Field Modulation Technique Research Articles

Hot-Electron Magnetophonon Effect in n-InSb at 77 K Investigated by Magnetic Field Modulation Technique

Second derivative of the transverse and longitudinal magnetoconductance is carried out by using a method of pulse electric field application combined with the magnetic field modulation technique. Resonant conductance minima shift to higher magnetic field side with increasing the electric field in the transverse configuration, while in the longitudinal configuration the ordinary maxima do not shift to higher magnetic field side but new conductance maxima are observed.

A Study of Magnetophonon Effect in n-InSb Using Field Modulation Technique

Precise measurements of the magnetophonon effect in n -InSb are made by making use of a magnetic field modulation and phase sensitive second harmonic detection technique. Obtained data show an excellent signal to noise ratio and up to the 14th extremum are resolved in the transverse configuration at 77 K. Second derivative of the magnetoresistance in the longitudinal configuration is extensively investigated in the temperature range of 89 to 171 K. A curve resolver analysis is applied to resolve new structure which appears between the ordinary magnetophonon resonance peaks and four peaks around the N =2 peak are resolved, which are assigned to the structure arising from the spin-conserving single and two LO phonon processes. Fourier transform technique is also adopted to obtain frequency spectrum of the magnetophonon structure. The higher harmonic terms and two LO phonon components are resolved for the first time by using a proper window function for Fourier analysis. The results are consistent with those...

Electric field dependence of the positions and amplitudes of magnetophonon oscillations in n-InSb at 77 K

The influence of pulsed electric fields on the magnetophonon structure in the transverse and longitudinal magnetoresistance of n-InSb at 77 K has been reexamined using a magnetic field modulation technique. For the transverse configuration, a shift to higher magnetic fields with increasing electric field is observed for the resistance maxima up to N = 8. The amplitudes decrease monotonously and disappear at about 60V/cm for N = 3. In the longitudinal case, the extrema shift to lower magnetic fields as the electric field is increased. In contrast to the transverse case, the amplitudes increase by a factor of 1.8 up to 15V/cm, and then either decrease or become saturated, depending on the harmonic number of the extremum under consideration. These experimental results are discussed within the context of calculations based on a quantum kinetic equation approach and predictions obtained from a simplified analytical theory.

Distribution function relaxation times in gallium arsenide : R. A. Warriner. Solid St. electron. Devices1, (3) 92 (April 1977)

The study of the magnetophonon resonance effect in semiconductors carried out in Osaka University is reviewed, covering theories, experimental techniques and results obtained. Experimental techniques are briefly described, where emphasis is placed on the magnetic field modulation technique. The effective mass is determined in III–V semiconductors at a wide range of lattice temperatures and its temperature dependence is discussed. Magnetophonon resonance associated with impurity state, zone-edge phonons, and intervalley phonons are also reviewed. At high electric and high magnetic fields, the magnetophonon resonance extrema in the magnetoconductivity exhibit splitting, which is shown to be interpreted in terms of the inelastic inter-Landau level scattering. Magnetophonon resonance of two-dimensional electron gas in heterojunctions is discussed and the sheet electron density dependence of the magnetophonon resonance amplitudes is explained in terms of the Landau level broadening due to remote impurity scattering.

Eddy currents in magnetic measurements

In the field modulation technique for magnetic measurements, the voltage signalV(H) from a pickup coil surrounding a metal cylinder of permeability μ=1+K(H) and conductivity σ=σ0[1+S(H)] in the presence of an alternating fieldh0 cos ωt superimposed on a steady fieldH (both parallel to the axis of the cylinder) provides a measure ofK(H). This technique is particularly useful for study of the de Haas-van Alphen effect, in whichK(H) oscillates withH, and the paper is mainly concerned with the effect of eddy currents on the relation betweenV(H) andK(H) and the practical implications for the use of the technique. It is also shown that if ω is high enough,S(H) (e.g., the oscillations of the Shubnikov-de Haas effect) and also information on the orientation dependence of σ can be extracted from suitable measurements onV(H) and its orientation dependence. The calculations fall into two main parts, corresponding to weak and strong modulation, i.e., according ash0 is small or appreciable compared with the period of the field dependence ofK andS. For weak modulation, results are obtained for arbitrary values ofK andS over the whole range of ω. It is shown that ifK(H) is not small,V(H) no longer faithfully reproduces the form ofK(H) once ω is high enough to make the skin depth of the eddy currents comparable to the radius of the cylinder. In general,V(H) contains not only the fundamental frequency ω, but also its harmonics, i.e.,V(H)=∑n=1∞Vn(H)eniωt, but it is only for strong modulation that the higher harmonics become appreciable. The variation of theVn with modulation current and ω is calculated under the special assumptions thatK andS ≪ 1 and thatK andS are simple harmonic functions ofH; for these special assumptions the weak modulation results forV1 obtained earlier fall out as a limiting case of the results for arbitrary modulation. Some of the theoretical predictions were tested experimentally on sodium and potassium crystals. Good agreement was found at frequencies up to such that the skin depth became comparable to or smaller than the sample radius, when appreciable discrepancies appeared. Some of these could be attributed to helicon resonances, the possibility of which was ignored in the theory, and some to sample inhomogeneity, the effect of which are briefly discussed in an appendix.

Magnetic-field-dependent electron scattering rates in bismuth alloys near the quantum limit

We have developed techniques which enable us to extract Dingle temperatures (quasi-particle scattering rates) from the shape of single quantum oscillations of the magnetization (de Haas-van Alphen effect) near the quantum limit. The wave shape of the magnetization oscillations is calculated near the quantum limit, as a function of quasi-particle scattering rate, including the effects of both band-structure and Fermi-level fluctuations. By comparison with the wave shape which is measured using a low-amplitude field-modulation technique near the quantum limit, the scattering rate may be extracted. Scattering rates are also obtained, for comparison purposes, in the high-quantum-phase (low-field) limit, using the Lifshitz-Kosevitch formula. Using these techniques we have determined electron ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ parallel to the binary direction) and hole ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ parallel to the trigonal direction) scattering rates, in both the low- and high-phase limits, for pure Bi and for Bi(Sb) and Bi(Si) dilute alloys. For Bi and Bi(Sb) the electron and hole scattering rates are independent of field strength as the quantum limit is approached. In contrast, Bi(Si) exhibits a monotonically rising scattering rate as a function of field as the quantum limit is approached, for both electrons and holes. A self-consistent average $T$-matrix formulation is used to calculate the scattering rate as a function of magnetic field in the diluteimpurity limit. Provided that the range of the impurity potential is taken into account, and that the calculation is done self-consistently, the results of model calculations of the scattering rate for both Bi(Sb) and Bi(Si) are in good qualitative and semi-quantitative agreement with experiment.

The absolute amplitude of the de Haas van Alphen effect in nickel

Measurements are reported for the absolute amplitude of the de Haas-van Alphen effect due to the neck in the FS of nickel along [111] using the field modulation technique. The results show that the amplitude can be adequately calculated using the Lifshitz-Kosevich theory, independent of the conduction electron g-factor.

Magnetic field modulation technique for the study of hot carrier oscillatory magnetoresistance phenomena

A new experimental technique is reported which allows the detection of the oscillatory components of the magnetoresistance of semiconductors subject to high electric fields, where the pulse length must be in the submicrosecond region in order to avoid lattice heating. It uses a combination of sampling and magnetic field modulation techniques. Its capability of resolving hot-electron magnetophonon structure in n–InSb at 77 and 4.2 K for up to N=10 Landau level spacings is demonstrated.

De Haas-van Alphen Effect and Fermi Surface of LaB6

The de Haas-van Alphen (dHvA) effect in LaB 6 single crystal has been studied in detail using the field modulation technique. Observed dHvA frequencies in the (010) and (1\bar10) planes range from the order of 10 6 to 10 8 gauss. The angular dependence of the dHvA frequencies and the disappearance of the oscillation in some angular regions indicate that the Fermi surface of LaB 6 consists of a multiply connected surface, large pieces of which are centered at the point X (or M) in the simple cubic Brillouin zone. The electron density calculated from the Fermi surface is 1.39×10 22 cm -3 which corresponds to just one electron per unit cell.

Cyclotron masses in ReO3 measured by the de Haas–van Alphen effect

Cyclotron masses in ReO3 have been determined from the temperature dependence of the de Haas–van Alphen (dHvA) amplitude. Three frequency branches for magnetic field directions in the (110) plane were investigated. The dHvA effect was detected by the low-frequency field-modulation technique using magnetic fields between 35 and 55 kOe at temperatures below 2.172 K. Measured cyclotron mass values are in reasonable agreement with the theoretical predictions of Mattheiss calculated by the augmented plane wave (APW) method. A small frequency branch in the region of the [110] direction with a frequency of 72.0 MG and a cyclotron mass of 1.07 m0 at [110] was detected in addition to the six frequency branches in the (110) plane which were reported previously. The new branch is attributed to an electron orbit resulting from magnetic breakdown between the β and γ APW Fermi surface sheets.

De Haas-van Alphen Effect in Manganese Phosphide

This paper is the first report on the experimental study of the de Haas-van Alphen (dHvA) effect in a magnetic compound. The dHvA oscillations in manganese phosphide are observed by low-frequency field-modulation techniques in the magnetic fields (H) applied along the c and b axes up to 94 kOe and at temperatures down to 1.1 K. The extremal area is determined as 3.23×10 -2 a.u. in the paramagnetic phase in the region of H =50∼94 kOe along the c axis. In the field along the b axis, the well-defined dHvA oscillations are observed in the paramagnetic phase in the region of H =40∼70 kOe and the extremal area is determined as 9.05×10 -3 a.u., and various abnormal oscillations are observed in the fan phase in the region of H =9∼37 kOe and it is concluded that the extremal area in the fan phase varies with the external magnetic field.

Magnetooptik und elektronische Struktur der magnetisch ordnenden Europiumchalkogenide

The absorption coefficient and the interband Faraday rotation of EuS, EuSe and EuTe thin films have been measured as function of the photon energy (1–6 eV), the temperature (2.7–300 K) and the applied magnetic field (0–11.5 kOe). In addition a magnetic field modulation technique has been developed, with a resolution of 2 ⋅ 10−4 deg. This allows the measurement of the Faraday rotation in fields of only 100 Oe, which is important for metamagnetic samples with low critical fields. A Kramers-Kronig transformation of the Faraday rotation leads to the circular dichroism and from these two quantities and the optical constants the off-diagonal elements of the conductivity tensor have been computed. From a comparison of this experimental result with values obtained from a modified atomic model, we deduce the character of the involved transitions and the spin polarization of the occupied ground states (4f 7,p(anion)). In addition the ratio of exchange splitting to band width of the empty 5d final state can be evaluated. The fine structure of the first main peak is discussed in terms of Kasuya's coupling scheme between the 4f 6 multiplett and the excited 5d electron. In the antiferromagnetic EuTe the temperature dependence of the Faraday rotation does not follow the net magnetization of the sample for all photon energies, but some transitions show a “ferromagnetic” behavior. This is interpreted in Slater's model of the magnetic Brillouin zone.

Erratum: Field modulation technique with synchronous detection for measuring magnetic properties in time-dependent fields

A method to measure magnetic quantities of ferrimagnetic and ferromagnetic samples under the effect of time‐dependent fields [Ha(t)] is presented. The method is based on the alternating field method together with the powerful technique of synchronous detection. Interesting quantities such as the total Bloch wall area present during the magnetization reversal, the reversible permeability, and its first derivative with respect to the magnetic field at any point of the hysteresis loop are plotted rapidly, even in the case of very small samples (for instance, iron whiskers). Reversible permeability is obtained without need of extapolation. The switching time and the dynamic coercive field are easily measured as well. The sensitivity of the method is very high, and the noise is widely rejected. The technique is applied to iron whiskers and polycrystalline YIG.

Conduction electron g-factor measurements in Au using the de Haas-van Alphen effect

The conduction electron g-factor in Au was measured with three different techniques using the de Haas-van Alphen effect. On the neck orbits, the three techniques are in very good agreement and show a variation in the g-factor of ~60%, with a minimum of 1.15 at 〈111〉. On the belly at an isolated spin splitting zero at 71.6 ° from 〈100〉 the g-factor was found to be 2.35. A calibration procedure for the field modulation technique which allows accurate measurement of absolute amplitudes is presented. Absolute amplitudes measured with this procedure compare favorably with those made by torque magnetometer. A detailed discussion of magnetic interaction is given, including the effects of the vector nature of the magnetization and local demagnetizing fields caused by finite sample size.

De Haas–van Alphen Effect in Antimony–Tellurium Alloys

The de Haas–van Alphen frequencies, cyclotron masses, and Dingle temperatures of antimony–tellurium alloys with up to 0.11 at. % Te were measured using the low frequency field modulation technique. The hole and electron frequencies decreased and increased respectively, as predicted by the rigid band model. At the highest concentration, the increase is about 25% that of pure Sb and the decrease is about 20%. The cyclotron masses of electrons and holes changed with concentration. This dependence resulted from the nonparabolicity of the Sb bands. Estimates of the Fermi surface volume of the alloys indicated that each Te atom contributes one electron to the alloy. The present results are compared with previous de Haas–van Alphen results on antimony–tin alloys.

Nonlinear reversible processes in YIG: An explanation for the Rayleigh loop anomalies

A magnetic field modulation technique with synchronous detection is applied to measure the reversible permeability μr and the derivative of the magnetization M with respect to the field H in YIG samples. The measurements develop a nonlinear and reversible dependence of M upon H (nearly M = aH + bH3) before the appearance of any Rayleigh behavior. If H is increased, the Rayleigh dependence in H2 is superimposed to the former, giving rise to anomalous Rayleigh loops. A model based on the elasticity of the Bloch wall is proposed and resolved. The theoretical solution fits the experimental curves.

Field modulation technique with synchronous detection for measuring magnetic properties in time-dependent fields

A method to measure magnetic quantities of ferrimagnetic and ferromagnetic samples under the effect of time-dependent fields [Ha(t)] is presented. The method is based on the alternating field method together with the powerful technique of synchronous detection. Interesting quantities such as the total Bloch wall area present during the magnetization reversal, the reversible permeability, and its first derivative with respect to the magnetic field at any point of the hysteresis loop are plotted rapidly, even in the case of very small samples (for instance, iron whiskers). Reversible permeability is obtained without need of extapolation. The switching time and the dynamic coercive field are easily measured as well. The sensitivity of the method is very high, and the noise is widely rejected. The technique is applied to iron whiskers and polycrystalline YIG.

The de Haas-van Alphen effect in InBi

By using the field modulation technique, the frequency spectrum of the de Haas-van Alphen effect in the semimetallic compound InBi has been investigated for fixed directions of the magnetic field, lying in three symmetry planes of the tetragonal unit cell. The experiments were confined to frequencies above 10 6 G. Specimens were spark cut from two, differently grown, single crystals. In both series of specimens, two continuous frequency branches were found, which almost agreed with one another and with previous work by Shapira et al. and others. They correspond to two slightly distorted ellipsoids of revolution, elongated along the c-direction, with a volume ratio of about two. Strong evidence is found, that low frequency branches, found in only one series of specimens and also found in previous work, are due to inclusions of In 5Bi 3 and/or In 2Bi crystals, having a strong crystal orientation relation to the InBi matrix.

Amplitude Modulation of de Haas-van Alphen Waveforms

We report detailed experimental measurements and calculations of the amplitude modulation (AM) of a high-frequency de Haas-van Alphen (dHvA) quantum-oscillation waveform, due to magnetic interaction with a low-frequency dHvA oscillation. Experiments were carried out using a pure Au single crystal with $H$ parallel to the 111g direction, at 36.1 kG and 2.0 K. Two new mechanisms by which AM can arise are described in detail: (i) AM can arise in conjunction with the frequency modulation (FM) due to magnetic interaction, through modulation of the Bessel-function arguments which appear in using the field-modulation technique. This FM-AM effect is an unavoidable consequence of using the field-modulation technique in the presence of magnetic interaction. The resulting AM waveforms can be totally different in appearance at different detection harmonics. (ii) AM can also arise via magnetic interaction and phase smearing in an inhomogeneous magnetic field. The observed AM, as a function of a linear magnetic field gradient, is in good qualitative agreement with the prediction of Hornfeldt, Ketterson, and Windmiller. Possible applications of AM effects are briefly discussed.

Techniques for the measurement of electron scattering using the de Haas-van Alphen effect: application to dislocations in copper

Measurement of the local electronic lifetimes via the de Haas-van Alphen (dHvA) effect depends on the development of reliable techniques for amplitude measurements in well-characterized crystals. Some methods for avoiding both systematic and random errors were developed in a study of the effect of lattice dislocations on the dHvA scattering temperature in copper, using the field-modulation technique. The techniques described here include characterization of crystal purity and microstructure; precise orientation of the crystal in situ; precise field homogenization; control of modulation amplitude; and avoiding errors due to incomplete penetration of the modulation field, magnetic interaction, and magneto-resistance oscillations. In addition, representative amplitude measurements are presented for copper crystals containing a well-defined array of lattice dislocations. The results demonstrate that consistently high values of the scattering temperature typically observed in earlier measurements have an explanation as a dislocation effect. This effect is several orders of magnitude stronger in dHvA measurements than in electrical resistivity, and will therefore be important in any application of the dHvA effect to study scattering problems.