Non-trivial band topology along with magnetism leads to different novel quantum phases. When time-reversal symmetry is broken in three-dimensional topological insulators (TIs) through, e.g., the proximity effect, different phases such as the quantum Hall phase or the quantum anomalous Hall(QAH) phase emerge, displaying interesting transport properties for spintronic applications. The QAH phase displays sidewall chiral edge states, which leads to the QAH effect. We have considered a heterostructure consisting of a TI, namely Bi[Formula: see text]Se[Formula: see text], sandwiched between two two-dimensional ferromagnetic monolayers of CrI[Formula: see text], to study how its topological and transport properties change due to the proximity effect. Combining DFT and tight-binding calculations, along with non-equilibrium Green's function formalism, we show that a well-defined exchange gap appears in the band structure in which spin-polarised edge states flow. In a finite slab, the nature of the surface states depends on both the cross-section and thickness of the system. Therefore, we also study the width and finite-size effects on the transmission and topological properties of this magnetised TI nanoribbon.

PdFe/Ir(111) has attracted tremendous attention for next-generation spintronics devices due to existence of magnetic skyrmions with the external magnetic field. Our density functional theoretical calculations in combination with spin dynamics simulation suggest that the spin spiral phase in fcc stacked PdFe/Ir(111) flips into the skyrmion lattice phase around B-ert similar to 6 T. This leads to the microscopic understanding of the thermodynamic and kinetic behaviours affected by the intrinsic spin-lattice couplings (SLCs) in this skyrmion material for magneto-mechanical properties. Here we calculate fully relativistic SLC parameters from first principle computations and investigate the effect of SLC on dynamical magnetic interactions in skyrmion multilayers PdFe/Ir(111). The exchange interactions arising from next nearest-neighbors (NN) in this material are highly frustrated and responsible for enhancing skyrmion stability. We report the larger spin-lattice effect on both dynamical Heisenberg exchanges and Dzyaloshinskii-Moriya interactions for next NN compared to NN which is in contrast with recently observed spin-lattice effect in bulk bcc Fe and CrI3 monolayer. Based on our analysis, we find that the effective measures of SLCs in fcc (hcp) stacking of PdFe/Ir(111) are similar to 2.71(similar to 2.36) and similar to 14.71(similar to 21.89) times stronger for NN and next NN respectively, compared to bcc Fe. The linear regime of displacement for SLC parameters is <= 0.02 angstrom which is 0.72% of the lattice constant for PdFe/Ir(111). The microscopic understanding of SLCs provided by our current study could help in designing spintronic devices based on thermodynamic properties of skyrmion multilayers.

Skyrmions having topologically protected field configurations with particle-like properties play an important role in various fields of science. Our present study focus on the generation of skyrmion from spin spiral in the magnetic multilayers of 4d/Fe/Ir(111) with 4d = Y, Zr, Nb, Mo, Ru, Rh. Here we investigate the impact of 4d transition metals on the isotropic Heisenberg exchanges and anti-symmetric Dzyaloshinskii-Moriya interactions originating from the broken inversion symmetry at the interface of 4d/Fe/Ir(111) multilayers. We find a strong exchange frustration due to the hybridization of the Fe-3d layer with both 4d and Ir-5d layers which modifies due to band filling effects of the 4d transition metals. We strengthen the analysis of exchange frustration by shedding light on the orbital decomposition of isotropic exchange interactions of Fe-3d orbitals. Our spin dynamics and Monte Carlo simulations indicate that the magnetic ground state of 4d/Fe/Ir(111) transition multilayers is a spin spiral in theab-plane with a period of 1 to 2.5 nm generated by magnetic moments of Fe atoms and propagating along thea-direction. The spiral wavelengths in Y/Fe/Ir(111) are much larger compared to Rh/Fe/Ir(111). In order to manipulate the skyrmion phase in 4d/Fe/Ir(111), we investigate the magnetic ground state of 4d/Fe/Ir(111) transition multilayers with different external magnetic field. An increasing external magnetic field of ∼12 T is responsible for deforming the spin spiral into a isolated skyrmion which flips into skyrmion lattice phase around ∼18 T in Rh/Fe/Ir(111). Our study predict that the stability of magnetic skyrmion phase in Rh/Fe/Ir(111) against thermal fluctuations is upto temperatureT⩽90 K.

YMn6Sn6 consists of two types of Mn-based kagome planes stacked along the c-axis having a complex magnetic interaction. We report a spin reconstruction in YMn6Sn6 from ferromagnetic (FM) into a combination of two incommensurate spin spirals (SSs) originating from two different types of Mn kagome planes driven by frustrated magnetic exchanges along the c-axis with the inclusion of the Hubbard U . The pitch angle and wave vector of the incommensurate SSs are similar to 89 . 3 degrees and similar to (0 0 0.248), respectively, which are in excellent agreement with the experiment. We employ an effective model Hamiltonian constructed out of exchange interactions to capture the experimentally observed nonequivalent nature of the two incommensurate SSs which also explain the FM-SS crossover due to antiferromagntic spin exchange with correlation. We further report the existence of a topological magnon with spin-orbit coupling in the incommensurate SS phase of YMn6Sn6 by calculating the topological invariants and Berry curvature profile. The location of the Dirac magnon in the energy landscape at 73 meV matches with another experimental report. We demonstrate the accuracy of our results by highlighting the experimental features in YMn6Sn6.

Much has been learned about the topological transport in real materials. We investigate the interplay between magnetism and topology in the magnetotransport of PrRhC2. The fourfold degeneracy reduces to twofold followed by nondegenerate Weyl nodes when the orientation of the magnetic quantization axis is changed from easy axis to body diagonal through face diagonal. This engenders chirality imbalance between positive and negative chirality Weyl nodes around the Fermi energy. We observe a significant enhancement in the chiral anomaly mediated response such as planar Hall conductivity and longitudinal magnetoconductivity, due to the emergence of chirality imbalance upon orienting the magnetic quantization axis to body diagonal. The angular variations of the above quantities for different magnetic quantization axes clearly refer to the typical signature of planar Hall effect in Weyl semimetals. We further investigate the profiles of anomalous Hall conductivities as a function of Fermi energy to explore the effects of symmetries as well as chirality imbalance on Berry curvature.

In this paper, we present a theoretical formulation of magnetization dynamics in disordered binary alloys, based on the Kubo linear response theory, interfaced with a seamless combination of three approaches: density functional-based tight-binding linear muffin-tin orbitals, generalized recursion and augmented space formalism. We applied this method to study the magnetization dynamics in chemically disordered FexCo1-x (x = 0.2, 0.5, 0.8) alloys. We found that the magnon energies decreased with an increase in Co concentration. Significant magnon softening was observed in Fe20Co80 at the Brillouin zone boundary. Magnon-electron scattering increased with increasing Co content, which in turn modified the hybridization between the Fe and Co atoms. This reduced the exchange energy between the atoms and softened down the magnon energy. The lowest magnon lifetime was found in Fe50Co50, where disorder was at a maximum. This clearly indicated that the damping of magnon energies in FexCo1-x was governed by hybridization between Fe and Co, whereas the magnon lifetime was controlled by disorder configuration. Our atomistic spin dynamics simulations show reasonable agreement with our theoretical approach in magnon dispersion for different alloy compositions.

Search for new topological quantum materials is the demand of time and the theoretical prediction plays a crucial role besides the obvious experimental verification. Divination of topological properties in already well-known narrow gap semiconductors is a flourishing area in quantum material. In this view we revisited the semiconductor compound in the chalcopyrite series, with a very small gap near the Fermi energy. Using the density functional theory-based first-principles calculations, we report a strong topologically nontrivial phase in chalcopyrite ZnGeSb2, which can act as a model system of strained HgTe. The calculations reveal the nonzero topological invariant (Z2), the presence of Dirac cone crossing in the surface spectral functions with spin-momentum locked spin texture. We also study the interplay between the structural parameters and electronic properties, and report the tunable topological properties due to a very small band gap, from nontrivial to trivial phase under the application of moderate hydrostatic pressure within approximate to 7 GPa. A small modification of a lattice parameter is enough to achieve this topological phase transition which is easily accomplished in an experimental laboratory. The calculations show that a discontinuity in the tetragonal distortion of noncentrosymmetric ZnGeSb2 plays a crucial role in driving this topological phase transition. Our results are further collaborated with a low energy k center dot p model Hamiltonian to validate our abinitio findings. We showed that the evaluation of the model band energy dispersion under the hydrostatic pressure is consistent with the obtained results.

Since thermal fluctuations become more important as dimensions shrink, it is expected that low-dimensional magnets are more sensitive to atomic displacement and phonons than bulk systems are. Here we present a fully relativistic first-principles study on the spin-lattice coupling, i.e., how the magnetic interactions depend on atomic displacement, of the prototypical two-dimensional ferromagnet CrI3. We extract an effective measure of the spin-lattice coupling in CrI3, which is up to ten times larger than what is found for bcc Fe. The magnetic exchange interactions, including Heisenberg and relativistic Dzyaloshinskii-Moriya interactions, are sensitive both to the in-plane motion of Cr atoms and out-of-plane motion of ligand atoms. We find that significant magnetic pair interactions change sign from ferromagnetic (FM) to antiferromagnetic (AFM) for atomic displacements larger than 0.16 (0.18) angstrom for Cr (I) atoms. We explain the observed strong spin-lattice coupling by analyzing the orbital decomposition of isotropic exchange interactions, involving different crystal-field-split Cr-3d orbitals. The competition between the AFM t(2g)-t(2g) and FM t(2g)-e(g) contributions depends on the bond angle formed by Cr and I atoms as well as Cr-Cr distance. In particular, if a Cr atom is displaced, the FM-AFM sign changes when the I-Cr-I bond angle approaches 90 degrees. The obtained spin-lattice coupling constants, along with the microscopic orbital analysis, can act as a guiding principle for further studies of the thermodynamic properties and combined magnon-phonon excitations in two-dimensional magnets.

Considering a noncentrosymmetric, nonmagnetic double Weyl semimetal (WSM) SrSi2, we investigate the electron and hole pockets in bulk Fermi surface behavior that enables us to characterize the material as a type-I WSM. We study the structural handedness of the material and correlate it with the distinct surface Fermi surface at two opposite surfaces following an energy evolution. The Fermi arc singlet becomes doublet with the onset of spin orbit coupling that is in accordance with the topological charge of the Weyl nodes (WNs). A finite energy separation between WNs of opposite chirality in SrSi2 allows us to compute circular photogalvanic effect (CPGE). Followed by the three band formula, we show that CPGE is only quantized for Fermi level chosen in the vicinity of WN residing at a higher value of energy. Surprisingly, for the other WN of opposite chirality in the lower value of energy, CPGE is not found to be quantized. Such a behavior of CPGE is in complete contrast to the time reversal breaking WSM where CPGE is quantized to two opposite plateau depending on the topological charge of the activated WN. We further analyze our finding by examining the momentum resolved CPGE. Finally we show that two band formula for CPGE is not able to capture the quantization that is apprehended by the three band formula.

We study the role of time reversal symmetry (TRS) in the circular photogalvanic (CPG) responses considering a chiral Weyl semimetal (WSM), while a quantized CPG response is guaranteed by both the broken inversion symmetry and broken mirror symmetries. The TRS broken WSM yields one left and one right chiral Weyl node (WN), while there are two left and right chiral WNs for a TRS invariant WSM. We show that these features can potentially cause the quantization of a CPG response at higher values compared to the topological charge of the underlying WSM. This is further supported by the fact that Berry curvature and velocity behave differently depending on whether the system preserves or breaks the TRS. We find the CPG responses for a TRS invariant type-II WSM to be quantized at two and four times the topological charge of the activated WNs while the chemical potentials are, respectively, chosen in the vicinity of the energies associated with the left and right chiral WNs. By contrast, irrespective of the above choice of the chemical potential, the quantization in the CPG response is directly given by the topological charge of the activated WNs for the TRS broken case. Interestingly, we notice a nonquantized peak in the CPG response when the energies of the WNs associated with opposite chiralities are close to each other, as is the case for the TRS invariant type-I WSM considered here. Moreover, we show that the tilt can significantly modify the CPG response as the velocity in the tilt direction changes, which enters into the CPG tensor through the Fermi distribution function. Given these exciting outcomes, the second-order CPG response emerges as a useful indicator to characterize the system under consideration. Furthermore, we investigate the momentum resolved structure of the CPG response to relate with the final results and strengthen our analysis from the perspective of the lattice models.