The Paramagnetic Meissner Effect (PME) in Metallic Superconductors

At a Glance

Metadata	Details
Publication Date	2023-06-19
Journal	Metals
Authors	M.R. Koblischka, L. Půst, Crosby-Soon Chang, Thomas Hauet, Anjela Koblischka‐Veneva
Institutions	Centre National de la Recherche Scientifique, Institut Jean Lamour
Citations	5
Analysis	Full AI Review Included

Technical Documentation & Analysis: Paramagnetic Meissner Effect (PME) in Metallic Superconductors

6CCVD Reference Document: PME-METALS-2023-1140 Date: October 26, 2023

Executive Summary

This review of the Paramagnetic Meissner Effect (PME) in metallic superconductors provides critical insights into unconventional superconducting behavior, directly relevant to advanced material engineering and quantum applications.

PME Confirmation: The PME (Wohlleben effect) is confirmed in s-wave metallic superconductors (Nb, Al, Pb, Ta, MgB₂), characterized by positive magnetization during field-cool measurements.
Mechanisms: PME is categorized as either Extrinsic (driven by flux compression, giant vortex states, and surface defects) or Intrinsic (driven by odd s-wave superconductivity or $\pi$-junctions).
Material Relevance: The research highlights Boron-Doped Diamond (BDD) thin films as a unique elemental superconductor exhibiting PME, confirming the viability of 6CCVD’s core material for advanced quantum research.
Surface Control is Key: Experimental results demonstrate that PME can be removed by surface abrasion or induced/enhanced by ion implantation, emphasizing the critical role of surface quality and defect engineering.
Advanced Metrology: Observation relies heavily on highly sensitive techniques, including SQUID magnetometry, AC susceptibility, and spatial mapping via Diamond Nitrogen-Vacancy (NV)-center magnetometry.
Geometric Dependence: PME manifestation is strongly dependent on sample geometry, requiring precise control over thin film thickness (down to 0.1 µm) and mesoscopic patterning (disks, nanowires).

Technical Specifications

The following hard data points were extracted from the review, focusing on material properties and experimental conditions relevant to superconducting material fabrication.

Parameter	Value	Unit	Context
Niobium (Nb) T_c,onset	9.20 - 9.28	K	Bulk disks, depending on surface treatment
Nb Disk Thickness (t)	127 - 250	µm	Standard samples used for PME studies
Characteristic Temperature T_p	9.05 (±0.05)	K	Temperature of maximum positive moment (Nb disk)
Characteristic Temperature T₁	9.15 (±0.05)	K	Temperature of minimum diamagnetic moment (Nb disk)
Nb Ginzburg-Landau Parameter ($\kappa$)	~0.8 - 1.0	N/A	Close to Type-I/Type-II border
BDD Thin Film T_c Range	2.1 - 5.8	K	Observed PME in Boron-Doped Diamond
Al Mesoscopic Disk Thickness	0.1	µm	Used for Giant Vortex State observation
Ion Implantation Depth (Kr-ions)	~120	nm	Depth required to induce PME in Nb disks
Applied DC Magnetic Field (H_ext)	1 - 200	mT	Range for PME observation in Nb disks
SQUID Moment Sensitivity	< 10^-6	emu	Required resolution for low-field PME measurements

Key Methodologies

The experimental observations of PME rely on precise control of temperature, magnetic field, and sample surface condition.

Field-Cooled Magnetometry (FC-C/FC-W): Measurement of magnetic moment m(T) at constant, small applied fields. PME is identified by positive magnetization (paramagnetic signal) upon cooling (FC-C) or warming (FC-W).
Magnetic Hysteresis Loops (MHLs): Detailed m(H) measurements performed near T_c using stationary SQUID techniques to minimize artifacts. MHL shape analysis distinguishes conventional vortex pinning from PME-related Giant Vortex states.
AC Susceptibility ($\chi$): Measurement of the real ($\chi$’) and imaginary ($\chi$”) components as a function of frequency (down to 1 Hz) and AC amplitude (h_ac). Anomalous positive peaks in $\chi$’ (Diffraction Paramagnetic Effect, DPE) are used to determine surface T_c.
Surface Engineering: Mechanical abrasion (reducing thickness by ~10%) was used to remove PME, while Kr-ion implantation (to a depth of 120 nm) was used to induce or enhance PME by creating controlled surface defects.
Magnetic Imaging Techniques:
- Scanning SQUID Microscopy (SSM) and Magneto-Optic Imaging (MOI) were used to visualize magnetic flux distribution and vortex clusters at 4.2 K.
- Diamond Nitrogen-Vacancy (NV)-center magnetometry was employed for non-invasive, spatially-resolved magnetic field sensing near the surface (probe volume $\approx$ 20 nm thick, 500 nm diameter).
Low-Energy Muon Spin Spectroscopy (LE-$\mu$SR): Used on hybrid trilayers (Au/Ho/Nb) to provide depth-resolved magnetic susceptibility, confirming intrinsic PME (odd s-wave superconductivity) in the non-superconducting Au layer.

6CCVD Solutions & Capabilities

The research on PME in metallic superconductors, particularly the focus on BDD, mesoscopic structures, and surface sensitivity, presents a direct opportunity for collaboration utilizing 6CCVD’s advanced MPCVD diamond capabilities.

Applicable Materials

To replicate or extend the research on PME, 6CCVD recommends the following materials, optimized for high-purity and precise geometry control:

Research Application	6CCVD Material Recommendation	Rationale
Intrinsic PME Studies ($\pi$-junctions, odd s-wave SC)	Boron-Doped Diamond (BDD) Thin Films	Direct match to the unique elemental superconductor (Ref. [107]). We offer precise B-doping control to tune T_c (2.1 K - 5.8 K range) and optimize $\pi$-junction networks.
Mesoscopic Structures (Al/Nb disks, nanowires)	High-Purity Single Crystal Diamond (SCD) Wafers	Ideal substrates for depositing and patterning high-quality metallic films (Nb, Al, Pb) due to diamond’s superior thermal management and chemical inertness.
Hybrid/Multilayer Systems (Au/Ho/Nb, V/Fe)	Polycrystalline Diamond (PCD) Plates	Available in large formats (up to 125 mm) for large-scale deposition of complex multilayer stacks requiring subsequent patterning or metalization.

Customization Potential

The PME research demands materials with highly controlled dimensions and surface characteristics, areas where 6CCVD excels:

Thickness Control: The paper investigates thin films down to 0.1 µm (Al mesoscopic disks). 6CCVD provides SCD and PCD layers with exceptional thickness uniformity from 0.1 µm up to 500 µm, enabling precise control over quantum confinement effects.
Surface Quality for Intrinsic PME: Since PME is highly sensitive to surface defects (abrading removes PME), 6CCVD offers ultra-smooth polishing (SCD R_a < 1 nm, PCD R_a < 5 nm). This pristine surface quality is essential for isolating intrinsic PME mechanisms from extrinsic flux compression effects.
Custom Metalization for Hybrid Systems: The study of intrinsic PME relies on hybrid structures (e.g., Au/Ho/Nb trilayers). 6CCVD offers in-house metalization capabilities including Au, Pt, Pd, Ti, W, and Cu, allowing researchers to fabricate custom superconductor/ferromagnet or superconductor/normal metal stacks.
Substrate Dimensions: While the paper focuses on small disks (6.4 mm diameter), 6CCVD can supply PCD wafers up to 125 mm for scaling up mesoscopic patterning experiments or magnetic imaging studies.

Engineering Support

Understanding and manipulating the PME requires deep expertise in material science and superconductivity.

6CCVD’s in-house PhD engineering team specializes in MPCVD diamond growth and surface modification. We offer consultation services to assist researchers in:

Material Selection: Choosing the optimal diamond type (SCD, PCD, BDD) and orientation for specific PME experiments.
Surface Preparation: Designing custom polishing or surface termination protocols to control the superconducting properties at the interface, critical for replicating or controlling the surface effects observed in the Nb disk studies (abrading/implantation).
Custom Structure Design: Assisting with the design and fabrication of custom thin film stacks and metalized patterns required for similar Superconducting Spintronics projects.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

The experimental data in the literature concerning the Paramagnetic Meissner Effect (PME) or also called Wohlleben effect are reviewed with the emphasis on the PME exhibited by metallic, s-wave superconductors. The PME was observed in field-cool cooling (FC-C) and field-cool warming (FC-W) m(T)-measurements on Al, Nb, Pb, Ta, in compounds such as, e.g., NbSe2, In-Sn, ZrB12, and others, and also in MgB2, the metallic superconductor with the highest transition temperature. Furthermore, samples with different shapes such as crystals, polycrystals, thin films, bi- and multilayers, nanocomposites, nanowires, mesoscopic objects, and porous materials exhibited the PME. The characteristic features of the PME, found mainly in Nb disks, such as the characteristic temperatures T1 and Tp and the apparative details of the various magnetic measurement techniques applied to observe the PME, are discussed. We also show that PME can be observed with the magnetic field applied parallel and perpendicular to the sample surface, that PME can be removed by abrading the sample surface, and that PME can be introduced or enhanced by irradiation processes. The PME can be observed as well in magnetization loops (MHLs, m(H)) in a narrow temperature window Tp<Tc, which enables the construction of a phase diagram for a superconducting sample exhibiting the PME. We found that the Nb disks still exhibit the PME after more than 20 years, and we present the efforts of magnetic imaging techniques (scanning SQUID microscopy, magneto-optics, diamond nitrogen-vacancy (NV)-center magnetometry, and low-energy muon spin spectroscopy, (LE-μSR)). Various attempts to explain PME behavior are discussed in detail. In particular, magnetic measurements of mesoscopic Al disks brought out important details employing the models of a giant vortex state and flux compression. Thus, we consider these approaches and demagnetization effects as the base to understand the formation of the paramagnetic signals in most of the materials investigated. New developments and novel directions for further experimental and theoretical analysis are also outlined.