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Effect of tensile stress on cobalt-based amorphous wires impedance near the magnetostriction compensation temperature
Journal Pre-proofs Effect of tensile stress on cobalt-based amorphous wires impedance near the magnetostriction compensation temperature D.A. Bukreev, M.S. Derevyanko, A.A. Moiseev, A.V. Semirov PII: DOI: Reference:
S0304-8853(19)30737-1 https://doi.org/10.1016/j.jmmm.2020.166436 MAGMA 166436
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Journal of Magnetism and Magnetic Materials
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22 February 2019 9 January 2020 9 January 2020
Please cite this article as: D.A. Bukreev, M.S. Derevyanko, A.A. Moiseev, A.V. Semirov, Effect of tensile stress on cobalt-based amorphous wires impedance near the magnetostriction compensation temperature, Journal of Magnetism and Magnetic Materials (2020), doi: https://doi.org/10.1016/j.jmmm.2020.166436
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Effect of tensile stress on cobalt-based amorphous wires impedance near the magnetostriction compensation temperature Bukreev D.A., Derevyanko M.S.*, Moiseev A.A., Semirov A.V. Irkutsk State University, 664003, Irkutsk, Russia * e-mail: [email protected] Abstract This study investigates the effect of tensile stress on the impedance of an amorphous Co66Fe4Ta2.5Si12.5B15 wire near the magnetostriction compensation temperature at approximately 170 K. When the wire is exposed to the tensile stress, the wire impedance modulus is found to demonstrate high temperature sensitivity of over 2%/K. This finding can help in designing of temperature sensors. Keywords Amorphous soft magnetic alloys, magnetostriction compensation temperature, magnetoimpedance Introduction High-frequency electrical properties of amorphous soft magnetic alloys exhibit strong sensitivity to various external influences. In particular, changes in electrical impedance under the influence of a magnetic field (magnetoimpedance effect – MI) [1,2], deformations (stressimpedance effect – SI) [3] and temperature [4–7] were discovered in wires, glass covered microwires, ribbons and films. The nature of this phenomenon can be explained within the framework of classical electrodynamics [1,2,8]. Based on the above-mentioned effects, it is possible to design magnetic field [9–12], magnetoelastic [13,14] and temperature [5,15] sensors. Investigations of these effects are also interesting from a fundamental point of view. For example, it was shown that it is possible to detect the features of magnetic anisotropy [16,17], the magnitude and sign of magnetostriction [18,19] using MI and SI. From both applied and fundamental points of view, investigation of the temperature effect on the impedance is very important. Firstly, it is necessary to determine the operating temperature range of the MI and SI based sensors and to solve the problems of a thermal stability increasing [20–22]. Secondly, it is possible to develop temperature sensors based on these investigations 1
[5,15]. Thirdly, temperature investigations of the impedance can be used as a tool for studying magnetic phase transitions [7,15,23–26], temperature effect on magnetic anisotropy and magnetostriction [19,27], as well as relaxation of residual quenching stresses [25]. In our opinion, investigations of the joint effect of the temperature and the mechanical stresses on the impedance are particularly interesting [19,28,29]. Such investigations allow to obtain data on the temperature effect on the magnetoelastic properties of amorphous soft magnetic alloys, which is important, because their magnetic anisotropy is predominantly magnetoelastic [30]. For example, investigation of the temperature effect on the impedance and MI of an elastically deformed Co-based ribbon allowed us to detect a change in the magnetostriction sign and the magnetostriction compensation temperature [19]. Similar investigations are very interesting especially in the case of amorphous soft magnetic wires produced by the in-rotating-water spinning method [31]. These wires have a much more complex distribution of the quenching stresses compared to ribbons [30,32], which can affect the temperature dependence of the impedance and MI in the presence of the external mechanical stresses. However, there aren't many publications about the joint effect of the temperature and the mechanical stresses on the amorphous wires impedance [28,29]. Therefore, further study of this problem is of interest. This paper is devoted to a study of the joint effect of the temperature and the mechanical stresses on the impedance modulus and MI of amorphous Co-based wires doped with tantalum in a wide frequency range of alternating current. The study is focused on the temperature and the stress influence on the impedance near the magnetostriction compensation temperature which is significantly lower than room temperature. Material and methods The amorphous wire produced by an in-rotating-water spinning method had the composition of Co66Fe4Ta2.5Si12.5B15. The wire radius was 65 μm. Samples of a 30 mm length were cut off from it. Electrical impedance modulus (𝑍) was measured using a magnetoimpedance spectroscopy measuring system based on Agilent 4294A impedance analyzer [33] in AC frequency range (𝑓) from 0.1 to 100 MHz. The alternating current of 1 mA flowed through the sample axially. The external magnetic field (𝐻) and the tensile stress (𝜎) were also oriented axially. The maximum of the magnetic field strength and the tensile stress value was 150 Oe and 440 MPa, respectively. Impedance measurements were carried out in the temperature (𝑇) range from 120 to 300 K. The MI was calculated as follows:
2
𝑀𝐼(𝐻) =
𝑍(𝐻) ― 𝑍(𝐻max) 𝑍(𝐻max)
× 100%,
(1)
where 𝑍(𝐻) и 𝑍(𝐻max) are the impedance moduli measured in the magnetic fields with strengths of 𝐻 and 𝐻max = 150 Oe, respectively. The relative temperature change of the impedance modulus (thermo-impedance effect, TI) was calculated as follows:
𝑇𝐼(𝑇) =
𝑍0(𝑇) ― 𝑍0(𝑇0) 𝑍0(𝑇0)
× 100%,
(2)
where 𝑍0 is the impedance modulus measured in the zero magnetic field and 𝑇0 is the starting temperature with the value of 120 K. Low temperatures can lead to irreversible changes in the magnetic properties of amorphous alloys [34,35]. Therefore, we controlled the reversibility of the temperature changes in the impedance. For this, the impedance was measured at room temperature before and after cooling to 120
K,
and
its
relative
change
was
calculated
as
follows:
𝑅𝐸𝑉 = 100% ∙
(𝑍𝑎𝑐(𝐻) ― 𝑍𝑏𝑐(𝐻)) 𝑍𝑏𝑐(𝐻), where 𝑍𝑏𝑐 and 𝑍𝑎𝑐 are the impedance moduli before and after cooling to 120 K, respectively. Measurements showed that the impedance varies slightly for all values of 𝐻 (Fig. 1). The nonzero values of 𝑅𝐸𝑉 are due to instrumental errors in the impedance and the magnetic field measurements. In general, temperature changes in the impedance can be considered reversible.
Fig. 1. The change in the impedance after cooling relative to the impedance before cooling. The data are given for magnetic field strengths from 0 to 150 Oe and AC frequencies of 10, 30 and 100 MHz.
The small-angle magnetization rotation (SAMR) method was used to measure the saturation magnetostriction (𝜆𝑠) [36]. Unlike the original SAMR method, magnetization oscillation was 3
excited by the alternating current [37]. Its frequency and amplitude were 100 kHz and 10 mA, respectively. Saturation magnetization values (𝑀𝑠) required for 𝜆𝑠 measurements by the SAMR method were defined from hysteresis loops obtained by the induction method. Results and discussion The different behavior of 𝑀𝐼(𝐻) under the influence of the tensile stress can be seen at the temperatures below and above 𝑇𝜆 ≈ 170 K. At temperatures below 𝑇𝜆, as the tensile stress increase, the ascending portion of 𝑀𝐼(𝐻) becomes larger, and the peak is shifted to the higher fields (Fig. 2, a). At the temperatures above 𝑇𝜆, an increase of σ leads to opposite changes (Fig. 2, b). Moreover, at a certain value of 𝜎, the ascending portion disappears.
Fig. 2. Magnetic field dependences of 𝑀𝐼 (see expression (1)) in Co66Fe4Ta2.5Si12.5B15 wires. The dependencies have been obtained at an AC frequency of 30 MHz at a) 120 K and b) 210 K. Tensile stresses were 0, 220 and 440 MPa.
In [28,29], the value (∆𝑍 𝑍)max = 100% ∙ (𝑍max ― 𝑍0) 𝑍0 was used to describe the effect of temperature and tensile stresses on MI in CoFeSiB wires. Here 𝑍max is the maximum value of the impedance modulus in a magnetic field. It is possible to estimate the change in the ascending portion on the 𝑀𝐼(𝐻) dependency by change in (∆𝑍 𝑍)max. It was found that there is a maximum in the temperature dependence of (∆𝑍 𝑍)max above room temperature, if the tensile stresses are absent [28]. It is associated with reversible relaxation of quenching stresses, which leads to a decrease in magnetoelastic anisotropy and, as a result, to an increase in (∆𝑍 𝑍)max [4,28,29]. In our case, reversible relaxation of the quenching stresses probably occurs at temperatures above 240 K, when (∆𝑍 𝑍)max increases with increasing 𝑇 (Fig. 3, curve 𝜎 = 0 MPa). In [28], it was also found that the increase in tensile stresses leads to the decrease in 4
(∆𝑍 𝑍)max, and also to the disappearance of a maximum in the temperature dependence of this quantity. Thus, it turns into a monotonously decreasing one. These changes are explained in terms of competition between internal and external stresses. When the temperature changes, the balance between them also changes, because internal stresses depend on temperature. In our case, (∆𝑍 𝑍)max similarly changes with increasing of the tensile stresses at the temperatures above 170 K (Fig. 3). At the lower temperatures, tensile stresses lead to an increase in (∆𝑍 𝑍)max, and this does not fit into the conceptions developed in [28]. Therefore, other conceptions are needed to use.
Fig. 3. Temperature dependences of (∆𝑍 𝑍)max = 100% ∙ (𝑍max ― 𝑍0) 𝑍0 obtained at tensile stresses of 0, 220, and 440 MPa. The AC frequency was 30 MHz.
Referring again to Figure 2. The ascending portion of 𝑀𝐼(𝐻) dependency shows that there is a circular component of magnetization in the wire volume corresponding to the skin depth. And the smaller 𝑀𝐼(𝐻 = 0), the larger the circular component [16,17]. Therefore, our findings suggest that the growth of the tensile stress leads to an increase in the circular component of the magnetization at the temperatures below 𝑇𝜆 and to its decrease at the temperatures above 𝑇𝜆. This is due to a change in the magnetostriction sign near 𝑇𝜆. According to the results, the 𝜆𝑠 has a negative value at the temperatures below 𝑇𝜆 ≈ 170 K and a positive one – at the temperatures above 𝑇𝜆 (fig. 4, curve 1). An increase in the temperature from 120 to 260 K leads to an increase in the magnetostriction. A further increase in the temperature leads to a slight decrease in 𝜆𝑠. In the case of the content in the alloy of two transition metals, the temperature dependence of the magnetostriction can be represented as follows [38,39] 𝜆𝑠,0(𝑇) = 𝛼1,0(𝜇0𝑀𝑠(𝑇))3 + 𝛼2,0(𝜇0𝑀𝑠(𝑇))2,
(3) 5
where the first term describes the contribution from a single-ion interaction, the second – from a two-ion one. The index “0” means that the influence of the mechanical stresses on the magnetostriction is not separately considered. According to [39], even a small Fe content in the Co-based alloy leads to the appearance of the two-ion contribution. Moreover, for close contents of Fe and Co, as in the alloy Co66Fe4Ta2.5Si12.5B15, the coefficient 𝛼1 < 0, and the coefficient 𝛼2 > 0. In this case, it is possible that magnetostriction reaches zero at a certain temperature (magnetostriction compensation temperature) and will have different signs above and below it. This is 𝑇𝜆 ≈ 170 K for Co66Fe4Ta2.5Si12.5B15 wires. In our case, the calculated magnetostriction values with help of the model of the one- and two-ion interactions are close to the measured one only at low and high temperatures (fig. 4). Therefore, below we consider the dependence of the magnetostriction on mechanical stresses [40– 42]: 𝜆𝑠 = 𝜆𝑠,0 ―𝛽𝜎,
(4)
where 𝜆𝑠,0 is the magnetostriction in the absence of the mechanical stresses, 𝛽 is a coefficient, usually taking a value from (1 ÷ 6) ∙ 10 ―10 MPa ―1. The coefficient 𝛽 can be changed with a temperature in a rather complicated way, as shown in the paper [43]. Internal stresses 𝜎𝑖 also change with the temperature [32]. Considering the latter and (3), the expression (4) can be written in the form: 𝜆𝑠(𝑇) = 𝛼1(𝜇0𝑀𝑠(𝑇))3 + 𝛼2(𝜇0𝑀𝑠(𝑇))2 ― 𝜆𝑠, 𝜎(𝑇),
(5)
where 𝜆𝑠, 𝜎(𝑇) = 𝛽(𝑇)𝜎𝑖(𝑇). Analyzing expression (5) and comparing of the curves 1 and 2 in fig. 4, it can be assumed that if the temperature changes, the term 𝜆𝑠, 𝜎(𝑇) undergoes non-monotonic and significant changes with a maximum of about 200 K and a minimum of about 260 K.
6
Fig. 4. Temperature dependence of the saturation magnetostriction 𝜆𝑠 of the Co66Fe4Ta2.5Si12.5B15 wire: curve 1 – measured values; curve 2 – calculated values by expression (3). The following values were used for calculations: 𝛼1,0 = 5.45 ∙ 10 ―5 Т ―3; 𝛼2,0 = 2.74 ∙ 10 ―5 Т ―2; the saturation magnetization values 𝑀𝑠 required for the calculations were obtained experimentally and are shown in the inset.
When 𝜆𝑠 is negative, the axial tensile stress orients the magnetization in the perpendicular direction to the wire length. It was shown above that this is a circular direction, because the ascending portion of 𝑀𝐼(𝐻) increases and 𝑀𝐼(𝐻 = 0) decreases with increasing stresses 𝜎 (fig. 2). When 𝜆𝑠 is positive, the axial tensile stress orients the magnetization in the axial direction. Near 𝑇𝜆, when the magnetostriction changes sign, the magnetization in the tensed wire is reoriented from the circular to the axial direction. Consequently, circular magnetic permeability and the impedance modulus determined by it will undergo considerable changes in the vicinity of the 𝑇𝜆. Really, near the 𝑇𝜆, the impedance modulus of the tensed wire demonstrates considerable growth with an increase in the temperature, which is expressed in terms of the thermo-impedance dependences, 𝑇𝐼(𝑇), as shown in Fig. 5. The thermo-impedance effect reaches the peak value at 180 K and decreases with a further increase in the temperature. Note that the sensitivity of the thermo-impedance effect in the temperature range from 140 to 180 K at the frequency of 100 MHz exceeds 2%/K, which can be used for temperature sensors development.
7
Fig. 5. Thermo-impedance effect in the Co66Fe4Ta2.5Si12.5B15 wires: a) the dependences were obtained at AC frequencies of 10, 30, and 100 MHz when tensile stresses σ were 0 MPa (filled markers) and 440 MPa (empty markers); b) the dependences were obtained at AC frequency of 30 MHz when tensile stress was 0, 150, 300, 440 MPa.
The peak of the 𝑇𝐼(𝑇) shifts to the higher temperatures with increasing of the tensile stress (fig. 5, b). This is because the mechanical stresses lead to a decrease in magnetostriction (see expression (4)), therefore the temperature at which the conditions for achieving the maximum 𝑇𝐼 value are fulfilled is increased with 𝜎 increase. At different AC frequencies, the peaks on the 𝑇𝐼(𝑇) dependencies are observed at different temperatures (fig. 5, a). If we consider the skin effect [1,8], we can assume that this may be due to the peculiarities of the radial distribution of internal stresses in the wire [30,32], which affect the magnetostriction. These results can be useful in studying the effect of a temperature on magnetic properties and MI in glass-coated microwires [7,22,44–46]. The metal nucleus and the glass coating of the microwire have different coefficients of the thermal expansion [47,48]. As a result of this, firstly, internal stresses caused by the microwire fabrication arise both in the nucleus and in the covering. They depend on the ratio of the nucleus diameter to the total diameter of the microwire. The smaller this ratio, the greater the internal mechanical stresses, which affect the magnetic properties and MI [26,49]. Secondly, a change in a temperature will lead to a change in internal stresses. As a result of this, a large TI caused by a change in the magnetostriction sign can be observed in glass-coated microwires without creating external mechanical stresses. Conclusions It was found that changes in the magnetic field dependences of the magnetoimpedance effect in the amorphous Co66Fe4Ta2.5Si12.5B15 wires caused by the tensile stress are different at the 8
temperatures below and above 170 K. At the temperatures below 170 K, they indicate the increase of the circular component of the magnetization with increasing the tensile stress, and at the temperatures above 170 K, they indicate its decrease. This result is due to the change in the magnetostriction sign from the negative to the positive at the temperature of 170 K, which is the magnetostriction compensation temperature of the amorphous Co66Fe4Ta2.5Si12.5B15 wires. It is also shown that the change in the magnetostriction sign provides for a strong increase in the impedance with the temperature increase in the range from 140 to 180 K. For example, at the frequency of 100 MHz, the temperature sensitivity of the impedance exceeds 2%/K, which can be used for temperature sensors development. Acknowledgments This work was supported by a project part of the Government Assignment for Scientific Research from the Ministry of Education and Science, Russia (No. 3.1941.2017/4.6). References [1]
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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
13
Highlights 1. Magnetostriction compensation temperature for Co66Fe4Ta2.5Si12.5B15 alloy was found. 2. Impedance varies greatly near the magnetostriction compensation temperature. 3. Strong impedance temperature changes may be used in the design of temperature sensors.
14
S0304-8853(19)30737-1 https://doi.org/10.1016/j.jmmm.2020.166436 MAGMA 166436
To appear in:
Journal of Magnetism and Magnetic Materials
Received Date: Revised Date: Accepted Date:
22 February 2019 9 January 2020 9 January 2020
Please cite this article as: D.A. Bukreev, M.S. Derevyanko, A.A. Moiseev, A.V. Semirov, Effect of tensile stress on cobalt-based amorphous wires impedance near the magnetostriction compensation temperature, Journal of Magnetism and Magnetic Materials (2020), doi: https://doi.org/10.1016/j.jmmm.2020.166436
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Effect of tensile stress on cobalt-based amorphous wires impedance near the magnetostriction compensation temperature Bukreev D.A., Derevyanko M.S.*, Moiseev A.A., Semirov A.V. Irkutsk State University, 664003, Irkutsk, Russia * e-mail: [email protected] Abstract This study investigates the effect of tensile stress on the impedance of an amorphous Co66Fe4Ta2.5Si12.5B15 wire near the magnetostriction compensation temperature at approximately 170 K. When the wire is exposed to the tensile stress, the wire impedance modulus is found to demonstrate high temperature sensitivity of over 2%/K. This finding can help in designing of temperature sensors. Keywords Amorphous soft magnetic alloys, magnetostriction compensation temperature, magnetoimpedance Introduction High-frequency electrical properties of amorphous soft magnetic alloys exhibit strong sensitivity to various external influences. In particular, changes in electrical impedance under the influence of a magnetic field (magnetoimpedance effect – MI) [1,2], deformations (stressimpedance effect – SI) [3] and temperature [4–7] were discovered in wires, glass covered microwires, ribbons and films. The nature of this phenomenon can be explained within the framework of classical electrodynamics [1,2,8]. Based on the above-mentioned effects, it is possible to design magnetic field [9–12], magnetoelastic [13,14] and temperature [5,15] sensors. Investigations of these effects are also interesting from a fundamental point of view. For example, it was shown that it is possible to detect the features of magnetic anisotropy [16,17], the magnitude and sign of magnetostriction [18,19] using MI and SI. From both applied and fundamental points of view, investigation of the temperature effect on the impedance is very important. Firstly, it is necessary to determine the operating temperature range of the MI and SI based sensors and to solve the problems of a thermal stability increasing [20–22]. Secondly, it is possible to develop temperature sensors based on these investigations 1
[5,15]. Thirdly, temperature investigations of the impedance can be used as a tool for studying magnetic phase transitions [7,15,23–26], temperature effect on magnetic anisotropy and magnetostriction [19,27], as well as relaxation of residual quenching stresses [25]. In our opinion, investigations of the joint effect of the temperature and the mechanical stresses on the impedance are particularly interesting [19,28,29]. Such investigations allow to obtain data on the temperature effect on the magnetoelastic properties of amorphous soft magnetic alloys, which is important, because their magnetic anisotropy is predominantly magnetoelastic [30]. For example, investigation of the temperature effect on the impedance and MI of an elastically deformed Co-based ribbon allowed us to detect a change in the magnetostriction sign and the magnetostriction compensation temperature [19]. Similar investigations are very interesting especially in the case of amorphous soft magnetic wires produced by the in-rotating-water spinning method [31]. These wires have a much more complex distribution of the quenching stresses compared to ribbons [30,32], which can affect the temperature dependence of the impedance and MI in the presence of the external mechanical stresses. However, there aren't many publications about the joint effect of the temperature and the mechanical stresses on the amorphous wires impedance [28,29]. Therefore, further study of this problem is of interest. This paper is devoted to a study of the joint effect of the temperature and the mechanical stresses on the impedance modulus and MI of amorphous Co-based wires doped with tantalum in a wide frequency range of alternating current. The study is focused on the temperature and the stress influence on the impedance near the magnetostriction compensation temperature which is significantly lower than room temperature. Material and methods The amorphous wire produced by an in-rotating-water spinning method had the composition of Co66Fe4Ta2.5Si12.5B15. The wire radius was 65 μm. Samples of a 30 mm length were cut off from it. Electrical impedance modulus (𝑍) was measured using a magnetoimpedance spectroscopy measuring system based on Agilent 4294A impedance analyzer [33] in AC frequency range (𝑓) from 0.1 to 100 MHz. The alternating current of 1 mA flowed through the sample axially. The external magnetic field (𝐻) and the tensile stress (𝜎) were also oriented axially. The maximum of the magnetic field strength and the tensile stress value was 150 Oe and 440 MPa, respectively. Impedance measurements were carried out in the temperature (𝑇) range from 120 to 300 K. The MI was calculated as follows:
2
𝑀𝐼(𝐻) =
𝑍(𝐻) ― 𝑍(𝐻max) 𝑍(𝐻max)
× 100%,
(1)
where 𝑍(𝐻) и 𝑍(𝐻max) are the impedance moduli measured in the magnetic fields with strengths of 𝐻 and 𝐻max = 150 Oe, respectively. The relative temperature change of the impedance modulus (thermo-impedance effect, TI) was calculated as follows:
𝑇𝐼(𝑇) =
𝑍0(𝑇) ― 𝑍0(𝑇0) 𝑍0(𝑇0)
× 100%,
(2)
where 𝑍0 is the impedance modulus measured in the zero magnetic field and 𝑇0 is the starting temperature with the value of 120 K. Low temperatures can lead to irreversible changes in the magnetic properties of amorphous alloys [34,35]. Therefore, we controlled the reversibility of the temperature changes in the impedance. For this, the impedance was measured at room temperature before and after cooling to 120
K,
and
its
relative
change
was
calculated
as
follows:
𝑅𝐸𝑉 = 100% ∙
(𝑍𝑎𝑐(𝐻) ― 𝑍𝑏𝑐(𝐻)) 𝑍𝑏𝑐(𝐻), where 𝑍𝑏𝑐 and 𝑍𝑎𝑐 are the impedance moduli before and after cooling to 120 K, respectively. Measurements showed that the impedance varies slightly for all values of 𝐻 (Fig. 1). The nonzero values of 𝑅𝐸𝑉 are due to instrumental errors in the impedance and the magnetic field measurements. In general, temperature changes in the impedance can be considered reversible.
Fig. 1. The change in the impedance after cooling relative to the impedance before cooling. The data are given for magnetic field strengths from 0 to 150 Oe and AC frequencies of 10, 30 and 100 MHz.
The small-angle magnetization rotation (SAMR) method was used to measure the saturation magnetostriction (𝜆𝑠) [36]. Unlike the original SAMR method, magnetization oscillation was 3
excited by the alternating current [37]. Its frequency and amplitude were 100 kHz and 10 mA, respectively. Saturation magnetization values (𝑀𝑠) required for 𝜆𝑠 measurements by the SAMR method were defined from hysteresis loops obtained by the induction method. Results and discussion The different behavior of 𝑀𝐼(𝐻) under the influence of the tensile stress can be seen at the temperatures below and above 𝑇𝜆 ≈ 170 K. At temperatures below 𝑇𝜆, as the tensile stress increase, the ascending portion of 𝑀𝐼(𝐻) becomes larger, and the peak is shifted to the higher fields (Fig. 2, a). At the temperatures above 𝑇𝜆, an increase of σ leads to opposite changes (Fig. 2, b). Moreover, at a certain value of 𝜎, the ascending portion disappears.
Fig. 2. Magnetic field dependences of 𝑀𝐼 (see expression (1)) in Co66Fe4Ta2.5Si12.5B15 wires. The dependencies have been obtained at an AC frequency of 30 MHz at a) 120 K and b) 210 K. Tensile stresses were 0, 220 and 440 MPa.
In [28,29], the value (∆𝑍 𝑍)max = 100% ∙ (𝑍max ― 𝑍0) 𝑍0 was used to describe the effect of temperature and tensile stresses on MI in CoFeSiB wires. Here 𝑍max is the maximum value of the impedance modulus in a magnetic field. It is possible to estimate the change in the ascending portion on the 𝑀𝐼(𝐻) dependency by change in (∆𝑍 𝑍)max. It was found that there is a maximum in the temperature dependence of (∆𝑍 𝑍)max above room temperature, if the tensile stresses are absent [28]. It is associated with reversible relaxation of quenching stresses, which leads to a decrease in magnetoelastic anisotropy and, as a result, to an increase in (∆𝑍 𝑍)max [4,28,29]. In our case, reversible relaxation of the quenching stresses probably occurs at temperatures above 240 K, when (∆𝑍 𝑍)max increases with increasing 𝑇 (Fig. 3, curve 𝜎 = 0 MPa). In [28], it was also found that the increase in tensile stresses leads to the decrease in 4
(∆𝑍 𝑍)max, and also to the disappearance of a maximum in the temperature dependence of this quantity. Thus, it turns into a monotonously decreasing one. These changes are explained in terms of competition between internal and external stresses. When the temperature changes, the balance between them also changes, because internal stresses depend on temperature. In our case, (∆𝑍 𝑍)max similarly changes with increasing of the tensile stresses at the temperatures above 170 K (Fig. 3). At the lower temperatures, tensile stresses lead to an increase in (∆𝑍 𝑍)max, and this does not fit into the conceptions developed in [28]. Therefore, other conceptions are needed to use.
Fig. 3. Temperature dependences of (∆𝑍 𝑍)max = 100% ∙ (𝑍max ― 𝑍0) 𝑍0 obtained at tensile stresses of 0, 220, and 440 MPa. The AC frequency was 30 MHz.
Referring again to Figure 2. The ascending portion of 𝑀𝐼(𝐻) dependency shows that there is a circular component of magnetization in the wire volume corresponding to the skin depth. And the smaller 𝑀𝐼(𝐻 = 0), the larger the circular component [16,17]. Therefore, our findings suggest that the growth of the tensile stress leads to an increase in the circular component of the magnetization at the temperatures below 𝑇𝜆 and to its decrease at the temperatures above 𝑇𝜆. This is due to a change in the magnetostriction sign near 𝑇𝜆. According to the results, the 𝜆𝑠 has a negative value at the temperatures below 𝑇𝜆 ≈ 170 K and a positive one – at the temperatures above 𝑇𝜆 (fig. 4, curve 1). An increase in the temperature from 120 to 260 K leads to an increase in the magnetostriction. A further increase in the temperature leads to a slight decrease in 𝜆𝑠. In the case of the content in the alloy of two transition metals, the temperature dependence of the magnetostriction can be represented as follows [38,39] 𝜆𝑠,0(𝑇) = 𝛼1,0(𝜇0𝑀𝑠(𝑇))3 + 𝛼2,0(𝜇0𝑀𝑠(𝑇))2,
(3) 5
where the first term describes the contribution from a single-ion interaction, the second – from a two-ion one. The index “0” means that the influence of the mechanical stresses on the magnetostriction is not separately considered. According to [39], even a small Fe content in the Co-based alloy leads to the appearance of the two-ion contribution. Moreover, for close contents of Fe and Co, as in the alloy Co66Fe4Ta2.5Si12.5B15, the coefficient 𝛼1 < 0, and the coefficient 𝛼2 > 0. In this case, it is possible that magnetostriction reaches zero at a certain temperature (magnetostriction compensation temperature) and will have different signs above and below it. This is 𝑇𝜆 ≈ 170 K for Co66Fe4Ta2.5Si12.5B15 wires. In our case, the calculated magnetostriction values with help of the model of the one- and two-ion interactions are close to the measured one only at low and high temperatures (fig. 4). Therefore, below we consider the dependence of the magnetostriction on mechanical stresses [40– 42]: 𝜆𝑠 = 𝜆𝑠,0 ―𝛽𝜎,
(4)
where 𝜆𝑠,0 is the magnetostriction in the absence of the mechanical stresses, 𝛽 is a coefficient, usually taking a value from (1 ÷ 6) ∙ 10 ―10 MPa ―1. The coefficient 𝛽 can be changed with a temperature in a rather complicated way, as shown in the paper [43]. Internal stresses 𝜎𝑖 also change with the temperature [32]. Considering the latter and (3), the expression (4) can be written in the form: 𝜆𝑠(𝑇) = 𝛼1(𝜇0𝑀𝑠(𝑇))3 + 𝛼2(𝜇0𝑀𝑠(𝑇))2 ― 𝜆𝑠, 𝜎(𝑇),
(5)
where 𝜆𝑠, 𝜎(𝑇) = 𝛽(𝑇)𝜎𝑖(𝑇). Analyzing expression (5) and comparing of the curves 1 and 2 in fig. 4, it can be assumed that if the temperature changes, the term 𝜆𝑠, 𝜎(𝑇) undergoes non-monotonic and significant changes with a maximum of about 200 K and a minimum of about 260 K.
6
Fig. 4. Temperature dependence of the saturation magnetostriction 𝜆𝑠 of the Co66Fe4Ta2.5Si12.5B15 wire: curve 1 – measured values; curve 2 – calculated values by expression (3). The following values were used for calculations: 𝛼1,0 = 5.45 ∙ 10 ―5 Т ―3; 𝛼2,0 = 2.74 ∙ 10 ―5 Т ―2; the saturation magnetization values 𝑀𝑠 required for the calculations were obtained experimentally and are shown in the inset.
When 𝜆𝑠 is negative, the axial tensile stress orients the magnetization in the perpendicular direction to the wire length. It was shown above that this is a circular direction, because the ascending portion of 𝑀𝐼(𝐻) increases and 𝑀𝐼(𝐻 = 0) decreases with increasing stresses 𝜎 (fig. 2). When 𝜆𝑠 is positive, the axial tensile stress orients the magnetization in the axial direction. Near 𝑇𝜆, when the magnetostriction changes sign, the magnetization in the tensed wire is reoriented from the circular to the axial direction. Consequently, circular magnetic permeability and the impedance modulus determined by it will undergo considerable changes in the vicinity of the 𝑇𝜆. Really, near the 𝑇𝜆, the impedance modulus of the tensed wire demonstrates considerable growth with an increase in the temperature, which is expressed in terms of the thermo-impedance dependences, 𝑇𝐼(𝑇), as shown in Fig. 5. The thermo-impedance effect reaches the peak value at 180 K and decreases with a further increase in the temperature. Note that the sensitivity of the thermo-impedance effect in the temperature range from 140 to 180 K at the frequency of 100 MHz exceeds 2%/K, which can be used for temperature sensors development.
7
Fig. 5. Thermo-impedance effect in the Co66Fe4Ta2.5Si12.5B15 wires: a) the dependences were obtained at AC frequencies of 10, 30, and 100 MHz when tensile stresses σ were 0 MPa (filled markers) and 440 MPa (empty markers); b) the dependences were obtained at AC frequency of 30 MHz when tensile stress was 0, 150, 300, 440 MPa.
The peak of the 𝑇𝐼(𝑇) shifts to the higher temperatures with increasing of the tensile stress (fig. 5, b). This is because the mechanical stresses lead to a decrease in magnetostriction (see expression (4)), therefore the temperature at which the conditions for achieving the maximum 𝑇𝐼 value are fulfilled is increased with 𝜎 increase. At different AC frequencies, the peaks on the 𝑇𝐼(𝑇) dependencies are observed at different temperatures (fig. 5, a). If we consider the skin effect [1,8], we can assume that this may be due to the peculiarities of the radial distribution of internal stresses in the wire [30,32], which affect the magnetostriction. These results can be useful in studying the effect of a temperature on magnetic properties and MI in glass-coated microwires [7,22,44–46]. The metal nucleus and the glass coating of the microwire have different coefficients of the thermal expansion [47,48]. As a result of this, firstly, internal stresses caused by the microwire fabrication arise both in the nucleus and in the covering. They depend on the ratio of the nucleus diameter to the total diameter of the microwire. The smaller this ratio, the greater the internal mechanical stresses, which affect the magnetic properties and MI [26,49]. Secondly, a change in a temperature will lead to a change in internal stresses. As a result of this, a large TI caused by a change in the magnetostriction sign can be observed in glass-coated microwires without creating external mechanical stresses. Conclusions It was found that changes in the magnetic field dependences of the magnetoimpedance effect in the amorphous Co66Fe4Ta2.5Si12.5B15 wires caused by the tensile stress are different at the 8
temperatures below and above 170 K. At the temperatures below 170 K, they indicate the increase of the circular component of the magnetization with increasing the tensile stress, and at the temperatures above 170 K, they indicate its decrease. This result is due to the change in the magnetostriction sign from the negative to the positive at the temperature of 170 K, which is the magnetostriction compensation temperature of the amorphous Co66Fe4Ta2.5Si12.5B15 wires. It is also shown that the change in the magnetostriction sign provides for a strong increase in the impedance with the temperature increase in the range from 140 to 180 K. For example, at the frequency of 100 MHz, the temperature sensitivity of the impedance exceeds 2%/K, which can be used for temperature sensors development. Acknowledgments This work was supported by a project part of the Government Assignment for Scientific Research from the Ministry of Education and Science, Russia (No. 3.1941.2017/4.6). References [1]
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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
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Highlights 1. Magnetostriction compensation temperature for Co66Fe4Ta2.5Si12.5B15 alloy was found. 2. Impedance varies greatly near the magnetostriction compensation temperature. 3. Strong impedance temperature changes may be used in the design of temperature sensors.
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