Reverse-magnetic-field reciprocity in conductive samples with extended contacts

Cornils, M.; Oliver, Paul

doi:10.1063/1.2951895

Cited by 23 publications

(15 citation statements)

References 22 publications

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“…Applied Mathematics and Physics current partitioning between left and right, which depends solely on the spacing of contacts (see Appendix A).With the principle of RMFR[23] [24][25] we can swap supply and sense contacts. Then the Hall potential on the outer boundary is constant if both current contacts are located on the inner boundary.…”

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confidence: 99%

The Classical Hall Effect in Multiply-Connected Plane Regions Part I: Topologies with Stream Function

Ausserlechner¹

2019

JAMP

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Typical Hall plates for practical magnetic field sensing purposes are plane, simply-connected regions with peripheral contacts. Their output voltage is the sum of even and odd functions of the applied magnetic field. They are commonly called offset and Hall voltage. Contemporary smart Hall sensor circuits extract the Hall voltage via spinning current Hall probe schemes, thereby cancelling out the offset very efficiently. The magnetic field response of such Hall plates can be computed via the electric potential or via the stream function. Conversely, Hall plates with holes show new phenomena: 1) the stream function exists only for a limited class of multiply-connected domains, and 2) a sub-class of 1) behaves like a Hall/Anti-Hall bar configuration, i.e., no Hall voltage appears between any two points on the hole boundary if current contacts are on their outer boundary. The paper studies the requirements under which these effects occur. Canonical cases of simply and doubly connected domains are computed analytically. The focus is on 2D multiply-connected Hall plates where all boundaries are insulating and where all current contacts are point sized.

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confidence: 99%

The Classical Hall Effect in Multiply-Connected Plane Regions Part I: Topologies with Stream Function

Ausserlechner¹

2019

JAMP

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“…To avoid the large changing offsets in transverse voltage measurements 31 , we apply the frequently used ‘Onsager reciprocity method’ 40 41 , which is not common in studies of MIT materials. Here, for each field the Hall voltage is measured in two complementary configuration, exemplified in Fig.…”

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confidence: 99%

High resolution Hall measurements across the VO2 metal-insulator transition reveal impact of spatial phase separation

Yamin

Strelniker

Sharoni

2016

Sci Rep

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Many strongly correlated transition metal oxides exhibit a metal-insulator transition (MIT), the manipulation of which is essential for their application as active device elements. However, such manipulation is hindered by lack of microscopic understanding of mechanisms involved in these transitions. A prototypical example is VO2, where previous studies indicated that the MIT resistance change correlate with changes in carrier density and mobility. We studied the MIT using Hall measurements with unprecedented resolution and accuracy, simultaneously with resistance measurements. Contrast to prior reports, we find that the MIT is not correlated with a change in mobility, but rather, is a macroscopic manifestation of the spatial phase separation which accompanies the MIT. Our results demonstrate that, surprisingly, properties of the nano-scale spatially-separated metallic and semiconducting domains actually retain their bulk properties. This study highlights the importance of taking into account local fluctuations and correlations when interpreting transport measurements in highly correlated systems.

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“…At zero magnetic field (B15b) differs slightly from (21) in [1] (in the second indices). There are two reasons for this discrepancy: 1) the contacts of the complementary device are shifted in the direction of lower indices in [1] (whereas they are shifted in the direction of larger indices in this paper), and 2) in Here is another argument which proves that [26]. With (B14a) this gives In Appendix C we check our formulae against finite element simulations to guarantee their correctness.…”

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confidence: 93%

Relations between Hall Plates with Complementary Contact Geometries

Ausserlechner¹

2019

JAMP

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Singly connected Hall plates with N peripheral contacts can be mapped onto the upper half of the z-plane by a conformal transformation. Recently, Homentcovschi and Bercia derived the General Formula for the electric field in this region. We present an alternative intuitive derivation based on conformal mapping arguments. Then we apply the General Formula to complementary Hall plates, where contacts and insulating boundaries are swapped. The resistance matrix of the complementary device at reverse magnetic field is expressed in terms of the conductance matrix of the original device at non-reverse magnetic field. These findings are used to prove several symmetry properties of Hall plates and their complementary counterparts at arbitrary magnetic field. Journal of Applied Mathematics and Physics mentary device (see (13a) in [6]).In [7] plane singly-connected Hall plates with four peripheral contacts and equal input and output resistances were considered. If magnetic field is impressed on such a device, it has the same output voltage as its complementary device, provided both are supplied by the same voltage source (see Figure 7 in this work). This was conjectured in [8] and proven in [7] and [9] for weak applied magnetic field (see (50) in [8], see Section 4, Appendix B, and Figure 8, all in [7]). Numerical inspection suggests that this also holds for strong magnetic field, but a rigorous proof has not been given so far. In [8] it was also implicitly mentioned that the product of input resistances of original and complementary Hall plates of that particular symmetry (i.e., input resistance equals output resistance) at zero magnetic field equals twice the square of the sheet resistance (see the paragraph after (50) in [8]).Complementary Hall plates with three extended contacts on the perimeter were studied in [10]. If such a device has single mirror symmetry, also its complementary device has single mirror symmetry. Then-analogous to above-the change of the potentials on the output contacts due to reversal of magnetic field polarity are identical in both original and complementary devices, if both devices are supplied with the same supply voltage on the other two contacts, and if the magnetic field is weak (see also Figure 6 in this work). This property also means that the ratio of Hall output signal over thermal noise under the constraint of fixed supply voltage and fixed input resistance is the same in the original Hall plate and in the complementary Hall plate [10] [11].In Section 2 we reconsider the General Formula of [12] for the electric field in the upper half of the z-plane with N contacts on the real axis. Thereby, we present a different derivation than the one given in [12]. This new approach shows how the stagnation points are linked to the electric field in the Hall plate. From this result we derive the resistance matrix of a general device at arbitrary magnetic field in Section 3. This is similar to [12]. In Section 4 we link the resistance matrices of original device and complementary device at reverse...

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Reverse-magnetic-field reciprocity in conductive samples with extended contacts

Cited by 23 publications

References 22 publications

The Classical Hall Effect in Multiply-Connected Plane Regions Part I: Topologies with Stream Function

The Classical Hall Effect in Multiply-Connected Plane Regions Part I: Topologies with Stream Function

High resolution Hall measurements across the VO2 metal-insulator transition reveal impact of spatial phase separation

Relations between Hall Plates with Complementary Contact Geometries

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