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Beyond topological electronic systems

Artificial spin ice and Penrose quasicrystals: topological defects and magnon resonances

Magnons, quanta of spin waves, are known to enable information processing with low power consumption at the nanoscale. Magnons also allows to probe fundamental interaction in a magnetic system via the study of magnetization dynamics. The MagTop characterization and processing group, in collaboration with D. Grundler’s group at EPFL, undertook an extensive study of understanding, and controlled manipulation of, magnon spectra in periodic and aperiodic magnetic nanostructures revealing the role of topological defects.

We probed periodic magnetic nanostructures called artificial spin ice that are made of a periodic network of nanomagnets on a kagome lattice [1,2]. We experimentally showed signature of topological defects in the magnon spectra. Using microwave switching experiments, we showed that such topological defects in the periodic nanostructures can initiate avalanches in a controlled manner within the magnetic nanostructure lattice.

Quasicrystals exhibit aperiodic long-range order and unconventional rotational symmetry, but no translational invariance. On a fundamental level, we probed the effect of exchange and dipolar interaction on the magnon spectra in a five-fold rotationally symmetric artificial quasicrystal lattice [3]. Using our knowledge of magnetization dynamics in these aperiodic structures, we also successfully demonstrated reprogrammable magnonic artificial quasicrystal. The spin wave propagation study of artificial quasicrystals showed presence of spin waves in diagonal directions in contrast to the periodic nanostructures. Our results suggest that a Penrose P3 quasicrystal tiling operates as a grating coupler inducing a manifold of both propagation directions and wavelengths. Such formation of magnonic minibands allows one to engineer better magnonic waveguides compared with periodic nanostructures [4]. We showed the ultra-short magnons spin wave interference and demonstrated unprecedentedly large extinction ratios of 31 dB and 25 dB for a binary 1/0 operation at small wavelengths of 155 nm and 69 nm, respectively. These ratios are promising in view of nanomagnonics and considerably larger than 19 dB achieved by the uni-directional long-wavelength spin waves exploited before [5].

[1] V. S. Bhat, S. Watanabe, K. Baumgaertl, A. Kleibert, M. A. W. Schoen, C. A .F. Vaz, and D. Grundler, Magnon Modes of Microstates and Microwave-Induced Avalanche in Kagome Artificial Spin Ice with Topological Defects, Phys. Rev. Lett. 125, 117208 (2020).
[2] V. S. Bhat and D. Grundle, Tuning interactions in reconfigurable kagome artificial spin ices for magnonics, Appl. Phys. Lett. 119, 092403 (2021).
[3] V. S. Bhat, S. Watanabe, F. Kronast, K. Baumgaertl, and D. Grundler, Spin Dynamics, Loop Formation and Cooperative Reversal in Artificial Quasicrystals with Tailored Exchange Coupling, arXiv:220508224.
[4] S. Watanabe, V. S. Bhat, K. Baumgaertl, M. Hamdi, and D. Grundler, Direct observation of multiband transport in magnonic Penrose quasicrystals via broadband and phase-resolved spectroscopy, Sci. Adv. 7, eabg3771 (2021).
[5] S. Watanabe, V. S. Bhat, A. Mucchietto, E.N. Dayi, S. Shan, and D. Grundler, Periodic and Aperiodic NiFe Nanomagnet/Ferrimagnet Hybrid Structures for 2D Magnon Steering and Interferometry with High Extinction Ratio, Adv. Mater. 01087 (2023).
Invited talk: V. S. Bhat,  Spatially Resolved Magnon Modes in Kagome Artificial Spin Ices with Topological Defects,  Magnetism and Magnetic Materials (MMM) Conference 2020, USA.

Interfacing ferromagnets and semiconductors: phonon-mediated exchange

How to control a long-range phonon-mediated exchange interaction discovered by photoluminescence of CdTe quantum well (QW) in a hybrid Co/(Mg,Cd)Te/CdTe/(Mg,Cd)Te heterostructure grown by MBE at IFPAN [V. L. Korenev et al., Nat. Phys. 12, 85 (2016)]? Figure presents two structures fabricated by MagTop/IFPAN MBE teams, which made it possible to affect this exchange by low voltage U and by the distance between the ferromagnetic layer and CdTe QW.

Hybrid structures grown in a two-chamber MBE set-up allowing for magnetooptical probing of exchange coupling between ferromagnetic layers (Co or Fe) and carriers in CdTe QW vs. voltage U (left panel) (after [1]) and distance d (right panel) (after [2]).

Specially designed ferromagnet-semiconductor hybrid nanostructures, grown by the MagTop/IFPAN MBE groups (see Figure), were used to study in details ferromagnetic proximity effects across an insulating barrier.

The first type of experiments was carried out on a structure consisting of a ferromagnetic Co layer (also acting as an electrostatic gate) and a semiconductor CdTe QW, separated by a thin nonmagnetic Cd1-yMgyTe barrier. The electric field was shown to control the phononic a.c. Stark effect—the indirect exchange mechanism that is mediated by elliptically polarized phonons emitted from the ferromagnet. The effective magnetic field of the p-d exchange interaction reaches up to 2.5 Tesla and can be turned on and off by application of bias voltage across the heterostructure, as low as 1 V [1].

Even more sophisticated structures were required for subsequent experiments. In this case, the non-magnetic barrier separating the CdTe QW from the Fe layer deposited (in-situ MBE) on the top surface had a „wedge” shape, i.e., its thickness varied in one of the directions perpendicular to the growth axis of the structure. This allowed us to unambiguously study the ferromagnetic proximity effect as a function of FM distance from the QW in one sample by moving the laser spot, which was used to observe the effect, along the gradient (see Figure). Only by designing the structure in this way could the coexistence of long-range and short-range ferromagnetic proximity effects be revealed. The former is observed for holes bound to shallow acceptors in the CdTe QW and can be electrostatically controlled (as discussed above), while the latter is observed for conduction band electrons due to the overlap of their wave functions with the d-electrons of Fe film. The coexistence of the two ferromagnetic proximity effects also indicates the presence of a non-trivial spin texture within the same heterostructure.

[1] L. Korenev, I. V. Kalitukha, I. A. Akimov, V. F. Sapega, E. A. Zhukov, E. Kirstein, O. S. Ken, D. Kudlacik, G. Karczewski, T. Wojtowicz, N. D. Ilyinskaya, N. M. Lebedeva, T. A. Komissarova, Yu. G. Kusrayev, D. R. Yakovlev, and M. Bayer, Low voltage control of exchange coupling in a ferromagnet-semiconductor quantum well hybrid structure, Nat. Commun. 10, 2899 (2019).
[2] I. V. Kalitukha, O. S. Ken, V. L. Korenev, I. A. Akimov, V. F. Sapega, D. R. Yakovlev, G. S. Dimitriev, L. Langer, G. Karczewski, S. Chusnutdinow, T. Wojtowicz, M. Bayer, Coexistence of Short- and Long-Range Ferromagnetic Proximity Effects in a Fe/(Cd,Mg)Te/CdTe Quantum Well Hybrid StructureNano Lett. 21, 2370 (2021).

A new class of transverse magneto-optical phenomena with potentials for applications in nanophotonic circuits

High-quality quantum structures produced by MagTop/IFPAN MBE groups became building blocks of hybrid plasmonic-semiconductor nanostructures, which were used by MagTop’s collaborators to demonstrate and study in details new phenomena of transverse magnetic routing of light emission (TMRLE), as well as to demonstrate optical controll of transverse electron spin components normal to the direction of light propagation. In these hybrids, the plasmonic metal grating of Au was fabricated by electron beam lithography and lift-off on the surface of a structure containing a diluted magnetic semiconductor Cd1-xMnxTe quantum well (QW).

Schematic representation of experimental setup to demonstrate the TMRLE effect. An external in-plane magnetic field B is applied to the plasmonic structure (left part). The angular distribution of light emitted by the structure is converted by a lens into a spatial distribution in the Fourier plane (right) and recorded by a two dimensional CCD matrix (after [1]).

Figure shows the structure in which transverse magnetic routing of light emission (TMRLE) was demonstrated [1]. Taking advantage of large spin splitting characteristic of DMS and spin-locking of light in plasmonic structures (analogous to carrier spin-locking in topological insulators) directionality of emission up to 60% was achieved at 10 K [1], which dropped to 15% at 20 K and in the magnetic field of 485 mT [2]. However, the TMRLE is not limited to magnetic nanostructures and can be strong also in nonmagnetic nanostructures possessing large intrinsic g-factor. Thus, there is hope that the effect of controlling the direction of light emission from nanometer-sized light sources by means of a transverse magnetic field can be used in the future to build nanophotonic logic circuits or magneto-optical memories, among others.

Plasmonics opens up also new possibilities in the field of optical spin control, which is the basis of ultrafast spintronics, allowing the polarization of light to be tailored at the nanoscale. Circularly polarized light combined with spin-orbit coupling makes it possible to manipulate the spins of electron states in condensed matter. However, the conventional approach is limited to longitudinal spin initialization along one particular axis, which is dictated by the direction of light propagation. Ultrafast optical excitation of electron spin on femtosecond time scales via plasmon-to-exciton spin conversion was demonstrated [3]. It was also shown that by using the spin of the incident photons as an additional degree of freedom, not only longitudinal but also transverse components of electron spin normal to the direction of light propagation can be adjusted on demand.

[1] F. Spitzer, A. N. Poddubny, I. A. Akimov, V. F. Sapega, L. Klompmaker, L. E. Kreilkamp, L. V. Litvin, R. Jede, G. Karczewski, M. Wiater, T. Wojtowicz, D. R. Yakovlev, M. Bayer, Routing the emission of a near-surface light source by a magnetic fieldNat. Phys. 14, 1043 (2018) corrections.
[2] L. Klompmaker, A. N. Poddubny, E. Yalcin, L. V. Litvin, R. Jede, G. Karczewski, S. Chusnutdinow, T. Wojtowicz, D. R. Yakovlev, M. Bayer, I. A. Akimov, Transverse magnetic routing of light emission in hybrid plasmonic-semiconductor nanostructures: Towards operation at room temperature, Phys. Rev. Research 4, 013058 (2022).
[3] I. A. Akimov, A. N. Poddubny, J. Vondran, Yu. V. Vorobyov, L. V. Litvin, R. Jede, G. Karczewski, S. Chusnutdinow, T. Wojtowicz, and M. Bayer, Plasmon-to-exciton spin conversion in semiconductor-metal hybrid nanostructures,  Phys. Rev. B 103, 085425 (2021).

Nematicity in solids: role of anisotropic spinodal decomposition and orbital polarization 

The origin of nematicity, i.e., in-plane rotational symmetry breaking, and in particular the relative role played by spontaneous unidirectional ordering of spin, orbital, or charge degrees of freedom, is a challenging issue of magnetism, unconventional superconductivity, and quantum Hall systems.  While MagTop’s and collaborators’ results indicated uneven dxz and dyz orbital occupation in a superconducting iron pnictide pointed to the important role of orbital polarization, experimental and theoretical results for In1xFexAs demonstrated that anisotropic distribution of Fe cations at the growth surface (that has a lower symmetry than the bulk) can lead to a quenched nematic order of alloy components, which then governs low-temperature magnetic and magnetotransport properties.

Non-uniform and anisotropic distribution of Fe cations in a 200 nm-wide slab of (In,Fe)As (black lines along the [1-10] crystallographic direction) according to HR-TEM (left panel) and the corresponding low-temperature anisotropic magnetoresistance (right panel) (after [2]).

By using x-ray linear dichroism technique, the collaboration showed that the imbalance between dxz and dyz orbital occupation is present in Eu(Fe1−xCox)2As2 single crystals deep in the tetragonal phase and also in the superconducting state, where the dxz orbital has a higher occupation as indicated by an x-ray linear dichroism magnitude of 1.5% [1]. The findings point to the importance of orbital polarization in the theoretical description of nematicity and superconductivity, particularly for determination of the superconducting gap symmetry, which is affected by orbital fluctuations.

In contrast, results gathered for dilute magnetic semiconductors and dilute topological materials, both obtained previously [see T. Dietl et al., Rev. Mod. Phys. 87, 1311 (2015)] and more recently [2], revealed experimentally the appearance of anisotropic distribution of transition metal (TM) cations.  A theoretical analysis showed that the effect results from a weaker chemical pd attraction between TM surface cation dimers residing along the [110] direction compared to the [1-10] case [2]. Under such conditions, epitaxial growth leads to a surplus of TM cations along [1-10] crystal orientation, in agreement with chemically resolved TEM image shown in Figure.

[1] D. Rybicki, M. Sikora, J. Stępień, Ł. Gondek, K. Goc, T. Strączek, M. Jurczyszyn, Cz. Kapusta, Z. Bukowski, M. Babij, M. Matusiak, M. Zając, Direct evidence of uneven dxz and dyz orbital occupation in the superconducting state of iron pnictide, Phys. Rev. B 102, 195126 (2020).
[2] Ye Yuan, R. Hübner, M. Birowska, Chi Xu, Mao Wang, S. Prucnal, R. Jakiela, K. Potzger, R. Böttger, S. Facsko, J. A. Majewski, M. Helm, M. Sawicki, Shengqiang Zhou, T. Dietl, Nematicity of correlated systems driven by anisotropic chemical phase separationPhys. Rev. Materials 2, 114601 (2018) [Editors’ Suggestion].
invited talks: T. Dietl, Phase separations and nematicity of transition metal impurities, IEEE NAP-2022 International Conference, Sep. 11-16, Kraków, Poland; Twenty-Fifth Congress and General Assembly of the International Union of Crystallography Prague, Prague , Czech Republic, 14 – 22 August, 2021; The 2nd Kavli ITS Workshop on Magnetic Semiconductors, Beijing, China, 15-16 January, 2020; Quantum Complex Matter, Superstripes 2019 Meeting, Ischia, Italy, 23-29 June, 2019

Topological systems with dissipation: the discovery of long-range entanglement

Making coupling to the reservoir a resource rather than an obstacle emerges as one of the most promising roads in topological quantum computing. MagTop’s researchers proposed a 1D non-Hermitian model, in which they revealed the presence of a hidden Chern number. They used this model to describe lasing in a polariton system and, most recently, to examine a chain of transmon devices, the qubits of the most mature quantum computers. The dynamics of this system with dissipation, examined employing the third quantization methods, revealed the presence of controllable long-range quantum entanglement between distant end states of the chain.

Non-Hermitian Bose-Hubbard transmon ABBA chain (A – blue, B – red) with the on-site and inter-site energies Ui and Ji, respectively. The dissipation strength is tuned by the coupling to the measurement circuit ki and loss caused by the quantum circuit refrigerator gi (QCR).

To open a new avenue in exploration of quantum effects in non-Hermitian topological systems, we proposed to utilize the mature superconducting quantum device technologies and introduced a transmon chain where the spatially-dependent dissipation, the ABBA-like pattern, is realized by tunable quantum circuit refrigerators [1]. By solving the many-body Lindblad master equation using a combination of the density matrix renormalization group and Prosen-Seligman third quantization approaches, we show that the topological end modes and the associated phase transition are visible in simple reflection measurements with experimentally realistic parameters. Most importantly, we demonstrated the possibility to generate genuine long-range quantum entanglement between the topologically protected end states. This can be done by time-evolving a Fock state with fixed number of bosons in the central site.

The crucial ingredient of that recent development is the so-called hidden Chern number in one-dimensional non-Hermitian topological systems proposed in our earlier work [2]. This Chern number manifests itself as topologically protected in-gap end states at zero real part of the energy. We show that the bulk-boundary correspondence coming from the hidden Chern number is robust and immune to the non-Hermitian skin effect. We introduce a minimal model Hamiltonian supporting topologically nontrivial phases in this symmetry class, derive its topological phase diagram, and calculate the end states originating from the hidden Chern number. This formalism was then used to describe lasing in a polariton system [3].

[1] W. Brzezicki, M. Silveri, M. Płodzień, F. Massel, T. Hyart, Non-Hermitian topological quantum states in a reservoir-engineered transmon chain, Phys. Rev. B 107, 115146 (2023).
[2] W. Brzezicki, T. Hyart, Hidden Chern number in one-dimensional non-Hermitian chiral-symmetric systems, Phys. Rev. B 100, 161105(R) (2019).
[3] P. Comaron, V. Shahnazaryan, W. Brzezicki, T. Hyart, M. Matuszewski, Non-Hermitian topological end-mode lasing in polariton systems,  Phys. Rev. Research 2, 022051(R) (2020).

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