{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T13:15:16Z","timestamp":1768828516414,"version":"3.49.0"},"reference-count":80,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2021,8,21]],"date-time":"2021-08-21T00:00:00Z","timestamp":1629504000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["Collaborative Research Centre 1261"],"award-info":[{"award-number":["Collaborative Research Centre 1261"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Surface acoustic wave (SAW) sensors for the detection of magnetic fields are currently being studied scientifically in many ways, especially since both their sensitivity as well as their detectivity could be significantly improved by the utilization of shear horizontal surface acoustic waves, i.e., Love waves, instead of Rayleigh waves. By now, low-frequency limits of detection (LOD) below 100 pT\/Hz can be achieved. However, the LOD can only be further improved by gaining a deep understanding of the existing sensor-intrinsic noise sources and their impact on the sensor\u2019s overall performance. This paper reports on a comprehensive study of the inherent noise of SAW delay line magnetic field sensors. In addition to the noise, however, the sensitivity is of importance, since both quantities are equally important for the LOD. Following the necessary explanations of the electrical and magnetic sensor properties, a further focus is on the losses within the sensor, since these are closely linked to the noise. The considered parameters are in particular the ambient magnetic bias field and the input power of the sensor. Depending on the sensor\u2019s operating point, various noise mechanisms contribute to f0 white phase noise, f\u22121 flicker phase noise, and f\u22122 random walk of phase. Flicker phase noise due to magnetic hysteresis losses, i.e. random fluctuations of the magnetization, is usually dominant under typical operating conditions. Noise characteristics are related to the overall magnetic and magnetic domain behavior. Both calculations and measurements show that the LOD cannot be further improved by increasing the sensitivity. Instead, the losses occurring in the magnetic material need to be decreased.<\/jats:p>","DOI":"10.3390\/s21165631","type":"journal-article","created":{"date-parts":[[2021,8,22]],"date-time":"2021-08-22T22:59:27Z","timestamp":1629673167000},"page":"5631","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Phase Noise of SAW Delay Line Magnetic Field Sensors"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9839-3890","authenticated-orcid":false,"given":"Phillip","family":"Durdaut","sequence":"first","affiliation":[{"name":"Microwave Engineering, Institute of Electrical Engineering and Information Technology, Faculty of Engineering, Kiel University, Kaiserstr. 2, 24143 Kiel, Germany"}]},{"given":"Cai","family":"M\u00fcller","sequence":"additional","affiliation":[{"name":"Nanoscale Magnetic Materials and Magnetic Domains, Institute for Materials Science, Faculty of Engineering, Kiel University, Kaiserstr. 2, 24143 Kiel, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6759-4208","authenticated-orcid":false,"given":"Anne","family":"Kittmann","sequence":"additional","affiliation":[{"name":"Inorganic Functional Materials, Institute for Materials Science, Faculty of Engineering, Kiel University, Kaiserstr. 2, 24143 Kiel, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4226-5827","authenticated-orcid":false,"given":"Viktor","family":"Schell","sequence":"additional","affiliation":[{"name":"Inorganic Functional Materials, Institute for Materials Science, Faculty of Engineering, Kiel University, Kaiserstr. 2, 24143 Kiel, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8012-6794","authenticated-orcid":false,"given":"Andreas","family":"Bahr","sequence":"additional","affiliation":[{"name":"Sensor System Electronics, Institute of Electrical Engineering and Information Technology, Faculty of Engineering, Kiel University, Kaiserstr. 2, 24143 Kiel, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2314-5179","authenticated-orcid":false,"given":"Eckhard","family":"Quandt","sequence":"additional","affiliation":[{"name":"Inorganic Functional Materials, Institute for Materials Science, Faculty of Engineering, Kiel University, Kaiserstr. 2, 24143 Kiel, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7882-7396","authenticated-orcid":false,"given":"Reinhard","family":"Kn\u00f6chel","sequence":"additional","affiliation":[{"name":"Microwave Engineering, Institute of Electrical Engineering and Information Technology, Faculty of Engineering, Kiel University, Kaiserstr. 2, 24143 Kiel, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9352-2868","authenticated-orcid":false,"given":"Michael","family":"H\u00f6ft","sequence":"additional","affiliation":[{"name":"Microwave Engineering, Institute of Electrical Engineering and Information Technology, Faculty of Engineering, Kiel University, Kaiserstr. 2, 24143 Kiel, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0237-6450","authenticated-orcid":false,"given":"Jeffrey","family":"McCord","sequence":"additional","affiliation":[{"name":"Nanoscale Magnetic Materials and Magnetic Domains, Institute for Materials Science, Faculty of Engineering, Kiel University, Kaiserstr. 2, 24143 Kiel, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1063\/1.1754276","article-title":"Direct Piezoelectric Coupling to Surface Elastic Waves","volume":"7","author":"White","year":"1965","journal-title":"Appl. Phys. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1109\/58.238094","article-title":"SAW Devices for Consumer Communication Applications","volume":"40","author":"Ruppel","year":"1993","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"White, R.M. (1985, January 16\u201318). Surface Acoustic Wave Sensors. Proceedings of the 1985 IEEE Ultrasonics Symposium, San Francisco, CA, USA.","DOI":"10.1109\/ULTSYM.1985.198558"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"021001","DOI":"10.1088\/1674-4926\/37\/2\/021001","article-title":"Surface acoustic wave devices for sensor applications","volume":"37","author":"Liu","year":"2016","journal-title":"J. Semicond."},{"key":"ref_5","unstructured":"Fischerauer, G., Mauder, A., and M\u00fcller, R. (2008). Acoustic Wave Devices. Sensors Set, Wiley-VCH."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2566","DOI":"10.1109\/TUFFC.2021.3069382","article-title":"Sensing Mechanism of Surface Acoustic Wave Magnetic Field Sensors Based on Ferromagnetic Films","volume":"68","author":"Yang","year":"2021","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_7","unstructured":"Smole, P., Ruile, W., Korden, C., Ludwig, A., Quandt, E., Krassnitzer, S., and Pongratz, P. (2003, January 4\u20138). Magnetically tunable SAW-resonator. Proceedings of the 2003 IEEE International Frequency Control Symposium and PDA Exhibition Jointly with the 17th European Frequency and Time Forum, Tampa, FL, USA. Number 2."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1049\/el:19750465","article-title":"Magnetically tuned surface-acoustic-wave phase shifter","volume":"11","author":"Ganguly","year":"1975","journal-title":"Electron. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1794","DOI":"10.1063\/1.324869","article-title":"Variable delay lines using magnetostrictive metallic glass film overlays","volume":"49","author":"Forester","year":"1978","journal-title":"J. Appl. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Robbins, W.P., and Simpson, E.U. (1978, January 25\u201327). Surface Acoustic Wave Properties of RF Sputtered Nickel Films on Lithium Niobate. Proceedings of the 1978 Ultrasonics Symposium, Cherry Hill, NJ, USA.","DOI":"10.1109\/ULTSYM.1978.197122"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1410","DOI":"10.1109\/TMAG.1979.1060442","article-title":"Applications of amorphous magnetic-layers in surface-acoustic-wave devices","volume":"15","author":"Webb","year":"1979","journal-title":"IEEE Trans. Magn."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"916","DOI":"10.1109\/TMAG.1980.1060738","article-title":"Variable SAW delay line using amorphous TbFe2 film","volume":"16","author":"Yamaguchi","year":"1980","journal-title":"IEEE Trans. Magn."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3181","DOI":"10.1109\/TMAG.1981.1061730","article-title":"Magnetostrictive properties of sputtered Co-Cr film on surface acoustic wave","volume":"17","author":"Hashimoto","year":"1981","journal-title":"IEEE Trans. Magn."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Altan, B., and Robbins, W. (1981, January 14\u201316). Tunable ZnO-Si SAW Devices Using Magnetostrictive Thin Films. Proceedings of the 1981 IEEE Ultrasonics Symposium, Chicago, IL, USA.","DOI":"10.1109\/ULTSYM.1981.197631"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Hietala, A., and Robbins, W. (1982, January 27\u201329). Properties of Sputtered Tb-Fe for Tunable SAW Device Applications. Proceedings of the 1982 Ultrasonics Symposium, San Diego, CA, USA.","DOI":"10.1109\/ULTSYM.1982.197845"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1016\/0925-8388(94)90571-1","article-title":"Surface acoustic waves on thin films of giant magnetostrictive alloys","volume":"211\u2013212","author":"Koeninger","year":"1994","journal-title":"J. Alloys Compd."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4100","DOI":"10.1109\/TMAG.2012.2201928","article-title":"Surface Acoustic Wave Magnetic Sensor using Galfenol Thin Film","volume":"48","author":"Li","year":"2012","journal-title":"IEEE Trans. Magn."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"114101","DOI":"10.1063\/1.4868530","article-title":"Multilayer magnetostrictive structure based surface acoustic wave devices","volume":"104","author":"Zhou","year":"2014","journal-title":"Appl. Phys. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"870","DOI":"10.1016\/j.proeng.2015.08.743","article-title":"Experimental Study of Multilayer Piezo-magnetic SAW Delay Line for Magnetic Sensor","volume":"120","author":"Elhosni","year":"2015","journal-title":"Procedia Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1063\/1.351863","article-title":"Love-type surface-acoustic waves propagating in amorphous iron-boron films with multilayer structure","volume":"72","author":"Yokokawa","year":"1992","journal-title":"J. Appl. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1109\/T-UFFC.1987.26931","article-title":"Magnetic Field Sensors Based on SAW Propagation in Magnetic Films","volume":"34","author":"Hanna","year":"1987","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Mazzamurro, A., Talbi, A., Dusch, Y., Elmazria, O., Pernod, P., Matar, O.B., and Tiercelin, N. (2018). Highly Sensitive Surface Acoustic Wave Magnetic Field Sensor Using Multilayered TbCo2\/FeCo Thin Film. Proceedings, 2.","DOI":"10.3390\/proceedings2130902"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"105040","DOI":"10.1088\/1361-665X\/aae011","article-title":"Magnetostrictive effect in micro-dotted FeCo film coated surface acoustic wave devices","volume":"27","author":"Wang","year":"2018","journal-title":"Smart Mater. Struct."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.sna.2020.111998","article-title":"Sensitivity and Noise Analysis of SAW Magnetic Field Sensors with varied Magnetostrictive Layer Thicknesses","volume":"311","author":"Kittmann","year":"2020","journal-title":"Sens. Actuators A Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"044001","DOI":"10.1103\/PhysRevApplied.13.044001","article-title":"Giant Magnetoelastic Coupling in a Love Acoustic Waveguide Based on TbCo2\/FeCo Nanostructured Film on ST-Cut Quartz","volume":"13","author":"Mazzamurro","year":"2020","journal-title":"Phys. Rev. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"082402","DOI":"10.1063\/1.5044478","article-title":"Self-biased vector magnetic sensor based on a Love-type surface acoustic wave resonator","volume":"113","author":"Liu","year":"2018","journal-title":"Appl. Phys. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"045036","DOI":"10.1088\/1361-665X\/ab7857","article-title":"Temperature compensated magnetic field sensor based on love waves","volume":"29","author":"Mishra","year":"2020","journal-title":"Smart Mater. Struct."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"11292","DOI":"10.1109\/JSEN.2020.2998826","article-title":"Enhanced Performance Love Wave Magnetic Field Sensors with Temperature Compensation","volume":"20","author":"Yang","year":"2020","journal-title":"IEEE Sens. J."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"073503","DOI":"10.1063\/1.5140562","article-title":"Magnetic anisotropy controlled FeCoSiB thin films for surface acoustic wave magnetic field sensors","volume":"116","author":"Schell","year":"2020","journal-title":"Appl. Phys. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"193501","DOI":"10.1063\/1.4919897","article-title":"Ultra-sensitive Hall sensors based on graphene encapsulated in hexagonal boron nitride","volume":"106","author":"Dauber","year":"2015","journal-title":"Appl. Phys. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1109\/JSEN.2005.843889","article-title":"An AMR sensor-based measurement system for magnetoelectrical resistivity tomography","volume":"5","author":"Zimmermann","year":"2005","journal-title":"IEEE Sens. J."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"10Q107","DOI":"10.1063\/1.1861375","article-title":"Low-frequency noise measurements on commercial magnetoresistive magnetic field sensors","volume":"97","author":"Stutzke","year":"2005","journal-title":"J. Appl. Phys."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1109\/JSEN.2012.2216521","article-title":"Characterization of an optimized off-diagonal GMI-based magnetometer","volume":"13","author":"Dufay","year":"2013","journal-title":"IEEE Sens. J."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/S0924-4247(03)00094-3","article-title":"Advances in fluxgate sensors","volume":"106","author":"Ripka","year":"2003","journal-title":"Sens. Actuators A Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"8000","DOI":"10.1109\/JSEN.2019.2914965","article-title":"Noise Analysis and Comparison of Phase- and Frequency-Detecting Readout Systems: Application to SAW Delay Line Magnetic Field Sensor","volume":"19","author":"Durdaut","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"024018","DOI":"10.1103\/PhysRevApplied.13.024018","article-title":"Direct Link between Specific Magnetic Domain Activities and Magnetic Noise in Modulated Magnetoelectric Sensors","volume":"13","author":"Urs","year":"2020","journal-title":"Phys. Rev. Appl."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1038\/s41598-017-18441-4","article-title":"Wide Band Low Noise Love Wave Magnetic Field Sensor System","volume":"8","author":"Kittmann","year":"2018","journal-title":"Sci. Rep."},{"key":"ref_38","unstructured":"Besser, L., and Gilmore, R. (2003). Practical RF Circuit Design for Modern Wireless Systems, Artech House."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/S0924-4247(96)01311-8","article-title":"A study of Love-wave acoustic sensors","volume":"56","author":"Du","year":"1996","journal-title":"Sens. Actuators A Phys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"333001","DOI":"10.1088\/0022-3727\/48\/33\/333001","article-title":"Progress in magnetic domain observation by advanced magneto-optical microscopy","volume":"48","author":"McCord","year":"2015","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"055605","DOI":"10.1063\/1.4943760","article-title":"Advanced magneto-optical microscopy: Imaging from picoseconds to centimeters - imaging spin waves and temperature distributions (invited)","volume":"6","author":"Urs","year":"2016","journal-title":"AIP Adv."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"3319","DOI":"10.1002\/pssa.200405475","article-title":"Influence of strain on the high-frequency magnetic properties of FeCoBSi thin films","volume":"201","author":"Glasmachers","year":"2004","journal-title":"Phys. Status Solidi A"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1038\/nmeth.2089","article-title":"NIH Image to ImageJ: 25 years of image analysis","volume":"9","author":"Schneider","year":"2012","journal-title":"Nat. Methods"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"5491","DOI":"10.1063\/1.1562732","article-title":"Kerr observations of asymmetric magnetization reversal processes in CoFe\/IrMn bilayer systems","volume":"93","author":"McCord","year":"2003","journal-title":"J. Appl. Phys."},{"key":"ref_45","unstructured":"Durdaut, P., Wolframm, H., and H\u00f6ft, M. (2020). Low-Frequency Magnetic Noise in Statically-Driven Solenoid for Biasing Magnetic Field Sensors. arXiv."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Durdaut, P., H\u00f6ft, M., Friedt, J.M., and Rubiola, E. (2019). Equivalence of Open-Loop and Closed-Loop Operation of SAW Resonators and Delay Lines. Sensors, 19.","DOI":"10.3390\/s19010185"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/LSENS.2019.2943129","article-title":"Frequency Response of SAW Delay Line Magnetic Field\/Current Sensor","volume":"3","author":"Labrenz","year":"2019","journal-title":"IEEE Sens. Lett."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Rubiola, E. (2009). Phase Noise and Frequency Stability in Oscillators, Cambridge University Press.","DOI":"10.1017\/CBO9780511812798"},{"key":"ref_49","unstructured":"(2009). IEEE Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology\u2014Random Instabilities. IEEE Stand., 1139."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"2613","DOI":"10.1109\/TUFFC.2012.2502","article-title":"Phase Noise in RF and Microwave Amplifiers","volume":"59","author":"Boudot","year":"2012","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_51","unstructured":"Sears, F.W., and Salinger, G.L. (1975). Thermodynamics, Kinetic Theory, and Statistical Thermodynamics, Addison-Wesley Publishing Company. [3rd ed.]."},{"key":"ref_52","unstructured":"Durdaut, P. (2020). Ausleseverfahren und Rauschmodellierung f\u00fcr magnetoelektrische und magnetoelastische Sensorsysteme, Shaker."},{"key":"ref_53","unstructured":"Pozar, D.M. (2012). Microwave Engineering, Wiley. [4th ed.]."},{"key":"ref_54","unstructured":"Yao, D., and Sullivan, C.R. (2009, January 20\u201324). Effect of Capacitance on Eddy-Current loss in Multi-Layer Magnetic Films for MHz Magnetic Components. Proceedings of the 2009 IEEE Energy Conversion Congress and Exposition, San Jose, CA, USA."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1002\/andp.18652020906","article-title":"Ueber die Aenderungen des magnetischen Moments, welche der Zug und das Hindurchleiten eines galvanischen Stroms in einem Stabe von Stahl oder Eisen hervorbringen","volume":"202","author":"Villari","year":"1865","journal-title":"Ann. Der Phys. Und Chem."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"K155","DOI":"10.1002\/pssa.2210850256","article-title":"Electrical Resistivity of Amorphous Co-Rich FeCo-SiB Alloys","volume":"85","author":"Kohmoto","year":"1984","journal-title":"Phys. Status Solidi A"},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Jungerman, R., Baer, R., and Bray, R. (1985, January 16\u201318). Delay Dependence of Phase Noise in SAW Filters. Proceedings of the 1985 Ultrasonics Symposium, San Francisco, CA, USA.","DOI":"10.1109\/ULTSYM.1985.198514"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1109\/58.330266","article-title":"1\/f noise in etched groove surface acoustic wave (SAW) resonators","volume":"41","author":"Parker","year":"1994","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1109\/TUFFC.2002.1002464","article-title":"Surface-related phase noise in SAW resonators","volume":"49","author":"Enguang","year":"2002","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Parker, T. (1979, January 26\u201328). 1\/f Phase Noise in Quartz Delay Lines and Resonators. Proceedings of the 1979 Ultrasonics Symposium, New Orleans, LA, USA.","DOI":"10.1109\/ULTSYM.1979.197330"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1049\/el:19790211","article-title":"1\/f phase noise in quartz s.a.w. devices","volume":"15","author":"Parker","year":"1979","journal-title":"Electron. Lett."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"2445","DOI":"10.1063\/1.1480458","article-title":"Advanced interferometric phase and amplitude noise measurements","volume":"73","author":"Rubiola","year":"2002","journal-title":"Rev. Sci. Instrum."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"16156","DOI":"10.1103\/PhysRevB.48.16156","article-title":"Fluctuation-dissipation relation for giant magnetoresistive 1\/f noise","volume":"48","author":"Hardner","year":"1993","journal-title":"Phys. Rev. B"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"6152","DOI":"10.1063\/1.366533","article-title":"1\/f noise in anisotropic and giant magnetoresistive elements","volume":"82","author":"Schep","year":"1997","journal-title":"J. Appl. Phys."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"3289","DOI":"10.1103\/PhysRevLett.85.3289","article-title":"Low-Frequency Magnetic Noise in Micron-Scale Magnetic Tunnel Junctions","volume":"85","author":"Ingvarsson","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"5363","DOI":"10.1063\/1.353732","article-title":"Low temperature properties of soft magnetic materials: Magnetic viscosity and 1\/ f thermal noise","volume":"73","author":"Durin","year":"1993","journal-title":"J. Appl. Phys."},{"key":"ref_67","unstructured":"Briaire, J. (2000). 1\/f Noise in Permalloy. [Ph.D. Thesis, Eindhoven University of Technology]."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"084904","DOI":"10.1063\/1.2885711","article-title":"Calculation of magnetic field noise from high-permeability magnetic shields and conducting objects with simple geometry","volume":"103","author":"Lee","year":"2008","journal-title":"J. Appl. Phys."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"023394","DOI":"10.1103\/PhysRevResearch.2.023394","article-title":"Diamond magnetometer enhanced by ferrite flux concentrators","volume":"2","author":"Fescenko","year":"2020","journal-title":"Phys. Rev. Res."},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Schmalz, J., Kittmann, A., Durdaut, P., Spetzler, B., Faupel, F., H\u00f6ft, M., Quandt, E., and Gerken, M. (2020). Multi-Mode Love-Wave SAW Magnetic-Field Sensors. Sensors, 20.","DOI":"10.3390\/s20123421"},{"key":"ref_71","unstructured":"Boll, R. (1979). Soft Magnetic Materials: Fundamentals, Alloys, Properties, Products, Applications, the Vacuumschmelze Handbook, Vacuumschmelze GmbH Hanau, Siemens AG Munich, Heyden & Sons Ltd."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"1126","DOI":"10.1016\/S0304-8853(01)00979-9","article-title":"High-frequency magnetoelastic materials for remote-interrogated stress sensors","volume":"242\u2013245","author":"Ludwig","year":"2002","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"2703","DOI":"10.1109\/TMAG.2004.832139","article-title":"High-Frequency Properties of FeCoSiB Thin Films With Crossed Anisotropy","volume":"40","author":"Frommberger","year":"2004","journal-title":"IEEE Trans. Magn."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"3443","DOI":"10.1109\/TMAG.2004.836740","article-title":"A phenomenological theory of damping in ferromagnetic materials","volume":"40","author":"Gilbert","year":"2004","journal-title":"IEEE Trans. Magn."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"093911","DOI":"10.1063\/1.2365382","article-title":"Domain wall induced modes of high-frequency response in ferromagnetic elements","volume":"100","author":"Queitsch","year":"2006","journal-title":"J. Appl. Phys."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"054410","DOI":"10.1103\/PhysRevB.90.054410","article-title":"Picosecond wide-field magneto-optical imaging of magnetization dynamics of amorphous film elements","volume":"90","author":"Mozooni","year":"2014","journal-title":"Phys. Rev. B"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1080\/13642818208246438","article-title":"Factors affecting domain wall mobility in thin ferromagnetic metal films","volume":"46","author":"Aharoni","year":"1982","journal-title":"Philos. Mag. B"},{"key":"ref_78","doi-asserted-by":"crossref","unstructured":"Frommberger, M., Ludwig, A., Zanke, C., Sehrbrock, A., and Quandt, E. (August, January 27). High frequency magnetic properties of FeCoBSi\/SiO2 and (FeCo\/CoB)\/SiO2 multilayer thin films. Proceedings of the 2003 IEEE International Magnetics Conference, Rome, Italy.","DOI":"10.1109\/TMAG.2003.816045"},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"1347","DOI":"10.1109\/JMEMS.2020.3014402","article-title":"Fundamental Noise Limits and Sensitivity of Piezoelectrically Driven Magnetoelastic Cantilevers","volume":"29","author":"Durdaut","year":"2020","journal-title":"J. Microelectromech. Syst."},{"key":"ref_80","unstructured":"Bertotti, G. (1998). Hysteresis in Magnetism: For Physicists, Materials Scientists and Engineers, Academic Press."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/16\/5631\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:48:33Z","timestamp":1760165313000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/16\/5631"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,21]]},"references-count":80,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2021,8]]}},"alternative-id":["s21165631"],"URL":"https:\/\/doi.org\/10.3390\/s21165631","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,21]]}}}