FI124670B - Device for detecting a magnetic field - Google Patents

Description

DEVICE FOR DETECTING MAGNETIC FIELD

The present invention relates to a device for detecting magnetic field.

5

In Figure la has been disclosed an example of a waveguide 100 with one narrow 101. Under ballistic regime in a cylindrical quantum waveguide 100, the kinetic energy E of an electron is the sumE = Et +El , where Et stands for the quan-10 tized energy of transverse electron motion and Et denotes the energy of longitudinal motion. The spectrum of Et consists of numbers Et(n) (thresholds) with « = 1,2,..., where Et(n) form an increasing sequence, £'i(l)>0, 2m a 15 m* being the transverse effective electron mass and d the diameter of waveguide 100 cross-section. Generally, electrons with the same full energy E can be in states with distinct transverse energies (distinct n ) .

20 When a waveguide cross-section varies along the axis, one can consider E = Et+Et as approximate relation. If the diame- ter d of the waveguide 100 decreases, then the quantized ^ energy of transverse electron motion Et increases. The full o energy E remains constant, so the energy of longitudinal σ> 25 motion El decreases, which is equivalent to arising a poten-x £ tial barrier for the longitudinal electron motion. Example of this potential barrier has been disclosed in Figure lb in m $5 which x-axis means the longitudinal direction of the wave- guide.

30 2

In turn increasing then diameter d of the waveguide forms a potential well. Therefore, varying a waveguide cross-section, it is possible to get a needed potential structure. Such a structure could be obtained, for example, by successive 5 sputtering various materials. However, in such a case the effect of non-elastic scattering by the interfaces of the materials would essentially shorten the electron free path.

If Et{n)>E , then the electron is reflected with probability 10 close to 1 (up to a small probability of under barrier transition) .

Figure 2a discloses a quantum waveguide 200 with two narrows 2 01, 2 02. If there are two narrows 2 01, 2 02 in a quantum 15 waveguide 200, then the domain 203 between narrows plays the role of a resonator 204. If the heights of the barriers are greater than the electron energy, there can occur resonant tunneling electrons through the resonator 204. Figure 2b discloses examples of the barrier potentials and resonant 20 energy levels (RL) in the case of two narrows in the wave guide .

The resonant tunneling phenomenon consists of the fact that, for an electron with energy E, the probability T(E) to pass 't q 25 from one part of the waveguide to the other through the res ell cc> onator has a sharp peak at E = Eres (possibly, T(Eres) = 1 ), g] where Eres denotes a "resonant" energy. The resonant energies ir practically coincide with the energy quasi-levels in the po- Q_ te, tential well created by the narrows. The width of the reso-

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to 30 nant peak depends on, for example, the diameter and form of co o the narrow.

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Figure 3a shows the computed dependence of the transition coefficient T on the dimensionless quantity k~Exn . The resonator geometry and the dimensions are depicted by Figure 3b. The length of the waveguide 11 may be, for example, 5 10-30 nm and the width of the narrow can be, for example 5 nm. Even for such a wide narrow (0.55 of the waveguide diameter) , there have been seen two clear resonant peaks at km 7.5 and at ^«8.7 . For k> 9.6 the energy of electrons approaching the resonator exceeds the potential barrier, so 10 T(k)m 1. The slight oscillations of T for k> 9.6 are related to over-barrier electron reflection. The width of the peaks sharply diminishes as the diameter d of the narrows decreases. The parameters of the system have been chosen so that the energy E of the electrons approaching the resona-15 tor satisfies £,(1) <E <Et(2) . IfE>Et(2) , there arises multichannel scattering. When entering the resonator, such an electron wave probably changes its transverse quantum number and respectively its longitudinal energy because of scattering by the potential barrier. It may happen that the reso-20 nant tunneling conditions are fulfilled for the new state. It is not improbable that the wave recovers its original state leaving the resonator. In consequence of this the dependence T(E) becomes rather complicated. Therefore the 't electrons with energy E such that Et(1) < E < Et(2) are optimal δ ^ 25 to be used.

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00 To control electron flows it is possible to use electric

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£ fields in the resonator generated by external electrodes.

The effect of such an electric field reduces to shifting the m ^ 30 resonant energy levels by the amount approximately equal to ^ the average potential energy of an electron in the resonator.

4

Some amplifiers based on the resonant tunneling phenomenon in quantum waveguides with narrows were suggested in Finnish patent no. 121489. In these devices, an electron flow is controlled by means of electric fields generated by external 5 electrodes.

The invention is intended to create a device for detecting magnetic field, which is simple to implement. The characteristic features of the device according to the invention are 10 stated in Claim 1.

The invention may be implemented in several different ways. According to first embodiment applying one resonator the device is very simple at its implementation. According to sec-15 ond embodiment applying two resonators the device is improved relating to temperature properties (less thermo sensitivity) . The applications of the devices are, for example, reading heads in the information storing devices and also in magnetic sensors. Other additional advantages achieved by 20 means of the invention appear in the description portion and its specific features from the accompanying Claims.

The invention, which is not restricted to the embodiments presented in the following, is described in greater details ''t 25 with reference to the accompanying drawings, in which δ c\j oo O Figure la shows an example of the waveguide with

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c\J one narrow, £ Figure lb shows an example of the barrier poten- co 30 tial of the waveguide disclosed in Fig- m ure la, oo o Figure 2a shows an example of the waveguide with two narrows, 5

Figure 2b shows examples of the barrier potentials of the waveguide disclosed in Figure 2a and resonant levels,

Figure 3a shows the computed dependence of the 5 transition coefficient T on the dimen- L· 77^2 sionless quantity K ~ ,

Figure 3b shows the resonator geometry in the case

Figure 3a,

Figure 4 shows one rough schematic diagram of the 10 device having one resonator,

Figure 5a - 5d show calculations relating to the device presented in Figure 4,

Figures 6a, 6b show energy level diagram of the first embodiment of the device of Figure 4 in 15 order to detect magnetic field,

Figures 7a, 7b show energy level diagram of the second embodiment of the device of Figure 4 in order to detect magnetic field,

Figure 8 shows one rough schematic diagram of the 20 device having two resonators,

Figures 9a, 9b show energy level diagram of the first embodiment of the device of Figure 8 in order to detect magnetic field, and Figures 10a, 10b show energy level diagram of the second 't q 25 embodiment of the device of Figure 8 in

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^ order to detect magnetic field.

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x Figure 4 shows one rough schematic diagram of the device 10

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according to first embodiment. In the invention by means of co 30 a magnetic field B localized in the resonator 21 is effected £2 to the electron flow going through the elongated quantum o

00 waveguide 11. If there is a magnetic field B of strength H

in the resonator 21, then the resonant energy Eres of the resonator 21 increases by μΗ for the electrons with spin 6 coinciding with magnetic field vector B and decreases by μΗ for those with spin of the opposite direction, μ being the electron spin magnetic momentum. As a result, any resonant energy level Eres of the resonator 21 splits into the two 5 levels. If a magnetic field B occupies a part of the resonator 21, then the resonant energy level shift is less than μΗ .

According to one example the resonant tunneling parameters 10 for the resonator 21 in magnetic field B may be next. Assume that the vector of a homogeneous magnetic field is orthogonal to the resonator axis, the diameter of the region 16 of the resonator 21 occupied by the magnetic field is about 0.4 of the diameter of the resonator 21 whereas the 15 center of the region coincides with that of the resonator 21. Figure 5a shows the calculated dependence of the resonant energy k2es on H for the electrons whose spin is directed as the magnetic field vector B. For 0<#<10 the dependence is practically linear, k2es=A + KH . In the same 20 range of H for the electrons with opposite spin orientation there holds k2es=A-KH . The transition coefficient T calculated for k2=k2es(H) is depicted by Figure 5b. For ^ 0 < H <10 the value T is practically independent of H and ° T. The steep decrease in T for if>15 stems from the § 25 Aharonov-Bohm phenomenon (the effect of magnetic field on ^ the wave function phase is different for the electrons ^ bypassing the magnetic field domain on different sides) .

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^ Figure 5c represents the transition coefficients as function C\l [£ in energy (the resonance curve), and Figure 5d depicts the co q 30 width of the resonance curve at half-height as function in

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magnetic field strength. Calculations show that the width of the resonance sharply decreases with decreasing the diameter of narrows.

7

The electron flows have been controlled by means of sufficiently small magnetic fields (in the dimensionless units 0< H < 10 ) . In such a case, the Aharonov-Bohm 5 phenomenon can be neglected.

The device 10 to detect magnetic fields B can be implemented by means of at least two types of devices. In Figure 4 has been disclosed the first embodiment of the device in which 10 the device 10 is implemented with one resonator 21. In Figure 8 has been disclosed the second embodiment of the device 10 which is implemented with two resonators 21, 19.

Here the device 10 means a subsystem formed of the quantum waveguide 11 that can be part of an electric circuit or some 15 higher level system.

Figure 4 shows an example of a one-resonator device 10 for detecting magnetic field i.e. magnetic fluxes. The device 10 includes a quantum waveguide 11 with a source and a drain 20 contacts 12, 13 at its ends 12', 13'. The contacts 12, 13 may be injecting metallic contacts. A voltage source 20 is connected to the source and drain contacts 12, 13. The voltage U provided by the voltage source may be, for example, 0,1 V. By means of that a voltage U is delivered ^ 25 for initiating an electron motion from the source contact 12 δ ^ to the drain contact 13. In other words, between the source

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S5 12 and the drain 13 an accelerating voltage U is delivered.

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£ The quantum waveguide 11 may be made of a high-resistance 30 semiconductor. The size and material of the waveguide 11 in have been chosen to provide the ballistic i.e. collision-^ free electron transport from the source 12 to the drain 13 in the conductivity zone. The device 10 is suitable for detecting magnetic fields B localized in nano-domains.

8

In addition, the waveguide 11 has now also two narrows 14, 15. The domain between these narrows 14, 15 serves as a quantum resonator 21. The depth of the narrows 14, 15 is 5 such that the domain between the narrows 14, 15 serves as a quantum resonator 21 for the electrons injected from the source contact 12 and moving to the drain contact 13 under ballistic i.e. collision-free regime.

10 Such narrows 14, 15 can be produced by electron litography or X-ray litography, for example. The cross-section of the waveguide 11 has been chosen so that Eres - EF » kBT, EF being the Fermi level at the contacts 12, 13. Thus, there are no electrons with energy E > Eres to enter the waveguide 15 11. Here kB is Bolzmann constant and T is a temperature.

In addition, the device 10 also includes analysing means 17 for detecting a magnetic field B to be measured and located in the region 16. The analysing means may include, for 20 example, a current meter 17 connected to the series with the voltage source 20. The analysing means 17 are arranged to identify the magnetic field B from the current through the resonator 21. The current may be present or absent when the magnetic field B effects to the resonator 21.

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^ Theoretically, the current density J through the system is ° determined by

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x J ~\g{E)v{E)T{E)fs{E)[\-fD{E-eU)]dE

cd the integration over the electrons moving from the source in lo 30 12, g(E) being the state density in the nondeformed ^ waveguide, v(E) the electron velocity along the waveguide axis, T(E) the probability for an electron with energy E to pass through the resonator 21. Finally, fs(E) is the Fermi 9 function for the electrons of the source 12, fD{E) being the same for the electrons of the drain 13.

The resonator's 21 geometry, for example, the length may be 5 arranged so that the resonance energy level Eres of the resonator 21 satisfies Eres > EFs + kBT, EFs being the Fermi level at the source 12. In other words, the resonance energy level Eies of the resonator 21 is &E higher than the Fermi level EFs in the source 12 with ΔΕ > kBT. The situation 10 corresponding to this has been disclosed in Figure 6a. Then practically there is no current in the device 10 because in the absence of magnetic field B, the electrons that could pass through the resonator 21 are absent from the incoming flow approaching the barrier from the source 12 (fs(E)& 0 for 15 E>EFs+kBT).

The resonance energy level Eres splits into two levels Eres+ and Eres- when a magnetic field B is supplied to the region 16 of the resonator 21. Figure 6b discloses the situation 20 corresponding to this. For the electrons of the source 12 whose spin direction coincides with the direction of the magnetic field vector B, the resonance energy level Eres increases to be Eres+. For the electrons of the source 12 't q whose spin in direction is opposite to the magnetic field c\j oq 25 vector B the resonant energy level Eres decreases to be Eres-· o

For a certain strength of such a field, the resonant energy c\j x level Ejres- of the resonator 21 for the electrons with spin cr directed oppositely to the magnetic field vector B reaches

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5) the Fermi level EFs in the source 12 and comes in the energy

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$2 30 domain EFd + kBT < Eres~ < EFs + kBT and there arises a current o 00 through the resonator 21.

10

The device 10 presented in Figure 4 may be implemented also in a second way. If the resonator's 21 geometry, for example, the length is chosen so that in the absence of magnetic field B in the region 16 of the resonator 21 a 5 resonant level Eres for the electrons is arranged in region Em - Eres> kBT , EFd being the Fermi level at the drain 13, there again will be no current. Figure 7a discloses the situation corresponding to this. In other words, the resonant energy level Eres of the resonator 21 is below than 10 the Fermi level EFd in the drain 13 i.e. Eres < EFd with AE>kBT ' This is because all the final electron states of the drain 13 have been occupied by the electrons.

When a magnetic field B is supplied to the region 16 of the 15 resonator 21, the resonant energy level Eres of the resonator 21 splits into two levels, Eres+ and Eres-. Figure 7b discloses the situation corresponding to this. In one of these levels Eres+ the resonant energy level Eres is increased by μΗ for the electrons with spin of the same direction as 20 the magnetic field vector B. For the electrons whose spin in direction is opposite to the magnetic field vector B the resonant energy level Eres decreases to be Eres-· For the electrons with spin of the same direction as the magnetic field vector B, the resonant energy level Eres+ reaches the g] 25 Fermi level EFd in the drain 13 from below for a certain g magnetic field B value to be Eres+· In other words, when EFs > g} Eres+ > EFd, there arises a current through resonator 21 due to the presence of free electron levels at the drain 13.

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g 30 However, the detecting devices 10 based on the above co £ principles of one resonator 21 may possess several c\j disadvantages. First, such a device 10 is of high thermosensitivity that is the magnetic field B strength needed for the through current depends on temperature: the 11 threshold strength of magnetic field is less for small temperatures. Second, even for small temperatures the threshold strength is sufficiently large; for T ~ 10 K, the needed resonance energy level splitting is about~ kBT which 5 is ~ 1CT3 eV for this temperature. The devices are of comparatively low sensitivity to magnetic field. The reason is that the current arises only if the resonant energy level

> k T

splits into two levels spaced at distance - B for the ~ EF -EF /2 first embodiment or at distance 1 2 for the second 10 embodiment presented above. For the device depicted by

Figures 7a and 7b, the needed splitting is >EFi~EF^ =eU .

In Figure 8 has been disclosed a second embodiment of the device 10 according to the invention. This device 10 with 15 two resonators 21, 19 have no disadvantages described above.

Such a device 10 is similar to those of the first type, however the waveguide 11 has now three narrows 14, 15, 27 forming two quantum resonators 21, 19 in series for the electrons injected from the source 12 and moving to the

20 drain 13 under ballistic i.e. collision-free regime. A

magnetic field B is localized in the region 28 of one of the resonator 19. The second resonator 21 chooses the electrons whose energy belongs to a given small interval (a monochrom- o ator).

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According to the first embodiment the geometry, for example, x the lengths of resonators 21, 19 are chosen so that the res-

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onance energy levels Eresi, EreS2 of the resonators 21, 19 co co in incide being below the Fermi level EFs at the source contact co ^ 30 12 and above the Fermi level EFd at the drain contact 13.

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Then there is a through electric current in the device 10 in the absence of magnetic field B. Figure 9a discloses this situation.

12

The geometry, for example, the lengths of the resonators 21, 19 are chosen so that, when a magnetic field B is supplied to the region 28 of one of the resonator 19, the resonant 5 energy level EreS2 of the resonator 19 splits for the electrons with opposite spins. Figure 9b presents the situation corresponing to this. Owing to this the splitted resonance levels EreS2+, EreS2- in the resonator 19 do not coincide with a resonance level Eresi in the other resonator 10 21 and current vanishes. In other words, with a magnetic field B on such that the resonance splitting i.e. the distance between the new resonance energy levels EreS2+, EreS2-of the resonator 19 with the field B is greater than the width of the resonance energy level Eresi, the current 15 vanishes. The width of the resonance energy level Eresi, EreS2 is determined by the depth of the narrows 14, 15, 27.

The width of resonance energy level peaks can be made quite small by diminishing the diameter of the narrows 14, 15, 27, 20 so the magnetic field sensitivity of the device 10 would be large. However, a strong decrease in the level width (which is equivalent to an increase of the quantum resonator quality factor) leads to some sacrifice of the device's acting speed. The duration of stay for an electron in a ''i 25 quantum resonator 19 is proportional to the product of the δ w flight time through the resonator 19 for a free electron and co o the resonator quality factor. Therefore an increase of the σ> quality factor reduces the device's acting speed, x

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co 30 According to one more embodiment is presented a device with

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co two resonators 21, 19, where a magnetic field B manifests o itself not by the disappearance but the rise of a current.

To this end the geometry, for example, the lengths of the resonators 21, 19 are chosen so that, in the absence of a 13 magnetic field B, the resonance energy levels Eresi, EreS2 are different relative to each other, and the distance between them exceeds their width; moreover, both levels Eresi/ EreS2 are between the Fermi levels EFs, EFd at the source and the 5 drain contacts 12, 13. Then, in the absence of a magnetic field B there is no current in the device 10. Figure 10a shows this situation.

With a magnetic field B on, the resonance energy level EreS2 10 of the resonator 19 splits to EreS2+, EreS2- and, for a certain magnetic field strength B, one of these new levels Eres2+ coincides with the resonant energy level Eresi of the other resonator 21, which results in the rise of a current in the device 10 registered by analyzing means 17. Figure 10b shows 15 this situation. The levels Eresi, EreS2- again become different as the field strength B increases and the current vanishes. Choosing the geometry of resonators 21, 19 to determine the dif f erence£resl ~Eres2 , it is possible to tune the device 10 for switching on/off with a certain magnetic field B.

20

In the above the resonance energy level of the resonator has been determined by the length of the resonator. However, other examples of this parameter are the sizes and the form of the cross-section of the waveguide and the form of the ? 25 ends of the resonator (opening and closing angle).

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1 Some examples of the material of the waveguide 11 in which

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^ the electrons are under ballistic regime may be mentioned x Q- GaAs or AlGaAs. The length L of resonator 19, 21 is connected 30 ed with the length of de Broglie wave λ. It fullfills L = m (ij ηλ for resonance tunneling (n = 1, 2, 3...) . The length λ is ^ connected with the electron energy and in GaAs case that is about 1-5 nm. It means that the resonator 19, 21 can be about 10 nm (maybe less) . Full length of the waveguide 11 14 can be about 20 - 30 nm: 5 - 10 nm waveguide at the left of resonator + 10 nm resonator + 5 - 10 nm at the right of resonator. Free path for electron is much more than this length, for example, over 1000 nm (especially at low temperatures).

5

It must be understood that the above description and the related figures are only intended to illustrate the present invention. The invention is thus in no way restricted to only the embodiments disclosed or stated in the Claims, but 10 many different variations and adaptations of the invention, which are possible within the scope on the inventive idea defined in the accompanying Claims, will be obvious to one skilled in the art.

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Claims (9)

Apparatus for detecting a magnetic field comprising: - a quantum waveguide (11) having source and sink contacts (12, 13), - a voltage source (20) connected to a source and sink contacts (12, 13) to initiate an electronic movement from a source. (12) for the throat (13) under ballistic conditions, - at least one quantum resonator (21) for electrons 10 formed by two narrow (14, 15) waveguides (11) and an area between the narrow (14, 15), - analyzing means (17) B) for detection in the region (16) of the resonator (21). Device according to Claim 1, characterized in that the analyzing means (17) are arranged to detect the magnetic field (B) on the basis of the current passing through the resonator (21). Device according to Claim 1 or 2, characterized in that the geometry of the resonator (21) is adapted to be selected such that - when the magnetic field (B) is off the region (16) of the resonator (21), the electron resonance level (Eres) is 251, when the magnetic field (B) is on, the resonator energy level (Eres_) of the resonator (21) i 00 cp for electrons whose spin Sj is opposite to the magnetic field vector jr (B) is to EFct + cd 30 kBT <Eres- <EFs + kBT generating current through the resonator CM to (21). co δ CM 19 Device according to Claim 1 or 2, characterized in that the geometry of the resonator (21) is adapted to be selected such that - when the magnetic field (B) is off the region (16) of the resonator (21), the electron resonance level (Eres) is <EFct - kBT, - with the magnetic field (B) turned on, the resonator energy level (Eres +) of the resonator (21) for electrons having a spin parallel to the magnetic field vector (B) 10 is adapted to satisfy EFs> Eres +> EFd, through. Device according to Claim 1 or 2, characterized in that the waveguide (11) comprises three narrow gaps (14, 15, 15 27) at a depth such that the two areas between the narrow gaps (14, 15, 27) act as quantum resonators (21, 19). from the source (12) to the sink (13) for electrons moving under ballistic conditions, and the magnetic field to be measured (B) is located in the region 20 (28) of one of the resonators (19). Device according to Claim 5, characterized in that the geometry of the resonators (21, 19) is chosen so that when the magnetic field (B) is off, the resonant energy levels (Eresi / EreS2) of the resonators (21, 19) are equal to Fermi. δ cm between wars (EFs, EFd) at source and throat contacts (12, 13) CO cp generating a current through device (10) which is recorded by O) cm analyzing means (17). x IX CL cc »30 7th Device according to Claim 6, characterized in that the resonant levels (EreS2 + / EreS2-) of the resonator (19) when the magnetic field (B) is on in one of the resonators (19) do not coincide with that of the other resonator (21). resonance level (Eresi) and the current is adapted to dissipate from the device (10). 20 Device according to Claim 5, characterized in that the geometry of the resonators (21, 19) is chosen such that - in the absence of the magnetic field (B), the resonant energy levels (Eresi, Eres2) of the resonators (21, 5 19) are different from each other, (Eresi, Eres2) the distance is adapted to be greater than the width of the resonant energy levels (Eresi r EreS2). 10) No power. Device according to Claim 8, characterized in that, when the magnetic field (B) is on, one of the resonator levels (EreS2 +) of the resonator (19) at a given field strength (B) of the magnetic field (B) coincides with the resonance level (Eresi) and generating a current to be recorded by the analyzing means (17), and when the magnetic field (B) is further adapted to grow, the levels (Eresi ^ EreS2 +) become different and the current is adapted to disappear. 't δ c \ j i oo o O) C \ l X cc CL CD CM LO LO CO O CM