Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “FERROMAGNETISM”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,783 records · Page 99
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Effect of interionic anisotropy on the phase states and spectra of a non-Heisenberg magnet with S = 1

We study the effect of interionic anisotropy on the phase states of a non-Heisenberg ferromagnet with magnetic ion spin S = 1. It is shown that depending on the relation between the interionic anisotropy constants, uniaxial and angular ferromagnetic and nonmagnetic phases exist in the system. We analyze the dynamic properties of the system in the vicinity of orientational phase transitions, as well as a phase transition in the magnetic moment magnitude. It is shown that orientational phase transitions in ferromagnetic and nematic phases can be first- as well as second-order.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Magnetic proximity effect at the interface between a cuprate superconductor and an oxide spin valve

A heterostructure that consists of the YBa{sub 2}Cu{sub 3}O{sub 7–δ} cuprate superconductor and the SrRuO{sub 3}/La{sub 0.7}Sr{sub 0.3}MnO{sub 3} ruthenate/manganite spin valve is investigated using SQUID magnetometry, ferromagnetic resonance, and neutron reflectometry. It is shown that a magnetic moment is induced due to the magnetic proximity effect in the superconducting part of the heterostructure, while the magnetic moment in the composite ferromagnetic interlayer is suppressed. The magnetization emerging in the superconductor coincides in order of magnitude with the results of calculations taking into account the induced magnetic moment of Cu atoms because of orbital reconstruction at the interface between the superconductor and the ferromagnet, as well as with the results of the model taking into account the variations in the density of states at a distance on the order of the coherence length in the superconductor. The experimentally obtained characteristic penetration depth of the magnetic moment in the superconductor considerably exceeds the coherence length of the cuprate superconductor, which indicates the predominance of the mechanism of induced magnetic moment of Cu atoms.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Causes of the Metamagnetism in a Disordered EuMn{sub 0.5}Co{sub 0.5}O{sub 3} Perovskite

The magnetic properties of the EuMn{sub 0.5}Co{sub 0.5}O{sub 3} perovskite synthesized under various conditions are studied in fields up to 140 kOe. The sample synthesized at T = 1500°C is shown to exhibit a metamagnetic phase transition, which is irreversible below T = 40 K, and the sample synthesized at T = 1200°C demonstrates the field dependence of magnetization that is typical of a ferromagnet. Both samples have T{sub C} = 123 K and approximately the same magnetization in high magnetic fields. The metamagnetism is assumed to be related to a transition from a noncollinear ferromagnetic phase to a collinear phase, and the presence of clusters with ordered Co{sup 2+} and Mn{sup 4+} ions leads to ferromagnetism. The noncollinear phase is formed due to the competition between positive Co{sup 2+}–Mn{sup 4+} and negative Mn{sup 4+}–Mn{sup 4+} and Co{sup 2+}–Co{sup 2+} interactions, which make almost the same contributions, and to the existence of a high magnetic anisotropy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Unusual Behavior of the Coercive Field in a (CoFeB){sub x}(LiNbO{sub y}){sub 100 –x} Nanocomposite with a High Content of Magnetic Ions in an Insulating Matrix

The temperature behavior of the coercive field H{sub c}(T) and the magnetic anisotropy in (CoFeB){sub x}(LiNbO{sub y}){sub 100 –x} nanocomposite films with a ferromagnetic alloy content x = 33–48 at % near the metal–insulator transition (x{sub c} ≈ 42 at %) have been studied by the magnetometry and ferromagnetic resonance methods. The films were ensembles of CoFe granules with lateral sizes of 2–4 nm, which are highly elongated (up to 10–15 nm) in the nanocomposite growth direction and embedded in a LiNbO{sub y} matrix with a high content of magnetic Fe{sup 2+} and Co{sup 2+} ions (up to 3 × 10{sup 22} cm{sup –3}). A nonmonotonic behavior of H{sub c}(T), viz., a sharp minimum at a temperature T{sub F} ≈ 50 K close to the blocking temperature (T{sub b}{sup ∗} ≈ 70 K) of the granule magnetic moment, has been detected in samples with x < 42 at %. The effective field of the perpendicular growth anisotropy (0.4–0.8 kOe) turns out to be an order of magnitude lower than the field of the granule shape anisotropy (about 7 kOe) and increases with x. The revealed peculiarities are explained by the fact that, apart from the ferromagnetic intergranular exchange interaction in an infinite cluster, the surface anisotropy effects involving magnetic ions in a thin layer adjacent to the cluster and responsible for the surface interaction fluctuations play a big role in the investigated percolation nanocomposites, enhancing the nanocomposite demagnetization at T ≈ T{sub F} ~ T{sub b}{sup ∗}.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Magnetic and Resistive Properties of Magnetite/Iridate Heterostructures

A technique is developed to grow epitaxial heterostructures consisting of strontium iridate (SrIrO{sub 3}) and lanthanum–strontium manganite (La{sub 0.7}Sr{sub 0.3}MnO{sub 3}). Their transport properties and ferromagnetic resonance spectra are measured. The parameters obtained are compared with the properties of individual iridate and manganite films. The results of resistive measurements point to conduction of the iridate/manganite interface. As temperature decreases, the ferromagnetic resonance line width increases and the resonance field decreases, which indicates the appearance of additional ferromagnetic ordering in the heterostructures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

DOE-EPSCoR. Exchange interactions in epitaxial intermetallic layered systems

The goal of this research is to develop a fundamental understanding of the exchange interactions in epitaxial intermetallic alloy thin films and multilayers, including films and multilayers of Fe-Pt, Co-Pt and Fe-P-Rh alloys deposited on MgO and Al 2 O 3 substrates. Our prior results have revealed that these materials have a rich variety of ferromagnetic, paramagnetic and antiferromagnetic phases which are sensitive functions of composition, substrate symmetry and layer thickness. Epitaxial antiferromagnetic films of FePt alloys exhibit a different phase diagram than bulk alloys. The antiferromagnetism of these materials has both spin ordering transitions and spin orienting transitions. The objectives include the study of exchange-inversion materials and the interface of these materials with ferromagnets. Our aim is to formulate a complete understanding of the magnetic ordering in these materials, as well as developing an understanding of how the spin structure is modified through contact with a ferromagnetic material at the interface. The ultimate goal is to develop the ability to tune the phase diagram of the materials to produce layered structures with tunable magnetic properties. The alloy systems that we will study have a degree of complexity and richness of magnetic phases that requires the use of the advanced tools offered by the DOE-operated national laboratory facilities, such as neutron and x-ray scattering to measure spin ordering, spin orientations, and element-specific magnetic moments. We plan to contribute to DOE’s mission of producing “Materials by Design” with properties determined by alloy composition and crystal structure. We have developed the methods for fabricating and have performed neutron diffraction experiments on some of the most interesting phases, and our work will serve to answer questions raised about the element-specific magnetizations using the magnetic x-ray dichroism techniques and interface magnetism in layered structures using polarized neutron reflectometry. Through application of these techniques to understand the materials fabricated in our laboratory, we will employ a tight feedback loop to tailor the magnetic properties on demand. Developing the ability to control magnetic anisotropy is essential for creating the next generation of magnetic storage media (for hard disks, for example), where individual bit sizes have already become smaller than 100nm in the largest dimension. Still smaller bits and higher storage density will require the ability to exquisitely tailor magnetic media properties at the atomic level, the ultimate goal of our study.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Self-Intercalation Tunable Interlayer Exchange Coupling in a Synthetic van der Waals Antiferromagnet

One of the most promising avenues in 2D materials research is the synthesis of antiferromagnets employing 2D van der Waals (vdW) magnets. However, it has proven challenging, due in part to the complicated fabrication process and undesired adsorbates as well as the significantly deteriorated ferromagnetism at atomic layers. Here, the engineering of the antiferromagnetic (AFM) interlayer exchange coupling between atomically thin yet ferromagnetic CrTe 2 layers in an ultra-high vacuum-free 2D magnetic crystal, Cr 5 Te 8 is reported. By self-introducing interstitial Cr atoms in the vdW gaps, the emergent AFM ordering and the resultant giant magnetoresistance effect are induced. A large negative magnetoresistance (10%) with a plateau-like feature is revealed, which is consistent with the AFM interlayer coupling between the adjacent CrTe 2 main layers in a temperature window of 30 K below the Néel temperature. Notably, the AFM state has a relatively weak interlayer exchange coupling, allowing a switching between the interlayer AFM and ferromagnetic states at moderate magnetic fields. Here this work represents a new route to engineering low-power devices that underpin the emerging spintronic technologies, and an ideal laboratory to study 2D magnetism.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Emergent Magnetic States and Tunable Exchange Bias at 3d Nitride Heterointerfaces

Abstract Interfacial magnetism stimulates the discovery of giant magnetoresistance (MR) and spin–orbital coupling across the heterointerfaces, facilitating the intimate correlation between spin transport and complex magnetic structures. Over decades, functional heterointerfaces composed of nitrides have seldom been explored due to the difficulty in synthesizing high‐quality nitride films with correct compositions. Here, the fabrication of single‐crystalline ferromagnetic Fe 3 N thin films with precisely controlled thicknesses is reported. As film thickness decreases, the magnetization dramatically deteriorates, and the electronic state changes from metallic to insulating. Strikingly, the high‐temperature ferromagnetism is maintained in a Fe 3 N layer with a thickness down to 2 u.c. (≈8 Å). The MR exhibits a strong in‐plane anisotropy; meanwhile, the anomalous Hall resistivity reverses its sign when the Fe 3 N layer thickness exceeds 5 u.c. Furthermore, a sizable exchange bias is observed at the interfaces between a ferromagnetic Fe 3 N and an antiferromagnetic CrN. The exchange bias field and saturation moment strongly depend on the controllable bending curvature using the cylinder diameter engineering technique, implying the tunable magnetic states under lattice deformation. This work provides a guideline for exploring functional nitride films and applying their interfacial phenomena for innovative perspectives toward practical applications.

Jin, Qiao↗
DOE OSTI2023

Strongly Correlated Exciton-Magnetization System for Optical Spin Pumping in CrBr 3 and CrI 3 .

Ferromagnetism in van der Waals systems, preserved down to a monolayer limit, attracted attention to a class of materials with general composition CrX 3 (X=I, Br, Cl), which are treated now as canonical two-dimensional ferromagnets. Their diverse magnetic properties, such as different easy axes or varying and controllable character of in-plane or interlayer ferromagnetic coupling, make them promising candidates for spintronic, photonic, optoelectronic, and other applications. Still, significantly different magneto-optical properties between the three materials, have been presenting a challenging puzzle for researchers over the last few years. Herewith, we demonstrate that despite similar structural and magnetic configurations, the coupling between excitons and magnetization is qualitatively different in CrBr 3 and CrI 3 films. Through a combination of the optical spin pumping experiments with the state-of-the-art theory describing bound excitonic states in the presence of magnetization, we concluded that the hole-magnetization coupling has the opposite sign in CrBr 3 and CrI 3 and also between the ground and excited exciton state. Consequently, we demonstrate efficient spin pumping capabilities in CrBr 3 driven by magnetization via spin-dependent absorption and unraveled the different origins of the magnetic hysteresis in CrBr 3 and CrI 3 are unraveled

36 MATERIALS SCIENCE↗
DOE OSTI2018

Chemical Synthesis of Magnetically Hard and Strong Rare Earth Metal Based Nanomagnets

Abstract We report a general chemical approach to synthesize strongly ferromagnetic rare‐earth metal (REM) based SmCo and SmFeN nanoparticles (NPs) with ultra‐large coercivity. The synthesis started with the preparation of hexagonal CoO+Sm 2 O 3 (denoted as SmCo‐O) multipods via decomposition of Sm(acac) 3 and Co(acac) 3 in oleylamine. These multipods were further reduced with Ca at 850 °C to form SmCo 5 NPs with sizes tunable from 50 to 200 nm. The 200 nm SmCo 5 NPs were dispersed in ethanol, and magnetically aligned in polyethylene glycol (PEG) matrix, yielding a PEG‐SmCo 5 NP composite with the room temperature coercivity ( H c ) of 49.2 kOe, the largest H c among all ferromagnetic NPs ever reported, and saturated magnetic moment ( M s ) of 88.7 emu g −1 , the highest value reported for SmCo 5 NPs. The method was extended to synthesize other ferromagnetic NPs of Sm 2 Co 17 , and, for the first time, of Sm 2 Fe 17 N 3 NPs with H c over 15 kOe and M s reaching 127.9 emu g −1 . These REM based NPs are important magnetic building blocks for fabrication of high‐performance permanent magnets, flexible magnets, and printable magnetic inks for energy and sensing applications.

Shen, Bo↗
DOE OSTI2018

Chemical Synthesis of Magnetically Hard and Strong Rare Earth Metal Based Nanomagnets

We report here a general chemical approach to synthesize strongly ferromagnetic rare-earth metal (REM) based SmCo and SmFeN nanoparticles (NPs) with ultra-large coercivity. The synthesis started with the preparation of hexagonal CoO+Sm 2 O 3 (denoted as SmCo-O) multipods via decomposition of Sm(acac) 3 and Co(acac) 3 in oleylamine. These multipods were further reduced with Ca at 850 °C to form SmCo 5 NPs with sizes tunable from 50 to 200 nm. The 200 nm SmCo 5 NPs were dispersed in ethanol, and magnetically aligned in polyethylene glycol (PEG) matrix, yielding a PEG-SmCo 5 NP composite with the room temperature coercivity (H c ) of 49.2 kOe, the largest H c among all ferromagnetic NPs ever reported, and saturated magnetic moment (M s ) of 88.7 emu g -1 , the highest value reported for SmCo 5 NPs. The method was extended to synthesize other ferromagnetic NPs of Sm 2 Co 17 , and, for the first time, of Sm 2 Fe 17 N 3 NPs with H c over 15 kOe and M s reaching 127.9 emu g -1 . These REM based NPs are important magnetic building blocks for fabrication of high-performance permanent magnets, flexible magnets, and printable magnetic inks for energy and sensing applications.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Escalated Phase Separation Driven Enhanced Magnetoresistance in Manganite/Iridate Epitaxial Heterostructures

Phase separation in manganites leads to unique magnetic and electronic properties. 50% Ca-doped LaMnO 3 (LCMO), at the boundary of ferromagnetic (FM) and antiferromagnetic (AFM) states in La 1-x Ca x MnO 3 (0 ≤ x ≤ 1), is an ideal system to study phase separation behavior. The investigation reveals the effect of a 5d-metal perovskite SrIrO 3 (SIO) on the phase separation, magnetic, and magnetoresistance (MR) properties of LCMO. Single-layer and bilayer LCMO films, both appear purely ferromagnetic along the in-plane (IP) magnetic field direction, but show the tendency of temperature-dependent ferromagnetic and antiferromagnetic or charge-ordered (CO) phase separation with the out-of-plane (OOP) applied field. The MR, and colossal magnetoresistance (CMR), observed in LCMO/SIO bilayers are two orders and an order of magnitude (in %) larger, respectively than that in the single-layer film. The coexistence of FM and AFM/CO phases is responsible for the CMR and MR enhancement in the LCMO/SIO bilayer, pointing toward the importance of the phase separation and competition of both the individual materials in enhancing their magnetic and electronic properties.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Orbital Hybridization and Magnetic Coupling at Cuprate–Manganite Interfaces Driven by Manganite Doping

Fundamental understanding of interface mechanisms that generate unexpected physical properties in the cuprate/manganite heterostructures is essential for possible applications as spintronic devices. In this study, CaCuO 2 /La 1–x Sr x MnO 3 (CCO/LSMO) superlattices are investigated, where the infinite-layer cuprate CCO does not have apical oxygen for Cu in the Ca-plane so that the Mn–O–Cu superexchange coupling can be only present at the MnO 2 –(La,Sr)O–CuO 2 interface. Two different doping states for the manganites are studied, namely x = 0.1 and x = 0.3, corresponding to the ferromagnetic insulating and ferromagnetic metallic states, respectively, in the manganite phase diagram. Linear and circular dichroism in X-ray absorption by synchrotron radiation at Cu and Mn L-edges clearly demonstrate that in the absence of apical oxygen in the cuprate block, the magnetic coupling between the LSMO and CCO is weakly ferromagnetic when LSMO is metallic, while it is antiferromagnetic when LSMO is insulating, along with an increased Cu 3d(3z 2 –r 2 ) and Mn 3d(3z 2 –r 2 ) orbital occupation. It is proposed that the Mn 3d valence band upward shift driven by the enhancement of Mn 3+ content in the underdoped sample enhances the orbital hybridization. The stronger hybridization at the interface MnO 2 –(La,Sr)O–CuO 2 gives rise to the antiferromagnetic coupling between cuprate and underdoped manganite.

36 MATERIALS SCIENCE↗
DOE OSTI2020

First-Principles Quantum Transport Modeling of Spin-Transfer and Spin-Orbit Torques in Magnetic Multilayers

A unified approach for computing (i) spin-transfer torque in magnetic trilayers like spin valve and magnetic tunnel junction, where injected charge current flows perpendicularly to interfaces, and (ii) spin-orbit torque in magnetic bilayers of the type ferromagnet/spin-orbit-coupled material, where injected charge current flows parallel to the interface, was reviewed. The experimentally explored and technologically relevant spin-orbit-coupled materials include 5d heavy metals, topological insulators, Weyl semimetals, and transition metal dichalcogenides. This approach requires to construct the torque operator for a given Hamiltonian of the device and the steady-state nonequilibrium density matrix, where the latter is expressed in terms of the nonequilibrium Green’s functions and split into three contributions. Tracing these contributions with the torque operator automatically yields field-like and damping-like components of spin-transfer torque or spin-orbit torque vector, which is particularly advantageous for spin-orbit torque where the direction of these components depends on the unknown-in-advance orientation of the current-driven nonequilibrium spin density in the presence of spin-orbit coupling. Illustrative examples are provided by computing spin-transfer torque in a one-dimensional toy model of a magnetic tunnel junction and realistic Co/Cu/Co spin valve, both of which are described by first-principles Hamiltonians obtained from noncollinear density functional theory calculations, as well as by computing spin-orbit torque in a ferromagnetic layer described by a tight-binding Hamiltonian which includes spin-orbit proximity effect within ferromagnetic monolayers assumed to be generated by the adjacent monolayer transition metal dichalcogenide. In addition, it is shown here how spin-orbit proximity effect, quantified by computing (via first-principles retarded Green’s function) spectral functions and spin textures on monolayers of realistic ferromagnetic material like Co in contact with heavy metal or monolayer transition metal dichalcogenide, can be tailored to enhance the magnitude of spin-orbit torque. Furthermore, errors made in the calculation of spin-transfer torque are quantified when using Hamiltonian from collinear density functional theory, with rigidly rotated magnetic moments to create noncollinear magnetization configurations, instead of proper (but computationally more expensive) self-consistent Hamiltonian obtained from noncollinear density functional theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Theoretical Study of Doped and Co-doped Gallium Nitride with (Cr, Ni): an LDA-SIC and Monte Carlo Study

Using a composition of first-principle density functional theory (DFT) calculations and Monte Carlo simulation with the calculation within the self-interaction-correction local-density approximation, the electronic, magnetic, and optical properties of doped and co-doped GaN (Ga{sub 1−x}Cr{sub x}N, Ga{sub 1−x}Ni{sub x}N) and GaN (Ga{sub 1−2x}Cr{sub x}Ni{sub x}N) (x = 0.03 and 0.06), respectively, have been investigated. Our results have proven that the half-metallic ferromagnetic state still persists of co-doped GaN. In comparing the total energies, ab initio calculations certify the magnetic-state stability of the ferromagnetic phase compared with the spin-glass state. The exchange interactions obtained from the ab initio calculations were used as input parameters in a classical Ising model by Monte Carlo simulation to confirm the half-metallic ferromagnetic states with high Neel temperature.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Ni Nanoparticle-Added Ni{sub x}/(Cu{sub 0.5}Tl{sub 0.5})Ba{sub 2}Ca{sub 2}Cu{sub 3}O{sub 10-δ} Superconductor Composites and Their Enhanced Flux Pinning Characteristics

Ni nanoparticle-added Ni{sub x}/(Cu{sub 0.5}Tl{sub 0.5})Ba{sub 2}Ca{sub 2} Cu{sub 3}O{sub 10-δ} superconductor composites are synthesized at normal pressure by two-step solid-state reaction method. The idea for adding ferromagnetic nanoparticles was to create artificial pinning centers at grain boundaries. The samples have shown orthorhombic crystal structure in which the cell parameters increase with an increase in the added concentration of Ni nanoparticles. This shows that due to the higher reactivity, Ni nanoparticles partially diffuse into the unit cell of (Cu{sub 0.5}Tl{sub 0.5})Ba{sub 2}Ca{sub 2}Cu{sub 3}O{sub 10-δ} superconductors. This also indicates as an evidence of the occupancy of these nanoparticles at grain boundaries. A metallic variation of resistivity from room temperature down to the onset of superconductivity is a typical feature of these samples with T{sub c}(R = 0) varying between 92 and 94 K. The magnitude of diamagnetism is significantly enhanced in 7 and 10% nanoparticle-added samples. The enhanced magnetization of ferromagnetic nanoparticles at reduced temperature plays a vital role in reducing the diamagnetism of nanosuperconductor composites. The softening of apical oxygen modes of type Cu(1)–O{sub A}–Cu(2) has confirmed the diffusion of Ni nanoparticles into the unit cell of the final compound. The excess conductivity analyses of conductivity data have shown that the values of B{sub c}(0), B{sub c1}, and J{sub c} are enhanced with the addition of Ni nanoparticles in the final compound. Variation of superconducting properties was attributed to pair breaking due to spin scattering across these ferromagnetic Ni nanoparticles. This shows that added Ni nanoparticles act as efficient pinning centers, which is also confirmed by the suppression of the London penetration depth.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Ab Initio Study of Structural, Electronic, and Magnetic Properties of A{sub 1−x}{sup III}Mn{sub x}B{sup VI}: In{sub 1−x}Mn{sub x}S-Diluted Magnetic Semiconductor

First-principles density functional calculations on the new class of diluted magnetic semiconductor A{sub 1−x}{sup III}Mn{sub x}B{sup VI} In{sub 1−x}Mn{sub x}S for x = 0.25 and 0.5 are investigated to study the structural, electronic, and magnetic properties, employing the full-potential linearized augmented plane wave method. Electronic band structures and density of states revealed a half-metallic character of In{sub 1−x}Mn{sub x}S and show the stability of anti-ferromagnetic states as compared with ferromagnetic states. The calculated exchange constants J{sub dd} are in good agreement with experimental and theoretical results on magnetic properties of single crystalline A{sub 1−x}{sup III}Mn{sub x}B{sup VI} in the anti-ferromagnetic case. Our predicated calculations on the s,p-d exchange constants N{sub 0}α and N{sub 0}β show that they are lower than in A{sub 1−x}{sup II}Mn{sub x}B{sup VI} DMS. The local environment is found tetrahedral as in the II–VI DMS and other (III,Mn) VI compounds. The total magnetic moment for In{sub 1−x}Mn{sub x}S for different concentrations is in accordance with the exact value 5 μ{sub B} and comes mainly from impurity Mn. The local magnetic moments of Mn ions are reduced from their free space charges values due to the p-d hybridization which produces small magnetic moments on the nonmagnetic In and S sites. The Curie temperature of In{sub 1−x}Mn{sub x}S is calculated within the mean field approximation and compared with other DMS systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Thermodynamics of Restricted Boltzmann Machines and Related Learning Dynamics

We investigate the thermodynamic properties of a restricted Boltzmann machine (RBM), a simple energy-based generative model used in the context of unsupervised learning. Assuming the information content of this model to be mainly reflected by the spectral properties of its weight matrix W, we try to make a realistic analysis by averaging over an appropriate statistical ensemble of RBMs. First, a phase diagram is derived. Otherwise similar to that of the Sherrington–Kirkpatrick (SK) model with ferromagnetic couplings, the RBM’s phase diagram presents a ferromagnetic phase which may or may not be of compositional type depending on the kurtosis of the distribution of the components of the singular vectors of W. Subsequently, the learning dynamics of the RBM is studied in the thermodynamic limit. A “typical” learning trajectory is shown to solve an effective dynamical equation, based on the aforementioned ensemble average and explicitly involving order parameters obtained from the thermodynamic analysis. In particular, this let us show how the evolution of the dominant singular values of W, and thus of the unstable modes, is driven by the input data. At the beginning of the training, in which the RBM is found to operate in the linear regime, the unstable modes reflect the dominant covariance modes of the data. In the non-linear regime, instead, the selected modes interact and eventually impose a matching of the order parameters to their empirical counterparts estimated from the data. Finally, we illustrate our considerations by performing experiments on both artificial and real data, showing in particular how the RBM operates in the ferromagnetic compositional phase.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗