Prof. dr hab. Józef Barnaś
- Tel: +48 61 829 5287
- Loc: wing J, 2nd floor, room 208
- Email: barnas@amu.edu.pl
Scientific degrees
Title of professor – 1999
Habilitation – 1993
PhD in physics – 1983
MSc in physics – 1974
Awards
2019 – Order of Polonia Restituta
2009 – Award of The Foundation for Polish Science (FNP)
2008 – Smoluchowski Medal
1999 – Award of Maria Curie-Skłodowska
1998 – Award of the Minister for National Education
Rector’s awards for scientific research (A. Mickiewicz University in Poznań)
Publications
2023 |
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10. | Wojciech Rudziński, Józef Barnaś, Anna Dyrdał Journal of Magnetism and Magnetic Materials, 588 , pp. 171463, 2023. @article{Rudzinski2023, title = {Spin waves in monolayers of transition-metal dichalcogenides with Dzyaloshinskii - Moriya interaction}, author = {Wojciech Rudziński and Józef Barnaś and Anna Dyrdał}, url = {https://doi.org/10.1016/j.jmmm.2023.171463}, doi = {10.1016/j.jmmm.2023.171463}, year = {2023}, date = {2023-12-15}, journal = {Journal of Magnetism and Magnetic Materials}, volume = {588}, pages = {171463}, abstract = {Dzyaloshinski–Moriya interaction, known also as the antisymmetric exchange coupling, leads to a variety of interesting spin phenomena, like spin canting, skyrmion formation, nonreciprocal spin wave propagation, and others. In this paper we analyze spin waves in monolayers of two-dimensional van–der–Waals materials, such as Vanadium–based dichalcogenides, VX2 (X=S, Se, Te) and other materials of similar symmetry. The considerations are limited to a collinear spin ground state, stabilized by a sufficiently strong magnetic anisotropy. The theoretical analysis is performed within the general spin wave theory based on the Holstein–Primakoff–Bogoliubov transformation.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Dzyaloshinski–Moriya interaction, known also as the antisymmetric exchange coupling, leads to a variety of interesting spin phenomena, like spin canting, skyrmion formation, nonreciprocal spin wave propagation, and others. In this paper we analyze spin waves in monolayers of two-dimensional van–der–Waals materials, such as Vanadium–based dichalcogenides, VX2 (X=S, Se, Te) and other materials of similar symmetry. The considerations are limited to a collinear spin ground state, stabilized by a sufficiently strong magnetic anisotropy. The theoretical analysis is performed within the general spin wave theory based on the Holstein–Primakoff–Bogoliubov transformation. |
9. | Mirali Jafari, Wojciech Rudziński, Józef Barnaś, Anna Dyrdał Electronic and magnetic properties of 2D vanadium-based transition metal dichalcogenides Scientific Reports, 13 , pp. 20947, 2023. @article{Jafari2023, title = {Electronic and magnetic properties of 2D vanadium-based transition metal dichalcogenides}, author = {Mirali Jafari and Wojciech Rudziński and Józef Barnaś and Anna Dyrdał}, url = {https://doi.org/10.1038/s41598-023-48141-1}, doi = {10.1038/s41598-023-48141-1}, year = {2023}, date = {2023-11-28}, journal = {Scientific Reports}, volume = {13}, pages = {20947}, abstract = {In this paper, electronic and magnetic properties of monolayers and bilayers of Vanadium-based transition metal dichalcogenides VX2 (X = S, Se, Te) in the H phase are investigated theoretically using methods based on DFT calculations as well as analytical methods based on effective spin Hamiltonians. The band structure has been computed for all systems, and then the results have been used to determine exchange parameters and magnetic anisotropy constants. These parameters are subsequently used for the determination of the Curie temperatures, hysteresis curves, and energy of spin-wave excitations. In the latter case, we compare analytical results based on effective spin Hamiltonian with those determined numerically by Quantum ATK software and find a good agreement. The determined Curie temperature for VTe2 monolayers and bilayers is below the room temperature (especially that for bilayers), while for the other two materials, i.e. for VS2 and VSe2, it is above the room temperature, in agreement with available experimental data.}, keywords = {}, pubstate = {published}, tppubtype = {article} } In this paper, electronic and magnetic properties of monolayers and bilayers of Vanadium-based transition metal dichalcogenides VX2 (X = S, Se, Te) in the H phase are investigated theoretically using methods based on DFT calculations as well as analytical methods based on effective spin Hamiltonians. The band structure has been computed for all systems, and then the results have been used to determine exchange parameters and magnetic anisotropy constants. These parameters are subsequently used for the determination of the Curie temperatures, hysteresis curves, and energy of spin-wave excitations. In the latter case, we compare analytical results based on effective spin Hamiltonian with those determined numerically by Quantum ATK software and find a good agreement. The determined Curie temperature for VTe2 monolayers and bilayers is below the room temperature (especially that for bilayers), while for the other two materials, i.e. for VS2 and VSe2, it is above the room temperature, in agreement with available experimental data. |
8. | Anna Dyrdał, Alireza Qaiumzadeh, Arne Brataas, Józef Barnaś Magnon-plasmon hybridization mediated by spin-orbit interaction in magnetic materials Physical Review B, 108 (4), pp. 045414, 2023. @article{Dyrdał2023, title = {Magnon-plasmon hybridization mediated by spin-orbit interaction in magnetic materials}, author = {Anna Dyrdał and Alireza Qaiumzadeh and Arne Brataas and Józef Barnaś}, url = {https://doi.org/10.1103/PhysRevB.108.045414}, doi = {10.1103/PhysRevB.108.045414}, year = {2023}, date = {2023-07-21}, journal = {Physical Review B}, volume = {108}, number = {4}, pages = {045414}, abstract = {We propose a mechanism for magnon-plasmon coupling and hybridization in ferromagnetic (FM) and antiferromagnetic (AFM) systems. The electric field associated with plasmon oscillations creates a nonequilibrium spin density via the inverse spin galvanic effect. This plasmon-induced spin density couples to magnons by an exchange interaction. The strength of magnon-plasmon coupling depends on the magnetoelectric susceptibility of the system and the wavevector at which the level repulsion has happened. This wavevector may be tuned by an applied magnetic field. In AFM systems, the degeneracy of two chiral magnons is broken in the presence of a magnetic field, and we find two separate hybrid modes for left-handed and right-handed AFM magnons. Furthermore, we show that magnon-plasmon coupling in AFM systems is enhanced because of strong intrasublattice spin dynamics. We argue that the recently discovered two-dimensional magnetic systems are ideal platforms to investigate proposed magnon-plasmon hybrid modes.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We propose a mechanism for magnon-plasmon coupling and hybridization in ferromagnetic (FM) and antiferromagnetic (AFM) systems. The electric field associated with plasmon oscillations creates a nonequilibrium spin density via the inverse spin galvanic effect. This plasmon-induced spin density couples to magnons by an exchange interaction. The strength of magnon-plasmon coupling depends on the magnetoelectric susceptibility of the system and the wavevector at which the level repulsion has happened. This wavevector may be tuned by an applied magnetic field. In AFM systems, the degeneracy of two chiral magnons is broken in the presence of a magnetic field, and we find two separate hybrid modes for left-handed and right-handed AFM magnons. Furthermore, we show that magnon-plasmon coupling in AFM systems is enhanced because of strong intrasublattice spin dynamics. We argue that the recently discovered two-dimensional magnetic systems are ideal platforms to investigate proposed magnon-plasmon hybrid modes. |
2022 |
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7. | X.-G. Wang, L. Chotorlishvili, G. Tatara, Anna Dyrdał, Guang-hua Guo, V. K. Dugaev, Józef Barnaś, S.S.P. Parkin, A. Ernst Skyrmion lattice hosted in synthetic antiferromagnets and helix modes Phys. Rev. B, 106 , pp. 104424, 2022. @article{Wang2022b, title = {Skyrmion lattice hosted in synthetic antiferromagnets and helix modes}, author = {X.-G. Wang and L. Chotorlishvili and G. Tatara and Anna Dyrdał and Guang-hua Guo and V. K. Dugaev and Józef Barnaś and S.S.P. Parkin and A. Ernst}, url = {https://journals.aps.org/prb/abstract/10.1103/PhysRevB.106.104424}, doi = {10.1103/PhysRevB.106.104424}, year = {2022}, date = {2022-09-20}, journal = {Phys. Rev. B}, volume = {106}, pages = {104424}, abstract = {Thin ferromagnetic films can possess unconventional magnetic properties, opening a new road for using them in spintronic technologies. In the present work exploiting three different methods, we comprehensively analyze phason excitations of a skyrmion lattice in synthetic antiferromagnets. To analyze phason excitations of the skyrmion lattice, we have constructed an analytical model based on three coupled helices and found a linear gapless mode. Micromagnetic simulations also support this result. Moreover, a similar result has been achieved within the rigid skyrmion lattice model based on the coupled Thiele's equations, when the coupling between skyrmions in different layers of the synthetic antiferromagnetic is comparable to or larger than the intralayer coupling. In addition, we also consider the orbital angular momentum and spin pumping current associated with phason excitations. Due to the gapless excitations in the case of skyrmion lattice, the pumping current is nonzero for the arbitrary frequency of pumping microwaves. In the case of individual skyrmions, no current is pumped when microwave frequency is inside the gap of the spectrum of individual skyrmions.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Thin ferromagnetic films can possess unconventional magnetic properties, opening a new road for using them in spintronic technologies. In the present work exploiting three different methods, we comprehensively analyze phason excitations of a skyrmion lattice in synthetic antiferromagnets. To analyze phason excitations of the skyrmion lattice, we have constructed an analytical model based on three coupled helices and found a linear gapless mode. Micromagnetic simulations also support this result. Moreover, a similar result has been achieved within the rigid skyrmion lattice model based on the coupled Thiele's equations, when the coupling between skyrmions in different layers of the synthetic antiferromagnetic is comparable to or larger than the intralayer coupling. In addition, we also consider the orbital angular momentum and spin pumping current associated with phason excitations. Due to the gapless excitations in the case of skyrmion lattice, the pumping current is nonzero for the arbitrary frequency of pumping microwaves. In the case of individual skyrmions, no current is pumped when microwave frequency is inside the gap of the spectrum of individual skyrmions. |
6. | X.-G. Wang, Guang-hua Guo, Anna Dyrdał, Józef Barnaś, V. K. Dugaev, S. S. P. Parkin, A. Ernst, L. Chotorlishvili Skyrmion Echo in a System of Interacting Skyrmions Phys. Rev. Lett., 129 , pp. 126101, 2022. @article{Wang2022, title = {Skyrmion Echo in a System of Interacting Skyrmions}, author = {X.-G. Wang and Guang-hua Guo and Anna Dyrdał and Józef Barnaś and V. K. Dugaev and S. S. P. Parkin and A. Ernst and L. Chotorlishvili}, url = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.126101}, doi = {10.1103/PhysRevLett.129.126101}, year = {2022}, date = {2022-09-14}, journal = {Phys. Rev. Lett.}, volume = {129}, pages = {126101}, abstract = {We consider helical rotation of skyrmions confined in the potentials formed by nanodisks. Based on numerical and analytical calculations we propose the skyrmion echo phenomenon. The physical mechanism of the skyrmion echo formation is also proposed. Because of the distortion of the lattice, impurities, or pinning effect, confined skyrmions experience slightly different local fields, which leads to dephasing of the initial signal. The interaction between skyrmions also can contribute to the dephasing process. However, switching the magnetization direction in the nanodiscs (e.g., by spin transfer torque) also switches the helical rotation of the skyrmions from clockwise to anticlockwise (or vice versa), and this restores the initial signal (which is the essence of skyrmion echo).}, keywords = {}, pubstate = {published}, tppubtype = {article} } We consider helical rotation of skyrmions confined in the potentials formed by nanodisks. Based on numerical and analytical calculations we propose the skyrmion echo phenomenon. The physical mechanism of the skyrmion echo formation is also proposed. Because of the distortion of the lattice, impurities, or pinning effect, confined skyrmions experience slightly different local fields, which leads to dephasing of the initial signal. The interaction between skyrmions also can contribute to the dephasing process. However, switching the magnetization direction in the nanodiscs (e.g., by spin transfer torque) also switches the helical rotation of the skyrmions from clockwise to anticlockwise (or vice versa), and this restores the initial signal (which is the essence of skyrmion echo). |
5. | L. Chotorlishvili, Xi-guang Wang, Anna Dyrdał, Guang-hua Guo, Vitalii K. Dugaev, Józef Barnaś, J. Berakdar Rectification of the spin Seebeck current in noncollinear antiferromagnets Phys. Rev. B, 106 (1), pp. 014417, 2022, ISSN: 2469-9969. @article{Chotorlishvili2022, title = {Rectification of the spin Seebeck current in noncollinear antiferromagnets}, author = {L. Chotorlishvili and Xi-guang Wang and Anna Dyrdał and Guang-hua Guo and Vitalii K. Dugaev and Józef Barnaś and J. Berakdar}, url = {https://journals.aps.org/prb/abstract/10.1103/PhysRevB.106.014417}, doi = {10.1103/PhysRevB.106.014417}, issn = {2469-9969}, year = {2022}, date = {2022-07-25}, journal = {Phys. Rev. B}, volume = {106}, number = {1}, pages = {014417}, abstract = {In the absence of an external magnetic field and a spin-polarized charge current, an antiferromagnetic system supports two degenerate magnon modes. An applied thermal bias activates the magnetic dynamics, leading to a magnon flow from the hot to the cold edge (magnonic spin Seebeck current). Both degenerate bands contribute to the magnon current but the orientations of the magnetic moments underlying the magnons are opposite in different bands. Therefore, while the magnon current is nonzero, the net spin current is zero. To obtain a nonzero net spin current, one needs to apply either a magnetic field or a spin-polarized charge current that lifts the bands' degeneracy. Here, attaching a thermal contact to one edge of a helical nanowire, we study three different magnonic spin currents: (i) the exchange, and (ii) Dzyaloshinskii–Moriya spin currents flowing along the helical nanowire, and (iii) magnonic spin current pumped into the adjacent normal-metal layer. We find that the combination of Dzyaloshinskii–Moriya interaction and external magnetic field substantially enhances the spin current compared to the current generated solely through a magnetic field. Due to nonreciprocal magnons and magnon dichroism effect, the Dzyaloshinskii–Moriya and exchange spin currents show left-right propagation asymmetry, with 20% of current rectification. The spin pumping current shows a slight asymmetry only in the case of a strong Dzyaloshinskii–Moriya interaction. The observed effects are explained in terms of the magnon dispersion relations and the magnon Doppler effect.}, keywords = {}, pubstate = {published}, tppubtype = {article} } In the absence of an external magnetic field and a spin-polarized charge current, an antiferromagnetic system supports two degenerate magnon modes. An applied thermal bias activates the magnetic dynamics, leading to a magnon flow from the hot to the cold edge (magnonic spin Seebeck current). Both degenerate bands contribute to the magnon current but the orientations of the magnetic moments underlying the magnons are opposite in different bands. Therefore, while the magnon current is nonzero, the net spin current is zero. To obtain a nonzero net spin current, one needs to apply either a magnetic field or a spin-polarized charge current that lifts the bands' degeneracy. Here, attaching a thermal contact to one edge of a helical nanowire, we study three different magnonic spin currents: (i) the exchange, and (ii) Dzyaloshinskii–Moriya spin currents flowing along the helical nanowire, and (iii) magnonic spin current pumped into the adjacent normal-metal layer. We find that the combination of Dzyaloshinskii–Moriya interaction and external magnetic field substantially enhances the spin current compared to the current generated solely through a magnetic field. Due to nonreciprocal magnons and magnon dichroism effect, the Dzyaloshinskii–Moriya and exchange spin currents show left-right propagation asymmetry, with 20% of current rectification. The spin pumping current shows a slight asymmetry only in the case of a strong Dzyaloshinskii–Moriya interaction. The observed effects are explained in terms of the magnon dispersion relations and the magnon Doppler effect. |
4. | Mir Ali Jafari, Małgorzata Wawrzyniak-Adamczewska, Stefan Stagraczyński, Anna Dyrdał, Józef Barnaś Spin valve effect in two-dimensional VSe2 system J. Magn. Magn. Mater., 548 , pp. 168921, 2022, ISSN: 0304-8853. @article{Jafari2022, title = {Spin valve effect in two-dimensional VSe2 system}, author = {Mir Ali Jafari and Małgorzata Wawrzyniak-Adamczewska and Stefan Stagraczyński and Anna Dyrdał and Józef Barnaś}, url = {https://www.sciencedirect.com/science/article/pii/S0304885321011215?via%3Dihub}, doi = {10.1016/j.jmmm.2021.168921}, issn = {0304-8853}, year = {2022}, date = {2022-03-15}, journal = {J. Magn. Magn. Mater.}, volume = {548}, pages = {168921}, abstract = {Vanadium based dichalcogenides, VSe2, are two-dimensional materials in which magnetic Vanadium atoms are arranged in a hexagonal lattice and are coupled ferromagnetically within the plane. However, adjacent atomic planes are coupled antiferromagnetically. This provides new and interesting opportunities for application in spintronics and data storage and processing technologies. A spin valve magnetoresistance may be achieved when magnetic moments of both atomic planes are driven to parallel alignment by an external magnetic field. The resistance change associated with the transition from antiparallel to parallel configuration is qualitatively similar to that observed in artificially layered metallic magnetic structures. Detailed electronic structure of VSe2 was obtained from DFT calculations. Then, the ballistic spin-valve magnetoresistance was determined within the Landauer formalism. In addition, we also analyze thermal and thermoelectric properties. Both phases of VSe2, denoted as H and T, are considered.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Vanadium based dichalcogenides, VSe2, are two-dimensional materials in which magnetic Vanadium atoms are arranged in a hexagonal lattice and are coupled ferromagnetically within the plane. However, adjacent atomic planes are coupled antiferromagnetically. This provides new and interesting opportunities for application in spintronics and data storage and processing technologies. A spin valve magnetoresistance may be achieved when magnetic moments of both atomic planes are driven to parallel alignment by an external magnetic field. The resistance change associated with the transition from antiparallel to parallel configuration is qualitatively similar to that observed in artificially layered metallic magnetic structures. Detailed electronic structure of VSe2 was obtained from DFT calculations. Then, the ballistic spin-valve magnetoresistance was determined within the Landauer formalism. In addition, we also analyze thermal and thermoelectric properties. Both phases of VSe2, denoted as H and T, are considered. |
3. | Kateryna Boboshko, Anna Dyrdał, Józef Barnaś Journal of Magnetism and Magnetic Materials, 545 , pp. 168698, 2022. @article{Boboshko2022, title = {Bilinear magnetoresistance in topological insulators: The role of spin–orbit scattering on impurities}, author = {Kateryna Boboshko and Anna Dyrdał and Józef Barnaś}, url = {https://www.sciencedirect.com/science/article/pii/S0304885321009318}, doi = {10.1016/j.jmmm.2021.168698}, year = {2022}, date = {2022-03-01}, journal = {Journal of Magnetism and Magnetic Materials}, volume = {545}, pages = {168698}, abstract = {Bilinear magnetoresistance (BMR) is a new kind of magnetoresistance, that scales linearly with electric and magnetic fields. This magnetoresistance occurs in systems with strong spin–orbit interaction. Additionally, this interaction also leads to quadratic magnetoresistance (QMR). We consider theoretically BMR and QMR in surface states of 3D topological insulators, and propose a new mechanism that leads to these effects. This mechanism is based on scattering on spin–orbit impurities. Accordingly, we assume the minimal model of surface electronic states in a single independent surface of a TI, and calculate both BMR and QMR induced as an interplay of current-induced spin polarization (or equivalently effective spin–orbit field) and spin–orbit scattering on impurities. We present detailed characteristics of both BMR and QMR, and compare our results with those obtained for TIs with spin-momentum locking inhomogeneities and hexagonal warping of the Dirac cones.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Bilinear magnetoresistance (BMR) is a new kind of magnetoresistance, that scales linearly with electric and magnetic fields. This magnetoresistance occurs in systems with strong spin–orbit interaction. Additionally, this interaction also leads to quadratic magnetoresistance (QMR). We consider theoretically BMR and QMR in surface states of 3D topological insulators, and propose a new mechanism that leads to these effects. This mechanism is based on scattering on spin–orbit impurities. Accordingly, we assume the minimal model of surface electronic states in a single independent surface of a TI, and calculate both BMR and QMR induced as an interplay of current-induced spin polarization (or equivalently effective spin–orbit field) and spin–orbit scattering on impurities. We present detailed characteristics of both BMR and QMR, and compare our results with those obtained for TIs with spin-momentum locking inhomogeneities and hexagonal warping of the Dirac cones. |
2. | V. A. Stephanovich, E. V. Kirichenko, V. K. Dugaev, Józef Barnaś Dynamic Friedel oscillations on the surface of a topological insulator Phys. Rev. B, 105 , pp. 075306, 2022. @article{Stephanovich2022, title = {Dynamic Friedel oscillations on the surface of a topological insulator}, author = {V. A. Stephanovich and E. V. Kirichenko and V. K. Dugaev and Józef Barnaś}, url = {https://journals.aps.org/prb/abstract/10.1103/PhysRevB.105.075306}, doi = {10.1103/PhysRevB.105.075306}, year = {2022}, date = {2022-02-14}, journal = {Phys. Rev. B}, volume = {105}, pages = {075306}, abstract = {We study theoretically the dynamic Friedel oscillations of electrons at the surface of a topological insulator (TI) that are generated by the rotation of a localized impurity spin. We show that the spin-orbit interaction (SOI) in Rashba form, which is an integral part of the TI Hamiltonian, yields a highly anisotropic response to the localized spin rotation. As a result, the response to a flip of a localized spin z projection involves the reaction of all x, y, and z components of the local magnetization. Additionally, the dynamic spin moment (and thus also Friedel oscillations) emitted by the localized dynamical spin depends on the orientation in the TI plane. The resulting unusual dynamics is due to the interplay of SOI and Ruderman-Kittel-Kasuya-Yoshida interactions. This provides the basis for manipulation of the spin transport in topological insulators decorated with localized impurity spins, which may be important for technological applications.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We study theoretically the dynamic Friedel oscillations of electrons at the surface of a topological insulator (TI) that are generated by the rotation of a localized impurity spin. We show that the spin-orbit interaction (SOI) in Rashba form, which is an integral part of the TI Hamiltonian, yields a highly anisotropic response to the localized spin rotation. As a result, the response to a flip of a localized spin z projection involves the reaction of all x, y, and z components of the local magnetization. Additionally, the dynamic spin moment (and thus also Friedel oscillations) emitted by the localized dynamical spin depends on the orientation in the TI plane. The resulting unusual dynamics is due to the interplay of SOI and Ruderman-Kittel-Kasuya-Yoshida interactions. This provides the basis for manipulation of the spin transport in topological insulators decorated with localized impurity spins, which may be important for technological applications. |
2021 |
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1. | Michał Inglot, Vitalii K. Dugaev, Anna Dyrdał, Józef Barnaś Phys. Rev. B, 104 (21), pp. 214408, 2021, ISSN: 2469-9969. @article{Inglot2021, title = {Graphene with Rashba spin-orbit interaction and coupling to a magnetic layer: Electron states localized at the domain wall}, author = {Michał Inglot and Vitalii K. Dugaev and Anna Dyrdał and Józef Barnaś}, url = {https://journals.aps.org/prb/abstract/10.1103/PhysRevB.104.214408}, doi = {10.1103/PhysRevB.104.214408}, issn = {2469-9969}, year = {2021}, date = {2021-12-06}, journal = {Phys. Rev. B}, volume = {104}, number = {21}, pages = {214408}, abstract = {Electron states localized at a magnetic domain wall in a graphene with Rashba spin-orbit interaction and coupled to a magnetic layer are studied theoretically. It is shown that two one-dimensional bands of edge modes propagating along the domain wall emerge in the energy gap for each Dirac point, and the modes associated with different Dirac points K and K′ are the same. The coefficients describing decay of the corresponding wave functions with distance from the domain wall contain generally real and imaginary terms. Numerical results on the local spin density and on the total spin expected in the edge states characterized by the wave number ky are presented and discussed. The Chern number for a single magnetic domain on graphene indicates that the system is in the quantum anomalous Hall phase, with two chiral modes at the edges. In turn, the number of modes localized at the domain wall is determined by the difference in Chern numbers on both sides of the wall. These numbers are equal to 2 and −2, respectively, so there are four modes localized at the domain wall.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Electron states localized at a magnetic domain wall in a graphene with Rashba spin-orbit interaction and coupled to a magnetic layer are studied theoretically. It is shown that two one-dimensional bands of edge modes propagating along the domain wall emerge in the energy gap for each Dirac point, and the modes associated with different Dirac points K and K′ are the same. The coefficients describing decay of the corresponding wave functions with distance from the domain wall contain generally real and imaginary terms. Numerical results on the local spin density and on the total spin expected in the edge states characterized by the wave number ky are presented and discussed. The Chern number for a single magnetic domain on graphene indicates that the system is in the quantum anomalous Hall phase, with two chiral modes at the edges. In turn, the number of modes localized at the domain wall is determined by the difference in Chern numbers on both sides of the wall. These numbers are equal to 2 and −2, respectively, so there are four modes localized at the domain wall. |