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arXiv:1908.07702 · Physical review. B./Physical review. B

Effects of staggered Dzyaloshinskii-Moriya interactions in a quasi-two-dimensional Shastry-Sutherland model

Tianqi Chen, Chu Guo, Pinaki Sengupta, Dario Poletti

Published Feb 18, 2020• 11 citations
arXivHTMLPDF

Abstract

Frustrated quantum spin systems exhibit exotic physics induced by external magnetic field with anisotropic interactions. Here, we study the effect of nonuniform Dzyaloshinskii-Moriya (DM) interactions on a quasi-two-dimensional Shastry-Sutherland lattice using a matrix product state algorithm. We first recover the magnetization plateau structure present in this geometry and then we show that both interdimer and intradimer DM interactions significantly modify the plateaux. The non-number-conserving intradimer interaction smoothens the shape of the magnetization curve, while the number-conserving interdimer interaction induces different small plateaux, which are signatures of the finite size of the system. Interestingly, the interdimer DM interaction induces chirality in the system. We thus characterize these chiral phases with particular emphasis to their robustness against intradimer DM interactions.

DOI
10.1103/physrevb.101.064417

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scientific writing and presentation skills also improved due to his suggestions.I am really very thankful for being so flexible and allowing me to choose the work and project which interests me most.

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Frustrated quantum spin systems exhibit exotic physics induced by external magnetic field with anisotropic interactions. Here, we study the effect of nonuniform Dzyaloshinskii-Moriya (DM) interactions on a quasi-two-dimensional Shastry-Sutherland lattice using a matrix product state algorithm. We first recover the magnetization plateau structure present in this geometry and then we show that both interdimer and intradimer DM interactions significantly modify the plateaux. The non-number-conserving intradimer interaction smoothens the shape of the magnetization curve, while the number-conserving interdimer interaction induces different small plateaux, which are signatures of the finite size of the system. Interestingly, the interdimer DM interaction induces chirality in the system. We thus characterize these chiral phases with particular emphasis to their robustness against intradimer DM interactions.
We investigate the effect of Dzyaloshinskii-Moriya (DM) interactions on torque measurements of quantum magnets with magnetization plateaux in the context of a frustrated spin-1/2 ladder. Using extensive DMRG simulations, we show that the DM contribution to the torque is peaked at the critical fields, and that the total torque is non-monotonous if the DM interaction is large enough compared to the g -tensor anisotropy. More remarkably, if the DM vectors point in a principal direction of the g -tensor, torque measurements close to this direction will show well-defined peaks even for small DM interaction, leading to a very sensitive way to detect the critical fields. We propose to test this effect in the two-dimensional plateau system SrCu 2 (BO 3 ) 2 .
Spin-1/2 Heisenberg model on the Shastry-Sutherland lattice is considered within the many-body perturbation theory developed from the exactly solved spin-1/2 Ising-Heisenberg model with the Heisenberg intradimer and Ising interdimer interactions. The former model is widely used for a description of magnetic properties of the layered compound SrCu _2 2 (BO _3 3 ) _2 2 , which exhibits a series of fractional magnetization plateaux at sufficiently low temperatures. Using the novel type of many-body perturbation theory we have found the effective model of interacting triplet excitations with the extended hard-core repulsion, which accurately recovers 1/8, 1/6 and 1/4 magnetization plateaux for moderate values of the interdimer coupling. A possible existence of a striking quantum phase of bound triplons is also revealed at low enough magnetic fields.
By using the density-matrix renormalization group method, the spin entanglement in the antiferromagnetic Heisenberg chain with the staggered Dzyaloshinskii-Moriya (DM) interactions is investigated. It is found that the staggered DM interactions remove the field-induced second order quantum phase transition of the system at the magnitude of magnetic field H＝2, and lead to the vanishing of the anomalous behavior of quantum entanglement. Also, the staggered DM interactions eliminate the divergence of entanglement range. It means the disappearance of the factorizing point in the model studied. Due to the presence of the staggered DM interactions, the system will never come to the state of saturated ferromagnetism under finite magnetic fields, thus maintaining the spin entanglement. The staggered DM interactions favor the tuning of the strength and range of spin entanglement.
Dzyaloshinskii–Moriya (DM) interactions cause many interesting physical features, such as topologically nontrivial magnetic skyrmions and chiral domain walls. These interactions become more pronounced in low-dimensional systems. We investigated a one-dimensional Heisenberg spin-1/2 chain with an asymmetric DM interaction. The results show that, upon applying a nonzero DM interaction, the Néel ground state transitions to a spin chiral phase. Moreover, using the mean-field approximation, we obtain the dispersion of the energy spectrum, from which the z-axis spin chirality is calculated as a function of the strength of the DM interaction for low-lying excitations. The results indicate that the DM interaction facilitates chirality for Dz ≤ J and induces a spin-gapped chiral state.
We investigate the interplay of Dzyaloshinskii-Moriya interactions and an external field in spin-1∕21∕21∕2 dimers. For isolated dimers and at low field, we derive simple expressions for the staggered and uniform magnetizations which show that the orientation of the uniform magnetization can deviate significantly from that of the external field. In fact, in the limit where the D\mathbf{D}D vector of the Dzyaloshinskii-Moriya interaction is parallel to the external field, the uniform magnetization actually becomes perpendicular to the field. For larger fields, we show that the staggered magnetization of an isolated dimer has a maximum close to one-half the polarization, with a large maximal value of $0.35g{\ensuremath{\mu}}_{B}$ in the limit of very small Dzyaloshinskii-Moriya interaction. We investigate the effect of interdimer coupling in the context of ladders with density-matrix renormalization-group (DMRG) calculations and show that, as long as the values of the Dzyaloshinskii-Moriya interaction and of the exchange interaction are compatible with respect to the development of a staggered magnetization, the simple picture that emerges for isolated dimers is also valid for weakly coupled dimers with minor modifications. The results are compared with torque measurements on Cu2(C5H12N2)2Cl4{\mathrm{Cu}}_{2}{({\mathrm{C}}_{5}{\mathrm{H}}_{12}{\mathrm{N}}_{2})}_{2}{\mathrm{Cl}}_{4}Cu2​(C5​H12​N2​)2​Cl4​.
The study of topological magnetic excitations have attracted widespread attention in the past few years.The wide variety of ground state phases realized in different two-dimensional magnets have emerged as versatile platforms for realizing magnetic analogues of topological phases uncovered in electronic systems over the past two decades.Dzyaloshinskii-Moriya(DM) interactions, that are ubiquitous in many quantum magnets, and has been demonstrated to induce a non-trivial topology in the magnetic excitations in many quantum magnets.In particular, signatures of DM-interaction induced topological features observed in the dispersion of magnetic excitations in the geometrically frustrated Shastry-Sutherland compound SrCu 2 (BO 3 ) 2 and honeycomb ferromagnet CrI 3 have provided the motivation behind the bulk of the research presented in this thesis.In the first chapter we introduce the background and motivation of our study.We showed that the vastly available materials with a possibility of nonzero symmetry allowed DM-interaction motivate us to study the minimal models of interacting spins related to the materials.In the second chapter we have described the methods that is used to study the spin systems.To describe the spin excitations in the long-range ordered system and dimerized system, we use Holstein-Primakoff transformation and bond-operator formalism respectively.The Schwinger Boson mean field theory is applicable for any generic magnetic ground state and useful to study the system at high temperatures compared with Holstein-Primakoff transformation.After transforming the Hamiltonian into a quadratic bosonic Hamiltonian, it is diagonalized by using Bogoliubov-Valatin transformation.Different observables like Berry-curvature, Chern-number, Dynamical Spin structure factor etc. are cal-vii culated by using the single particle wave-function obtained from Bogoliubov-Valatin transformation.A non-zero Berry curvature is a signature of topologically protected edge states in a stripe geometry of a lattice and a systematic way of calculating edge states is also explained in the second chapter.Moreover in the second chapter the usefulness of symmetry in obtaining band degeneracies and the allowed spin-spin interaction terms are also described.The past theoretical studies show the presence of topological magnons in honeycomb ferromagnetic models due to presence of DM-interaction on a next-nearest neighbour bonds.Recently this kind of DM-interaction is detected in the honeycomb ferromagnet CrI 3 .This type of DM-interaction induces chiral edge states of magnon in the system and so we named it as chiral DM-interaction.In the third chapter we show that breaking of inversion symmetry at the center of honeycomb structure gives rise to a extra DM-interaction which we named as anti-chiral DM-interaction.We studied the system by using Schwinger Boson mean field theory and Holstein-Primakoff transformation and show that when the antichiral DM-interaction dominates over the chiral DM-interaction, the direction of velocity of the edge states become in the same direction (antichiral edge states).Due to conservation of total number of spins in the system a bulk current flows in the opposite direction relative to the antichiral edge current.In this study we suggested the way to break the inversion symmetries in the materials CrSrTe 3 , CrGrTe 3 , AFe 2 (PO 4 ) 2 (A=Ba, Cs, K, La) to achieve antichiral DM-interaction.The presence of antichiral edge states can be detected by using inelastic neutron scattering by detecting the band tilting at K and K points of magnon bands.Moreover we showed that spin noise spectroscopy at the edges is useful measurements to detect the presence of antichiral edge modes.Magnetic force microscopy is also a promising tool to detect the antichiral magnons at edges.The underlying spin-Hamiltonian of the antiferromagnetic systems in the materials like rare-earth tetraborides(RB 4 , R=Er,Tm) and U 2 Pd 2 In can be described by using extended Shastry-Sutherland models.In previous theoretical studies it is shown that there is a non-collinear spin-state known as flux state exists in the Shastry-Sutherland model in presence of out of plane DM-interaction.Although the presence of perpendicular component of DM-interactions in the rare-earth materials are not known, it can be induced artificially by using circularly polarized light or using heavy-metal alloys.In the fourth chapter, we studied the magnetic excitations in the flux state on Shastry-Sutherland lattice in-First of all, I would like to thank my research supervisor Prof. Pinaki Sengupta for his continuous support and guidance throughout my Ph.D. study on and off the field.whenever I went to his office with a problem he always welcomed me and assisted me.He has encouraged and inspired me to become an independent researcher and developed my critical thinking.I am really grateful to him as a person who introduced me the field of research.Moreover my scientific writing and presentation skills also improved due to his suggestions.I am really very thankful for being so flexible and allowing me to choose the work and project which interests me most.