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Temperature-driven enhancement and sign reversal of field-like torque in Py/FePS$_3$ bilayers
Authors:
Dhananjaya Mahapatra,
Anudeepa Ghosh,
Harekrishna Bhunia,
Bipul Pal,
Partha Mitra
Abstract:
Electrical manipulation of magnetization via current-induced spin orbit torques offers a promising route toward nonvolatile and energy efficient spintronic devices. In this work, we present a comprehensive investigation of SOTs in Py/FePS$_3$ bilayer devices, where Py/FePS$_3$ is a layered van der Waals antiferromagnetic insulator. Using low frequency harmonic Hall measurements, we quantify both f…
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Electrical manipulation of magnetization via current-induced spin orbit torques offers a promising route toward nonvolatile and energy efficient spintronic devices. In this work, we present a comprehensive investigation of SOTs in Py/FePS$_3$ bilayer devices, where Py/FePS$_3$ is a layered van der Waals antiferromagnetic insulator. Using low frequency harmonic Hall measurements, we quantify both field like and damping like torque components and examine their dependence on temperature. We find that interfacing Py with Py/FePS$_3$ leads to a pronounced enhancement of the field-like torque efficiency compared to Py reference devices, while the damping-like torque remains largely unaffected. Strikingly, the field like torque efficiency exhibits a strong temperature dependence, including a clear sign reversal upon cooling. This behavior occurs despite negligible charge current flow through the Py/FePS$_3$ layer, indicating that the observed torque modulation arises from interfacial effects rather than bulk transport. The close correlation between the temperature evolution of the field like torque and the antiferromagnetic ordering of Py/FePS$_3$ highlights the active role of antiferromagnetic insulators in controlling spin orbit torque symmetry and efficiency, and suggests new pathways for torque engineering in magnetic heterostructures.
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Submitted 28 February, 2026;
originally announced March 2026.
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Interface tuned Enhanced and Low Temperature Quenching of Orbital Hall Currents Induce Torque and magnetoresistance in Light Metal/Nickel Bilayers
Authors:
Dhananjaya Mahapatra,
Harekrishna Bhunia,
Manu S Pattelath,
Partha Mitra
Abstract:
We investigate orbital current induced effects arising from the orbital Hall effect in light-metal/ferromagnet bilayers. Thin films of Ti in ohmic contact with Ni were studied using second-harmonic longitudinal and transverse voltage measurements under an applied a.c. current. From these signals, we extract the orbital Hall torque (OHT) efficiency and the unidirectional orbital magnetoresistance (…
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We investigate orbital current induced effects arising from the orbital Hall effect in light-metal/ferromagnet bilayers. Thin films of Ti in ohmic contact with Ni were studied using second-harmonic longitudinal and transverse voltage measurements under an applied a.c. current. From these signals, we extract the orbital Hall torque (OHT) efficiency and the unidirectional orbital magnetoresistance (UOMR). Insertion of a Cu interlayer between the Ni/Ti interface leads to an enhancement of both OHT efficiency and UOMR compared to both Ni/Ti and Ni/Cu bilayers. Furthermore, systematic variation of Ti thickness reveals that both OHT efficiency and UOMR increase with increasing Ti thickness, indicating that the observed phenomena predominantly originate from the bulk orbital Hall effect rather than purely from interfacial mechanisms and Lowering the temperature leads to a clear reduction in both the orbital Hall torque (OHT) efficiency and the unidirectional orbital magnetoresistance (UOMR). The nearly linear and correlated temperature dependence of both parameters suggests a common underlying mechanism, namely, the orbital Hall effect in the light-metal layer, which governs both the generation of orbital current and its subsequent influence on the ferromagnet through orbital torque and orbital magnetoresistance.
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Submitted 12 November, 2025;
originally announced November 2025.
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Decoupling of Spin-Orbit Torque Components in Py/W Bilayers unveiled through variation of W-resistivity
Authors:
Abu Bakkar Miah,
Dhananjaya Mahapatra,
Soumik Aon,
Harekrishna Bhunia,
Partha Mitra
Abstract:
Harmonic Hall measurements were performed on a series of ferromagnetic metal/heavy metal (FM/HM) bilayers consisting of Permalloy (Py) as the FM and beta-Tungsten (W) as the HM, and the efficiencies of the two orthogonal components of the spin-orbit torque (SOT) were extracted. Two sets of Hall bar-shaped devices, differing in the aspect ratio of the voltage pickup line width and the current chann…
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Harmonic Hall measurements were performed on a series of ferromagnetic metal/heavy metal (FM/HM) bilayers consisting of Permalloy (Py) as the FM and beta-Tungsten (W) as the HM, and the efficiencies of the two orthogonal components of the spin-orbit torque (SOT) were extracted. Two sets of Hall bar-shaped devices, differing in the aspect ratio of the voltage pickup line width and the current channel width, were studied. Within each set, the resistivity of the W layer was systematically varied over a wide range (approximately 150-1000 micro-Ohm-cm). To account for geometry-induced variations in current distribution, numerical simulations were performed, and a correction protocol was developed to normalize the torque efficiencies obtained from the conventional analysis. After applying the correction, the Slonczewski-like (anti-damping, in-plane) torque efficiency exhibited a consistent dependence on W resistivity across both device sets. In contrast, the field-like (out-of-plane) torque efficiency remained largely independent of W resistivity, reinforcing its interfacial character.
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Submitted 17 December, 2025; v1 submitted 7 March, 2025;
originally announced March 2025.
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Evidence of orbital Hall current induced correlation in second harmonic response of longitudinal and transverse voltage in light metal-ferromagnet bilayers
Authors:
Dhananjaya Mahapatra,
Abu Bakkar Miah,
HareKrishna Bhunia,
Soumik Aon,
Partha Mitra
Abstract:
We investigate the effect of orbital current arising from orbital Hall effect in thin films of Nb and Ti in ohmic contact with ferromagnetic Ni in the second harmonic longitudinal and transverse voltages in response to an a.c. current applied to the bilayer structures. Our experiments were analogous to those on Heavy Metal-Ferromagnet bilayers and we extract the Orbital Hall Torque efficiency and…
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We investigate the effect of orbital current arising from orbital Hall effect in thin films of Nb and Ti in ohmic contact with ferromagnetic Ni in the second harmonic longitudinal and transverse voltages in response to an a.c. current applied to the bilayer structures. Our experiments were analogous to those on Heavy Metal-Ferromagnet bilayers and we extract the Orbital Hall Torque efficiency and unidirectional magnetoresistance (UMR). Through second-harmonic measurements, we investigate orbital Hall torque and UMR in bilayer devices composed of ferromagnetic materials (FM), such as Ni and NiFe, paired with light metals (LM), such as Ti and Nb. Our results demonstrate that LM/Ni bilayers exhibit enhanced damping-like torque and unidirectional magnetoresistance (UMR) compared to LM/NiFe bilayers. This enhancement suggests that angular momentum is generated via the orbital Hall effect within the light metal, where it undergoes orbital-to-spin conversion within the Ni ferromagnet, ultimately transferring to the magnetization of the ferromagnetic layer. Torque and UMR are also absent in single-layer devices, highlighting the necessity of the bilayer structure for orbital current generation.
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Submitted 11 June, 2025; v1 submitted 13 November, 2024;
originally announced November 2024.
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Anomalous Inverse Spin Hall Effect (AISHE) due to Unconventional Spin Currents in Ferromagnetic Films with Tailored Interfacial Magnetic Anisotropy
Authors:
Soumik Aon,
Harekrishna Bhunia,
Pratap Kumar Pal,
Abu Bakkar Miah,
Dhananjaya Mahapatra,
Anjan Barman,
Partha Mitra
Abstract:
A single layer ferromagnetic film magnetized in the plane of an ac current flow, exhibits a characteristic Hall voltage with harmonic and second harmonic components, which is attributed to the presence of spin currents with polarization non-collinear with the magnetization. A set of 30 nm thick permalloy (Py) films used in this study are deposited at an oblique angle with respect to the substrate…
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A single layer ferromagnetic film magnetized in the plane of an ac current flow, exhibits a characteristic Hall voltage with harmonic and second harmonic components, which is attributed to the presence of spin currents with polarization non-collinear with the magnetization. A set of 30 nm thick permalloy (Py) films used in this study are deposited at an oblique angle with respect to the substrate plane which induces an in-plane easy axis in the magnetization of the initial nucleating layers of the films which is distinct from the overall bulk magnetic properties of the film. This unusual magnetic texture provides a platform for the direct detection of inverse spin Hall effect in Hall bar shaped macroscopic devices at room temperatures which we denote as Anomalous Inverse Spin Hall Effect (AISHE). Control samples fabricated by normal deposition of permalloy with slow rotation of substrate shows significant reduction of the harmonic Hall signal that further substantiates the model. The analysis of the second harmonic Hall signal corroborates the presence of spin-orbit torque arising from the unconventional spin-currents in the single-layer ferromagnets.
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Submitted 6 May, 2024;
originally announced May 2024.
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Direct Electrical Detection of Spin Chemical Potential Due to Spin Hall Effect in $β$-Tungsten and Platinum Using a Pair of Ferromagnetic and Normal Metal Voltage probes
Authors:
Soumik Aon,
Abu Bakkar Miah,
Arpita Mandal,
Harekrishna Bhunia,
Dhananjaya Mahapatra,
Partha Mitra
Abstract:
The phenomenon of Spin Hall Effect (SHE) generates a pure spin current transverse to an applied current in materials with strong spin-orbit coupling, although not detectable through conventional electrical measurement. An intuitive Hall effect like measurement configuration is implemented to directly measure pure spin chemical potential of the accumulated spins at the edges of heavy metal (HM) cha…
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The phenomenon of Spin Hall Effect (SHE) generates a pure spin current transverse to an applied current in materials with strong spin-orbit coupling, although not detectable through conventional electrical measurement. An intuitive Hall effect like measurement configuration is implemented to directly measure pure spin chemical potential of the accumulated spins at the edges of heavy metal (HM) channels that generates large SHE. A pair of transverse linearly aligned voltage probes in placed in ohmic contact with the top surface of HM , one being a ferromagnetic metal (FM) with non-zero spin polarization and other is the reference metal (RM) with zero polarization of carriers. This combination of FM/RM electrodes is shown to induce an additional voltage proportional to a spin accumulation potential, which is anti symmetric with respect to opposite orientations of FM controlled by a 2D vector magnet. Proof of concept of the measurement scheme is verified by comparing the signs of voltages for HM channels of Tungsten (W) and Platinum (Pt) which are known to generate opposite spin accumulation under similar conditions of applied current. The same devices are also able to detect the reciprocal effect, inverse spin Hall effect (ISHE) by swapping the current and voltage leads and the results are consistent with reciprocity principle. Further, exploiting a characteristic feature of W thin film deposition, a series of devices were fabricated with W resistivity varying over a wide range of 10 - 750 $μΩ$-cm and the calculated spin Hall resistivity exhibits a pronounced power law dependence on resistivity. Our measurement scheme combined with almost two decades of HM resistivity variation provides the ideal platform required to test the underlying microscopic mechanism responsible for SHE/ISHE.
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Submitted 5 April, 2024;
originally announced April 2024.
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Anisotropic magneto-photothermal voltage in Sb2Te3 topological insulator thin films
Authors:
Subhadip Manna,
Sambhu G Nath,
Samrat Roy,
Soumik Aon,
Sayani Pal,
Kanav Sharma,
Dhananjaya Mahapatra,
Partha Mitra,
Sourin Das,
Bipul Pal,
Chiranjib Mitra
Abstract:
We studied longitudinal and Hall photothermal voltages under a planar magnetic field scan in epitaxial thin films of the Topological Insulator (TI) Sb2Te3, grown using pulsed laser deposition (PLD). Unlike prior research that utilised polarised light-induced photocurrent to investigate the TI, our study introduces advancements based on unpolarized light-induced local heating. This method yields a…
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We studied longitudinal and Hall photothermal voltages under a planar magnetic field scan in epitaxial thin films of the Topological Insulator (TI) Sb2Te3, grown using pulsed laser deposition (PLD). Unlike prior research that utilised polarised light-induced photocurrent to investigate the TI, our study introduces advancements based on unpolarized light-induced local heating. This method yields a thermoelectric response exhibiting a direct signature of strong spin-orbit coupling. Our analysis reveals three distinct contributions when fitting the photothermal voltage data to the angular dependence of the planar magnetic field. The interaction between the applied magnetic field and the thermal gradient on the bulk band orbitals enables the differentiation between the ordinary Nernst effect from the out-of-plane thermal gradient and an extraordinary magneto-thermal contribution from the planar thermal gradient. The fitting of our data to theoretical models indicates that these effects primarily arise from the bulk states of the TI rather than the surface states. These findings highlight PLD-grown epitaxial topological insulator thin films as promising candidates for optoelectronic devices, including sensors and actuators. Such devices offer controllable responses through position-dependent, non-invasive local heating via focused incident light and variations in the applied magnetic field direction.
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Submitted 15 March, 2024;
originally announced March 2024.
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Modulating Spin Current Induced Effective Damping in $β-W/Py$ Heterostructures by a Systematic Variation in Resistivity of the Sputtered Deposited $β-W$ films
Authors:
Soumik Aon,
Sayani Pal,
Subhadip Manna,
Chiranjib Mitra,
Partha Mitra
Abstract:
Utilizing the spin-induced pumping from a ferromagnet (FM) into a heavy metal (HM) under the ferromagnetic resonance (FMR) condition, we report an enhancement in effective damping in $β$- W/Py bilayers by systematically varying resistivity ($ρ_{W}$) of $β$-W films. Different resistivity ranging from 100 $μΩ$-cm to 1400 $μΩ$-cm with a thickness of 8 nm can be achieved by varying the argon pressure…
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Utilizing the spin-induced pumping from a ferromagnet (FM) into a heavy metal (HM) under the ferromagnetic resonance (FMR) condition, we report an enhancement in effective damping in $β$- W/Py bilayers by systematically varying resistivity ($ρ_{W}$) of $β$-W films. Different resistivity ranging from 100 $μΩ$-cm to 1400 $μΩ$-cm with a thickness of 8 nm can be achieved by varying the argon pressure ($P_{Ar}$) during the growth by the method of sputtering. The coefficient of effective damping $α_{eff}$ is observed to increase from 0.010 to 0.025 with $ρ_{W}$, which can be modulated by $P_{Ar}$. We observe a modest dependence of $α_{eff}$ on the sputtering power ($p_{S}$) while keeping the $P_{Ar}$ constant. $α_{eff}$ dependence on both $P_{Ar}$ and $p_{S}$ suggests that there exists a strong correlation between $α_{eff}$ and $ρ_{W}$. It is thus possible to utilize $ρ_{W}$ as a tuning parameter to regulate the $α_{eff}$, which can be advantageous for faster magnetization dynamics switching. The thickness dependence study of Py in the aforementioned bilayers manifests a higher spin mixing conductance ($g^{\uparrow\downarrow}_{eff}$) which suggests a strong spin pumping from Py into the $β$-W layer. The effective spin current ($J_{S(eff)}$) is also evaluated by considering the spin-back flow in this process. Intrinsic spin mixing conductance ($g^{\uparrow\downarrow}_{W}$) and spin diffusion length ($λ_{SD}$) of $β$-W are additionally investigated using thickness variations in $β$-W. Furthermore, the low-temperature study in $β$-W/Py reveals an intriguing temperature dependence in $α_{eff}$ which is quite different from $α_{b}$ of single Py layer and the enhancement in $α_{eff}$ at low temperature can be attributed to the spin-induced pumping from Py layer into $β$-W.
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Submitted 5 August, 2023;
originally announced August 2023.
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Role of electron and hole doping in NdNi1_xVxO3 Nanostructure
Authors:
Raktima Basu,
Reshma Kumawat,
Mrinmay Sahu,
Abu Bakkar Miah,
Partha Mitra,
Goutam Dev Mukherjee
Abstract:
Neodymium nickelate, NdNiO3 attracts attraction due to the simultaneous occurrence of several phase transitions around the same temperature. The electronic properties of NdNiO3 are extremely complex as structural distortion, electron correlation, charge ordering, and orbital overlapping play significant roles in the transitions. We report the effects of electron and hole injection via doping a sin…
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Neodymium nickelate, NdNiO3 attracts attraction due to the simultaneous occurrence of several phase transitions around the same temperature. The electronic properties of NdNiO3 are extremely complex as structural distortion, electron correlation, charge ordering, and orbital overlapping play significant roles in the transitions. We report the effects of electron and hole injection via doping a single 3d metal, V, in the NdNiO3 nanostructures to understand the variations in the electronic properties without any structural distortion. A reversible resistivity modulation more than five orders of magnitude via hole doping and complete suppression of metal to insulator transition via electron doping is observed along with the switching of major charge carriers. The modulation of electronic properties without any structural distortion and external strain opens up new directions to consider the NdNi1_xVxO3 nanostructures applicable as emerging electronic devices.
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Submitted 5 September, 2022;
originally announced September 2022.
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AI without networks
Authors:
Partha P Mitra,
Clément Sire
Abstract:
Contemporary Artificial Intelligence (AI) stands on two legs: large training data corpora and many-parameter artificial neural networks (ANNs). The data corpora are needed to represent the complexity and heterogeneity of the world. The role of the networks is less transparent due to the obscure dependence of the network parameters and outputs on the training data and inputs. This raises problems,…
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Contemporary Artificial Intelligence (AI) stands on two legs: large training data corpora and many-parameter artificial neural networks (ANNs). The data corpora are needed to represent the complexity and heterogeneity of the world. The role of the networks is less transparent due to the obscure dependence of the network parameters and outputs on the training data and inputs. This raises problems, ranging from technical-scientific to legal-ethical. We hypothesize that a transparent approach to machine learning is possible without using networks at all. By generalizing a parameter-free, statistically consistent data interpolation method, which we analyze theoretically in detail, we develop a network-free framework for AI incorporating generative modeling. We demonstrate this framework with examples from three different disciplines - ethology, control theory, and mathematics. Our generative Hilbert framework applied to the trajectories of small groups of swimming fish outperformed state-of-the-art traditional mathematical behavioral models and current ANN-based models. We demonstrate pure data interpolation based control by stabilizing an inverted pendulum and a driven logistic map around unstable fixed points. Finally, we present a mathematical application by predicting zeros of the Riemann Zeta function, achieving comparable performance as a transformer network. We do not suggest that the proposed framework will always outperform networks as over-parameterized networks can interpolate. However, our framework is theoretically sound, transparent, deterministic, and parameter free: remarkably, it does not require any compute-expensive training, does not involve optimization, has no model selection, and is easily reproduced and ported. We also propose an easily computed method of credit assignment based on this framework, to help address ethical-legal challenges raised by generative AI.
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Submitted 5 June, 2024; v1 submitted 7 June, 2021;
originally announced June 2021.
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Cooling arbitrary near-critical systems using hyperbolic quenches
Authors:
Prahar Mitra,
Matteo Ippoliti,
R. N. Bhatt,
S. L. Sondhi,
Kartiek Agarwal
Abstract:
We describe a quench protocol that allows the rapid preparation of ground states of arbitrary interacting conformal field theories in $1+1$ dimensions. We start from the ground state of a related gapped relativistic quantum field theory and consider sudden quenches along the space-like trajectories $t^2 - x^2 = T^2_0$ (parameterized by $T_0$) to a conformal field theory. Using only arguments of sy…
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We describe a quench protocol that allows the rapid preparation of ground states of arbitrary interacting conformal field theories in $1+1$ dimensions. We start from the ground state of a related gapped relativistic quantum field theory and consider sudden quenches along the space-like trajectories $t^2 - x^2 = T^2_0$ (parameterized by $T_0$) to a conformal field theory. Using only arguments of symmetry and conformal invariance, we show that the post-quench stress-energy tensor of the conformal field theory is uniquely constrained up to an overall scaling factor. Crucially, the $\textit{geometry}$ of the quench necessitates that the system approach the vacuum energy density over all space except the singular lines $x = \pm t$. The above arguments are verified using an exact treatment of the quench for the Gaussian scalar field theory (equivalently, the Luttinger liquid), and numerically for the quantum $O(N)$ model in the large-$N$ limit. Additionally, for the Gaussian theory, we find in fact that even when starting from certain excited states, the quench conserves entropy, and is thus also suitable for rapidly preparing excited states. Our methods serve as a fast, alternative route to reservoir-based cooling to prepare quantum states of interest.
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Submitted 5 September, 2018;
originally announced September 2018.
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Overfitting or perfect fitting? Risk bounds for classification and regression rules that interpolate
Authors:
Mikhail Belkin,
Daniel Hsu,
Partha Mitra
Abstract:
Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated classifiers appears to be ubiquitous in high-dimensional data, having been observed in deep networks, kernel machines, boosting and random forests. Their performanc…
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Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated classifiers appears to be ubiquitous in high-dimensional data, having been observed in deep networks, kernel machines, boosting and random forests. Their performance is consistently robust even when the data contain large amounts of label noise.
Very little theory is available to explain these observations. The vast majority of theoretical analyses of generalization allows for interpolation only when there is little or no label noise. This paper takes a step toward a theoretical foundation for interpolated classifiers by analyzing local interpolating schemes, including geometric simplicial interpolation algorithm and singularly weighted $k$-nearest neighbor schemes. Consistency or near-consistency is proved for these schemes in classification and regression problems. Moreover, the nearest neighbor schemes exhibit optimal rates under some standard statistical assumptions.
Finally, this paper suggests a way to explain the phenomenon of adversarial examples, which are seemingly ubiquitous in modern machine learning, and also discusses some connections to kernel machines and random forests in the interpolated regime.
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Submitted 26 October, 2018; v1 submitted 13 June, 2018;
originally announced June 2018.
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Phase transitions in distributed control systems with multiplicative noise
Authors:
Nicolas Allegra,
Bassam Bamieh,
Partha P. Mitra,
Clément Sire
Abstract:
Contemporary technological challenges often involve many degrees of freedom in a distributed or networked setting. Three aspects are notable: the variables are usually associated with the nodes of a graph with limited communication resources, hindering centralized control; the communication is subjected to noise; and the number of variables can be very large. These three aspects make tools and tec…
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Contemporary technological challenges often involve many degrees of freedom in a distributed or networked setting. Three aspects are notable: the variables are usually associated with the nodes of a graph with limited communication resources, hindering centralized control; the communication is subjected to noise; and the number of variables can be very large. These three aspects make tools and techniques from statistical physics particularly suitable for the performance analysis of such networked systems in the limit of many variables (analogous to the thermodynamic limit in statistical physics). Perhaps not surprisingly, phase-transition like phenomena appear in these systems, where a sharp change in performance can be observed with a smooth parameter variation, with the change becoming discontinuous or singular in the limit of infinite system size. In this paper we analyze the so called network consensus problem, prototypical of the above considerations, that has been previously analyzed mostly in the context of additive noise. We show that qualitatively new phase-transition like phenomena appear for this problem in the presence of multiplicative noise. Depending on dimensions and on the presence or absence of a conservation law, the system performance shows a discontinuous change at a threshold value of the multiplicative noise strength. In the absence of the conservation law, and for graph spectral dimension less than two, the multiplicative noise threshold (the stability margin of the control problem) is zero. This is reminiscent of the absence of robust controllers for certain classes of centralized control problems. Although our study involves a toy model we believe that the qualitative features are generic, with implication for the robust stability of distributed control systems, as well as the effect of roundoff errors and communication noise on distributed algorithms.
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Submitted 29 August, 2017; v1 submitted 3 October, 2016;
originally announced October 2016.
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Critical Behavior and Universality Classes for an Algorithmic Phase Transition in Sparse Reconstruction
Authors:
Mohammad Ramezanali,
Partha P. Mitra,
Anirvan M. Sengupta
Abstract:
Recovery of an $N$-dimensional, $K$-sparse solution $\mathbf{x}$ from an $M$-dimensional vector of measurements $\mathbf{y}$ for multivariate linear regression can be accomplished by minimizing a suitably penalized least-mean-square cost $||\mathbf{y}-\mathbf{H} \mathbf{x}||_2^2+λV(\mathbf{x})$. Here $\mathbf{H}$ is a known matrix and $V(\mathbf{x})$ is an algorithm-dependent sparsity-inducing pen…
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Recovery of an $N$-dimensional, $K$-sparse solution $\mathbf{x}$ from an $M$-dimensional vector of measurements $\mathbf{y}$ for multivariate linear regression can be accomplished by minimizing a suitably penalized least-mean-square cost $||\mathbf{y}-\mathbf{H} \mathbf{x}||_2^2+λV(\mathbf{x})$. Here $\mathbf{H}$ is a known matrix and $V(\mathbf{x})$ is an algorithm-dependent sparsity-inducing penalty. For `random' $\mathbf{H}$, in the limit $λ\rightarrow 0$ and $M,N,K\rightarrow \infty$, keeping $ρ=K/N$ and $α=M/N$ fixed, exact recovery is possible for $α$ past a critical value $α_c = α(ρ)$. Assuming $\mathbf{x}$ has iid entries, the critical curve exhibits some universality, in that its shape does not depend on the distribution of $\mathbf{x}$. However, the algorithmic phase transition occurring at $α=α_c$ and associated universality classes remain ill-understood from a statistical physics perspective, i.e. in terms of scaling exponents near the critical curve. In this article, we analyze the mean-field equations for two algorithms, Basis Pursuit ($V(\mathbf{x})=||\mathbf{x}||_{1} $) and Elastic Net ($V(\mathbf{x})= ||\mathbf{x}||_{1} + \tfrac{g}{2} ||\mathbf{x}||_{2}^2$) and show that they belong to different universality classes in the sense of scaling exponents, with Mean Squared Error (MSE) of the recovered vector scaling as $λ^\frac{4}{3}$ and $λ$ respectively, for small $λ$ on the critical line. In the presence of additive noise, we find that, when $α>α_c$, MSE is minimized at a non-zero value for $λ$, whereas at $α=α_c$, MSE always increases with $λ$.
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Submitted 28 October, 2019; v1 submitted 29 September, 2015;
originally announced September 2015.
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The cavity method for analysis of large-scale penalized regression
Authors:
Mohammad Ramezanali,
Partha P. Mitra,
Anirvan M. Sengupta
Abstract:
Penalized regression methods aim to retrieve reliable predictors among a large set of putative ones from a limited amount of measurements. In particular, penalized regression with singular penalty functions is important for sparse reconstruction algorithms. For large-scale problems, these algorithms exhibit sharp phase transition boundaries where sparse retrieval breaks down. Large optimization pr…
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Penalized regression methods aim to retrieve reliable predictors among a large set of putative ones from a limited amount of measurements. In particular, penalized regression with singular penalty functions is important for sparse reconstruction algorithms. For large-scale problems, these algorithms exhibit sharp phase transition boundaries where sparse retrieval breaks down. Large optimization problems associated with sparse reconstruction have been analyzed in the literature by setting up corresponding statistical mechanical models at a finite temperature. Using replica method for mean field approximation, and subsequently taking a zero temperature limit, this approach reproduces the algorithmic phase transition boundaries. Unfortunately, the replica trick and the non-trivial zero temperature limit obscure the underlying reasons for the failure of a sparse reconstruction algorithm, and of penalized regression methods, in general. In this paper, we employ the ``cavity method'' to give an alternative derivation of the mean field equations, working directly in the zero-temperature limit. This derivation provides insight into the origin of the different terms in the self-consistency conditions. The cavity method naturally involves a quantity, the average local susceptibility, whose behavior distinguishes different phases in this system. This susceptibility can be generalized for analysis of a broader class of sparse reconstruction algorithms.
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Submitted 25 November, 2015; v1 submitted 13 January, 2015;
originally announced January 2015.
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Understanding the Effect of Uniaxial Tensile Strain on the Early Stages of Sensitization in AISI 304 Austenitic Stainless Steel
Authors:
P. S. Chowdhurya,
S. K. Guchhait,
P. K. Mitra,
P. Mukherjee,
N. Gayathri,
M. K. Mitra
Abstract:
In the present study, an attempt has been made to understand the effect of different competing mechanisms controlling the overall degree of sensitization (DOS) of deformed austenitic stainless steel at the early stage of sensitization. The Double Loop Electrochemical Potentiokinetic Reactivation (DL-EPR) studies were performed to characterize the Degree of Sensitization (DOS) as functions of pre-d…
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In the present study, an attempt has been made to understand the effect of different competing mechanisms controlling the overall degree of sensitization (DOS) of deformed austenitic stainless steel at the early stage of sensitization. The Double Loop Electrochemical Potentiokinetic Reactivation (DL-EPR) studies were performed to characterize the Degree of Sensitization (DOS) as functions of pre-defined strain and sensitization temperature. X-ray Diffraction (XRD) and Scanning Electron Microscopy (SEM) were used to explain the phenomena qualitatively. A non monotonous behaviour in the variation of DOS has been observed with deformation and sensitization temperature. The presence of Deformation Induced Martensites (DIM) and their transformation into tempered martensites (alpha + Fe3C) at higher temperatures was found to play major roles in controlling the overall sensitization and desensitization processes.
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Submitted 7 March, 2014;
originally announced March 2014.
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Localization and the Anomalous Hall Effect in a "Dirty" Metallic Ferromagnet
Authors:
P. Mitra,
N. Kumar,
N. Samarth
Abstract:
We report magnetoresistance measurements over an extensive temperature range (0.1 K $\leq T \leq$ 100 K) in a disordered ferromagnetic semiconductor (\gma). The study focuses on a series of metallic \gma~ epilayers that lie in the vicinity of the metal-insulator transition ($k_F l_e\sim 1$). At low temperatures ($T < 4$ K), we first confirm the results of earlier studies that the longitudinal cond…
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We report magnetoresistance measurements over an extensive temperature range (0.1 K $\leq T \leq$ 100 K) in a disordered ferromagnetic semiconductor (\gma). The study focuses on a series of metallic \gma~ epilayers that lie in the vicinity of the metal-insulator transition ($k_F l_e\sim 1$). At low temperatures ($T < 4$ K), we first confirm the results of earlier studies that the longitudinal conductivity shows a $T^{1/3}$ dependence, consistent with quantum corrections from carrier localization in a ``dirty'' metal. In addition, we find that the anomalous Hall conductivity exhibits universal behavior in this temperature range, with no pronounced quantum corrections. We argue that observed scaling relationship between the low temperature longitudinal and transverse resistivity, taken in conjunction with the absence of quantum corrections to the anomalous Hall conductivity, is consistent with the side-jump mechanism for the anomalous Hall effect. In contrast, at high temperatures ($T \gtrsim 4$ K), neither the longitudinal nor the anomalous Hall conductivity exhibit universal behavior, indicating the dominance of inelastic scattering contributions down to liquid helium temperatures.
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Submitted 14 June, 2010; v1 submitted 14 August, 2008;
originally announced August 2008.
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Quasi-reversible Magnetoresistance in Exchange Spring Tunnel Junctions
Authors:
M. Zhu,
M. J. Wilson,
P. Mitra,
P. Schiffer,
N. Samarth
Abstract:
We report a large, quasi-reversible tunnel magnetoresistance in exchange-biased ferromagnetic semiconductor tunnel junctions wherein a soft ferromagnetic semiconductor (\gma) is exchange coupled to a hard ferromagnetic metal (MnAs). Our observations are consistent with the formation of a region of inhomogeneous magnetization (an "exchange spring") within the biased \gma layer. The distinctive tu…
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We report a large, quasi-reversible tunnel magnetoresistance in exchange-biased ferromagnetic semiconductor tunnel junctions wherein a soft ferromagnetic semiconductor (\gma) is exchange coupled to a hard ferromagnetic metal (MnAs). Our observations are consistent with the formation of a region of inhomogeneous magnetization (an "exchange spring") within the biased \gma layer. The distinctive tunneling anisotropic magnetoresistance of \gma produces a pronounced sensitivity of the magnetoresistance to the state of the exchange spring.
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Submitted 17 July, 2008;
originally announced July 2008.
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Spin Valve Effect in Self-exchange Biased Ferromagnetic Metal/Semiconductor Bilayers
Authors:
M. Zhu,
M. J. Wilson,
B. L. Sheu,
P. Mitra,
P. Schiffer,
N. Samarth
Abstract:
We report magnetization and magetoresistance measurements in hybrid ferromagnetic metal/semiconductor heterostructures comprised of MnAs/(Ga,Mn)As bilayers. Our measurements show that the (metallic) MnAs and (semiconducting) (Ga,Mn)As layers are exchange coupled, re- sulting in an exchange biasing of the magnetically softer (Ga,Mn)As layer that weakens with layer thickness. Magnetoresistance mea…
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We report magnetization and magetoresistance measurements in hybrid ferromagnetic metal/semiconductor heterostructures comprised of MnAs/(Ga,Mn)As bilayers. Our measurements show that the (metallic) MnAs and (semiconducting) (Ga,Mn)As layers are exchange coupled, re- sulting in an exchange biasing of the magnetically softer (Ga,Mn)As layer that weakens with layer thickness. Magnetoresistance measurements in the current-perpendicular-to-the-plane geometry show a spin valve effect in these self-exchange biased bilayers. Similar measurements in MnAs/p- GaAs/(Ga,Mn)As trilayers show that the exchange coupling diminishes with spatial separation between the layers.
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Submitted 15 August, 2007;
originally announced August 2007.
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Weak localization correction to the anomalous Hall effect in polycrystalline Fe films
Authors:
P. Mitra,
A. F. Hebard,
K. A. Muttalib,
P. Woelfle
Abstract:
In situ transport measurements have been made on ultrathin ($<$100 Å thick) polycrystalline Fe films as a function of temperature and magnetic field for a wide range of disorder strengths. For sheet resistances $R_{xx}$ less than $\sim 3kΩ$, we find a logarithmic temperature dependence of the anomalous Hall conductivity $σ_{xy}$ which is shown for the first time to be due to a universal scale de…
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In situ transport measurements have been made on ultrathin ($<$100 Å thick) polycrystalline Fe films as a function of temperature and magnetic field for a wide range of disorder strengths. For sheet resistances $R_{xx}$ less than $\sim 3kΩ$, we find a logarithmic temperature dependence of the anomalous Hall conductivity $σ_{xy}$ which is shown for the first time to be due to a universal scale dependent weak localization correction within the skew scattering model. For higher sheet resistance, granularity becomes important and the break down of universal behavior becomes manifest as the prefactors to $σ_{xx}$ and $σ_{xy}$ decrease at different rates with increasing disorder.
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Submitted 22 May, 2007; v1 submitted 8 June, 2006;
originally announced June 2006.
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Schrodinger equation with a spatially and temporally random potential: Effects of cross-phase modulation in optical communication
Authors:
A. G. Green,
P. B. Littlewood,
P. P. Mitra,
L. G. L. Wegener
Abstract:
We model the effects of cross-phase modulation in frequency (or wavelength) division multiplexed optical communications systems, using a Schrödinger equation with a spatially and temporally random potential. Green's functions for the propagation of light in this system are calculated using Feynman path-integral and diagrammatic techniques. This propagation leads to a non-Gaussian joint distribut…
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We model the effects of cross-phase modulation in frequency (or wavelength) division multiplexed optical communications systems, using a Schrödinger equation with a spatially and temporally random potential. Green's functions for the propagation of light in this system are calculated using Feynman path-integral and diagrammatic techniques. This propagation leads to a non-Gaussian joint distribution of the input and output optical fields. We use these results to determine the amplitude and timing jitter of a signal pulse and to estimate the system capacity in analog communication.
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Submitted 16 October, 2002;
originally announced October 2002.
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Nonlinear limits to the information capacity of optical fiber communications
Authors:
Partha P. Mitra,
Jason B. Stark
Abstract:
The exponential growth in the rate at which information can be communicated through an optical fiber is a key element in the so called information revolution. However, like all exponential growth laws, there are physical limits to be considered. The nonlinear nature of the propagation of light in optical fiber has made these limits difficult to elucidate. Here we obtain basic insights into the l…
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The exponential growth in the rate at which information can be communicated through an optical fiber is a key element in the so called information revolution. However, like all exponential growth laws, there are physical limits to be considered. The nonlinear nature of the propagation of light in optical fiber has made these limits difficult to elucidate. Here we obtain basic insights into the limits to the information capacity of an optical fiber arising from these nonlinearities. The key simplification lies in relating the nonlinear channel to a linear channel with multiplicative noise, for which we are able to obtain analytical results. In fundamental distinction to the linear additive noise case, the capacity does not grow indefinitely with increasing signal power, but has a maximal value. The ideas presented here have broader implications for other nonlinear information channels, such as those involved in sensory transduction in neurobiology. These have been often examined using additive noise linear channel models, and as we show here, nonlinearities can change the picture qualitatively.
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Submitted 7 November, 2000;
originally announced November 2000.
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Capacity of multivariate channels with multiplicative noise: I.Random matrix techniques and large-N expansions for full transfer matrices
Authors:
Anirvan Mayukh Sengupta,
Partha Pratim Mitra
Abstract:
We study memoryless, discrete time, matrix channels with additive white Gaussian noise and input power constraints of the form $Y_i = \sum_j H_{ij} X_j + Z_i$, where $Y_i$ ,$X_j$ and $Z_i$ are complex, $i=1..m$, $j=1..n$, and $H$ is a complex $m\times n$ matrix with some degree of randomness in its entries. The additive Gaussian noise vector is assumed to have uncorrelated entries. Let $H$ be a…
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We study memoryless, discrete time, matrix channels with additive white Gaussian noise and input power constraints of the form $Y_i = \sum_j H_{ij} X_j + Z_i$, where $Y_i$ ,$X_j$ and $Z_i$ are complex, $i=1..m$, $j=1..n$, and $H$ is a complex $m\times n$ matrix with some degree of randomness in its entries. The additive Gaussian noise vector is assumed to have uncorrelated entries. Let $H$ be a full matrix (non-sparse) with pairwise correlations between matrix entries of the form $ E[H_{ik} H^*_{jl}] = {1\over n}C_{ij} D_{kl} $, where $C$,$D$ are positive definite Hermitian matrices. Simplicities arise in the limit of large matrix sizes (the so called large-N limit) which allow us to obtain several exact expressions relating to the channel capacity. We study the probability distribution of the quantity $ f(H) = \log \det (1+P H^{\dagger}S H) $. $S$ is non-negative definite and hermitian, with $Tr S=n$. Note that the expectation $E[f(H)]$, maximised over $S$, gives the capacity of the above channel with an input power constraint in the case $H$ is known at the receiver but not at the transmitter. For arbitrary $C$,$D$ exact expressions are obtained for the expectation and variance of $f(H)$ in the large matrix size limit. For $C=D=I$, where $I$ is the identity matrix, expressions are in addition obtained for the full moment generating function for arbitrary (finite) matrix size in the large signal to noise limit. Finally, we obtain the channel capacity where the channel matrix is partly known and partly unknown and of the form $αI+ βH$, $α,β$ being known constants and entries of $H$ i.i.d. Gaussian with variance $1/n$. Channels of the form described above are of interest for wireless transmission with multiple antennae and receivers.
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Submitted 31 October, 2000;
originally announced October 2000.
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The Channel Capacity of a Fiber Optics Communication System: perturbation theory
Authors:
Evgenii Narimanov,
Partha Mitra
Abstract:
We consider the communication channel given by a fiber optical transmission line. We develop a method to perturbatively calculate the information capacity of a nonlinear channel, given the corresponding evolution equation. Using this technique, we compute the decrease of the channel capacity to the leading order in the perturbative parameter for fiber optics communication systems.
We consider the communication channel given by a fiber optical transmission line. We develop a method to perturbatively calculate the information capacity of a nonlinear channel, given the corresponding evolution equation. Using this technique, we compute the decrease of the channel capacity to the leading order in the perturbative parameter for fiber optics communication systems.
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Submitted 20 July, 2000; v1 submitted 12 July, 2000;
originally announced July 2000.
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Distributions of Singular Values for Some Random Matrices
Authors:
A. M. Sengupta,
P. P. Mitra
Abstract:
The Singular Value Decomposition is a matrix decomposition technique widely used in the analysis of multivariate data, such as complex space-time images obtained in both physical and biological systems. In this paper, we examine the distribution of Singular Values of low rank matrices corrupted by additive noise. Past studies have been limited to uniform uncorrelated noise. Using diagrammatic an…
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The Singular Value Decomposition is a matrix decomposition technique widely used in the analysis of multivariate data, such as complex space-time images obtained in both physical and biological systems. In this paper, we examine the distribution of Singular Values of low rank matrices corrupted by additive noise. Past studies have been limited to uniform uncorrelated noise. Using diagrammatic and saddle point integration techniques, we extend these results to heterogeneous and correlated noise sources. We also provide perturbative estimates of error bars on the reconstructed low rank matrix obtained by truncating a Singular Value Decomposition.
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Submitted 25 September, 1997;
originally announced September 1997.
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Exclusion statistics and many-particle states
Authors:
P. Mitra
Abstract:
The thermodynamic distribution function for exclusion statistics is derived. Creation and annihilation operators for particles obeying such statistics are discussed. A connection with anyons is pointed out.
The thermodynamic distribution function for exclusion statistics is derived. Creation and annihilation operators for particles obeying such statistics are discussed. A connection with anyons is pointed out.
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Submitted 30 November, 1994;
originally announced November 1994.
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Understanding Far-Infrared Absorption in the S=1 Antiferromagnetic Chain Compound NENP
Authors:
Partha P. Mitra,
Bertrand I. Halperin
Abstract:
Infrared transmission measurements on the $S=1$ antiferromagnetic chain compound NENP in applied magnetic fields show a sharp absorption line at the field-shifted Haldane gap. This violates a wave-vector selection rule of the Hamiltonian normally used for NENP, as the gap excitations occur at the Brillouin zone boundary. We argue that the crystal structure admits terms which can explain the abso…
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Infrared transmission measurements on the $S=1$ antiferromagnetic chain compound NENP in applied magnetic fields show a sharp absorption line at the field-shifted Haldane gap. This violates a wave-vector selection rule of the Hamiltonian normally used for NENP, as the gap excitations occur at the Brillouin zone boundary. We argue that the crystal structure admits terms which can explain the absorption lines. In addition, in an applied field, staggered orientations of the g-tensors produce a staggered magnetic field. This can explain the observation of a finite gap at all applied fields.
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Submitted 16 September, 1993;
originally announced September 1993.