Measurements of the magnetic properties of conduction electrons
At a Glance
Section titled āAt a Glanceā| Metadata | Details |
|---|---|
| Publication Date | 2020-05-23 |
| Journal | Physics-Uspekhi |
| Authors | V.M. Pudalov |
| Citations | 8 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled āExecutive SummaryāThis review provides a comprehensive analysis of methods for measuring electron magnetization and susceptibility, focusing on techniques applicable to small, non-magnetic, low-dimensional electron systems (2D electron gas, nanosystems).
- Sensitivity Breakthrough: The review details the evolution from traditional, low-sensitivity laboratory magnetometers (e.g., torsion, VSM) to highly sensitive micro-console magnetometers (MCMs) and SQUID-based systems, necessary for studying samples with 108 to 109 electrons.
- Thermodynamic Focus: Capacitive āfloating gateā and modulation techniques (MMTM) are highlighted as the most fruitful modern methods, enabling the measurement of chemical potential derivatives (dĀµ/dB) and providing absolute thermodynamic data.
- Spin Correlation Results: Thermodynamic measurements successfully revealed strong electron-electron correlation effects in 2D systems, including negative compressibility and significant renormalization of spin susceptibility (up to 5x enhancement).
- Local Spin Sensing: The paper covers local methods for probing spin magnetization, including detection of the Spin Hall Effect (SHE) via optical (Kerr rotation) and electrical (Inverse SHE) techniques.
- Nanoscale Magnetometry: Nitrogen-Vacancy (NV) centers in diamond are presented as atomic-scale magnetic sensors, offering high spatial resolution (1-10 nm) and high sensitivity (4.3 nT/sqrt(Hz)) even at room temperature.
- Applications: These advanced techniques are crucial for research in spintronics, quantum computing, QHE metrology, and biophysics (e.g., imaging intracellular dynamics).
Technical Specifications
Section titled āTechnical Specificationsā| Parameter | Value | Unit | Context |
|---|---|---|---|
| Torsion Magnetometer Sensitivity (Torque) | 10-12 | J/T | Eisenstein et al. design (equivalent to 1011 Bohr magnetons) |
| Torsion Magnetometer Resolution (Angle) | ~1 | Āµrad | Detectable rotation angle |
| Microconsole Magnetometer (MCM) Thickness | 10 | Āµm | Typical bending element thickness |
| Microconsole Magnetometer (MCM) Sensitivity | 3 x 106 | ĀµB | Ferromagnet semiconductor (0.1 T field, 1 Hz bandwidth) |
| Vibrating Sample Magnetometer (VSM) Susceptibility Sensitivity | 2 x 10-10 | dĻ/Ļ | Frequency bandwidth 2 x 10-2 Hz |
| SQUID Magnetometer Noise Level (Flux) | 3.5 x 10-5 | Ī¦o/sqrt(Hz) | Zero field noise level |
| NV-Center Spatial Resolution | 1 to 10 | nm | Nanoscale magnetic sensing |
| NV-Center Threshold Sensitivity (Room Temp) | 4.3 | nT/sqrt(Hz) | Single NV-center in atmospheric environment |
| NV-Center Spin Relaxation Time (T2) | 100 | Āµs | NV-centers within 5 nm of diamond surface |
| Spin Diffusion Length (Ls) | 1.9 | Āµm | InGaAs, T = 20 K (Optical SHE detection) |
| Scanning SQUID Microscope (SSM) Spatial Resolution | ~20 | nm | Direct current SQUIDs |
| Scanning SQUID Microscope (SSM) Detected Flux | 10-3 to 10-5 | Ī¦o/sqrt(Hz) | Pickup loop diameter ~1 Āµm |
| Si-MOS Structure Leakage Resistance (R) | > 1013 | Ohm | Required for āfloating gateā measurements (C ā 1 nF, t ~ 104 s) |
Key Methodologies
Section titled āKey Methodologiesā-
Electromechanical Magnetometry (Torsion/MCM):
- Measures the mechanical torque (L = M x B) acting on an anisotropic sample in a uniform magnetic field.
- The torque is compensated by the elastic deformation of a thread (torsion) or a micro-console beam (MCM).
- Deformation is detected using highly sensitive capacitive sensors (measuring changes in gap d or area S) or optical sensors (laser reflection).
- MCM sensitivity is enhanced because the bending angle is inversely proportional to the sample thickness cubed (d3).
-
Modulation Capacitive Method (MMTM) for Spin Magnetization:
- A thermodynamic technique used primarily for 2D systems, applying the magnetic field strictly parallel (B||) to the 2D plane to exclude orbital effects.
- The gate voltage (Vg) is modulated at high frequency (e.g., 100 kHz) to modulate the electron concentration (Īns).
- The resulting recharging current (Ī“I) is measured, which is directly proportional to the magnetization per electron derivative (āM/ān) via the Maxwell relation (āM/ān = -āĀµ/āB).
-
Quantum Oscillation Interference (Vector Field):
- Uses a vector magnet to apply both perpendicular (Bā„) and parallel (B||) magnetic field components.
- Bā„ quantizes Landau levels, while B|| induces Zeeman splitting, leading to unequal spin subband populations.
- Spin susceptibility (Ļ*) is determined by analyzing the beating frequency of Shubnikov-de Haas (SdH) oscillations as a function of the total field (Btot).
-
Spin Hall Effect (SHE) Detection:
- Optical Detection (Direct SHE): Charge current flow induces spin accumulation at sample edges due to Spin-Orbit Interaction (SOI). This polarization is detected non-locally using Kerr rotation microscopy with micron-scale spatial resolution.
- Electrical Detection (Inverse SHE): Spin-polarized carriers are injected (e.g., from a ferromagnetic contact). The resulting spin current induces a transverse Hall voltage (VSH) in the nonmagnetic material, measured non-locally away from the injector.
-
NV-Center Magnetometry (ODMR):
- Utilizes the negatively charged Nitrogen-Vacancy (NV-) center in diamond as an atomic-scale sensor.
- The NV-center spin state (ground state 3A2) is polarized optically (e.g., 532 nm laser) and read out via spin-dependent photoluminescence (637-800 nm).
- External magnetic fields shift the spin sublevels (ms = Ā±1), which is detected by applying resonant microwave radiation (Optically Detected Magnetic Resonance, ODMR), causing a sharp drop in fluorescence intensity.
Commercial Applications
Section titled āCommercial Applicationsā| Industry/Field | Application/Product | Technology Used |
|---|---|---|
| Spintronics & Quantum Computing | Development of spin logic elements, spin current sensors, and effective information storage devices. | SHE/ISHE (Optical & Electrical Detection) |
| Metrology and Standards | Contactless estimation of true residual resistance in the Quantum Hall Effect (QHE) regime. | Thermodynamic Methods (Capacitive/Electrometric) |
| Magnetic Storage & Electronics | Characterization of read/write magnetic heads; measurement of stray fields from magnetic domains in hard disk drives. | NV-Center Magnetometry |
| Condensed Matter Physics | Imaging magnetic flux vortices in superconductors, domain walls, and exotic magnetic structures (skyrmions, spin ice). | NV-Center Magnetometry, Scanning SQUID Magnetometers (SSM) |
| Biophysics and Neuroscience | Intracellular dynamics detection in living cells; imaging magneto-marked cancer cells; molecular imaging via NMR/MRI techniques. | NV-Center Magnetometry |
| Materials Science Research | Absolute measurement of magnetization and susceptibility in low-dimensional systems (2D electron gas, quantum wells). | Microconsole Magnetometers (MCM), MMTM |
View Original Abstract
Abstract We consider various methods and techniques that are used in experimental condensed matter physics for measuring electron magnetization and susceptibility. The list of considered methods for macroscopic measurements includes magnetomechanical, electromagnetic, modulation-type, and thermodynamic methods based on chemical potential variation measurements. We also consider local methods of magnetic measurements based on the spin Hall effect and nitrogen-substituted vacancies (NV centers). Scanning probe magnetometers-microscopes are considered, such as the magnetic resonance force microscope, SQUID microscope, and Hall microscope. The review focuses on the electron spin magnetization measurements in nonmagnetic materials and systems, particularly in low-dimensional electron systems in semiconductors and in nanosystems that have come to the forefront in recent years.