2022 Abstracts Orbitronics

Peter OPPENEER

Spin-orbit torques (SOTs) in heavy-metal/ferromagnetic heterostructures have become a promising tool to achieve efficiently magnetization reversal using electrical current pulses [1]. SOTs have also been instrumental for current-induced magnetization switching in antiferromagnets (AFMs) with reduced symmetry [2]. It is generally accepted that the microscopic origin of SOTs is the relativistic spin-orbit coupling (SOC) of the heavy metal that provides charge-to-spin conversion, but the precise microscopic origins of SOTs are still being debated, with the spin Hall effect (SHE) due to nonlocal spin currents and the spin Rashba-Edelstein effect (SREE) due to local spin polarization at the interface being the primary candidates.
We employ first-principles calculations to investigate computationally the electrically induced out-of-equilibrium spin and orbital polarizations in symmetry-broken anti-ferromagnets CuMnAs and Mn2Au [3] as well as in Pt/3d-metal (Co, Ni, Cu) bilayer films and pure 3d-metal films [4]. We use linear-response theory to compute the full spin and orbital conductivity tensors and the induced spin and orbital polarizations. For the symmetry-broken AFMs we find that the dominant effect is the locally induced orbital polarization, i.e., an orbital Rashba-Edelstein effect (OREE) that is about 50x larger than the SREE. The OREE moreover does not require SOC and, because of symmetry, the induced orbital polarizations always exhibit (staggered) Rashba symmetry whereas the SREE, generated from the OREE through SOC, can exhibit Dresselhaus or Rashba symmetry.
For the Pt/3d-metal bilayer systems we compute similarly that the electrically induced transverse orbital polarization is exceedingly larger (~100 x) than the induced spin polarization and present even without SOC, in contrast to the spin polarization. This pin-points that also in the Pt/3d-metal bilayers the electrically induced orbital polarization due to the OREE and the orbital Hall effect (OHE) [5] are the primary responses, whereas the SREE and SHE are induced from these through SOC. We further compute atom-resolved response quantities that allow us to identify the induced spin-polarizations that lead to fieldlike (FL) SOTs and dampinglike (DL) SOTs and compare their relative magnitude, dependence on the magnetization direction, as well as their Pt-layer thickness dependence. We find that the DL SOT component is due to the magnetic SHE at the Pt/Co and Pt/Ni interfaces. Lastly, we calculate the electrically induced orbital polarization in non-magnetic metal films and show that it has a profile across the film that is distinctly different from that of the induced spin polarization.

References
[1] I.M. Miron, K. Garello, G. Gaudin, et al., Nature 476, 189 (2011)
[2] P. Wadley, B. Howells, J. Železný, et al., Science 351, 587 (2016)
[3] L. Salemi, M. Berritta, et al., Nat. Commun. 10, 5381 (2019)
[4] L. Salemi, M. Berritta, and P.M. Oppeneer, Phys. Rev. Mater. 5, 074407 (2021)
[5] D. Go, D. Jo, Ch. Kim, and H.-W. Lee, Phys. Rev. Lett. 121, 086602 (2018)

Ivo SOUZA

We express the Kubo formula for the spatially-dispersive optical conductivity in terms of three types of matrix elements between valence and conduction Bloch states: the first is the off-diagonal Berry connection matrix which, as is well known, describes electric-dipole interband transitions. The other two describe magnetic-dipole and electric-quadrupole transitions; they are, respectively, interband generalizations of the intrinsic orbital moment of a wavepacket [1], and of the quantum metric tensor [2]. This form of the spatially-dispersive conductivity is physically transparent due to the gauge invariance and origin independence of its individual terms; this is in contrast to the standard quantum multipole theory [3], where the individual terms are origin dependent and limited to bounded samples. The relation between the two formulations is established by considering the limit of a crystal composed of nonoverlapping molecules. Numerical results are presented for optical rotation and nonreciprocal directional dichroism in a tight-binding model of a chiral trigonal crystal.

[1] D. Xiao, M. C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys. 82, 1959 (2010)
[2] R. Cheng, Quantum Geometric Tensor (Fubini-Study Metric) in Simple Quantum System: A pedagogical Introduction, arXiv:1012.1337v2 (2013)
[3] R. E. Raab and O. L. De Lange, Multipole theory in electromagnetism: classical, quantum, and symmetry aspects, with applications, Oxford University Press (2004)

David VANDERBILT

The so-called "modern theory" of orbital magnetization was developed some 15-20 years ago. It takes the form of a reciprocal-space integral involving Berry curvatures and related quantities. A derivation based on semiclassical electron dynamics and another based on the Wannier representation led to identical expressions that could be implemented in modern first-principles electronic structure codes. In the first part of this talk, I will give a brief pedagogical review of these developments.
I will then discuss recent work in which we consider a crystal whose bulk magnetization vanishes by symmetry, but whose surface magnetization does not. An interesting question, then, is whether the surface orbital magnetization is well defined, and if so, how it can be calculated. Recently, Bianco and Resta derived a formulation of the orbital magnetization in terms of a local marker which, when integrated over the unit cell, correctly returns the bulk orbital magnetization. I will discuss whether, and under what conditions, a surface orbital magnetization is well defined, and point out ambiguities in the formulation in terms of a local marker. Calculations of surface magnetization and the resulting hinge currents will be illustrated in the context of tight-binding model Hamiltonians. I will also point out connections to the theory of the axion magnetoelectric coupling and surface anomalous Hall conductivity.

Sara VAROTTO

Spin-charge interconversion represents a promising viable solution for energy efficient electronics beyond CMOS architecture [1]. Broken inversion symmetry enables efficient and electrically tunable conversions. However, the electric field control remains volatile in semiconductors. This brought interest in ferroelectric Rashba semiconductors (FERSC), where semiconductivity, large spin–orbit coupling and non-volatility are intertwined.
The father compound of FERSCs is germanium telluride (GeTe), a CMOS-compatible semiconductor characterized by a giant Rashba-type spin-orbit coupling at room temperature, arising from the symmetry breaking induced by ferroelectric displacement. Importantly, calculations revealed that the spin orientation of each Rashba sub-band is inverted upon ferroelectric polarization reversal. We demonstrated such link in epitaxial GeTe(111) thin films on silicon, by our spin and angle resolved photoemission measurements on two surfaces with inward or outward spontaneous polarization [2]. Thus, FERSCs allow for ferroelectric control of the spin-resolved band structure in semiconductors, with intriguing implications on the spin transport properties.
Here we demonstrate the non-volatile, ferroelectric control of spin-to-charge conversion at room temperature in GeTe(111)//Si films [3]. First, we prove the feasibility of the ferroelectric switching, despite the high density of free carriers. The switching is induced by voltage pulses applied to a gate electrode, while the readout of the written state is performed by electro-resistive measurements of the GeTe/metal junction. By gate dependent spin-pumping at ferromagnetic resonance, we observe a spin-to-charge conversion as efficient as in Pt, and we show that its sign is switched for two opposite ferroelectric states. Density functional theory calculations reveal the consistency of these observation with spin Hall effect in thin GeTe films.
Our results open a route towards devices combining spin-based logic and memory integrated into a silicon-compatible material, where ferroelectricity can be employed as state variable to tune the spin-to-charge conversion.

[1] S. Manipatruni et al., Nature 565, 35–42 (2019)
[2] D. Di Sante et al., Adv. Mater. 25, 509-513 (2013)
[3] C. Rinaldi et al., Nano Letters, (2018); DOI: 10.1021/acs.nanolett.7b04829
[4] S. Varotto et al., arXiv:2103.07646 (2021)