Dilute magnetic semiconductors are attractive areas of specialty in semiconductor technology, material engineering, and condensed matter system. The model employed to manipulate the Hamiltonian of the system is the Heisenberg Model. By considering a cloud of electron gas and employing equation of state, the fractions ofdemagnetization factors were determined. Besides, the thermodynamic relation between magnetization and temperature is determined by analyzing the Helmholtz free energy.In this research,some of the pecular properties of magnetic semiconductor nanoparticles is reviewed. Most importantly, the ferromagnetic resonance is studied for medical imaging applications. ForFMR probes, the sample magnetization results from themagnetic moments of dipolar-coupled but unpairedelectrons. The relation between magnetization and magnetic flux density will be described by tuning magnetization, M to zero and then increasing it gradually. The resulting frequency versus magnetization curve is downward parabolic curves, resembling Gaussian distribution function which is sharper at tips. The side width sharpening is due to ferromagnetic spin confinement with increasing magnetic ion Mn²⁺ concentration. The basic parameters ascribing the resulting ferromagnetic resonance condition are investigated. By using the 3D exchange interaction model, the value of demagnetization factor that contributes to the formation of magnetization Peaks (0.1 & 0.9) is then determined. Furthermore, the angular dependence of ferromagnetic absorption frequency is investigated. It is expected that the ferromagnetic absorption frequency is directly proportional to the magnetic flux density, B.Fromferromagnetic resonance studies, the nature of magnetic property is studied in Zn_1−xMn_xO and Zn_xFe_2–xO₃nanoparticles. This property enables leveraging the significance of Zn_xFe_2–xO₃ andZn_1–xMn_xOnanoparticles in AI enhanced magnetic resonance imaging and immunotherapy.

Keywords: Ferromagnetic resonance, flux density, medical imaging, demagnetization factors, resonance frequency

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1. Shatnawi M, Alsmadi AM, Bsoul I, Salameh B, Mathai M, Alnawashi G, et al. Influence of Mn doping on the magnetic and optical properties of ZnO nanocrystalline particles. Results in Physics. 2016 Jan 1;6:1064–71.
2. Fischer P, Sanz-Hernández D, Streubel R, Fernández-Pacheco A. Launching a new dimension with 3D magnetic nanostructures. APL Materials. 2020 Jan 1;8(1).
3. Ochsenbein ST, Feng Y, Whitaker KM, Badaeva E, Liu WK, Li X, et al. Charge-controlled magnetism in colloidal doped semiconductor nanocrystals. Nature nanotechnology. 2009 Oct;4(10):681–7.
4. Nam-Trung N. Micro-magnetofluidics: interactions between magnetism and fluid flow on the microscale. Microfluidics and Nanofluidics. 2012;12(1–4):1–6.
5. Kittel C. Theory of the structure of ferromagnetic domains in films and small particles. Physical Review. 1946 Dec 1;70(11–12):965.
6. Coffey WT, Kalmykov YP. Thermal fluctuations of magnetic nanoparticles: Fifty years after Brown. J Appld Physc. 2012 Dec 15;112(12).
7. Benguettat-El Mokhtari I, Schmool DS. Ferromagnetic resonance in magnetic oxide nanoparticules: a short review of theory and experiment. Magnetochemistry. 2023 Jul 25;9(8):191.
8. Chen JQ, Chen C, Sun JJ, Zhang JW, Liu ZH, Qin L, et al. Linewidth measurement of a narrow-linewidth laser: principles, methods, and systems. Sensors. 2024 Jun 5;24(11):3656.
9. Sibera D, Jędrzejewski R, Mizeracki J, Presz A, Narkiewicz U, Łojkowski W. Synthesis and Characterization of ZnO Doped with Fe_2O_3-Hydrothermal Synthesis and Calcination Process. Acta Physica Polonica A. 2009 Dec;116(S).
10. Zhao MH, Wang ZL, Mao SX. Piezoelectric characterization of individual zinc oxide nanobelt probed by piezoresponse force microscope. Nano Letters. 2004 Apr 14;4(4):587–90.
11. Wu X, Wei Z, Zhang L, Wang X, Yang H, Jiang J. Optical and magnetic properties of Fe doped ZnO nanoparticles obtained by hydrothermal synthesis. J Nanomat. 2014;2014(1):792102.
12. Scherer C, Figueiredo Neto AM. Ferrofluids: properties and applications. Braziln J Physics. 2005;35:718–27.
13. Foti G, Longo C. Deep learning and AI in reducing magnetic resonance imaging scanning time: advantages and pitfalls in clinical practice. Polish J Radiolg. 2024 Sep 13;89:e443.
14. Hu Z, Song X, Ding L, Cai Y, Yu L, Zhang Let et al. Engineering Fe/Mn-doped zinc oxide nanosonosensitizers for ultrasound-activated and multiple ferroptosis-augmented nanodynamic tumor suppression. Materials Today Bio. 2022 Dec 1;16:100452.
15. Ventola CL. The nanomedicine revolution: part 1: emerging concepts. Pharmacy and Therapeutics. 2012 Sep;37(9):512.
16. Janisch R, Gopal P, Spaldin NA. Transition metal-doped TiO2 and ZnO—present status of the field. J Phys Condns Matter. 2005 Jun 24;17(27):R657.
17. Tognarelli JM, Dawood M, Shariff MI, Grover VP, Crossey MM, Cox IJ, et al. Magnetic resonance spectroscopy: principles and techniques: lessons for clinicians. J Clinical Experim Hepatolg. 2015 Dec 1;5(4):320–8.
18. Fischbach F, Bruhn H. Assessment of in vivo 1H magnetic resonance spectroscopy in the liver: a review. Liver Intl. 2008 Mar;28(3):297–307.
19. Bałanda M. AC susceptibility studies of phase transitions and magnetic relaxation: Conventional, molecular and low-dimensional magnets. Acta Physica Polonica A. 2013 Dec;124(6):964–76.
20. Pradhan AK, Hunter D, Zhang K, Dadson JB, Mohanty S, Williams TM, et al. Magnetic and spectroscopic characteristics of ZnMnO system. Applied Surface Science. 2005 Dec 15;252(5):1628–33.
21. Simpson DA, Ryan RG, Hall LT, Panchenko E, Drew SC, Petrou S, et al. Quantum Magne Resonc Microspy. arXiv preprint arXiv:1702.04418. 2017 Feb 14.
22. Sushkov AO, Lovchinsky I, Chisholm N, Walsworth RL, Park H, Lukin MD. Magnetic resonance detection of individual proton spins using quantum reporters. Physical Review Letters. 2014 Nov 7;113(19):197601.
23. Lee KW. Ferromagnetic and transport properties of Mn-doped ZnO. J Korean Phys Society. 2008 Jan;52(1):106–11.
24. Yuwita PE, Ardianti AD, Mas’udah KW. Structural, optical, and magnetic properties of Mn-doped ZnO nanoparticles synthesized by coprecipitation method. In: IOP Conference Series: Materials Science and Engineering. IOP Publishing. 2019 Apr 1;515(1):012065.
25. Park KH, YYS EK, Son LS, Oh SK, Yu SC, Kang HJ. Magnetic and structural properties of Mn: ZnO thin film grown on sapphire (0001) substrates by using pulsed laser deposition. J Korean Phys Soc. 2009 Dec 15;55(6):2685–8.
26. Sato K, Bergqvist L, Kudrnovský J, Dederichs PH, Eriksson O, Turek I, et al. First-principles theory of dilute magnetic semiconductors. Revw Modern Physc. 2010 Apr;82(2):1633–90.
27. Celinski Z, Urquhart KB, Heinrich B. Using ferromagnetic resonance to measure the magnetic moments of ultrathin films. J Mag Magnetic Matl. 1997 Feb 1;166(1–2):6–26.
28. Vegesna SV, Bhat VJ, Bürger D, Dellith J, Skorupa I, Schmidt OG, et al. Increased static dielectric constant in ZnMnO and ZnCoO thin films with bound magnetic polarons. Scientific Reports. 2020 Apr 21;10(1):6698.
29. Kupriyanova GS, Orlova AN. Simulation of the FMR Line Shape. Physics Procedia. 2016 Jan 1;82:32–7.
30. Kobelev AV, Shvachko YN, Ustinov VV. Angular dependence of the FMR linewidth and the anisotropy of the relaxation time in iron garnets. The Physc Metals Metallogphy. 2016 Jan;117:9–15.
31. Koshihara SY, Oiwa A, Hirasawa AM, Katsumoto S, Iye Y, Urano C, et al. Ferromagnetic order induced by photogenerated carriers in magnetic III–V semiconductor heterostructures of (In, Mn) As/GaSb. Physical Review Letters. 1997 Jun 16;78(24):4617.
32. Murzakhanov F, Mamin G, Voloshin A, Klimashina E, Putlyaev V, Doronin V, et al. Conventional electron paramagnetic resonance of Mn2+ in synthetic hydroxyapatite at different concentrations of the doped manganese. In: IOP Conference Series: Earth and Environmental Science. IOP Publishing. 2018 May 1;155(1):012006.
33. Liu Y, Shah S, Tan J. Computational modeling of nanoparticle targeted drug delivery. Rev Nanosci Nanotechnol. [Internet]. 2012;1:66–83.
34. Valezi DF, Vicentin BL, Mantovani AC, Di Mauro E. Applications of electron magnetic resonance in the study of soils, minerals, and iron oxides. In: Experimental methods in the physical sciences. Academic Press. 2019 Jan 1;50:203–217.
35. Hervé M, Peter M, Balashov T, Wulfhekel W. Towards laterally resolved ferromagnetic resonance with spin-polarized scanning tunneling microscopy. Nanomaterials. 2019 May 31;9(6):827.
36. Dobosz B, Krzyminiewski R, Kurczewska J, Schroeder G. The influence of surface modification, coating agents and pH value of aqueous solutions on physical properties of magnetite nanoparticles investigated by ESR method. J Mag Magnetic Matl. 2017 May 1;429:203–10.

Dilute magnetic semiconductors are attractive areas of specialty in semiconductor technology, material engineering, and condensed matter system. The model employed to manipulate the Hamiltonian of the system is the Heisenberg Model. By considering a cloud of electron gas and employing equation of state, the fractions ofdemagnetization factors were determined. Besides, the thermodynamic relation between magnetization and temperature is determined by analyzing the Helmholtz free energy.In this research,some of the pecular properties of magnetic semiconductor nanoparticles is reviewed. Most importantly, the ferromagnetic resonance is studied for medical imaging applications. ForFMR probes, the sample magnetization results from themagnetic moments of dipolar-coupled but unpairedelectrons. The relation between magnetization and magnetic flux density will be described by tuning magnetization, M to zero and then increasing it gradually. The resulting frequency versus magnetization curve is downward parabolic curves, resembling Gaussian distribution function which is sharper at tips. The side width sharpening is due to ferromagnetic spin confinement with increasing magnetic ion Mn²⁺ concentration. The basic parameters ascribing the resulting ferromagnetic resonance condition are investigated. By using the 3D exchange interaction model, the value of demagnetization factor that contributes to the formation of magnetization Peaks (0.1 & 0.9) is then determined. Furthermore, the angular dependence of ferromagnetic absorption frequency is investigated. It is expected that the ferromagnetic absorption frequency is directly proportional to the magnetic flux density, B.Fromferromagnetic resonance studies, the nature of magnetic property is studied in Zn_1−xMn_xO and Zn_xFe_2–xO₃nanoparticles. This property enables leveraging the significance of Zn_xFe_2–xO₃ andZn_1–xMn_xOnanoparticles in AI enhanced magnetic resonance imaging and immunotherapy.

Keywords: Ferromagnetic resonance, flux density, medical imaging, demagnetization factors, resonance frequency

🔒 This is a subscription article

Full text is available to subscribers and institutional members. Please choose an option below to access it.

1. Shatnawi M, Alsmadi AM, Bsoul I, Salameh B, Mathai M, Alnawashi G, et al. Influence of Mn doping on the magnetic and optical properties of ZnO nanocrystalline particles. Results in Physics. 2016 Jan 1;6:1064–71.
2. Fischer P, Sanz-Hernández D, Streubel R, Fernández-Pacheco A. Launching a new dimension with 3D magnetic nanostructures. APL Materials. 2020 Jan 1;8(1).
3. Ochsenbein ST, Feng Y, Whitaker KM, Badaeva E, Liu WK, Li X, et al. Charge-controlled magnetism in colloidal doped semiconductor nanocrystals. Nature nanotechnology. 2009 Oct;4(10):681–7.
4. Nam-Trung N. Micro-magnetofluidics: interactions between magnetism and fluid flow on the microscale. Microfluidics and Nanofluidics. 2012;12(1–4):1–6.
5. Kittel C. Theory of the structure of ferromagnetic domains in films and small particles. Physical Review. 1946 Dec 1;70(11–12):965.
6. Coffey WT, Kalmykov YP. Thermal fluctuations of magnetic nanoparticles: Fifty years after Brown. J Appld Physc. 2012 Dec 15;112(12).
7. Benguettat-El Mokhtari I, Schmool DS. Ferromagnetic resonance in magnetic oxide nanoparticules: a short review of theory and experiment. Magnetochemistry. 2023 Jul 25;9(8):191.
8. Chen JQ, Chen C, Sun JJ, Zhang JW, Liu ZH, Qin L, et al. Linewidth measurement of a narrow-linewidth laser: principles, methods, and systems. Sensors. 2024 Jun 5;24(11):3656.
9. Sibera D, Jędrzejewski R, Mizeracki J, Presz A, Narkiewicz U, Łojkowski W. Synthesis and Characterization of ZnO Doped with Fe_2O_3-Hydrothermal Synthesis and Calcination Process. Acta Physica Polonica A. 2009 Dec;116(S).
10. Zhao MH, Wang ZL, Mao SX. Piezoelectric characterization of individual zinc oxide nanobelt probed by piezoresponse force microscope. Nano Letters. 2004 Apr 14;4(4):587–90.
11. Wu X, Wei Z, Zhang L, Wang X, Yang H, Jiang J. Optical and magnetic properties of Fe doped ZnO nanoparticles obtained by hydrothermal synthesis. J Nanomat. 2014;2014(1):792102.
12. Scherer C, Figueiredo Neto AM. Ferrofluids: properties and applications. Braziln J Physics. 2005;35:718–27.
13. Foti G, Longo C. Deep learning and AI in reducing magnetic resonance imaging scanning time: advantages and pitfalls in clinical practice. Polish J Radiolg. 2024 Sep 13;89:e443.
14. Hu Z, Song X, Ding L, Cai Y, Yu L, Zhang Let et al. Engineering Fe/Mn-doped zinc oxide nanosonosensitizers for ultrasound-activated and multiple ferroptosis-augmented nanodynamic tumor suppression. Materials Today Bio. 2022 Dec 1;16:100452.
15. Ventola CL. The nanomedicine revolution: part 1: emerging concepts. Pharmacy and Therapeutics. 2012 Sep;37(9):512.
16. Janisch R, Gopal P, Spaldin NA. Transition metal-doped TiO2 and ZnO—present status of the field. J Phys Condns Matter. 2005 Jun 24;17(27):R657.
17. Tognarelli JM, Dawood M, Shariff MI, Grover VP, Crossey MM, Cox IJ, et al. Magnetic resonance spectroscopy: principles and techniques: lessons for clinicians. J Clinical Experim Hepatolg. 2015 Dec 1;5(4):320–8.
18. Fischbach F, Bruhn H. Assessment of in vivo 1H magnetic resonance spectroscopy in the liver: a review. Liver Intl. 2008 Mar;28(3):297–307.
19. Bałanda M. AC susceptibility studies of phase transitions and magnetic relaxation: Conventional, molecular and low-dimensional magnets. Acta Physica Polonica A. 2013 Dec;124(6):964–76.
20. Pradhan AK, Hunter D, Zhang K, Dadson JB, Mohanty S, Williams TM, et al. Magnetic and spectroscopic characteristics of ZnMnO system. Applied Surface Science. 2005 Dec 15;252(5):1628–33.
21. Simpson DA, Ryan RG, Hall LT, Panchenko E, Drew SC, Petrou S, et al. Quantum Magne Resonc Microspy. arXiv preprint arXiv:1702.04418. 2017 Feb 14.
22. Sushkov AO, Lovchinsky I, Chisholm N, Walsworth RL, Park H, Lukin MD. Magnetic resonance detection of individual proton spins using quantum reporters. Physical Review Letters. 2014 Nov 7;113(19):197601.
23. Lee KW. Ferromagnetic and transport properties of Mn-doped ZnO. J Korean Phys Society. 2008 Jan;52(1):106–11.
24. Yuwita PE, Ardianti AD, Mas’udah KW. Structural, optical, and magnetic properties of Mn-doped ZnO nanoparticles synthesized by coprecipitation method. In: IOP Conference Series: Materials Science and Engineering. IOP Publishing. 2019 Apr 1;515(1):012065.
25. Park KH, YYS EK, Son LS, Oh SK, Yu SC, Kang HJ. Magnetic and structural properties of Mn: ZnO thin film grown on sapphire (0001) substrates by using pulsed laser deposition. J Korean Phys Soc. 2009 Dec 15;55(6):2685–8.
26. Sato K, Bergqvist L, Kudrnovský J, Dederichs PH, Eriksson O, Turek I, et al. First-principles theory of dilute magnetic semiconductors. Revw Modern Physc. 2010 Apr;82(2):1633–90.
27. Celinski Z, Urquhart KB, Heinrich B. Using ferromagnetic resonance to measure the magnetic moments of ultrathin films. J Mag Magnetic Matl. 1997 Feb 1;166(1–2):6–26.
28. Vegesna SV, Bhat VJ, Bürger D, Dellith J, Skorupa I, Schmidt OG, et al. Increased static dielectric constant in ZnMnO and ZnCoO thin films with bound magnetic polarons. Scientific Reports. 2020 Apr 21;10(1):6698.
29. Kupriyanova GS, Orlova AN. Simulation of the FMR Line Shape. Physics Procedia. 2016 Jan 1;82:32–7.
30. Kobelev AV, Shvachko YN, Ustinov VV. Angular dependence of the FMR linewidth and the anisotropy of the relaxation time in iron garnets. The Physc Metals Metallogphy. 2016 Jan;117:9–15.
31. Koshihara SY, Oiwa A, Hirasawa AM, Katsumoto S, Iye Y, Urano C, et al. Ferromagnetic order induced by photogenerated carriers in magnetic III–V semiconductor heterostructures of (In, Mn) As/GaSb. Physical Review Letters. 1997 Jun 16;78(24):4617.
32. Murzakhanov F, Mamin G, Voloshin A, Klimashina E, Putlyaev V, Doronin V, et al. Conventional electron paramagnetic resonance of Mn2+ in synthetic hydroxyapatite at different concentrations of the doped manganese. In: IOP Conference Series: Earth and Environmental Science. IOP Publishing. 2018 May 1;155(1):012006.
33. Liu Y, Shah S, Tan J. Computational modeling of nanoparticle targeted drug delivery. Rev Nanosci Nanotechnol. [Internet]. 2012;1:66–83.
34. Valezi DF, Vicentin BL, Mantovani AC, Di Mauro E. Applications of electron magnetic resonance in the study of soils, minerals, and iron oxides. In: Experimental methods in the physical sciences. Academic Press. 2019 Jan 1;50:203–217.
35. Hervé M, Peter M, Balashov T, Wulfhekel W. Towards laterally resolved ferromagnetic resonance with spin-polarized scanning tunneling microscopy. Nanomaterials. 2019 May 31;9(6):827.
36. Dobosz B, Krzyminiewski R, Kurczewska J, Schroeder G. The influence of surface modification, coating agents and pH value of aqueous solutions on physical properties of magnetite nanoparticles investigated by ESR method. J Mag Magnetic Matl. 2017 May 1;429:203–10.