320
F. Vanderveken et al.
In the second part of this chapter, the coupling between magnetic and elastic
waves, due to the direct and inverse magnetoelastic interactions, was described.
By combining the magnetoelastic interaction terms with the magnetodynamic and
the elastodynamic equations, the magnetoelastic eigensystem has been derived for
an arbitrary in-plane magnetization orientation. Within this framework, both the
exchange and dipolar interaction have been taken into account. Previous descriptions of magnetoelastic waves in infinitesimally thin films have been extended to
thin films of finite thickness by considering the appropriate dipolar field based on
the magnetostatic Green’s function. Two limiting cases, i.e. static magnetization perpendicular or parallel to the propagation direction, have been studied in more detail
and their dispersion relations and eigenstates have been mathematically and graphically described. In addition, several properties of magnetoelastic waves, such as the
energy transfer length and the magnetoelastic bandgap, and concepts, such as wave
anticrossings and polarization rotations, have been discussed in detail. The fundamental framework of magnetoelastic phenomena and waves described in this chapter
can be utilised for the theoretical description and modeling of the next generation of
magnetoelectric transducers. These transducers need to operate at GHz frequencies
and should be miniaturized to the nanometer scale. Despite the technical challenges,
such transducers show high potential for efficient energy transfer between the electric
and magnetic domains.
Acknowledgements This work has been supported by imec’s industrial affiliate program on
beyond-CMOS logic and by the European Union’s Horizon 2020 research and innovation program
within the FET-OPEN project CHIRON under grant agreement No. 801055. F.V. acknowledges
financial support from the Research Foundation – Flanders (FWO) through grant No. 1S05719N.
References
1. Z. Diao, Z. Li, S. Wang, Y. Ding, A. Panchula, E. Chen, L. Wang, Y. Huai, Spin-transfer torque
switching in magnetic tunnel junctions and spin-transfer torque random access memory. J.
Phys.-Condens. Matter 19, 165209 (2007)
2. M. Bapna, B. Parks, S.D. Oberdick, H. Almasi, W. Wang, S.A. Majetich, Spin-orbit-torque
switching in 20-nm perpendicular magnetic tunnel junctions. Phys. Rev. Appl. 10, 024013
(2018)
3. N.I. Polzikovaa, S.G. Alekseev, I.I. Pyataikin, I.M. Kotelyanskii, V.A. Luzanov, A.P. Orlov,
Acoustic spin pumping in magnetoelectric bulk acoustic wave resonator. AIP Adv. 6, 056306
(2016)
4. S. Cherepov, P.K. Amiri, J.G. Alzate, K. Wong, M. Lewis, P. Upadhyaya, J. Nath, M. Bao, A.
Bur, T. Wu, G.P. Carman, A. Khitun, K.L. Wang, Electric-field-induced spin wave generation
using multiferroic magnetoelectric cells. Appl. Phys. Lett. 104, 082403 (2014)
5. N.I. Polzikova, S.G. Alekseev, V.A. Luzanov, A.O. Raevskiy, Electroacoustic excitation of spin
waves and their detection due to the inverse spin hall effect. Phys. Solid State 60, 2211–2217
(2018)
6. M. Balinskiy, A.C. Chavez, A. Barra, H. Chiang, G.P. Carman, A. Khitun, Magnetoelectric
spin wave modulator based on synthetic multiferroic structure. Sci. Rep. 8, 10867 (2018)
7. H. Zhou, A. Talbi, N. Tiercelin, O. Bou Matar, Multilayer magnetostrictive structure based
surface acoustic wave devices. Appl. Phys. Lett. 104, 114101 (2014)
F. Vanderveken et al.
In the second part of this chapter, the coupling between magnetic and elastic
waves, due to the direct and inverse magnetoelastic interactions, was described.
By combining the magnetoelastic interaction terms with the magnetodynamic and
the elastodynamic equations, the magnetoelastic eigensystem has been derived for
an arbitrary in-plane magnetization orientation. Within this framework, both the
exchange and dipolar interaction have been taken into account. Previous descriptions of magnetoelastic waves in infinitesimally thin films have been extended to
thin films of finite thickness by considering the appropriate dipolar field based on
the magnetostatic Green’s function. Two limiting cases, i.e. static magnetization perpendicular or parallel to the propagation direction, have been studied in more detail
and their dispersion relations and eigenstates have been mathematically and graphically described. In addition, several properties of magnetoelastic waves, such as the
energy transfer length and the magnetoelastic bandgap, and concepts, such as wave
anticrossings and polarization rotations, have been discussed in detail. The fundamental framework of magnetoelastic phenomena and waves described in this chapter
can be utilised for the theoretical description and modeling of the next generation of
magnetoelectric transducers. These transducers need to operate at GHz frequencies
and should be miniaturized to the nanometer scale. Despite the technical challenges,
such transducers show high potential for efficient energy transfer between the electric
and magnetic domains.
Acknowledgements This work has been supported by imec’s industrial affiliate program on
beyond-CMOS logic and by the European Union’s Horizon 2020 research and innovation program
within the FET-OPEN project CHIRON under grant agreement No. 801055. F.V. acknowledges
financial support from the Research Foundation – Flanders (FWO) through grant No. 1S05719N.
References
1. Z. Diao, Z. Li, S. Wang, Y. Ding, A. Panchula, E. Chen, L. Wang, Y. Huai, Spin-transfer torque
switching in magnetic tunnel junctions and spin-transfer torque random access memory. J.
Phys.-Condens. Matter 19, 165209 (2007)
2. M. Bapna, B. Parks, S.D. Oberdick, H. Almasi, W. Wang, S.A. Majetich, Spin-orbit-torque
switching in 20-nm perpendicular magnetic tunnel junctions. Phys. Rev. Appl. 10, 024013
(2018)
3. N.I. Polzikovaa, S.G. Alekseev, I.I. Pyataikin, I.M. Kotelyanskii, V.A. Luzanov, A.P. Orlov,
Acoustic spin pumping in magnetoelectric bulk acoustic wave resonator. AIP Adv. 6, 056306
(2016)
4. S. Cherepov, P.K. Amiri, J.G. Alzate, K. Wong, M. Lewis, P. Upadhyaya, J. Nath, M. Bao, A.
Bur, T. Wu, G.P. Carman, A. Khitun, K.L. Wang, Electric-field-induced spin wave generation
using multiferroic magnetoelectric cells. Appl. Phys. Lett. 104, 082403 (2014)
5. N.I. Polzikova, S.G. Alekseev, V.A. Luzanov, A.O. Raevskiy, Electroacoustic excitation of spin
waves and their detection due to the inverse spin hall effect. Phys. Solid State 60, 2211–2217
(2018)
6. M. Balinskiy, A.C. Chavez, A. Barra, H. Chiang, G.P. Carman, A. Khitun, Magnetoelectric
spin wave modulator based on synthetic multiferroic structure. Sci. Rep. 8, 10867 (2018)
7. H. Zhou, A. Talbi, N. Tiercelin, O. Bou Matar, Multilayer magnetostrictive structure based
surface acoustic wave devices. Appl. Phys. Lett. 104, 114101 (2014)