Comment on angeo-2021-59

The reconstruction of Mercury’s internal magnetic field enables us to take a look into the inner heart of Mercury. In view of the BepiColombo mission, Mercury’s magnetosphere is simulated using a hybrid plasma code and the multipoles of the internal magnetic field are estimated from the virtual spacecraft data using three distinct reconstruction methods: the truncated singular value decomposition, the Tikhonov regularization and Capon’s minimum variance projection. The study shows that a precise determination of Mercury’s internal field beyond the octupole, up to the dotriacontapole is possible and that Capon’s method provides the same high performance as the Tikhonov regularization, which is superior to the performance of the truncated singular value decomposition.

The "M\"ossbauer" technique was used to measure the internal magnetic fields and isomer shifts of ${\mathrm{Fe}}^{57}$ atoms residing at various sites in the FeSi series. The relative abundances of the various sites present in a given alloy were obtained by measuring the relative intensities of the components in the resolved spectrum of the alloy. Alloys with Si content varying from 0 to \ensuremath{\sim}27 at.% were studied. In the disordered region (10 at.% Si) three different type sites were observed. These corresponded to Fe atoms having 8, 7, and 6 nearest-neighbor Fe atoms. The internal field decreased by $0.08 {H}_{\mathrm{Fe}}$ for each Si nearest neighbor. In the ordered region the alloys try to go into a ${\mathrm{Fe}}_{3}$Al type structure. Sites having 8 through 3 nearest-neighbor iron atoms were observed. For $A$-type sites (4 nearest-neighbor Fe atoms and 4 nearest-neighbor Si atoms at 25 at.% Si), the internal field decreased by $0.14 {H}_{\mathrm{Fe}}$ for each Si nearest neighbor. Over the whole series the isomer shift indicated that there was progressively less electronic charge density at the origin as the number of nearest-neighbor Si atoms increased. A measure of the relative intensities of the various magnetic field components in the spectra of an alloy series is shown to give direct evidence on the type of ordering. No tendency to form intermediate compounds other than ${\mathrm{Fe}}_{3}$Si was observed. An average internal magnetic field for each alloy could be obtained from the data. This average internal field does not vary in the same way as the magnetization on the FeSi series.

The internal magnetic fields and isomer shifts of ${\mathrm{Fe}}^{57}$ nuclei in a number of iron-rich bcc binary alloy systems were measured by the M\ossbauer technique. The added solute atoms Al, Si, Mn, Cr, or V give structure to the individual lines of the spectra indicating that their effects are quite localized. These line shapes were analyzed by a computer program which interpreted them in terms of the effects of the solute atoms in the first five neighbor shells. It appears justifiable to attribute the observed hyperfine-field shifts in the FeAl series to the spatial variation of the spin polarization of the $4s$ conduction electrons around an Fe atom in pure iron. The observed $4s$ spin-polarization variation with distance had oscillations with a ${k}_{F}\ensuremath{\simeq}(1.0\ensuremath{-}1.2)\ifmmode\times\else\texttimes\fi{}{10}^{8}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ corresponding to 0.4-0.6 electrons/atom in the $4s$ conduction band. These oscillations are compared with those obtained by recent improved calculations of the indirect exchange polarization which take into account the full $k$ dependence of the conduction-electron wave functions. For all the alloy series reported here, internal field shifts at the first and second nearest neighbors decreased the internal field. This indicates that the $4s$ electrons produce an antiferromagnetic contribution to the magnetic coupling in iron. The average internal field of each alloy was also obtained, and for all the alloy series described here this quantity decreases more rapidly than the moment per Fe atom as a function of solute-atom concentration. The isomer shifts due to solute atoms in the first three neighbor shells are also reported.

The Earth’s internal magnetic field controls to a degree the strength, geographic positioning, and structure of currents flowing in the ionosphere and magnetosphere, which produce their own (external) magnetic fields. The secular variation of the Earth’s internal magnetic field can therefore lead to long-term changes in the externally produced magnetic field as well. Here we will examine this more closely. First, we obtain scaling relations to describe how the strength of magnetic perturbations associated with various different current systems in the ionosphere and magnetosphere depends on the internal magnetic field intensity. Second, we discuss how changes in the orientation of a simple dipolar magnetic field will affect the current systems. Third, we use model simulations to study how actual changes in the Earth’s internal magnetic field between 1908 and 2008 have affected some of the relevant current systems. The influence of the internal magnetic field on low- to mid-latitude currents in the ionosphere is relatively well understood, while the effects on high-latitude current systems and currents in the magnetosphere still pose considerable challenges.

Context.Stellar internal magnetic fields have recently been shown to leave a detectable signature on period spacing patterns of gravity modes.Aims.We aim to investigate the effect of the obliquity of a mixed (poloidal and toroidal) dipolar internal fossil magnetic field with respect to the rotation axis on the frequency of gravity modes in rapidly rotating stars.Methods.We used the traditional approximation of rotation to compute non-magnetic modes, and a perturbative treatment of the magnetic field to compute the corresponding frequency shifts. We applied the new formalism to HD 43317, a magnetic, rapidly rotating, slowly pulsating B-type star, whose field has an obliquity angle of about 80°.Results.We find that frequency shifts induced by the magnetic field on high-radial-order gravity modes are larger with increasing obliquity angle, when the magnetic axis is closer to the equatorial region, where these modes are trapped. The maximum value is reached for an obliquity angle of 90°. This trend is observed for all mode geometries.Conclusions.Our results predict that the signature of an internal oblique dipolar magnetic field is detectable using asteroseismology of gravity modes.

Direct magnetoelectric (ME) effect in two‐layered Tb0.12Dy0.2Fe0.68/Epoxy − PbZr0.53Ti0.47O3 composites containing magnetostrictive layers of the epoxy with distributed in it Tb0.12Dy0.2Fe0.68 granules and piezoelectric layers of the PbZr0.53Ti0.47O3 ceramics was studied. It was found, that the gradient distribution of Tb0.12Dy0.2Fe0.68 granules in magnetostrictive layers induces the internal (self‐biased) magnetic field. This field leads to the increase in ME responses in composites with the gradient distribution of Tb0.12Dy0.2Fe0.68 granules in magnetostrictive layers as compared with ME responses in composites with the random distribution of Tb0.12Dy0.2Fe0.68 granules in magnetostrictive layers, which does not induce the internal magnetic field. We revealed the possibility of controlling and determining values of the internal magnetic field in composites and conditions for obtaining optimal ME responses.

The development of a system for heading determination of a small underwater vehicle is described. The system uses a Kalman filter to fuse information from a pair of inclinometers and a tri-axial magnetometer. The magnetometer can be corrupted by variations in the Earth's field caused by: external objects and internal magnetic fields. The internal field is assumed to consist of static and thruster dependent parts. We show how to use inclinometer data to adjust for a limited set of external field variation. We also show how to calibrate the magnetometer to compensate for static and thruster dependent internal fields.

The presence of a time-reversal symmetry-breaking field in the hidden order and superconducting states of URu2Si2 has been studied by muon spin relaxation (μSR) spectroscopy. The development of an internal magnetic field has been observed in the hidden order state. Longitudinal-field μSR experiments have shown that the internal magnetic field is static on the time scale of μSR. The presence of both a- and c-axis components of the internal magnetic field at the muon sites was revealed by transverse-field μSR experiments. This is in contrast to the pressure-induced antiferromagnetic state, where the internal magnetic field is parallel to the c-axis. We also found that the muon spin relaxation rate is further enhanced below the superconducting phase transition temperature, indicating further development of the internal magnetic field.

The internal magnetic fields of Mn and Sn nuclei in Ni 2 MnSn, Co 2 MnSn and Ni 2 MnSb were measured with the spin-echo N. M. R. method, as well as their thermo-magnetic curves. The Curie temperatures measured of Ni 2 MnSn and Ni 2 MnSb were different from Castellitz's data, and a sluggish change of the magnetization in Ni 2 MnSb was observed, near the Curie temperature. The NMR signals of Mn nuclei were observed in Co 2 MnSn, Ni 2 MnSn and Ni 2 MnSb. The internal magnetic fields were 352.3, 312.7 and 285 kOe, respectively. An unexpected resonance signal appeared in Ni 2 MnSb and was interpreted as originating from Mn atoms occupying non-regular sites. The resonance signals of Sn nuclei were also observed in Co 2 MnSn and Ni 2 MnSn. The internal magnetic fields were 153.8 and 150.4 kOe, respectively. The difference in the internal magnetic fields of the above compounds from those of Cu 2 MnSn can be tentatively attributed to the difference in the conduction electron polarization by RKKY interaction.

In this paper, a new open-loop model for a magnetorheological-based actuator is presented. The model consists of two parts relating the output torque of the actuator to its internal magnetic field, and the internal magnetic field to the applied current. Each part possesses its own hysteretic behavior. The first part uses a novel nonlinear adaptive model that relates the internal magnetic field to the applied current. The second part uses an open-loop Bingham model to relate the output torque to an internal magnetic field. The model facilitates accurate control of the actuator using its input current. It also eliminates the need for force/torque sensors for providing feedback signals. The accuracy of the constructed model is validated through simulations. The model is assessed against a widely accepted hysteresis modeling approach, known as the Preisach model and its advantages are highlighted. Experimental results using the prototyped actuation mechanism further verify the accuracy of the model and demonstrate its effectiveness.

Magnetic field assisted centrifugal acceleration thin-layer chromatography: An approach to investigate the magnetic field effects on separation parameters including retention factor difference, selectivity factor, and resolution

Kelvin–Helmholtz instability in a twisting solar polar coronal hole jet observed by SDO/AIA

Mössbauer nuclei 119mSn were doped into the grain boundary of ultra fine grained iron specimens. Various parameters such as internal magnetic field, Debye temperatures and thermal jump frequency were measured. The parameters showed that tin atoms segregated at the grain boundary are contributing a less amount of outer shell electrons to bonds with the neighboring atoms and the average force constant is reduced below that of tin in solid solution in the iron matrix. The differences, however, were small while a large difference was noticed in its internal magnetic field. The absence in the internal magnetic field suggests that iron atoms next to tin in the grain boundary are in a special state with respect to their d-level and may explain the embrittlement of steel. The oxygen-induced embrittlement which was suggested from experiments of pure iron may be a different mechanism peculiar to pure iron.

Context. Asymmetries in the observed rotational splittings of a multiplet contain information about the star’s rotation profile and internal magnetic field. Moreover, the frequency regularities of multiplets can be used for mode identification. However, to exploit this information, highly accurate theoretical predictions are needed. Aims. We aim to quantify the difference in the predicted mode asymmetries between a 1D perturbative method and a 2D method that includes a 2D stellar structure model, which takes rotation into account. We then place these differences between 1D and 2D methods in the context of asteroseismic measurements of internal magnetic fields. We only focus on the asymmetries and not on possible additional frequency peaks that can arise when the magnetic and rotation axis are misaligned. Methods. We coupled the 1D pulsation codes GYRE and StORM to the 2D stellar structure code ESTER and compared the oscillation predictions with the results from the 2D TOP pulsation code. We focused on zero-age main-sequence models representative of rotating β Cephei pulsators spinning at up to 20 per cent of the critical Keplerian rotation rate. Specifically, we investigated low-radial-order gravity and pressure modes. Results. We find a generally good agreement between the oscillation frequencies resulting from the 1D and 2D pulsation codes. We report differences in predicted mode multiplet asymmetries of mostly below 0.06 d −1 . Since the magnetic asymmetries are small compared to the differences in the rotational asymmetries resulting from the 1D and 2D predictions, accurate measurements of the magnetic field are in most cases challenging. Conclusions. Differences in the predicted mode asymmetries of a rotating star between 1D perturbative methods and 2D non-perturbative methods can greatly hinder accurate measurements of internal magnetic fields in main-sequence pulsators with low-order modes. Nevertheless, reasonably accurate measurements could be possible with n pg ≥ 2 modes if the internal rotation is roughly below 10 per cent of the Keplerian critical rotation frequency for (aligned) magnetic fields of the order of a few hundred kilogauss. While the differences between the 1D and 2D frequency predictions are mostly too large for internal magnetic field detections, the rotational asymmetries predicted by StORM are in general accurate enough for asteroseismic modelling of the stellar rotation in main-sequence stars with identified low-order modes.

NMR spectra of 63,65Cu in an internal magnetic field were studied experimentally. The electric field gradient (EFG) at Cu nuclei in chalcopyrite CuFeS2 was evaluated ab initio by using a cluster approach. Calculations were carried out in the framework of the self-consistent field restricted open-shell Hartree–Fock method (SCF-LCAO-ROHF). The largest cluster for which calculations were carried out had the formula Cu9Fe10S28 n (R ~ 6 A, 47 atoms), where n is the cluster charge. The best agreement of the quadrupole parameters (quadrupole frequency νQ and EFG tensor asymmetry parameter η) that were determined experimentally (νQ = 1.29 MHz, η = 0.34) and were calculated (νQ = 1.40 MHz, η = 0.50) was obtained for the cluster Cu9Fe10S28 −4. Maps of electron-density distribution in the neighborhood of the Cu quadrupolar nucleus were built for the cluster Cu9Fe10S28 −4. It was suggested based on an analysis of the obtained electron-density distribution that the bond in chalcopyrite is not covalent. The energy-level diagram that was calculated in the ROHF high-spin approximation defined rather well chalcopyrite as a semiconductor with a very narrow LUMO–HOMO gap and was consistent with the notion of chalcopyrite as a gapless semiconductor.