The damping of a ferromagnetic system, ie the energy dissipation of the precessing moments, can be roughly categorized in Gilbert and non-Gilbert type damping. The Gilbert-type damping, introduced phenomenologically by Landau and Lifshiftz, is known as LL damping:
Another form of this damping, that better reflects the physics, was introduced by Gilbert [Gilbert] as:
Both forms are equivalent when the damping parameters are renormalized. Gilbert-type damping can be derived from the ansatz of a viscous damping in the ferromagnetic system. It grows linear with frequency and describes the damping due to the spin-flip-on-electron and magnon-phonon processes.
In metals, the spin-flip process scales with the squared spin-orbit couling constant which can be manipulated by changing the effective atomic number Z, eg by doping a ferromagnet with non-magnetic material [Scheck].
The non-Gilbert type damping is diverse. A significant contribution is due to the transfer of energy from one magnon mode to another -- the multi-magnon processes. In thin films the dominating process is the 2-magnon process, where the energy of the main uniform mode dissipates into a non-uniform, degenerate mode [Barsukov2010]. The multimagnon processes depend on the magnonic dispersion and the scattering potential. The first is controlled by the exchange interaction, magnetic anisotorpy and geometry of the sample. The scattering potential is defined by the defects [Barsukov2010]. For instance, in epitaxial cubic (001)-films the crystalline defects are oriented along the <100> and <110> in-plane axes. The 2-magnon damping is enhanced in the direction perpendicular to the defects. This leads to an increase of damping with four-fold symmetry in the film plane [Barsukov2012, Zakeri2007].
The scattering potential can also be artificially introduced to the sample. For instance, the oblique deposition of a film can create periodic defects, such as shown below. The scattering potential can also be induced by creating defects by sputtering, ion milling, ion implantation etc in combination with e-beam lithography.
Fig.: Topography of a film prepared using oblique deposition method. The oblique material beam creates stripe-like defects perpendicular to the beam's direction. This phenomenon is general as shown in (b): The wind carries and deposits sand grains which build stripe-like waves perpendicular to the wind direction. [(a) is adapted from Bubendorff et al., Europhys. Lett. 75(1), 119 (2006); (b) Playa del Ingles, Tenerife by IB.]
The 2-magnon scattering shows non-linear dependence on the frequency -- an arcsin-like dependence is typical. However, strongly periodic defects make the scattering process resonant with respect to the defects periodicity and the wave vector of the magnons involved. This leads to a more complicated behavior with resonant increase of the damping at specific frequencies [Barsukov2011].
[Gilbert] T.L. Gilbert, IEEE Trans. Magn. 40(6), 3443 (2004)
[Scheck] C. Scheck, L. Cheng, I. Barsukov, Z. Frait, and W.E. Bailey, Phys. Rev. Lett. 98, 117601 (2007), DOI: 10.1103/PhysRevLett.98.117601
[Barsukov2010] I. Barsukov, R. Meckenstock, J. Lindner, M. Möller, C. Hassel, O. Posth, M. Farle
IEEE Trans. Magn. 46, 2252 (2010), DOI: 10.1109/TMAG.2010.2044482
[Barsukov2012] I. Barsukov, P. Landeros, R. Meckenstock, J. Lindner, D. Spoddig, Zi-An Li, B. Krumme, H. Wende, D.L. Mills, and M. Farle, Phys. Rev. B 85, 014420 (2012), DOI: 10.1103/PhysRevB.85.014420
[Zakeri2007] Kh. Zakeri, J. Lindner, I. Barsukov, R. Meckenstock, M. Farle, U. von Hörsten, H. Wende, W. Keune, J. Rocker, S. S. Kalarickal, K. Lenz, W. Kuch, K. Baberschke and Z. Frait, Phys. Rev. B 76, 104416 (2007), DOI: 10.1103/PhysRevB.76.104416
[Barsukov2011] I. Barsukov, F. M. Römer, R. Meckenstock, K. Lenz, J. Lindner, S. Hemken to Krax, A. Banholzer, M. Körner, J. Grebing, J. Fassbender, and M. Farle, Phys. Rev. B 84, 140410(R) (2011), DOI: 10.1103/PhysRevB.84.140410
Magnetic Nanoparticles from Aqueous Solution
NiOx-passivated nickel nanoparticles were grown on small platinum seeds, which served as catalysts for the reduction of Ni2+ with hydrazine, in aqueous solutions of the cationic surfactant cetyltrimethylammonium bromide [Grzelczak]. Structural characterization shows the polycrystaline structure of the particles and the presence of metallic Ni, as well as NiOx and Ni(OH)2. The magnetic properties were studied by SQUID and FMR. An induced magnetic moment on the Pt seed has been observed by XMCD.
[Grzelczak] Marek Grzelczak, Jorge Pérez-Juste, Benito Rodríguez-González, Marina Spasova, Igor Barsukov, Michael Farle, and Luis M. Liz-Marzán, Chem. Mater. 20 (16), 5399 (2008), DOI: 10.1021/cm800665s
Ferromagnetic Resonance is a powerful technique for studying static and dynamic magnetic properties of ferromagnets. Combining this spectroscopy technique with the scanning microscopy allows for investigations on the nanometer scale. The scanning technique was realized by a thermal scanning microscop. It is capable to directly measure the heat locally generated by the ferromagnetic resonance in the sample.
Fig.: The setup is divided in two parts: the conventional FMR and the microscopy (in the red box). The conventional FMR consists of a microwave cavity placed between the pole pieces of an electromagnet.
[SThM2006] R. Meckenstock, I. Barsukov, C. Bircan, A. Remhoff, D. Dietzel, D. Spoddig
J. Appl. Phys. 99, 08C706 (2006), DOI: 10.1063/1.2171929
[SThMFMR2007] R. Meckenstock, I. Barsukov, O. Posth, J. Lindner, A. Butko, and D. Spoddig
Appl. Phys. Lett. 91, 142507 (2007), DOI: 10.1063/1.2794026
Spin-Torque Ferromagnetic Resonance with Field Modulation
This technique gives great improvement in sensitivity over the conventional ST-FMR measurements and circumvents the drawbacks of the conventional ST-FMR. Application of this technique to nanoscale magnetic tunnel junctions (MTJs) gives reliable information on magnetization dynamics for an arbitrary magnetic state of the MTJ, including the collinear conguration. The high sensitivity of the technique allows to measure the entire spectrum of low-frequency standing spin waves in MTJs in great detail.
Fig.: Spin torque driven FMR spectra of a 170 x 90 nm^2 elliptical MTJ nanopillar with external magnetic field of 30 mT in easy axis: (a) with amplitude modulation (conventional ST-FMR). (b) Field modulation removes large frequency-dependent background of non-magnetic origin and exposes several spin wave eigenmodes of the MTJ.
[STT-FMR2015] A. M. Gonçalves, I. Barsukov, Y.-J. Chen, L. Yang, J. A. Katine, and I. N. Krivorotov
Appl. Phys. Lett. 103, 172406 (2013), DOI:10.1063/1.4826927
Magnetic Phase Transitions in CoFeB/MgO based multilayers and MTJs
CoFeB alloys are of particular importance for spintronics applications, widely used in Magnetic Tunnel Junctions. Ultra-thin layers of CoFeB/MgO exhibit strong perpendicular magnetic anisotropy (PMA). We have studied PMA in the temperature range of 4-300 K and found that the anisotorpy field depends linearly on the temperature. Its thickness dependence indicates non-interfacial contributions to PMA. Easy-cone anisotropy is found in a narrow thickness range throughout the entire temperature range. Surprisingly, the anisotropy is found to vary with the magnetitude of the external magnetic field, suggesting the presence of an interfacial anti-ferromagnetic layer. By conducting magnetoresistance measurements and magnetometry in thin films and MTJ nanopillars, we confirm the presence of such interfacial layer and identify it to likely be an Iron oxide undergoing Morin-type transition at about 150 K.
Temperature-dependent easy-cone magnetic anisotropy in CoFeB
Yu Fu, I. Barsukov, Jing Li, A. M. Gonçalves, C. C. Kuo, M. Farle, I. N. Krivorotov
Appl. Phys. Lett. accepted (2016)
Magnetic phase transitions in Ta/CoFeB/MgO multilayers
I. Barsukov, Yu Fu, C. Safranski, Y.-J. Chen, B. Youngblood, A. M. Gonçalves, M. Spasova, M. Farle, J. A. Katine, C. C. Kuo, I. N. Krivorotov
Appl. Phys. Lett. 106, 192407 (2015), http://dx.doi.org/10.1063/1.4921306
Field-dependent perpendicular magnetic anisotropy in CoFeB thin films
I. Barsukov, Yu Fu, A. M. Gonçalves, M. Spasova, M. Farle, L. C. Sampaio, R. E. Arias, I. N. Krivorotov
Appl. Phys. Lett. 105, 152403 (2014), http://dx.doi.org/10.1063/1.4897939