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The Fermi–Dirac and Bose–Einstein statistics are considered to be key concepts in quantum mechanics, and they are used to explain the occupancy limit of electron orbitals. We investigate the physical origin of these two statistics and uncover that the key determining factor is whether an individual electron spin is measurable or not. Microscopically, a system with individually measurable electron spins corresponds to the presence of Larmor spin precession in electron–electron interactions, while the non-measurability of individual electron spins corresponds to the absence of Larmor spin precession. Both interaction types are possible, and the favored interaction type is thermodynamically determined. The absence of Larmor spin precession is realized in coherent electron states, and coherent electrons therefore obey Bose–Einstein statistics. [ABSTRACT FROM AUTHOR]

In a Wilberforce pendulum, two mechanical oscillators are coupled: one pertains to the longitudinal (tension) motion and the other to the rotational (twisting) motion. It is shown that the longitudinal magnetic moment of circular currents, and similarly the magnetic moment of a spin-chain, can exhibit a Wilberforce-like vibration. The longitudinal oscillation is related to the Langevin diamagnetism, while the twisting motion is superimposed on the magnetic moment and spin precession. The calculations show that the coupling term is nonlinear in this (longitudinal) vibrating and (magnetic moment) precession system. By increasing the strength of the coupling we arrive at a spectrum, where further vibrational modes can be associated with the rotation of the precession. This means that the extent of the change in coherence can be demonstrated. Since the coupling strength can be different due to local effects, this can be an important factor from the point of view of signal propagation and in preserving signal shapes. The amount specifying the dissipation is introduced to express the degree of deviation. A relationship exists between the parameter characteristic of the coupling strength and how its quantity influences decoherence and dissipation. [ABSTRACT FROM AUTHOR]

The advancement of technical means for determining soil density in precision (controlled) agriculture necessitates the enhancement of non-destructive flow interaction methods. There is also a need to improve methods for assessing soil density, as existing deviations from optimal values adversely affect the yield of agricultural crops. This research aims to establish the density of the composites in the granulometric composition of soil by determining the self- induction voltage in a changing magnetic field. The research methods are adapted to determine the relationships of Larmor precession under variable inductive current for the density of each composite in the granulometric soil composition. Experimental investigations were conducted by measuring the self-induction voltage of a solenoid acting as a sensor for each of the composites located within the core. The processing of experimental results was carried out according to the principles of mathematical statistics and probability theory, using approximations in the Excel and Statistica software packages. Based on the results of the experimental investigations, models of the relationships between the density p (1.0-1.5 g/cm³) of soil composites and the self- induction voltage εL = 184-192 mV, with a generator voltage of 5 V and determination coefficients R² = 0.95-0.99, have been established. These models enable the assessment of soil density with high accuracy, thereby facilitating the optimisation of agronomic processes. It has been determined that these models can be used with a high degree of reliability as calibration characteristics for the design of technical means for flow-based non-destructive measurement of the density of the main soil types in Ukraine. Furthermore, it has been identified that future research should focus on a more in-depth investigation of the relationships between magnetic permeability and the agrophysical characteristics of soil within the locally defined inductive field of the sensor (solenoid). An applied aspect of the obtained results is the further development of adaptive machinery and monitoring systems for soil conditions, aimed at achieving optimal cultivation indicators, as well as their utilisation by research institutions and instrument-making enterprises [ABSTRACT FROM AUTHOR]

This work studies the Clifford algebra approach to the density matrix. We discuss elementary examples of pure and mixed states by writing the density matrix as an element of the Clifford algebra of the three-dimensional space C l 3 . We also revisit the phenomenon of Larmor precession within the framework of Clifford algebra. Additionally, we discuss the geometrical interpretation of the so-called Clifford Density Element (CDE) for pure states in analogy to the Bloch sphere of conventional quantum theory. Finally, we discuss the dynamics of the CDE, which obeys an algebraic form of the Liouville von–Neumann equation. [ABSTRACT FROM AUTHOR]

Magnetic resonance imaging (MRI) is a widely used clinical diagnostic tool, which is based on the principle of nuclear magnetic resonance of hydrogen atoms in human body. The Larmor frequency of precession of the hydrogen atoms is determined by the strength of static magnetic field (B0) of MRI. A higher B0 can directly improve signal-to-noise ratio (SNR) of MRI. However, this method involves expensive hardware installation, which could have adverse effects of tissue-heating and make MRI unsafe for patients with medical implants. Hence, efforts have been made to increase the SNR of MRI without increasing B0. An effective solution in this direction would be to boost the radiofrequency (RF) magnetic fields emitted by the body part undergoing scan, particularly by using metamaterials. The higher the received RF signal strength, the greater the SNR of MRI. For a metamaterial to be used as an "add-on" in commercial scanners, its dimensions need to be designed appropriately so that it fits in the available gap between the transceiver coil and the human body. In this article, a 10-mm-thick metallo-dielectric metamaterial is designed by a stacking of alternate square-shaped capacitive patches and inductive apertures for enhancing the RF magnetic flux density and hence, the SNR of a 1.5 T MRI system. The inter-layer electromagnetic coupling in the stacked structure is deployed for spatial localization of magnetic fields at the resonant frequency (∼64 MHz) which is equal to the Larmor frequency of 1.5 T MRI. An equivalent circuit model, comprising a lumped-element third order bandpass filter, validated the transmissivity characteristics of the metamaterial obtained using full-wave simulations. Magnetic flux density enhancement by a factor of 55 is obtained when the metamaterial add-on is placed between a surface coil and a bio-model of human head. [ABSTRACT FROM AUTHOR]

Coherent spin dynamics of electrons in CdSe colloidal nanoplatelets are investigated by time-resolved pump–probe Faraday rotation at room and cryogenic temperatures. We measure electron spin precession in a magnetic field and determine g-factors of 1.83 and 1.72 at low temperatures for nanoplatelets with a thickness of 3 and 4 monolayers, respectively. The dephasing time of spin precession T 2 * amounts to a few nanoseconds and has a weak dependence on temperature, while the longitudinal spin relaxation time T 1 exceeds 10 ns even at room temperature. Observations of single and double electron spin–flips confirm that the nanoplatelets are negatively charged. The spin–flip Raman scattering technique reveals g-factor anisotropy by up to 10% in nanoplatelets with thicknesses of 3, 4, and 5 monolayers. In the ensemble with a random orientation of nanoplatelets, our theoretical analysis shows that the measured Larmor precession frequency corresponds to the in-plane electron g-factor. We conclude that the experimentally observed electron spin dephasing and its acceleration in the magnetic field are not provided by the electron g-factor anisotropy and can be related to the localization of the resident electrons and fluctuations of the localization potential. [ABSTRACT FROM AUTHOR]

In a Wilberforce pendulum, two mechanical oscillators are coupled: one pertains to the longitudinal (tension) motion and the other to the rotational (twisting) motion. It is shown that the longitudinal magnetic moment of circular currents, and similarly the magnetic moment of a spin-chain, can exhibit a Wilberforce-like vibration. The longitudinal oscillation is related to the Langevin diamagnetism, while the twisting motion is superimposed on the magnetic moment and spin precession. The calculations show that the coupling term is nonlinear in this (longitudinal) vibrating and (magnetic moment) precession system. By increasing the strength of the coupling we arrive at a spectrum, where further vibrational modes can be associated with the rotation of the precession. This means that the extent of the change in coherence can be demonstrated. Since the coupling strength can be different due to local effects, this can be an important factor from the point of view of signal propagation and in preserving signal shapes. The amount specifying the dissipation is introduced to express the degree of deviation. A relationship exists between the parameter characteristic of the coupling strength and how its quantity influences decoherence and dissipation.

We propose a scheme for a Bell–Bloom atomic magnetometer based on a single beam. In our approach, the light is periodically modulated synchronously with Larmor precession. As a result, the light that interacts with atoms is alternately polychromatic and monochromatic. When the light is polychromatic, the ±1st sidebands of the light are optically resonant with the atoms, and the atoms are polarized by pumping. When the light is monochromatic, a differential detection technique extracts the Faraday-rotation signal of the light, and the polarization of the light is probed. We demonstrate an experimental implementation of the Bell–Bloom magnetometer that achieves a sensitivity for magnetic-field detection of 0.25 pT/Hz1/2 at 1 Hz. Our scheme is suitable for developing compact, miniaturized magnetometers. [ABSTRACT FROM AUTHOR]

Parameter values extending over multiple temperatures/columns were assumed to have the same value for all the temperatures in question. A smaller quadrupole doublet component, with a relative spectral area fraction being below 3.5%, can be identified as high-spin Fe SP 3+ sp with parameters of I i ( I T i = 60 K) 0.52 mm s SP -1 sp and I E i SB Q sb ( I T i = 60 K) 0.62 mm s SP -1 sp (Table S3), which was presumably formed via low-level oxidation of the sample during its handling. [Extracted from the article]

Many-electron systems undergo a collective Larmor precession in the presence of a magnetic field. In a paramagnetic metal, the resulting spin wave provides insight into the correlation effects generated by the electron-electron interaction. Here, we use dynamical mean-field theory to investigate the collective Larmor precession in the strongly correlated regime, where dynamical correlation effects such as quasiparticle lifetimes and non-quasiparticle states are essential. We study the spin excitation spectrum, which includes a dispersive Larmor mode as well as electron-hole excitations that lead to Stoner damping. We also extract the momentum-resolved damping of slow spin waves. The accurate theoretical description of these phenomena relies on the Ward identity, which guarantees a precise cancellation of self-energy and vertex corrections at long wavelengths. Our findings pave the way towards a better understanding of spin wave damping in correlated materials. The authors provide an application of dynamical mean-field theory to the spin dynamics in strongly correlated electron systems showing the impact of dynamic electron-electron self-energies and vertex functions on the Larmor mode and damping processes. The results show the superior nature of the methodology against simpler random-phase approximation techniques. [ABSTRACT FROM AUTHOR]

Coherent spin dynamics of charge carriers in CsPbBr 3 perovskite nanocrystals are studied in a temperature range of 4–300 K and in magnetic fields of up to 500 mT using time-resolved pump-probe Faraday rotation and differential transmission techniques. We detect electron spin Larmor precession in the entire temperature range. At temperatures below 50 K, hole spin precession is also observed. The temperature dependences of spin-related parameters, such as Landè g-factor and spin dephasing time are measured and analyzed. The electron g-factor increases with growing temperature, which can not be described by the temperature-induced band gap renormalization. We find that photocharging of the nanocrystals with either electrons or holes depends on the sample cooling regime, namely the cooling rate and illumination conditions. The type of the charge carrier provided by the photocharging can be identified via the carrier spin Larmor precession. [ABSTRACT FROM AUTHOR]

Vector field measurement is demonstrated with an all-optical scalar atomic magnetometer using intrinsic parameters related to its scalar operation. The Bell-Bloom type atomic magnetometer measures the Larmor precession of cesium atoms through on-resonant absorption of a probe beam. While the AC component of the probe signal is used for the field magnitude measurement, the probe DC signal contains information about the polar angle, defined as the angle between the magnetic field and the probe beam. Additional polar angle information is obtained from the light-shift-induced magnetic field caused by the frequency modulation of the probe beam. With a measurement time of 100 ms, better than 0.02° sensitivity has been achieved using a commercial miniaturized sensor at the optimal sensor orientation. The angle measurement accuracy is checked against an optical encoder over the entire polar angle range of 0°–180°. Better than 1° error is recorded over most set polar angles. Azimuthal angle measurement is also exhibited with two orthogonally oriented sensors. [ABSTRACT FROM AUTHOR]

In this work, we look to compare three methods of feedback for the ultimate purpose of measuring the transverse vector components of a magnetic field using a synchronous light-pulse atomic scalar magnetometer with a few tens of fT/ Hz sensitivity in Earth-field-scale magnetic environments. By applying modulation in the magnetic field to orthogonal axes, the respective vector components may, in principle, be separated from the scalar measurement. Success of this technique depends in significant part on the ability to measure and respond to these perturbations with low measurement uncertainty. Using high-speed least-squares fitting, the phase response of the atomic spins relative to the first harmonic of the optical pump pulse repetition rate is monitored and correspondingly adjusted into resonance with the natural Larmor precession frequency. This paper seeks to motivate and compare three distinct methods of feedback for this purpose. As a first step toward the full development of this technique, the present work uses a simplified version with modulation applied only along the bias field. All three methods investigated herein are shown to provide results that match well with the scalar magnetometer measurements and to depend on both the applied modulation amplitude and optimal feedback response to achieve low relative uncertainty. [ABSTRACT FROM AUTHOR]

Fiber‐coupled atomic magnetometer (AM) based on a spin‐exchange relaxation‐free (SERF) regime has been a promising candidate for cryogenic devices for traditional magnetoencephalography (MEG) systems, as it has a flexible structure and a small lateral section for biomedical applications. The principles, key technologies, and applications of fiber‐coupled AM based on the atomic spin effect are reviewed in this paper. The principle of fiber‐coupled AM is introduced, the characteristics of conventional and fiber‐coupled AMs are compared, and the development history and current situation are reviewed. In addition, according to the demands for MEG applications, the key technologies of fiber‐coupled AM are summarized, and the bottleneck problems and future development directions for weak magnetic measurement are analyzed. [ABSTRACT FROM AUTHOR]

Graph: Figure 2(a) A 2D charge transport measurement map at RT showing the effect on the sheet resistance, , of applying a back gate voltage, Vbg, and top gate voltage, Vtg. (b) The same charge transport measurements transformed into a map as a function of carrier density, n, and electric displacement field, D. In both maps the symbols are shown where the spin transport measurements were made. b(inset) Sheet resistance close and parallel to the Dirac ridge (n 0). Also, "In doing so, we sweep a perpendicular magnetic field strength across a range of ±200 mT, which causes the diffusing electronic spins to experience Larmor precession, and fit the spin signal with the Hanle equation SP 22 sp ." now reads "In doing so, we sweep magnetic field strength perpendicular to the plane of the graphene (see Figure 1b), B SB sb , across a range of ±200 mT, which causes the diffusing electronic spins to experience Larmor precession, and fit the spin signal with the Hanle equation SP 22 sp .". [Extracted from the article]

[Display omitted] Ortho and para water are the two nuclear isomers where the hydrogen protons align to give a total nuclear spin of 1 or 0. The equilibrium ratio of 3:1 is established slowly in freshly evaporated water vapour while the isomers behave distinct gasses, with their own partial pressures. Magnetic-field-induced ortho ⟷ para transformations are expected to alter the evaporation rate. Evaporation from beakers of deionized water and a 6 M solution of urea is monitored simultaneously for periods from 1 to 60 h with and without a 500 mT magnetic field, while logging the ambient temperature and humidity. Balances with the two beakers are shielded in the same Perspex container. Many runs have been conducted over a two-year period. The evaporation rate of water is found to increase by 12 ± 7% of in the field but that of water with dissolved urea decreases by 28 ± 6%. Two effects are at play. One is dephasing of the Larmor precession of adjacent protons on a water molecule in a field gradient, which tends to equalize the isomer populations. The other is Lorentz stress on the moving charge dipole, which can increase the proportion of the ortho isomer. From analysis of the time and field dependence of the evaporation, we infer that the ortho fraction is 39 ± 1% in fresh vapour from water and 60 ± 5% in fresh vapour from urea. [ABSTRACT FROM AUTHOR]

The method for locating hidden subsurface non-metallic pipelines made of high-molecular compounds (polyethylene, polystyrene, PVC, polypropylene) is proposed. It is based on the self-reactance properties of liquids in pipelines, which become apparent under the forced polarization of liquid by turning the magnetic axis of their protons at some angle in relation to the Earth's magnetic field. The precession of the liquid proton axis in the direction to the Earth's magnetic field appears after the end of the polarization pulse action. It results in the appearance of the variable magnetic field of free nuclear precession with Larmor frequency thus testifying to the location of subsurface pipeline with liquid. Proton precession time depends on the liquid and serves as a sign for recognition of the liquid type in a pipeline. [ABSTRACT FROM AUTHOR]

The measurement of a time-varying magnetic field is different from a constant magnetic field, due to its field intensity variation with time. Usually, the time-varying magnetic field measurement converts the solution of the magnetic induction intensity into the calculation of the induced electromotive force (EMF); then, the magnetic induction intensity is obtained by the time integration of the EMF, but the process is vulnerable to external interference. In this paper, a non-steady state nuclear magnetic resonance (NSS-NMR) scheme for the measurement of a time-varying magnetic field is proposed. In a time-varying magnetic field environment, an RF excitation signal with a certain frequency bandwidth is applied to excite the nuclear spin system. The NSS-NMR signal, which varies with time in the frequency range corresponding to the frequency bandwidth of the RF excitation, could finally be obtained after a series of processing of the probe output signal. During the NSS-NMR experiment, an orthogonal dual-coil probe is adopted to synchronously generate the RF excitation and induce the probe output signal. Moreover, a directional coupler that utilized in the experiment outputs a reference signal from the coupling port for the subsequent signal processing. The experimental results show that the weak NSS-NMR signal is indeed observed. The longitudinal time-varying magnetic field ranges from 0.576 T to 0.582 T, which is inverted by the Larmor precession relationship, have been successfully detected based on the so-called NSS-NMR effect. [ABSTRACT FROM AUTHOR]

To realize the very objective of spintronics, namely the development of ultra-high frequency and energy-efficient electronic devices, an ultrafast and scalable approach to switch magnetic bits is required. Magnetization switching with spin currents generated by the spin–orbit interaction at ferromagnetic/non-magnetic interfaces is one of such scalable approaches, where the ultimate switching speed is limited by the Larmor precession frequency. Understanding the magnetization precession dynamics induced by spin–orbit torques (SOTs) is therefore of great importance. Here we demonstrate generation of ultrashort SOT pulses that excite Larmor precession at an epitaxial Fe/GaAs interface by converting femtosecond laser pulses into high-amplitude current pulses in an electrically biased p-i-n photodiode. We control the polarity, amplitude, and duration of the current pulses and, most importantly, also their propagation direction with respect to the crystal orientation. The SOT origin of the excited Larmor precession was revealed by a detailed analysis of the precession phase and amplitude at different experimental conditions. [ABSTRACT FROM AUTHOR]

Antiferromagnetic insulators 3 d transition-metal monoxides (TMOs), MnO, FeO, CoO, and NiO, are promising materials that open a new avenue for ultra-high speed operation physics in THz regime. Here, we investigate magnon dispersion and antiferromagnetic resonance (AFMR) frequencies of higher and lower modes (ω α and ω β) using semi-classical Larmor precession equation, in which magnetocrystalline anisotropy (MCA), magnetic dipole–dipole interaction (MDI), and spin-exchange interactions are considered. The calculated AFMR frequencies for MnO and NiO are in quantitative agreement with the experiments, where the inclusion of rhombohedral distortion is found to be necessary for ω β. In contrast, our results for FeO and CoO are only in qualitative agreement with the experiments. We also discuss the AFMR frequencies under the influence of magnetic parameters, particularly those related to the MCA and MDI. The calculations reveal that the AFMR frequencies exhibit different behavior with respect to magnetic parameters variation, depending on the magnetic easy axis of in-plane within (111) or out-of-plane with respect to (111). By analyzing the AFMR frequencies with respect to the magnetic parameters variation, we identify magnetic interactions that play the role in the AFMR frequencies of 3 d TMOs and partially explain the experimentally observed AFMR frequencies of FeO and CoO. Inclusion of non-negligible spin–orbit coupling effect such as spin-splitting may fully capture the experimentally observed AFMR frequencies of FeO and CoO. • Spin precession shape shows how MCA and MDI affects AFMR frequencies in 3 d TMOs. • Rhombohedral distortion impacts AFMR frequencies in NiO and MnO. • SOC–induced MCA mainly determines AFMR frequencies in FeO and CoO. [ABSTRACT FROM AUTHOR]

Spin exchange relaxation free (SERF) atomic magnetometer (AM), based on the Larmor precession of alkali atoms, is considered a promising candidate for magnetoencephalography (MEG) systems with the advantages of high sensitivity and no need for cryogenic devices. The footprint of the sensor header contains alkali vapor cell and bulk optical elements determining the spatial resolution of the MEG system. Optical fiber could separate the vapor cell far from other parts of the sensor header to improve the spatial resolution. However, coupling between glass cell and fibers limits the coupling loss of the light. Here, we describe the design of a fiber-based alkali vapor cell that could alleviate these issues. A pair of fiber cables combining a polarization maintaining fiber (PMF) and hollow-core photonic crystal fibers (HC-PCFs) are enclosed in a vacuum-sealed T-shape glass tube filled with alkali atoms. The fiber cell ensures a flexible integration with most fiber systems. The fiber structure, with an air gap between HC-PCFs, provides a large interaction volume between light and atoms. The vapor of the alkali atoms diffuses into the air core of the HC-PCF from the glass tube by heating. The alkali atoms still contained in SERF regime are within the wall relaxation rates of 12,764 s−1 in the coating fiber cell. The insertion loss due to fiber coupling is analyzed. The coupling efficiency could be 91%, with the fiber structure consisting of a 40 μm diameter HC-PCF and a 1 mm air gap. The limit sensitivity under this condition is simulated at 14.7 fT/Hz1/2. The fabrication technique and the light insertion loss are discussed. The fiber alkali vapor cell is of compact size and has flexible integration with the fiber atomic spin precession detection system. [ABSTRACT FROM AUTHOR]

It is crucial to develop a green solid-state fan (SSF) with high corona wind intensity and minimal ozone emission. The application of a magnetic field might be a feasible alternative. A magnetic field enhanced SSF with a simple structure was proposed. This research used a physical model to quantitatively investigate the effects of a magnetic field on corona wind velocity and body force. Under the influence of a magnetic field, the variation of voltammetry characteristics, corona wind strength, flow distribution, and ozone concentration were explored experimentally using a prototype SSF. With the aid of a magnetic field, the corona wind velocity and body force increased, according to the findings. The traveling route of electrons seems to shift rapidly. The SSF with a magnetic field has a lower corona current, lower ozone formation, greater flow yield, and a decline in ozone molecules when compared to the SSF without a magnetic field. The greatest corona wind velocity measured was 2.54 m/s when a 6.5 kV-voltage, a 5 mm-discharge gap, and a 24.28 mT-magnetic flux intensity were applied. The outcomes of this study might aid in the improvement of corona wind intensity and the development of green SSFs for cooling electronics. [ABSTRACT FROM AUTHOR]

The behavior of spins undergoing Larmor precession in the presence of time varying fields is of interest to many research fields. The frequency shifts and relaxation resulting from these fields are related to their power spectrum, determined from the Fourier Transform of the auto-correlation functions of the time varying field. Using the method of images C. M. Swank, A. K. Petukhov, and R. Golub (2012 and 2016) calculated the position-position auto-correlation function for particles moving in a rectangular cell with specular scattering walls. In this work we present a heuristic model that applies the method of images to the case of Lambert scattering walls. The results of this model are compared to simulation and show remarkably good agreement from the ballistic to diffusive regime of gas collisions, for both square and general rectangular cells. • Method of images used to calculate correlation functions in the case of Lambert scattering walls. • Resulting model is valid from ballistic to diffusive regime of gas collisions. • Model is valid for square and rectangular cells. • Model shows good agreement with simulations. • Application to gradient induced relaxation and frequency shifts in NMR. [ABSTRACT FROM AUTHOR]

We report the design and performance of a nonmagnetic drift stable optically pumped cesium magnetometer with a measured sensitivity of 35 fT at 200 s integration time and stability below 50 fT between 70 and 600 s. The sensor is based on the nonlinear magneto-optical rotation effect: in a Bell–Bloom configuration, a higher order polarization moment (alignment) of Cs atoms is created with a pump laser beam in an anti-relaxation coated Pyrex cell under vacuum, filled with Cs vapor at room temperature. The polarization plane of light passing through the cell is modulated due the precession of the atoms in an external magnetic field of 2.1 μT, used to optically determine the Larmor precession frequency. Operation is based on a sequence of optical pumping and observation of freely precessing spins at a repetition rate of 8 Hz. This free precession decay readout scheme separates optical pumping and probing and, thus, ensures a systematically highly clean measurement. Due to the residual offset of the sensor of <15 pT together with negligible crosstalk of adjacent sensors, this device is uniquely suitable for a variety of experiments in low-energy particle physics with extreme precision, here as a highly stable and systematically clean reference probe in search for time-reversal symmetry violating electric dipole moments. [ABSTRACT FROM AUTHOR]

The ensemble average phase Graph HT ht poses interesting challenges to the experiment. An observable sensitive to this relative precession rate would therefore provide a direct measurement of Graph HT ht . Since then, many more diagrams contributing to Graph HT ht have been evaluated. For a particle with momentum and spin vectors in a plane perpendicular to ->B, a classical calculation of the difference of these frequencies yields Graph HT ht (6) so that Graph HT ht (7) A relativistic calculation modifies the expression for I SB s sb i and I SB c sb i , but the difference 6 remains unaffected. [Extracted from the article]

A proton precession magnetometer (PPM) is a traditional quantum magnetometer based on the Larmor precession of hydrogen protons in Earth's magnetic field. PPMs are widely used in various fields, such as magnetic observation and detection of buried objects. A coaxial solenoid is typically used to construct the PPM sensor. However, the Larmor signal slowly weakens when the axial direction of the sensor gradually approaches the direction of Earth's magnetic field. Thus, a dead zone exists when Earth's magnetic field is nearly parallel to the axis of the sensor. An omnidirectional sensor with an "8"-type structure is designed in this study. The signal quality is slightly affected by the orientation of the sensor owing to the orthogonal polarized magnetic field components. The measured signal-to-noise ratio (SNR) of the Larmor signal is approximately 31/1, and the decay constant of the free induced decay (FID) signal is 0.95 s. The electrical parameters of the sensor coil are optimized and the polarization power is 8.0 W. Multiple hourly observations of Earth's magnetic field in noisy and quiet environments indicate the satisfactory consistency of the measurement results of the two PPMs with the proposed sensor. The standard deviations (STDs) of the measured results for a single instrument in noisy and quiet environments are 6.4 and 0.076 nT, respectively, which effectively reflect the environmental noise level. The sensitivity of the instrument is estimated to be 0.04 nT at a 5 s cycling rate for the two synchronized instruments. This is higher than the sensitivity of most commercial magnetometers of 0.1 nT. [ABSTRACT FROM AUTHOR]

Mn-based hard magnets are potentially suitable for advanced ultra-high frequency spintronics applications because they exhibit the Larmor precession of magnetization at THz wave-range frequencies with low magnetic relaxation. However, the low magnetic relaxation properties are not well understood; thus, a more detailed study is necessary. In this study, magnetization precessions in L10 Mn1.54Ga, D022 Mn2.12Ga, and C38 MnAlGe epitaxial films grown on MgO substrates were investigated using an all-optical pump-probe method under a magnetic field of ~20 kOe. The coherent magnetization precessions at frequencies of more than 0.1, 0.2, and 0.3 THz for the C38 MnAlGe, L10 Mn1.54Ga, and D022 Mn2.12Ga films, respectively, were clearly measured. The effective damping constant for the C38 MnAlGe film was smaller than the previously reported value measured at 10 kOe by a factor of 2, whereas those showed a large angular dependence. The effective damping constants for the L10 Mn1.54Ga and D022 Mn2.12Ga films were independent of the field angle and approximately identical to the values measured at 10 kOe. Thus, it was concluded that the values for the Gilbert damping constant, α, were 0.008 and 0.012 for the L10 Mn1.54Ga and D022 Mn2.12Ga films, respectively. The possible origin of the discrepancy between the experimental and theoretical a values for these films is discussed. [ABSTRACT FROM AUTHOR]

In aqueous systems with immobilized macromolecules, including biological tissue, the longitudinal spin relaxation of water protons is primarily induced by exchange-mediated orientational randomization (EMOR) of intra- and intermolecular magnetic dipole-dipole couplings. Starting from the stochastic Liouville equation, we have developed a non-perturbative theory that can describe relaxation by the dipolar EMOR mechanism over the full range of exchange rates, dipole couplings, and Larmor frequencies. Here, we implement the general dipolar EMOR theory for a macromolecule-bound three-spin system, where one, two, or all three spins exchange with the bulk solution phase. In contrast to the previously studied two-spin system with a single dipole coupling, there are now three dipole couplings, so relaxation is affected by distinct correlations as well as by self-correlations. Moreover, relaxation can now couple the magnetizations with three-spin modes and, in the presence of a static dipole coupling, with two-spin modes. As a result of this complexity, three secondary dispersion steps with different physical origins can appear in the longitudinal relaxation dispersion profile, in addition to the primary dispersion step at the Larmor frequency matching the exchange rate. Furthermore, and in contrast to the two-spin system, longitudinal relaxation can be significantly affected by chemical shifts and by the odd-valued ("imaginary") part of the spectral density function. We anticipate that the detailed studies of two-spin and three-spin systems that have now been completed will provide the foundation for developing an approximate multi-spin dipolar EMOR theory sufficiently accurate and computationally efficient to allow quantitative molecular-level interpretation of frequency-dependent water-proton longitudinal relaxation data from biophysical model systems and soft biological tissue. [ABSTRACT FROM AUTHOR]

TWe present results of a pulsed dynamic nuclear polarization (DNP) study at 0.35 T (9.7 GHz/ 14.7 MHz for electron/¹H Larmor frequency) using a lab frame-rotating frame cross polarization experiment that employs electron spin locking fields that match the ¹H nuclear Larmor frequency, the so called NOVEL (nuclear orientation via electron spin locking) condition. We apply the method to a series of DNP samples including a single crystal of diphenyl nitroxide (DPNO) doped benzophenone (BzP), 1,3-bisdiphenylene-2-phenylallyl (BDPA) doped polystyrene (PS), and sulfonated-BDPA (SA-BDPA) doped glycerol/water glassy matrices. The optimal Hartman-Hahn matching condition is achieved when the nutation frequency of the electron matches the Larmor frequency of the proton, ω1S = ω0I, together with possible higher order matching conditions at lower efficiencies. The magnetization transfer from electron to protons occurs on the time scale of ~100 ns, consistent with the electron-proton couplings on the order of 1-10 MHz in these samples. In a fully protonated single crystal DPNO/BzP, at 270 K, we obtained a maximum signal enhancement of ε = 165 and the corresponding gain in sensitivity of ε(T1/TB)1/2 = 230 due to the reduction in the buildup time under DNP. In a sample of partially deuterated PS doped with BDPA, we obtained an enhancement of 323 which is a factor of ~3.2 higher compared to the protonated version of the same sample and accounts for 49% of the theoretical limit. For the SA-BDPA doped glycerol/water glassy matrix at 80 K, the sample condition used in most applications of DNP in nuclear magnetic resonance, we also observed a significant enhancement. Our findings demonstrate that pulsed DNP via the NOVEL sequence is highly efficient and can potentially surpass continuous wave DNP mechanisms such as the solid effect and cross effect which scale unfavorably with increasing magnetic field. Furthermore, pulsed DNP is also a promising avenue for DNP at high temperature. [ABSTRACT FROM AUTHOR]

We investigate the spin-Hall conductivity (SHC) in the two-dimensional spin–orbit coupled systems by taking spin precession into account. The influence of spin precession on the spin-Hall current in the presence of disorder is investigated. Perturbation method leads to the result that the spin dynamics is composed of Larmor (periodic) and non-Larmor (non-periodic) precession. The non-Larmor component of spin is found to be the same result obtained from the Kubo formula in the short time limit. The Larmor component of spin, i.e., spin precession in the unperturbed system, was neglected in the previous studies, but it plays an important role in the linear response theory. The Larmor precession of spin should be zero after time average over several complete periods because there is no specific orientation perpendicular to the plane. By using the requirement of vanishing time-averaged Larmor precession of spin, we calculate the time-averaged non-Larmor SHC for k-cubic Rashba system by using the conventional definition of the spin current. Our result is 2.1(q/8π) which is very close to the experimental value 2.2(q/8π) by Wunderlich et al [2005 Phys. Rev. Lett. 94 , 047204], where −q is the electric charge. [ABSTRACT FROM AUTHOR]

Abstract A superluminescent diode (SLD) as an alternative of laser is used to detect optical rotation for atomic spin precession. A more uniform Gauss configuration without additional beam shaping and a relatively high power of the SLD have a potential for atomic magnetometers, which is demonstrated in theory and experiments. In addition, the robustness and compactness enable a more practical way for optical rotation detections, especially for applications in magnetoencephalography systems.

Abstract We propose an in-situ method to calibrate the coil constants of the optical atomic magnetometer. This method is based on measuring the Larmor precession of spin polarized alkali metal atoms and has been demonstrated on a K-Rb hybrid atomic magnetometer. Oscillation fields of different frequencies are swept on the transverse coil. By extracting the resonance frequency through phase-frequency analysis of electron spin projection, the coil constants are calibrated to be 323.1 ± 0.28 nT/mA, 108 ± 0.04 nT/Ma, and 185.8 ± 1.03 nT/mA along the X, Y, and Z directions, respectively.

A ring magnet enhancement method was developed and utilized for boosting the signal intensity of the analysis of scintillation crystals by radio frequency glow discharge mass spectrometry (rf-GD-MS). Three scintillation crystals of BGO, LYSO and GGAG were applied to observe the performance of the ring magnet method. The investigations suggested that the signal intensities obtained for 209Bi, 175Lu and 158Gd with the ring magnet were 7810–27 600 times those obtained without a magnet and were enhanced by a factor of 1.9–2.3 compared with the previously reported stacked magnet and array magnet methods. The results also suggested that the signal intensity was enhanced as the rf power increases from 25 W to 70 W (with a frequency of 13.56 MHz) and a sharp rise up to 4.8 MPa and then decreased with the increase of discharge pressure from 2.2 to 8.4 MPa. The validation results with two NIST samples indicated that the relative errors were within 13% and the lowest detection limit could reach as low as 0.0023 μg g−1 (24Mg, with 40 W and 4.8 MPa) for the ring magnet. The enhancement mechanism of this method was further proposed in which electrons could undergo distinct Larmor precession with a ring magnet, which could increase the collisions between the electrons and other particles to increase the ionization efficiency. Moreover, this work not only shed light on the possible enhancement mechanism by the ring magnet but also provided an effective determination method for the artificial crystals. [ABSTRACT FROM AUTHOR]

Alignment of nonspherical grains with magnetic fields is an important problem, as it lays the foundation of probing magnetic fields with polarized dust thermal emissions. In this paper, we investigate the feasibility of magnetic alignment in protoplanetary disks (PPDs). We use an alignment condition that Larmor precession should be fast compared with the damping timescale. We first show that the Larmor precession timescale is some 3 orders of magnitude longer than the damping time for millimeter-sized grains under conditions typical of PPDs, making the magnetic alignment unlikely. The precession time can be shortened by superparamagnetic inclusions (SPIs), but the reduction factor strongly depends on the size of the SPI clusters, which we find is limited by the so-called "Néel's relaxation process." In particular, the size limit of SPIs is set by the so-called "anisotropic energy constant" of the SPI material, which describes the energy barrier needed to change the direction of the magnetic moment of an SPI. For the most common iron-bearing materials, we find maximum SPI sizes corresponding to a reduction factor of the Larmor precession timescale of order 103. We also find that reaching this maximum reduction factor requires fine-tuning on the SPI sizes. Lastly, we illustrate the effects of the SPI size limits on magnetic alignment of dust grains with a simple disk model, and we conclude that it is unlikely for relatively large grains of order 100 μm or more to be aligned with magnetic fields, even with SPIs. [ABSTRACT FROM AUTHOR]

Geometrical frustration, quantum entanglement, and disorder may prevent long-range ordering of localized spins with strong exchange interactions, resulting in an exotic state of matter. k-(BEDT-TTF)2Cu2(CN)3 is considered the prime candidate for this elusive quantum spin liquid state, but its ground-state properties remain puzzling. We present a multifrequency electron spin resonance (ESR) study down to millikelvin temperatures, revealing a rapid drop of the spin susceptibility at 6 kelvin. This opening of a spin gap, accompanied by structural modifications, is consistent with the formation of a valence bond solid ground state. We identify an impurity contribution to the ESR response that becomes dominant when the intrinsic spins form singlets. Probing the electrons directly manifests the pivotal role of defects for the low-energy properties of quantum spin systems without magnetic order. [ABSTRACT FROM AUTHOR]

For the further development of spin‐echo techniques to label elastic scattering it is necessary to perform simulations of the Larmor precession of neutron spins in a magnetic field. The details of some of these techniques as implemented at the reactor in Delft are simulated. First, the workings of the magnetized foil flipper are simulated. A full virtual spin‐echo small‐angle neutron scattering instrument is built and tested without and with a realistic scattering sample. It is essential for these simulations to have a simulated sample that also describes the transmitted beam of unscattered neutrons, which usually is not implemented for the simulation of conventional small‐angle neutron scattering (SANS) instruments. Finally, the workings of a spin‐echo modulated small‐angle neutron scattering (SEMSANS) instrument are simulated. The simulations are in good agreement with theory and experiments. This setup can be extended to include realistic magnetic field distributions to fully predict the features of future Larmor labelling elastic‐scattering instruments. Configurations can now be simulated for more complicated combinations of SANS with SEMSANS. [ABSTRACT FROM AUTHOR]

Research on the location and shape of a beam spot at a target altitude can lay the foundation for understanding and diagnosing the long-range propagation of relativistic electron beams. Only a few studies have focused on this approach. In this study, a terrestrial atmosphere with a 3-D geomagnetic field was constructed in accordance with the International Geomagnetic Reference Field model and a relevant atmosphere model. Monte Carlo simulations were applied to the long-range propagation of relativistic (1–10 MeV) electron beams in the altitude range of 200–300 km. The results showed that when beams with various parameters were emitted in one location, the centers of the beam spots were distributed in concentric circles with different radii. The direction of the geomagnetic field determined the locations of the circle centers, whereas the beam energy and pitch angle determined the radii. When the initial gyrophase changed, the center of the beam spot rotated through the same angle. The beam spot was distributed as a partial ring with a width mainly related to the initial beam radius when the energy spread was relatively small. If the energy spread exceeded the limit, the beam spot was ring-shaped; the ring width was determined by both the initial beam radius and the energy spread. [ABSTRACT FROM AUTHOR]

Ionization of two-photon excited states 5 p 5 (2 P 3 / 2) 6 p [ 3 / 2 , 5 / 2 ] 2 , M = 2 (jl-coupling) of xenon atoms by circularly polarized probe light was studied experimentally in a supersonic beam. The observed photoionization signals revealed oscillation structure due to the Larmor precession of atomic states in an external magnetic field. We derived analytical formulas for the photoelectron current and explained the diversity in the structure of the detected oscillations in terms of the principal lines among multiplet components of optical transitions. The obtained numerical data demonstrate collapse and revival (beating) behavior of the photocurrent due to nonlinearity of Zeeman shifts in the presence of the Paschen–Back effect. Our results indicate the possibility of implementing Doppler-free spectroscopy involving bound-free transitions. [ABSTRACT FROM AUTHOR]

Abstract In this paper we show how the IBM superconducting chips can be a powerful tool for teaching foundations of quantum mechanics for undergraduate students (for graduates as well, in some cases). To this end, we briefly discuss about the main elements of the IBM Quantum Experience platform necessary to understand this paper, i.e., how to implement operations and single-qubit measurements. We experimentally study the dynamics of single spin systems interacting with static and time-dependent magnetic fields. First, we study the resonant behavior of a single spin coupled to a time-dependent rotating magnetic field. To end, we study the Larmor precession phenomenon. In both cases we show the theoretical and real experimental implementation. This article could be useful in introductory courses on quantum mechanics and nuclear magnetic resonance foundations, for example.

Radiative torques (RATs) or mechanical torques acting on irregular grains can induce the alignment of dust grains in respect to the alignment axis (AA), which can be either the direction of the magnetic field or the direction of the radiation. We show that carbonaceous grains can be aligned with their axes both parallel and perpendicular to the AA, and we explore the conditions where the particular mode of alignment takes place. We identify a new process of alignment of charged carbonaceous grains in a turbulent, magnetized interstellar medium with respect to an electric field. This field acts on grains accelerated in a turbulent medium and gyrorotating about a magnetic field. The electric field can also arise from the temporal variations of the magnetic field strength in turbulent, compressible media. The direction of the electric field is perpendicular to the magnetic field, and the carbonaceous grains precess in the electric field because of their electric moments. If this precession is faster than Larmor precession in the magnetic field, the alignment of such grains is with their long axes parallel to the magnetic field. We explore the parameter space for which the new mechanism aligns grains with long axes parallel to the magnetic field. We compare this mechanism with another process that provides the same type of alignment, namely, the RAT alignment of grains with insufficiently fast internal relaxation. We describe the conditions for which the particular mode of carbonaceous grain alignment is realized and discuss what information can be obtained by measuring the resulting polarization. [ABSTRACT FROM AUTHOR]

Inertial navigation systems generally consist of timing, acceleration, and orientation measurement units. Although much progress has been made towards developing primary timing sources such as atomic clocks, acceleration and orientation measurement units often require calibration. Nuclear Magnetic Resonance (NMR) gyroscopes, which rely on continuous measurement of the simultaneous Larmor precession of two co-located polarized noble gases, can be configured to have scale factors that depend to first order only on fundamental constants. The noble gases are polarized by spin-exchange collisions with co-located optically pumped alkali-metal atoms. The alkali-metal atoms are also used to detect the phase of precession of the polarized noble gas nuclei. Here we present a version of an NMR gyroscope designed to suppress systematic errors from the alkali-metal atoms. We demonstrate rotation rate angle random walk (ARW) sensitivity of 16 μ Hz / Hz and bias instability of ∼800 nHz. [ABSTRACT FROM AUTHOR]

We created software to simulate the Larmor precession in a setup for SESANS with adiabatic/radio frequency flippers in magnets designed to measure the time-of-flight on pulsed or stationary neutron sources. The values and spatial configurations of the magnetic fields of the existing prototype magnets we used as input data. For an empty setup, we calculate the polarization of a "divergent ribbon beam" 2 cm high, depending on the neutron wavelength λ. In the "scattering experiment", we show how to convert λ to the "spin-echo length" δ. For λ = 10 Å, flippers at a distance of 140 cm and a radio frequency 1 MHz we find δ ≈ 10 μm. Extension to δ = 20 μm is realistic. [ABSTRACT FROM AUTHOR]

The spin self-sustaining atomic magnetometer has the advantage of 1/τ measurement and great development potential in many applications. In this paper, we investigated the main elements that affect the stability and accuracy of the self-sustaining magnetometer and proposed the methods to improve its performance based on the measurement results. The correlation coefficient between fluctuations of the magnetic field generated by coils and the spin Larmor precession frequency is 0.97, which mainly dominates the stability in a short term. The accuracy of the magnetometer is affected by the power and frequency of the pump light. The Larmor precession frequency coefficient related to the pump light power is 26 mHz/mW, and the effect on the Larmor precession frequency is minimized when the pump light frequency is red detuned by 200 MHz from the 85Rb transition D1 line F = 3 to F′ = 3. The 1/τ measurement time after these corrections can be extended to 10 s, and the sensitivity achieved is 149 fT/ Hz , which is close to the quantum projection noise limit of the system. [ABSTRACT FROM AUTHOR]

The paper aims to apply the octonions to explore the precessional angular velocities of several particles in the electromagnetic and gravitational fields. Some scholars utilize the octonions to research the electromagnetic and gravitational fields. One formula can be derived from the octonion torque, calculating the precessional angular velocity generated by the gyroscopic torque. When the octonion force is equal to zero, it is able to deduce the force equilibrium equation and precession equilibrium equation and so forth. From the force equilibrium equation, one can infer the angular velocity of revolution for the particles. Meanwhile, from the precession equilibrium equation, it is capable of ascertaining the precessional angular velocity induced by the torque derivative, including the angular velocity of Larmor precession. Especially, some ingredients of torque derivative are in direct proportion to the field strengths. The study reveals that the precessional angular velocity induced by the torque derivative is independent of that generated by the torque. The precessional angular velocity, induced by the torque derivative, is relevant to the torque derivative and the spatial dimension of precessional velocity. It will be of great benefit to understanding further the precessional angular velocity of the spin angular momentum. [ABSTRACT FROM AUTHOR]

We demonstrate a portable all-optical intrinsic scalar magnetic gradiometer composed of miniaturized cesium vapor cells and vertical-cavity surface-emitting lasers (VCSELs). Two cells, with inner dimensions of 5 mm × 5 mm × 5 mm and separated by a baseline of 5 cm, are driven by one VCSEL, and the resulting Larmor precessions are probed by a second VCSEL through optical rotation. The off-resonant linearly polarized probe light interrogates two cells at the same time, and the output of the intrinsic gradiometer is proportional to the magnetic field gradient measured over the given baseline. This intrinsic gradiometer scheme has the advantage of avoiding added noise from combining two scalar magnetometers. We achieve a sensitivity better than 18 fT/cm/√Hz in the gradient measurement. Ultra-sensitive short-baseline magnetic gradiometers can potentially play an important role in many practical applications, such as nondestructive evaluation and unexploded ordnance detection. Another application of the gradiometer is for magnetocardiography (MCG) in an unshielded environment. Real-time MCG signals can be extracted from the raw gradiometer readings. The demonstrated gradiometer greatly simplifies the MCG setup and may lead to a ubiquitous MCG measurement in the future. [ABSTRACT FROM AUTHOR]

A novel method to determine the spin polarization and its distribution for a spin-exchange relaxation-free (SERF) atomic magnetometer are proposed in this paper. The Larmor precession frequency is measured using the fast Fourier transform (FFT) analysis result of the transient response of the magnetometer under the excitation of a series of the step-changed magnetic field. The spin polarization is extracted from the slow-down factor of the precession frequency. The variation of the spin polarization with different pump light intensities and the distribution of the spin polarization along the direction of the pump light are analyzed, and the experimental results are well consistent with the theoretical predictions. The expanded uncertainties of the experimental results vary from 2% to 11% with the increase of the spin polarization and the reason for this variation is analyzed. The advantage of this method is that it allows the accurate measurement of the spin polarization in the pump beam direction within the SERF regime operating state, and it is unaffected by the large optical depth of the vapor cell. [ABSTRACT FROM AUTHOR]

In this work, the design of a pulsed magnetic field generator, with user-selective pulsed modulation frequency is described. The ability to operate at various frequencies (single-frequency below 10 MHz) makes the system valuable to several areas such as medical treatments and pulsed switching systems. In this work, the pulsed magnetic field generator is designed to create localized field effects in portable magnetic resonance systems. Users may operate at a Larmor precession frequency between 100 kHz - 10 MHz and can achieve high currents through the load. Certain tunability can also be obtained by varying the load inductance or switching device conditions. In summary, this paper will describe the design considerations and challenges for portable monophasic pulsed magnetic field systems. [ABSTRACT FROM AUTHOR]

In this paper we show how the IBM superconducting chips can be a powerful tool for teaching foundations of quantum mechanics for undergraduate students (for graduates as well, in some cases). To this end, we briefly discuss about the main elements of the IBM Quantum Experience platform necessary to understand this paper, i.e., how to implement operations and single-qubit measurements. We experimentally study the dynamics of single spin systems interacting with static and time-dependent magnetic fields. First, we study the resonant behavior of a single spin coupled to a time-dependent rotating magnetic field. To end, we study the Larmor precession phenomenon. In both cases we show the theoretical and real experimental implementation. This article could be useful in introductory courses on quantum mechanics and nuclear magnetic resonance foundations, for example. [ABSTRACT FROM AUTHOR]