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 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 χ of the magnetic material. We derive an analytical expression for χ 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 (Fe90Co10)78Si12B10 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.

[1]  Alfred Ludwig,et al.  Magnetically tunable SAW-resonator , 2003, IEEE International Frequency Control Symposium and PDA Exhibition Jointly with the 17th European Frequency and Time Forum, 2003. Proceedings of the 2003.

[2]  T. Gilbert.  A phenomenological theory of damping in ferromagnetic materials , 2004, IEEE Transactions on Magnetics.

[3]  T. F. Rogers,et al.  Magnetically Induced Ultrasonic Velocity Changes in Polycrystalline Nickel , 1952 .

[4]  W. P. Mason.  Domain Wall Relaxation in Nickel , 1951 .

[5]  Eckhard Quandt,et al.  Mechanical-Resonance-Enhanced Thin-Film Magnetoelectric Heterostructures for Magnetometers, Mechanical Antennas, Tunable RF Inductors, and Filters , 2019, Materials.

[6]  Jens Reermann,et al.  Multimode delta-E effect magnetic field sensors with adapted electrodes , 2016 .

[7]  Jun Ou-Yang,et al.  Influence of the delta-E effect on a surface acoustic wave resonator , 2019, Applied Physics Letters.

[8]  Phillip Durdaut,et al.  Wide Band Low Noise Love Wave Magnetic Field Sensor System , 2018, Scientific Reports.

[9]  Amikam Aharoni,et al.  Demagnetizing factors for rectangular ferromagnetic prisms , 1998 .

[10]  Omar Elmazria,et al.  Highly Sensitive Surface Acoustic Wave Magnetic Field Sensor Using Multilayered TbCo2/FeCo Thin Film , 2018, Proceedings.

[11]  E. Quandt,et al.  Permeability and Magnetic Properties of Ferromagnetic NiFe/FeCoBSi Bilayers for High-Frequency Applications , 2007, IEEE Transactions on Magnetics.

[12]  Sebastian Zabel,et al.  Phase modulated magnetoelectric delta-E effect sensor for sub-nano tesla magnetic fields , 2015 .

[13]  R. F. Wiegert,et al.  Magnetoelastic surface acoustic wave attenuation and anisotropic magnetoresistance in Ni3Fe thin films , 2002 .

[14]  O. Bou Matar,et al.  Multilayer magnetostrictive structure based surface acoustic wave devices , 2014 .

[15]  M. Brandt,et al.  Elastically driven ferromagnetic resonance in nickel thin films. , 2010, Physical review letters.

[16]  H. Hoffmann,et al.  Theory of magnetization ripple , 1968 .

[17]  Sebastian Zabel,et al.  Microelectromechanical magnetic field sensor based on ΔE effect , 2014 .

[18]  J. Livingston,et al.  Magnetomechanical Properties of Amorphous Metals , 1982, April 16.

[19]  K. Mackay,et al.  Elastic properties of magnetostrictive thin films using bending and torsion resonances of a bimorph , 2000 .

[20]  M. Rinaldi,et al.  Self-Biased 215MHz Magnetoelectric NEMS Resonator for Ultra-Sensitive DC Magnetic Field Detection , 2013, Scientific Reports.

[21]  R. F. Wiegert,et al.  Enhanced magnetically tunable attenuation and relative velocity of 0.6 GHz Rayleigh waves in nickel thin films , 1989 .

[22]  G. Srinivasan,et al.  VOLTAGE CONTROL OF MAGNETISM IN MULTIFERROIC HETEROSTRUCTURES AND DEVICES , 2012 .

[23]  Tsuyoshi Uchiyama,et al.  Giant magneto-impedance in Co-rich amorphous wires and films , 1995 .

[24]  Tianxiang Nan,et al.  Ultra-sensitive NEMS magnetoelectric sensor for picotesla DC magnetic field detection , 2017 .

[25]  Supratik Datta,et al.  Stress and magnetic field dependent Young's modulus in single crystal iron-gallium alloys , 2010 .

[26]  W. P. Mason.  Rotational Relaxation in Nickel at High Frequencies , 1953 .

[27]  R. Gross,et al.  Surface acoustic wave driven ferromagnetic resonance in nickel thin films: Theory and experiment , 2012, 1208.0001.

[28]  A. K. Ganguly,et al.  Applications of amorphous magnetic-layers in surface-acoustic-wave devices , 1979 .

[29]  Jun Ou-Yang,et al.  Self-biased vector magnetic sensor based on a Love-type surface acoustic wave resonator , 2018 .

[30]  Sami Hage-Ali,et al.  Unipolar and Bipolar High-Magnetic-Field Sensors Based on Surface Acoustic Wave Resonators , 2017 .

[31]  Hao-Miao Zhou,et al.  A general one-dimension nonlinear magneto-elastic coupled constitutive model for magnetostrictive materials , 2015 .

[32]  Eckhard Quandt,et al.  Fully integrable magnetic field sensor based on delta-E effect , 2011 .

[33]  E. Quandt,et al.  Optimization of the /spl Delta/E-effect in thin films and multilayers by magnetic field annealing , 2002 .

[34]  C. Kittel.  On the Theory of Ferromagnetic Resonance Absorption , 1948 .

[35]  Yu Hui,et al.  High Resolution Magnetometer Based on a High Frequency Magnetoelectric MEMS-CMOS Oscillator , 2015, Journal of Microelectromechanical Systems.

[36]  P. Squire,et al.  Phenomenological model for magnetization, magnetostriction and ΔE effect in field-annealed amorphous ribbons , 1990 .

[37]  Marcel Bauer,et al.  Modern Magnetic Materials Principles And Applications , 2016 .

[38]  Luděk Kraus,et al.  GMI modeling and material optimization , 2003 .

[39]  P. Squire,et al.  Domain model for magnetoelastic behaviour of uniaxial ferromagnets , 1995 .

[40]  O. Bou Matar,et al.  Band gap tunability of magneto-elastic phononic crystal , 2012 .

[41]  E. Wohlfarth,et al.  A mechanism of magnetic hysteresis in heterogeneous alloys , 1991 .

[42]  A. K. Ganguly,et al.  Magnetoelastic surface waves on the (110) plane of highly magnetostrictive cubic crystals , 1978 .

[43]  Yana Jia,et al.  Enhanced sensitivity of temperature-compensated SAW-based current sensor using the magnetostrictive effect , 2017 .

[44]  L. Daniel,et al.  Measurement and Analytical Modeling of the $\Delta E$ Effect in a Bulk Iron-Cobalt Alloy , 2010, IEEE Transactions on Magnetics.

[45]  Laurent Daniel,et al.  An analytical model for the Δ E effect in magnetic materials , 2009 .

[46]  A. K. Ganguly,et al.  Magnetoelastic surface waves in a magnetic film–piezoelectric substrate configuration , 1976 .

[47]  A H Reid,et al.  Beyond a phenomenological description of magnetostriction , 2017, Nature Communications.

[48]  S. Hanna,et al.  Magnetic Field Sensors Based on SAW Propagation in Magnetic Films , 1987, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[49]  E. Lee,et al.  Magnetostriction and Magnetomechanical Effects , 1955 .

[50]  Andreas Neudert,et al.  Dynamic anisotropy in amorphous CoZrTa films , 2004 .

[51]  T. M. Crawford,et al.  Inductive measurement of ultrafast magnetization dynamics in thin-film Permalloy , 1999 .

[52]  J. Rantschler,et al.  Ripple field effect on high-frequency measurements of FeTiN films , 2003 .

[53]  W. Robbins,et al.  A simple phenomenological model of tunable SAW devices using magnetostrictive thin films , 1988, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[54]  M. Levy,et al.  Magnetic field dependence of 600 MHz SAW velocity changes for thin Ni films , 1988, IEEE 1988 Ultrasonics Symposium Proceedings..