Frequency Dependency of the Delta-E Effect and the Sensitivity of Delta-E Effect Magnetic Field Sensors
In recent years the delta-E effect has been used for detecting low frequency and low amplitude magnetic fields. Delta-E effect sensors utilize a forced mechanical resonator that is detuned by the delta-E effect upon application of a magnetic field. Typical frequencies of operation are from several k...
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| Format: | Article |
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MDPI AG
2019-11-01
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| Series: | Sensors |
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| Online Access: | https://www.mdpi.com/1424-8220/19/21/4769 |
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| author | Benjamin Spetzler Elizaveta V. Golubeva Cai Müller Jeffrey McCord Franz Faupel |
| author_facet | Benjamin Spetzler Elizaveta V. Golubeva Cai Müller Jeffrey McCord Franz Faupel |
| author_sort | Benjamin Spetzler |
| collection | DOAJ |
| description | In recent years the delta-E effect has been used for detecting low frequency and low amplitude magnetic fields. Delta-E effect sensors utilize a forced mechanical resonator that is detuned by the delta-E effect upon application of a magnetic field. Typical frequencies of operation are from several kHz to the upper MHz regime. Different models have been used to describe the delta-E effect in those devices, but the frequency dependency has mainly been neglected. With this work we present a simple description of the delta-E effect as a function of the differential magnetic susceptibility <inline-formula> <math display="inline"> <semantics> <mi>χ</mi> </semantics> </math> </inline-formula> of the magnetic material. We derive an analytical expression for <inline-formula> <math display="inline"> <semantics> <mi>χ</mi> </semantics> </math> </inline-formula> that permits describing the frequency dependency of the delta-E effect of the Young’s modulus and the magnetic sensitivity. Calculations are compared with measurements on soft-magnetic <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mrow> <mi>Fe</mi> </mrow> <mrow> <mn>90</mn> </mrow> </msub> <msub> <mrow> <mi>Co</mi> </mrow> <mrow> <mn>10</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>78</mn> </mrow> </msub> <msub> <mrow> <mi>Si</mi> </mrow> <mrow> <mn>12</mn> </mrow> </msub> <msub> <mi mathvariant="normal">B</mi> <mrow> <mn>10</mn> </mrow> </msub> </mrow> </semantics> </math> </inline-formula> thin films. We show that the frequency of operation can have a strong influence on the delta-E effect and the magnetic sensitivity of delta-E effect sensors. Overall, the delta-E effect reduces with increasing frequency and results in a stiffening of the Young’s modulus above the ferromagnetic resonance frequency. The details depend on the Gilbert damping. Whereas for large Gilbert damping the sensitivity continuously decreases with frequency, typical damping values result in an amplification close to the ferromagnetic resonance frequency. |
| first_indexed | 2024-04-11T12:45:19Z |
| format | Article |
| id | doaj.art-aa946e1d54254694acac5f0546b5abe3 |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-04-11T12:45:19Z |
| publishDate | 2019-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-aa946e1d54254694acac5f0546b5abe32022-12-22T04:23:23ZengMDPI AGSensors1424-82202019-11-011921476910.3390/s19214769s19214769Frequency Dependency of the Delta-E Effect and the Sensitivity of Delta-E Effect Magnetic Field SensorsBenjamin Spetzler0Elizaveta V. Golubeva1Cai Müller2Jeffrey McCord3Franz Faupel4Kiel University, 24118 Kiel, GermanyKiel University, 24118 Kiel, GermanyKiel University, 24118 Kiel, GermanyKiel University, 24118 Kiel, GermanyKiel University, 24118 Kiel, GermanyIn recent years the delta-E effect has been used for detecting low frequency and low amplitude magnetic fields. Delta-E effect sensors utilize a forced mechanical resonator that is detuned by the delta-E effect upon application of a magnetic field. Typical frequencies of operation are from several kHz to the upper MHz regime. Different models have been used to describe the delta-E effect in those devices, but the frequency dependency has mainly been neglected. With this work we present a simple description of the delta-E effect as a function of the differential magnetic susceptibility <inline-formula> <math display="inline"> <semantics> <mi>χ</mi> </semantics> </math> </inline-formula> of the magnetic material. We derive an analytical expression for <inline-formula> <math display="inline"> <semantics> <mi>χ</mi> </semantics> </math> </inline-formula> that permits describing the frequency dependency of the delta-E effect of the Young’s modulus and the magnetic sensitivity. Calculations are compared with measurements on soft-magnetic <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mrow> <mi>Fe</mi> </mrow> <mrow> <mn>90</mn> </mrow> </msub> <msub> <mrow> <mi>Co</mi> </mrow> <mrow> <mn>10</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>78</mn> </mrow> </msub> <msub> <mrow> <mi>Si</mi> </mrow> <mrow> <mn>12</mn> </mrow> </msub> <msub> <mi mathvariant="normal">B</mi> <mrow> <mn>10</mn> </mrow> </msub> </mrow> </semantics> </math> </inline-formula> thin films. We show that the frequency of operation can have a strong influence on the delta-E effect and the magnetic sensitivity of delta-E effect sensors. Overall, the delta-E effect reduces with increasing frequency and results in a stiffening of the Young’s modulus above the ferromagnetic resonance frequency. The details depend on the Gilbert damping. Whereas for large Gilbert damping the sensitivity continuously decreases with frequency, typical damping values result in an amplification close to the ferromagnetic resonance frequency.https://www.mdpi.com/1424-8220/19/21/4769delta-e effectmagnetoelasticityresonatorsmagnetic field sensingdynamic susceptibilitysurface acoustic wave (saw) |
| spellingShingle | Benjamin Spetzler Elizaveta V. Golubeva Cai Müller Jeffrey McCord Franz Faupel Frequency Dependency of the Delta-E Effect and the Sensitivity of Delta-E Effect Magnetic Field Sensors Sensors delta-e effect magnetoelasticity resonators magnetic field sensing dynamic susceptibility surface acoustic wave (saw) |
| title | Frequency Dependency of the Delta-E Effect and the Sensitivity of Delta-E Effect Magnetic Field Sensors |
| title_full | Frequency Dependency of the Delta-E Effect and the Sensitivity of Delta-E Effect Magnetic Field Sensors |
| title_fullStr | Frequency Dependency of the Delta-E Effect and the Sensitivity of Delta-E Effect Magnetic Field Sensors |
| title_full_unstemmed | Frequency Dependency of the Delta-E Effect and the Sensitivity of Delta-E Effect Magnetic Field Sensors |
| title_short | Frequency Dependency of the Delta-E Effect and the Sensitivity of Delta-E Effect Magnetic Field Sensors |
| title_sort | frequency dependency of the delta e effect and the sensitivity of delta e effect magnetic field sensors |
| topic | delta-e effect magnetoelasticity resonators magnetic field sensing dynamic susceptibility surface acoustic wave (saw) |
| url | https://www.mdpi.com/1424-8220/19/21/4769 |
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