeping an external field PRESERVED_PLACEHOLDER_^^^^6 OR ti:\66^^^^ past the local coercive field PRESERVED_PLACEHOLDER_^^^^6 OR ti:\6^^^^7. In a partitioned FM–NM–FM structure with two FM bars of different thicknesses, PRESERVED_PLACEHOLDER_^^^^6 OR ti:\6^^^^8 and PRESERVED_PLACEHOLDER_^^^^6 OR ti:\6^^^^9, so pulses satisfying

PRESERVED_PLACEHOLDER_^^^^6 OR ti:\6hall memresistance6^^^^

flip only one FM segment, while larger fields flip both. The four combinations PRESERVED_PLACEHOLDER_^^^^6 OR ti:\6query6^^^^ then yield four distinct zero-field voltages

PRESERVED_PLACEHOLDER_^^^^6 OR ti:\6all:\6^^^^

This is an explicit multi-bit Hall-memory readout based on static magnetic states rather than dynamic resistive switching (&&&^^^^6query6^^^^&&&).

Experimentally, all voltages were measured with a dc current PRESERVED_PLACEHOLDER_^^^^6 OR ti:\6 OR all:\6^^^^. In the three-terminal ^^^^6all:\6hall memresistance6^^^^ nm CoPRESERVED_PLACEHOLDER_^^^^6 OR ti:\6 OR ti:\6^^^^PdPRESERVED_PLACEHOLDER_^^^^6 OR ti:\6 OR ti:\6^^^^ device, the antisymmetric detection efficiency PRESERVED_PLACEHOLDER_^^^^6 OR ti:\66^^^^ was approximately PRESERVED_PLACEHOLDER_^^^^6 OR ti:\6^^^^7 at ^^^^6 OR all:\6hall memresistance6hall memresistance6^^^^ K and PRESERVED_PLACEHOLDER_^^^^6 OR ti:\6^^^^8 at 77 K. In the partitioned ^^^^6all:\6hall memresistance6^^^^ nm FM + ^^^^6query6hall memresistance6hall memresistance6^^^^ nm CuAu device, PRESERVED_PLACEHOLDER_^^^^6 OR ti:\6^^^^9 at room temperature and $R_{\uparrow\uparrow}$^^^^6hall memresistance6^^^^ at 77 K, with total resistance reduced by a factor $R_{\uparrow\uparrow}$^^^^6query6^^^^ relative to a single FM. In the FM$R_{\uparrow\uparrow}$^^^^6all:\6^^^^–NM–FMR↑↑R_{\uparrow\uparrow}^^^^6 OR all:\6^^^^ cell, the efficiency

$R_{\uparrow\uparrow}$^^^^6 OR ti:\6^^^^

was approximately $R_{\uparrow\uparrow}$^^^^6 OR ti:\6^^^^, the minimum spacing between adjacent read levels was on the order of tens of microvolts at $R_{\uparrow\uparrow}$6, and no drift was observed over days. The antisymmetric spikes scaled strictly linearly with $R_{\uparrow\uparrow}$7, reversed sign under $R_{\uparrow\uparrow}$8, and flipped sign when measured along the opposite edge, confirming a mixed-symmetry Hall origin rather than a true nonreciprocal effect (&&&^^^^6query6^^^^&&&).

^^^^6 OR ti:\6^^^^. Quantum anomalous Hall and topological memristive implementations

A quantum anomalous Hall realization stores non-volatile binary information directly in quantized Hall resistance levels. In a twisted-bilayer graphene on hBN moiré stack near three-quarter filling, spontaneous ferromagnetism yields a zero-field QAHE with first Chern number $R_{\uparrow\uparrow}$9 and

$R_{\uparrow\downarrow}$^^^^6hall memresistance6^^^^

so the two logic states are

$R_{\uparrow\downarrow}$^^^^6query6^^^^

The four-terminal cell writes by controlled hysteretic switching between the two Hall states using nanoampere currents of opposite polarities, and reads non-destructively by sensing the sign of the transverse Hall voltage at a current $R_{\uparrow\downarrow}$^^^^6all:\6^^^^ chosen inside the no-switching window $R_{\uparrow\downarrow}$^^^^6 OR all:\6^^^^ (&&&^^^^6all:\6^^^^&&&).

The reported thresholds at ^^^^6 OR ti:\6^^^^ K and zero magnetic field are $R_{\uparrow\downarrow}$^^^^6 OR ti:\6^^^^ and $R_{\uparrow\downarrow}$^^^^6 OR ti:\6^^^^. A practical read bias is $R_{\uparrow\downarrow}$6, for which $R_{\uparrow\downarrow}$7 is positive for the stored “^^^^6query6^^^^” state and negative for the stored “^^^^6hall memresistance6^^^^” state. The excitation gap is described by

$R_{\uparrow\downarrow}$8

with $R_{\uparrow\downarrow}$9. At the architecture level, each QAHE cell is placed in series with a two-terminal mixed-ionic-electronic-conduction selector with ON/OFF ratio $i(t)$^^^^6hall memresistance6^^^^ and leakage $i(t)$^^^^6query6^^^^, enabling a ^^^^6 OR all:\6^^^^D cross-point array with $i(t)$^^^^6all:\6^^^^ biasing. Reported cell metrics are a cell area of $i(t)$^^^^6 OR all:\6^^^^, write powers of approximately $i(t)$^^^^6 OR ti:\6^^^^ for “^^^^6hall memresistance6^^^^” and $i(t)$^^^^6 OR ti:\6^^^^ for “^^^^6query6^^^^”, read power $i(t)$6, and latency of $i(t)$7–$i(t)$8 (&&&^^^^6all:\6^^^^&&&).

A separate topological route combines floating-gate memristive behavior with a six-terminal Hall bar in the quantum spin Hall regime. The device is an inverted InAs/GaInSb/InAs trilayer quantum well with intrinsic floating-gate behavior arising from charge traps in a SiO$i(t)$9/SiN dielectric. When the drain and top-gate are shorted, trap charge $\phi_m$^^^^6hall memresistance6^^^^ shifts the gate potential by

$\phi_m$^^^^6query6^^^^

and the normalized trap occupation

$\phi_m$^^^^6all:\6^^^^

acts as the internal state variable. The memristor model is

$\phi_m$^^^^6 OR all:\6^^^^

with

$\phi_m$^^^^6 OR ti:\6^^^^

In this platform, one resistance state is governed by dissipationless helical edge channels with

$\phi_m$^^^^6 OR ti:\6^^^^

while the other is an incoherent bulk-conduction state with typical differential resistance $\phi_m$6–$\phi_m$7 for $\phi_m$8 V sweeps outside gap alignment (&&&^^^^6query66^^^^&&&).

The memristive loop is observed for current sweeps of $\phi_m$9 at PRESERVED_PLACEHOLDER_^^^^6query6hall memresistance6hall memresistance6^^^^ K, with two distinct voltages at PRESERVED_PLACEHOLDER_^^^^6query6hall memresistance6query6^^^^ corresponding to bulk and edge conduction. A linearized fit

PRESERVED_PLACEHOLDER_^^^^6query6hall memresistance6all:\6^^^^

gives PRESERVED_PLACEHOLDER_^^^^6query6hall memresistance6 OR all:\6^^^^ and PRESERVED_PLACEHOLDER_^^^^6query6hall memresistance6 OR ti:\6^^^^. By tuning the back gate, the high-resistance plateau crosses zero bias near PRESERVED_PLACEHOLDER_^^^^6query6hall memresistance6 OR ti:\6^^^^ V, and the maximum high/low resistance ratio reaches PRESERVED_PLACEHOLDER_^^^^6query6hall memresistance66^^^^ for PRESERVED_PLACEHOLDER_^^^^6query6hall memresistance6^^^^7 V sweeps. In transistor mode, PRESERVED_PLACEHOLDER_^^^^6query6hall memresistance6^^^^8 appears when the Fermi level lies in the gap; in the same regime PRESERVED_PLACEHOLDER_^^^^6query6hall memresistance6^^^^9 remains zero at small magnetic fields and no broken-symmetry quantum Hall plateaus appear up to PRESERVED_PLACEHOLDER_^^^^6query6query6hall memresistance6^^^^ T, consistent with time-reversal-invariant topological transport. The floating-gate state is stable over PRESERVED_PLACEHOLDER_^^^^6query6query6query6^^^^ s and over more than PRESERVED_PLACEHOLDER_^^^^6query6query6all:\6^^^^ full PRESERVED_PLACEHOLDER_^^^^6query6query6 OR all:\6^^^^ V sweeps, with typical power PRESERVED_PLACEHOLDER_^^^^6query6query6 OR ti:\6^^^^ in the edge state and up to PRESERVED_PLACEHOLDER_^^^^6query6query6 OR ti:\6^^^^ in the bulk state (&&&^^^^6query66^^^^&&&).

These two implementations represent different limits of Hall-based memory. The QAHE device uses quantized transverse Hall resistance as the stored variable itself, whereas the topological field-effect memristor uses a Hall-bar topological transport platform in which memory is carried by trap occupation and read out through a history-dependent switch between coherent edge transport and incoherent bulk transport.

^^^^6 OR ti:\6^^^^. Antiferromagnetic Hall-memristors

In antiferromagnetic Hall-memristors, Hall-memresistance is defined explicitly as a transverse Hall resistance that depends on the history of the applied electric field through a slowly varying internal antiferromagnetic order parameter, namely the Néel vector. Under a fixed longitudinal current PRESERVED_PLACEHOLDER_^^^^6query6query66^^^^, the Hall voltage PRESERVED_PLACEHOLDER_^^^^6query6query6^^^^7 therefore remembers prior current or field pulses. The microscopic mechanism combines a nonlinear Hall effect, which generates a transverse current density quadratic in the applied field, with a nonlinear Edelstein effect, which uses the same quadratic field dependence to induce a nonequilibrium spin polarization that slowly tilts the Néel vector (&&&^^^^6 OR all:\6^^^^&&&).

The constitutive relations are

PRESERVED_PLACEHOLDER_^^^^6query6query6^^^^8

PRESERVED_PLACEHOLDER_^^^^6query6query6^^^^9

and, using PRESERVED_PLACEHOLDER_^^^^6query6all:\6hall memresistance6^^^^ as the state variable,

PRESERVED_PLACEHOLDER_^^^^6query6all:\6query6^^^^

For CuMnAs, the symmetry analysis starts from space group PRESERVED_PLACEHOLDER_^^^^6query6all:\6all:\6^^^^: each Mn sublattice is locally noncentrosymmetric even though combined PRESERVED_PLACEHOLDER_^^^^6query6all:\6 OR all:\6^^^^ symmetry remains. Under the site point group PRESERVED_PLACEHOLDER_^^^^6query6all:\6 OR ti:\6^^^^, the allowed intrinsic second-order tensors are

PRESERVED_PLACEHOLDER_^^^^6query6all:\6 OR ti:\6^^^^

Thus a pulse PRESERVED_PLACEHOLDER_^^^^6query6all:\66^^^^ writes PRESERVED_PLACEHOLDER_^^^^6query6all:\6^^^^7 via the nonlinear Edelstein effect, and a low-amplitude read field probes the stored state through the nonlinear Hall response (&&&^^^^6 OR all:\6^^^^&&&).

The paper develops both a tilted massive Dirac toy model and a CuMnAs lattice model. The toy Hamiltonian is

PRESERVED_PLACEHOLDER_^^^^6query6all:\6^^^^8

with PRESERVED_PLACEHOLDER_^^^^6query6all:\6^^^^9. In the lattice realization, the PRESERVED_PLACEHOLDER_^^^^6query6 OR all:\6hall memresistance6^^^^ antiferromagnetic Hamiltonian contains

PRESERVED_PLACEHOLDER_^^^^6query6 OR all:\6query6^^^^

and staggered spin-orbit-coupled fields

PRESERVED_PLACEHOLDER_^^^^6query6 OR all:\6all:\6^^^^

The nonlinear Hall conductivity is then obtained from an intrinsic Kubo-type expression involving Berry connections, and numerically shows strong dependence on PRESERVED_PLACEHOLDER_^^^^6query6 OR all:\6 OR all:\6^^^^ and chemical potential (&&&^^^^6 OR all:\6^^^^&&&).

The four-terminal geometry separates write and read paths. Terminals PRESERVED_PLACEHOLDER_^^^^6query6 OR all:\6 OR ti:\6^^^^ inject a longitudinal current PRESERVED_PLACEHOLDER_^^^^6query6 OR all:\6 OR ti:\6^^^^ or field PRESERVED_PLACEHOLDER_^^^^6query6 OR all:\66^^^^; terminals PRESERVED_PLACEHOLDER_^^^^6query6 OR all:\6^^^^7 measure the transverse Hall voltage PRESERVED_PLACEHOLDER_^^^^6query6 OR all:\6^^^^8. Writing uses pulses of amplitude PRESERVED_PLACEHOLDER_^^^^6query6 OR all:\6^^^^9 and duration PRESERVED_PLACEHOLDER_^^^^6query6 OR ti:\6hall memresistance6^^^^, which tilt the Néel vector by PRESERVED_PLACEHOLDER_^^^^6query6 OR ti:\6query6^^^^. Reading uses a smaller field PRESERVED_PLACEHOLDER_^^^^6query6 OR ti:\6all:\6^^^^ to avoid disturbing the state. The Hall-memristance is defined by

PRESERVED_PLACEHOLDER_^^^^6query6 OR ti:\6 OR all:\6^^^^

The state evolution is modeled by a Landau–Khalatnikov-type equation,

PRESERVED_PLACEHOLDER_^^^^6query6 OR ti:\6 OR ti:\6^^^^

which yields hysteresis in PRESERVED_PLACEHOLDER_^^^^6query6 OR ti:\6 OR ti:\6^^^^ versus PRESERVED_PLACEHOLDER_^^^^6query6 OR ti:\66^^^^ (&&&^^^^6 OR all:\6^^^^&&&).

For CuMnAs, the material parameters used include PRESERVED_PLACEHOLDER_^^^^6query6 OR ti:\6^^^^7 eV, PRESERVED_PLACEHOLDER_^^^^6query6 OR ti:\6^^^^8 eV, PRESERVED_PLACEHOLDER_^^^^6query6 OR ti:\6^^^^9 eV, PRESERVED_PLACEHOLDER_^^^^6query6 OR ti:\6hall memresistance6^^^^, PRESERVED_PLACEHOLDER_^^^^6query6 OR ti:\6query6^^^^, and pulse amplitude PRESERVED_PLACEHOLDER_^^^^6query6 OR ti:\6all:\6^^^^. The nonlinear Hall-memconductance PRESERVED_PLACEHOLDER_^^^^6query6 OR ti:\6 OR all:\6^^^^ reaches up to PRESERVED_PLACEHOLDER_^^^^6query6 OR ti:\6 OR ti:\6^^^^ per PRESERVED_PLACEHOLDER_^^^^6query6 OR ti:\6 OR ti:\6^^^^ near avoided-crossing hot spots, and the normalized hysteresis-loop area peaks at PRESERVED_PLACEHOLDER_^^^^6query6 OR ti:\66^^^^, indicating robust nonvolatile behavior for a broad range of GHz–THz writing frequencies. CuMnAs has PRESERVED_PLACEHOLDER_^^^^6query6 OR ti:\6^^^^7 K, implying room-temperature stability of the stored state. Although exact switching energy and retention time are not yet measured, the authors estimate a switching energy in the fJ–pJ range and retention times PRESERVED_PLACEHOLDER_^^^^6query6 OR ti:\6^^^^8 that can be engineered into the ns–PRESERVED_PLACEHOLDER_^^^^6query6 OR ti:\6^^^^9s window (&&&^^^^6 OR all:\6^^^^&&&).

6. Related Hall-derived magnetoresistive phenomena and recurrent misconceptions

Several recurring interpretive issues accompany Hall-memresistance. One is the assumption that every pinched hysteresis loop must cross the origin. The feedback spin-valve analysis shows that this is true for homogeneous memristive systems but not for generalized heterogeneous memristive systems, where a nonzero additive term PRESERVED_PLACEHOLDER_^^^^6query66hall memresistance6^^^^ permits off-origin self-crossing. Another is the assumption that odd-in-field longitudinal signals in mixed-symmetry Hall devices represent genuine nonreciprocal transport. In the engineered CoPd structures, the observed effect is instead explained as the superposition of Ohmic and Hall voltages in a directionally inhomogeneous conductor, and the strict linearity in current, sign reversal under PRESERVED_PLACEHOLDER_^^^^6query66query6^^^^, and edge dependence all support that interpretation &&&^^^^6hall memresistance6^^^^&&&); (&&&^^^^6query6^^^^&&&)].

A related but distinct line of work is spin Hall magnetoresistance in heavy-metal/magnetic-insulator bilayers. In Pt/BaPRESERVED_PLACEHOLDER_^^^^6query66all:\6^^^^CoGePRESERVED_PLACEHOLDER_^^^^6query66 OR all:\6^^^^OPRESERVED_PLACEHOLDER_^^^^6query66 OR ti:\6^^^^, the resistance modulation arises from the spin Hall effect, inverse spin Hall effect, and spin-current dissipation at the interface. When the spin accumulation PRESERVED_PLACEHOLDER_^^^^6query66 OR ti:\6^^^^ is parallel to the magnetic order parameter PRESERVED_PLACEHOLDER_^^^^6query666^^^^, reflection dominates and the resistance is low; when PRESERVED_PLACEHOLDER_^^^^6query66^^^^7, spin-transfer torque or other spin-dissipation channels increase absorption and the resistance is high. The standard SMR ratio is

PRESERVED_PLACEHOLDER_^^^^6query66^^^^8

At PRESERVED_PLACEHOLDER_^^^^6query66^^^^9 K and PRESERVED_PLACEHOLDER_^^^^6query6max_results6hall memresistance6^^^^ T, the maximum in-plane SMR ratio is approximately PRESERVED_PLACEHOLDER_^^^^6query6max_results6query6^^^^ for PRESERVED_PLACEHOLDER_^^^^6query6max_results6all:\6^^^^ and about PRESERVED_PLACEHOLDER_^^^^6query6max_results6 OR all:\6^^^^ for PRESERVED_PLACEHOLDER_^^^^6query6max_results6 OR ti:\6^^^^, with angular dependence PRESERVED_PLACEHOLDER_^^^^6query6max_results6 OR ti:\6^^^^ and a current-direction anisotropy following PRESERVED_PLACEHOLDER_^^^^6query6^^^^76 (&&&^^^^6all:\6 OR ti:\6^^^^&&&).

The Pt/BaPRESERVED_PLACEHOLDER_^^^^6query6^^^^77CoGePRESERVED_PLACEHOLDER_^^^^6query6 study is not presented as Hall-memresistance, but it is relevant because it extends the Hall-derived magnetoresistance landscape into anisotropic altermagnetic interfaces. The work rules out several alternative explanations for the anisotropy, including domain-population differences, electric-polarization coupling, crystalline anisotropic magnetoresistance of Pt, and magnetic proximity effects, and proposes that the data may be understood through anisotropic altermagnetic ordering. This suggests that Hall-memresistance sits within a broader hierarchy of Hall-mediated spintronic responses in which symmetry, interfacial spin conversion, topological transport, and slow magnetic state variables can all shape the observable resistance (&&&^^^^6all:\6 OR ti:\6^^^^&&&).

Taken together, the available literature spans classical Hall feedback, engineered Hall-coefficient inhomogeneity, quantized Hall state storage, topological edge-state memristance, and nonlinear Hall/Edelstein antiferromagnetic memory. Hall-memresistance is therefore best characterized as a research program in which Hall physics is promoted from a passive probe of electronic structure to an active ingredient of memory-resistive functionality.