In this paper we study the effect of magnetostriction of Co-rich amorphous microwire to the noise of the orthogonal fluxgates based on such wires. The magnetostriction was modified by changing the relative amount of iron x with the respect of the total amount of cobalt and iron in the alloy. Specifically we changed x in the composition (Co1xFex)75Si15B10 casting wires with the following values of x: 0.05, 0.055, 0.06, 0.062, 0.065, 0.07 and 0.08. We found out that the noise indeed depends on the composition of the wire: while it is minimum (2.5 pT/Hz) for x between 0.06 and 0.062 where the magnetostriction is vanishing (λs ≈ 10−7) it significantly increases to tens of pT/Hz for both positive and negative magnetostriction when λs becomes one order of magnitude bigger. We verified that once the composition returns a magnetostriction low enough (around x = 0.06) then the noise does not depend on mechanical stress anymore. In fact the noise of a sensor with x = 0.06 is the identical in its natural curved state and when bended straight; for vanishing magnetostriction the bending does not affect at all the noise, as on the contrary it happens with larger magnetostriction. This suggests that once the wire has composition with x = 0.06 the remaining noise is not caused by mechanical stress. Finally we show how to overcome the problem of offset arising after annealing if continuous annealing current is used. We explain how this could be due by the fact that magnetostriction changes with temperature and even a wire with vanishing magnetostriction at room temperature can became significantly magnetostrictive at annealing temperature. For this reason we propose a method of annealing consisting rising the temperature of the wire while the wire is kept in its natural curved state. In this way no mechanical stress is applied to the wire during the annealing process, when the temperature is high enough to make it magnetostrictive even if it is non-magnetostrictive at room temperature. We show how this method suppresses the offset and significantly reduces the noise.

Fundamental mode orthogonal fluxgates (FM-OFG) are currently the vectorial sensors of magnetic field operating at room temperature providing the lowest noise. Proposed by Sasada for the first time in 20021 they have been improved till reaching 630 fT/Hz at 1 Hz and fT/Hz noise floor.2 Such low noise attracted increasing attention of the scientific community.3–9 

Most of the noise of FM-OFG which has been reduced so far was attributed by Barkhausen noise which arises when domain wall movement occurs if the magnetization falls out of saturation in case the dc component of the excitation current Idc is not sufficiently larger than the ac component Iac. This has been demonstrated by the fact that the 1/f noise of the sensor is strongly correlated to the energy of the circumferential minor BH loop once the magnetization falls out of saturation.10 It was then verified that increasing the circumferential anisotropy by annealing under circumferential field significantly reduces the noise because for the same value of Idc and Iac the magnetization remains more in saturation.11 

Other methods have been used to reduce the noise of FM-OFG, such as optimizing the geometry (length and diameter) to reduce the effect of the demagnetizing factor12 or use of multiple wires. The development of FM-OFG has now reached a stage where the noise is so low that any further reduction can be achieved only using different techniques. Unfortunately, once removed the Barkhausen noise little is still known about what causes the remaining noise.

In this paper we try to answer this question by analysing a possible source of the remaining noise in FM-OFG, the magnetostriction. Amorphous magnetic wires used as core for FM-OFG are produced by water quenching method13 on a spinning wheel; this method produces wires with a natural curvature corresponding to the radius of the wheel. Then the wire is bended in straight direction to be used as core for FM-OFG. By doing so a mechanical stress is introduced in the wire since the external side of the curved wire is compressed and the inner side is extended. Additionally, other mechanical stresses to the magnetic microwire can arise, for instance due to thermal expansion of the wire itself or of the substrate on which the wire is attached. It is well know that magnetostriction could affect the noise of fluxgate sensors since the magnetization of ferromagnetic material with non-vanishing magnetostriction changes when mechanical stress is applied to the material. This leads to different value of the magnetization due to mechanical stress for the same value of magnetic field applied to the core of the sensor; this means that the output voltage of the sensor will change for the same magnetic field measured by the sensor, which - by definition - is noise. However, currently we still do not know to which extend this mechanism affects this particular type of fluxgate and if there is any method to limit it.

We investigated this potential source of noise casting wires with different composition, thus changing the magnetostriction, and then using these wires as core for FM-OFG whose noise was characterized.

The typical composition of amorphous microwires used for FM-OFG is (Co0.94Fe0.06)72.5Si12.5B15. For a similar composition, namely (Co1xFex)75Si15B10, the minimum magnetostriction is achieved for x = 0.06 as shown in Ref. 14. In this case the composition is only slightly different, mainly regarding the metalloid components (Si and B). However, it has been shown that the nearly zero magnetostriction is achieved around the same proportion of Co and Fe (0.94 to 0.06 respectively), the amount of Fe necessary to achieve vanishing magnetostriction only slightly decreases if the metalloid components increase.15 If we change the proportions between Fe and Co, the magnetostriction changes sign: if the amount of Fe is below 0.06 of total (Fe+Co) amount the magnetostriction is negative, whereas if the amount of Fe is above 0.06 the magnetostriction is positive.

As an order of magnitude, defined as x the relative amount of Fe, if x = 0.06 the magnetostriction coefficient λs ≈ 10−7 for x = 0.04 at room temperature the magnetostriction coefficient becomes λs ≈ − 10−6 and for x = 0.08 we achieve λs ≈ + 1.3 ⋅ 10−6. This values are typical values of magnetostriction for these alloys referred at room temperature as measured and described in a previous paper.14 In this manuscript we did not repeat the same measurement of magnetostriction. In order to achieve microwires with both positive and negative magnetostriction we casted wire with (Co1xFex)72.5Si12.5B15 composition, for the following values of x: 0.05, 0.055, 0.06, 0.062, 0.065, 0.07 and 0.08. All wires had diameter between 120 and 130 μm.

For each composition we manufactured three FM-OFGs using two 8 cm long sections of the casted wires at 3mm distance. The wires have been soldered on a FR-4 printed circuit board. A picture of the sensor can be seen in Ref. 16. Each sensor was manufactured using wires from a different batch (different master alloy and casting process). This was done in order to avoid that random variables in the casting process could artificially affect the results. As we will see later the results were very consistent, since the noise achieved for every composition is very similar for every batch of production of any composition. This means the property of the wires are very similar once we set a composition.

Also, we characterized the wires by vibrating sample magnetometer in order to verify that all the wires were amorphous, since the coercivity was in all cases below 30 A/m.

A 1200 turns pick-up coil was then wound around plastic tube with 6 mm diameter surrounding the printed circuit board with the magnetic wires. We measured the sensitivity of the magnetometer by changing the frequency of the excitation current in a Helmholtz coil with 58 cm diameter and we found out that in all cases the resonation was around 40 kHz. Therefore, we chose 40 kHz as excitation frequency to maximize the sensitivity. Then, we varied the value of the ac and dc component of the excitation current verifying the noise changed accordingly to the noise model of the sensor10 to be sure the measured noise was indeed the noise of the sensor and not due to other sources. Finally, the minimum noise was achieved, for every sensor, with Idc = 50mA and Iac = 40mA which then became the excitation parameters. The details of the magnetometer used for production of the excitation current and the demodulation of the first harmonic of the voltage induced in pick-up coil are given elsewhere.16 

The noise was characterized by inserting the sensor in a 3 layer shielding and the output of the magnetometer was digitized by a ADS1299EEG acquisition board. The power spectral density was then calculated and the results are summarized in Fig. 1 and Fig. 2, where the value of the noise at 1 Hz and noise floor are respectively shown for different amount of Fe, and therefore different magnetostriction. In Fig. 1 we can see that the minimum noise at 1 Hz (typical reference value for 1/f noise) is minimum for a relative amount of Fe around 0.06 and 0.062. In this case the noise approaches 2.5 pT/Hz, which is a typical value of noise for a this type of sensors based on two as-cast wires (lower noise is achieved only with annealed wires). The same level of noise is achieved using commercial AC20 wires from Unitika. The noise, however, significantly increases as we increase or decrease the amount of Fe from the ideal value of x between 0.06 and 0.062. For x = 0.055 and x = 0.065, that is for both positive and negative magnetostriction, the noise at 1 Hz rises to about to 5.5 to 6 pT/Hz, which is more than twice the minimum noise for optimal x. For even larger or lower value of x (5 for negative magnetostriction, and 7 or 8 for positive magnetostriction) the noise even gets to several tens of pT/Hz. These results are very interesting from two points of view. First of all, we found that the magnetostriction in this type of amorphous magnetic wires significantly affect the noise of the sensor. We can say that one order of magnitude change in the magnetostriction constant (from λs ≈ 10−7 to λs ≈ 10−6) causes one order of magnitude change in the 1/f noise of the fluxgate (from unit to tens of pT/Hz). The second interesting remark is that once the composition is based on alloy with x between 0.06 and 0.062 (that is magnetostriction around λs ≈ 10−7) the noise is already minimum and does not show any possibility of reduction. In other words, these results do not show any room for reduction of noise by even further decrease of magnetostriction as the noise appear already at a minimum point for x between 0.06 and 0.062. For such composition it appears the magnetostriction does not play a role anymore. Fig. 2 shows similar results for the value of the noise floor. However, the minimum value of the noise floor (between 500 and 700 fT/Hz) is met for an wider range of Fe amount x between 0.055 and 0.065 while is increases over 1 pT/Hz only for x = 0.05 or x > = 0.07. There results suggest that the noise floor is more independent on the magnetostriction than the 1/f noise.

FIG. 1.

Noise spectral density at 1 Hz of fundamental mode orthogonal fluxgate based on amorphous wires with different relative amount of Fe.

FIG. 1.

Noise spectral density at 1 Hz of fundamental mode orthogonal fluxgate based on amorphous wires with different relative amount of Fe.

Close modal
FIG. 2.

Noise floor of fundamental mode orthogonal fluxgate based on amorphous wires with different relative amount of Fe.

FIG. 2.

Noise floor of fundamental mode orthogonal fluxgate based on amorphous wires with different relative amount of Fe.

Close modal

We wanted to confirm that once the amount of Fe is around x between 0.06 and 0.062 then the magnetostriction is low enough to have negligible effect on the noise. Therefore, we performed the following experiment. A wire with x = 0.06 was used as core of a FM-OFG in two different conditions: soldered on the sensor’s head leaving it in its natural curvature or bended in straight direction as typically done. These two conditions are shown in Fig. 3. In order to have room for a naturally curved wire we employed a single wire instead of two wires; also the size of the sensor’s head was doubled from 5 to 10 mm. The coil wound around this larger sensor’s head had 1600 turns in two layers. These two differences will bring to larger noise due to the fact that we have a single wire instead of two, and that the pick-up coil has larger diameter, therefore is less efficient in picking-up the axial flux of the microwires. Nevertheless, once taken into account that we expect larger noise, the relative comparison between the naturally curved wire and the bended straight wire will still indicate if the magnetostriction plays a role or not to the noise. It should be noted here that a naturally bended wire still works as fluxgate even if it is not bent in straight direction in the same way a traditional ring-core fluxgate is sensitive to magnetic field in the direction of the pick-up coil despite the core is curved with the respect of the direction of the pick-up coil. In this case the resonance frequency is larger than the previous experiment because of different inductance (we have only one wire) and different pick-up coil. We obtained resonance at 60 kHz, thus we excited the sensor using Idc = 50mA and Idc = 40mA at 60 kHz. Fig. 4 shows the noise obtained under these conditions with naturally curved wire and the very same wire bent to be straight. As expected the noise is larger than the one obtained in the previous experiment (around 6 pT/Hz). Quite interestingly, however, the noise is absolutely identical in both cases. There is no significant difference we can observe between the two noise spectra. This confirms that once the magnetostriction coefficient is around λs ≈ 10−7 it doesn’t play any role anymore in the remaining noise, since even a large mechanical deformation such as the bending to make the wire straight does not affect the noise of the sensor. As an additional confirmation we repeated the same experiment using a wire with x = 0.055 in its natural curved state or bent to be straight. In this case the bending make the noise significantly different. In Fig. 5 we can see that while the noise at 1 Hz is about 13 pT/Hz when the wire is in its natural curved state, it rises to more than 30 pT/Hz when the wire is bent in straight direction. An indication of what occurs in this wire when bent can be derived from Fig. 6 where the circumferential hysteresis loops, measured according to Ref. 17 are shown in both curved and bent states. It appears that because of the magnetostriction a component of the magnetization is brought to axial direction. This is confirmed by the fact that the offset, already quite large (3.2 μT), of the curved wire increases to 6.5 μT when the wire is bent straight. We repeated the same experiment with different sections of wire with x = 0.055 and the noise always increased when the wire in bent together with the offset.

FIG. 3.

A: classical structure of a 2 wire sensor head; B: sensor head with one naturally curve magnetic wire; C: same sensor head as B but with bent straight wire.

FIG. 3.

A: classical structure of a 2 wire sensor head; B: sensor head with one naturally curve magnetic wire; C: same sensor head as B but with bent straight wire.

Close modal
FIG. 4.

Noise spectra of a fluxgate based on a single wire with vanishing magnetostriction (x = 0.06) in its naturally curved state (blue) and bent in straight direction (red).

FIG. 4.

Noise spectra of a fluxgate based on a single wire with vanishing magnetostriction (x = 0.06) in its naturally curved state (blue) and bent in straight direction (red).

Close modal
FIG. 5.

Noise spectra of a fluxgate based on a single wire with negative magnetostriction (x = 0.055) in its naturally curved state (blue) and bent in straight direction (red).

FIG. 5.

Noise spectra of a fluxgate based on a single wire with negative magnetostriction (x = 0.055) in its naturally curved state (blue) and bent in straight direction (red).

Close modal
FIG. 6.

Circumferential Hysteresis loop of a microwire with x = 0.055 in its naturally curved state (blue) and bent in straight direction (red). For better observation of the difference we plotted only the upper half of the curve, give the symmetry of the loop.

FIG. 6.

Circumferential Hysteresis loop of a microwire with x = 0.055 in its naturally curved state (blue) and bent in straight direction (red). For better observation of the difference we plotted only the upper half of the curve, give the symmetry of the loop.

Close modal

As we mentioned, annealing the wire under the presence of circumferential field is an effective method to reduce the noise of FM-OFG, since it increases the circumferential anisotropy. One the problems of annealing these magnetic wires is that from time to time the offset appears to increase after annealing together with the noise. So far the reason why the offset and the noise randomly increased instead of decreasing was not clear. One solution was, however, given. In Ref. 2 the current used for Joule annealing was periodically flipped. In this way the component of the magnetization which happens to be in axial direction during annealing is periodically flipped and its net contribution vanishes (this is the same principle used by Sasada in Ref. 18 to suppress the offset of the FM-OFG). Despite this method proved to work it was not clear why annealing a wire with x = 0.06 Fe, therefore vanishing magnetostriction, was bringing a component of the magnetization to lay in axial direction. This appears in contradiction with the results summarized in Fig. 3, where we saw that the characteristics of a wire with x = 0.06 Fe are not affected by mechanical stress, so that a wire behaves in the very same way if it bent straight or left naturally curved. How possibly such wire could generate an axial magnetization, and then an increment of offset and noise when annealed? The answer can be seen in the dependence of the magnetostriction on the temperature. The values previously reported, and taken from Ref. 13, are given for room temperature. If the temperature rises, however, they change. For instance, a wire with 0.06 Fe has λs ≈ 10−7 at room temperature, but it rises to λs ≈ 0.5 ⋅ 10−6 for temperature as low as 200 °C. At such temperature, at which typically annealing is performed, we cannot consider the magnetostriction of the wire vanishing anymore. Since annealing was performed with wire bent straight, once the wire reaches temperature large enough the mechanical stress due to the bending makes a component of the magnetization axial because of the magnetostriction newly acquired thanks to the temperature. While at room temperature we can neglect the effect of the magnetostriction on a wire with 0.06 Fe, when we anneal it the magnetostriction is not negligible anymore and we should take into account. As a confirmation we tried the following experiment: we annealed a wire with 0.06 Fe in its naturally curved state, instead of making it straight before annealing. Then we annealed it with 370 mA for 1 minute in a shielding, in order to suppress the axial field of the Earth. We did not use any flipping but we always kept the same polarity of the annealing current. This would generate a huge offset as shown in Ref. 2. On the contrary we obtained the opposite behaviour: the offset, which was 1.35 μT before annealing, dropped to only 98 nT after annealing, despite we did not use any flipping of the annealing current. Correspondingly the noise dropped from 7 pT/Hz at 1 Hz before annealing to 2.3 pT/Hz after annealing the wire in its naturally curved state. We measured again the noise making the same wire straight after annealing, and interestingly the noise did not change as previously seen in Fig. 3 for as cast wire with x = 0.06 Fe (Fig. 7). These results suggests that even after annealing, once the wire is brought back to room temperature, because of composition with x = 0.06 Fe, the noise still does not depend on the vanishing magnetostriction and the bending has no effect on the noise. The bending has, however, effect on the wire during annealing, since at higher temperature the magnetostriction increases. If then you anneal keeping the wire straight this will introduce axial magnetization and give rise to large offset as shown in Ref. 2, on the contrary, if it is kept at its natural curvature (like in this experiment) no stress is applied to the wire and despite the magnetostriction rise due to temperature no magnetization is induced in axial direction, despite continuos current without flipping. Despite we derive that the best option of annealing amorphous microwire for FM-OFG is the perform annealing keeping them in their natural curved state and then to make them straight after annealing.

FIG. 7.

Noise of a fluxgate based on a wire with x = 0.06 Fe in its naturally curved state (blue), after annealing still being curved (red) and after annealing but bent straight (black).

FIG. 7.

Noise of a fluxgate based on a wire with x = 0.06 Fe in its naturally curved state (blue), after annealing still being curved (red) and after annealing but bent straight (black).

Close modal

In this paper we investigated the effect of the magnetostriction to the noise of fundamental mode orthogonal fluxgates. We found out that even a small change in the composition of the wire leads to significant change of the noise in the 1/f region and that the minimum noise is achieved if the relative amount of Fe with the respect of the total Fe+Co amount is between 0.06 and 0.062. We proved that once this composition is achieved the noise then does not depend on the mechanical stress since it is identical with the wire in its natural shape and when bent straight. This means that the source of the remaining noise must be found elsewhere, for instance in the structure of the wire which is not entirely saturated in its centre by the excitation current due to low circumferential field. In this case a new type of amorphous wire with non-magnetic core could be investigated.

For these type of wires we suggest a better method for annealing based on the knowledge that even a wire with vanishing magnetostriction at room temperature becomes positively magnetostrictive at higher temperature such as the ones at which annealing is performed. Therefore, we propose to anneal the wires while in their natural shape and not straight as usually done, to avoid any mechanical stress during annealing. This method provided a significant offset and noise reduction.

This work was supported by the mobility grant “International Mobility of Researchers in CTU,” No. CZ.02.2.69/0.0/0.0/16_027/0008465.

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