Seminaria

Dnia 2023-01-31 o godzinie 13:15 w sali 2011 Wydziału Fizyki odbędzie się wykład, na którym  dr hab. Marek Cinal z Instytutu Chemii Fizycznej PAN w Warszawie, wygłosi wykład pt:

Magnetic anisotropy and Gilbert damping in layered systems – calculation methods, spatial breakdown and quantum oscillations

Serdecznie zapraszamy

Andrzej Maziewski

Jerzy Przeszowski

„Magnetic anisotropy and Gilbert damping in layered systems – calculation methods, spatial breakdown and quantum oscillations”

dr hab. Marek Cinal
Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland

Magnetic anisotropy is a property of magnetic materials of fundamental importance for their magnetic structure, magnetization dynamics and applications such as high-density magnetic recording. In particular, magnetic tunnel junctions with perpendicular magnetic anisotropy (PMA) can be used as cells of non-volatile magnetic random access memory (MRAM) where the magnetization is switched with spin-transfer torque (STT) due to spin-polarized electric current flowing through the junction. Even faster and denser MRAMs are now being developed that, instead of using STT, take advantage of the spin-orbit torque (SOT) which comes from the spin current resulting from the spin Hall and Rashba effects due to in-plane current in a ferromagnet/heavy metal bilayer with strong spin-orbit coupling (SOC). The efficiency of such devices also strongly depends on the Gilbert damping which describes spin relaxation in ferromagnetic metals and thus determines how fast the reversal of magnetization takes place.

The magnetic anisotropy originates from two interactions. The magnetic dipole-dipole interaction gives rise to the energy dependence on the sample geometry (shape anisotropy) and, for films, promotes in-plane magnetization. The other term is magnetocrystalline anisotropy (MCA) which results from the SOC and is enhanced by the interfaces present in magnetic layered structures which can lead to PMA in ultrathin films, like Co/Pt and Co/Pd bilayers. The SOC is also the origin of the Gilbert damping so both the MCA and the Gilbert damping strongly depend on the electronic structure of magnetic materials.

The MCA energy, orbital magnetic moment and the Gilbert damping constant are investigated for fcc Co/NM layered systems including nonmagnetic transition metals NM= Cu, Ag, Au, Pd and Pt. The calculation methods, mutual relations, spatial breakdowns and oscillatory thickness dependences are examined [1]. In addition, magnetic anisotropy of ferromagnetic films with stepped surface and the resulting tilted magnetization [2] are shortly discussed while possible application of magnetization tilting for field-free switching in SOTMRAM devices is indicated.

It is shown [1] that the inclusion of the usually neglected intraband term in the second-order perturbation theory (PT) expression for the MCA energy [3] is vital as this term is finite for systems without the inversion symmetry and comparable to the interband term. Further, the validity of the PT formula for systems with strong SOC, like the Co/Pt bilayer, is examined. The oscillations of MCA energy and the orbital moment are discussed and quantum-well states responsible for these oscillations are identified. The orbital moment of Co is found to oscillate with different periods and amplitudes for different magnetization directions due to the specific symmetry of the involved d orbitals. The Bruno relation [3] between the MCA energy and the orbital moment anisotropy (OMA) is found to well reproduce the oscillations of the MCA energy versus the Co thickness but fail to approximate its mean value [1]. It is also shown that the spatial breakdown of the MCA energy into atomic layer contributions is not unique as two distinct methods lead to significantly different spatial decompositions. In addition, no clear correlation between the layer MCA and OMA terms, like a local Bruno relation, is found.

The Gilbert damping constant is calculated in the torque-correlation model [4] and the results for Co films as well as Co/NM bilayers and Co/NM1/NM2 trilayers are presented. The nonlocal origin of the Gilbert damping is discussed and visualized with its atomic layer contributions [5,6]. A remarkable enhancement of the damping constant in Co/NM1/NM2 trilayers is obtained due to adding the caps NM2=Pd, Pt, and it decays with the thickness of the spacers NM1=Cu, Ag, Au in agreement with experiment. It is shown that magnetization in Co is damped remotely by the strong SOC in NM2 via the quantum states that span over the whole trilayer.

[1] M. Cinal, Phys. Rev. B 105, 104403 (2022).

[2] M. Dąbrowski, M. Cinal, A.K. Schmid, J. Kirschner, and M. Przybylski, Phys. Rev. B 99, 184420 (2019).

[3] P. Bruno, Phys. Rev. B 39, 865 (1989).

[4] V. Kamberský, Czech. J. Phys. B 26, 1366 (1976).

[5] E. Barati, M. Cinal, D. M. Edwards, and A. Umerski, Phys. Rev. B 90, 014420 (2014).

[6] E. Barati and M. Cinal, Phys. Rev. B 91, 214435 (2015); 95, 134440 (2017).