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arXiv:1701.01465 · Physical review. B./Physical review. B

Phase diagram of weakly coupled Heisenberg spin chains subject to a uniform Dzyaloshinskii-Moriya interaction

Wen Jin, Oleg A. Starykh

Published Jun 8, 2017• 13 citations
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Abstract

Motivated by recent experiments on spin chain materials ${\mathrm{K}}_{2}{\mathrm{CuSO}}_{4}{\mathrm{Cl}}_{2}$ and ${\mathrm{K}}_{2}{\mathrm{CuSO}}_{4}{\mathrm{Br}}_{2}$, we theoretically investigate the problem of weakly coupled spin chains (chain exchange $J$, interchain ${J}^{\ensuremath{'}}$) subject to a staggered between chains, but uniform within a given chain, Dzyaloshinskii-Moriya (DM) interaction of magnitude $D$. In the experimentally relevant limit ${J}^{\ensuremath{'}}\ensuremath{\ll}D\ensuremath{\ll}J$ of the strong DM interaction the spins on the neighboring chains are forced to rotate in opposite directions, effectively resulting in a cancellation of the interchain interaction between components of spins in the plane normal to the vector $\mathbit{D}$. This has the effect of promoting a two-dimensional collinear spin density wave state, which preserves U(1) symmetry of rotations about the $\mathbit{D}$ axis. We also investigate response of this interesting system to an external magnetic field $\mathbit{h}$ and obtain the h-D phase diagrams for the two important configurations $\mathbit{h}\ensuremath{\parallel}\mathbit{D}$ and $\mathbit{h}\ensuremath{\perp}\mathbit{D}$.

DOI
10.1103/physrevb.95.214404

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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.
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​.
We theoretically study the joint influence of uniform Dzyaloshinskii-Moriya (DM) interactions, symmetric exchange anisotropy (with its axis parallel to the DM vector), and arbitrarily oriented magnetic fields on one-dimensional spin 1∕21∕21∕2 antiferromagnets. We show that the zero-temperature phase diagram contains three competing phases: (i) an antiferromagnet with Neel vector in the plane spanned by the DM vector and the magnetic field, (ii) a dimerized antiferromagnet with Neel vector perpendicular to both the DM vector and the magnetic field, and (iii) a gapless Luttinger liquid. Phase (i) is destroyed by a small magnetic field component along the DM vector and is furthermore unstable beyond a critical value of easy-plane anisotropy, which we estimate using Abelian and non-Abelian bosonization along with perturbative renormalization group. We propose a mathematical equivalent of the spin model in a one-dimensional Josephson junction array located in proximity to a bulk superconductor. We discuss the analogues of the magnetic phases in the superconducting context and comment on their experimental viability.
We have considered and alternating Heisenberg spin chain with nearest-neighbor (J1J_1J1​), next-nearest neighbor (J2J_2J2​) antiferromagnetic couplings along with z-component of the Dzyaloshinskii-Moriya(DM) (DzD_zDz​) interactions. The Hamiltonian has been studied using (a) Linear Spin-Wave Theory(LSWT) and (b) Density Matrix Renormalization Group (DMRG). The system had been reported earlier as a classical ferrimagnet only when nearest neighbor exchange interactions are present. Both the antiferromagnetic next-nearest neighbor interactions and DM interactions introduce strong quantum fluctuations and due to which all the signatures of ferrimagnetism vanishes. We find that the nonzero J2J_2J2​ introduces strong quantum fluctuations in each of the spin sites due to which the z-components of both spin-1 and spin-1/2 sites average out to be zero. The ground state becomes a singlet. The presence of J1J_1J1​ along with DzD_zDz​ introduces a short range order but develops long range order along the XY plane. J1J_1J1​ along with J2J_2J2​ induces competing phases with structure factor showing sharp and wide peaks, at two different angles reflecting the spin spiral structure locally as well as in the underlying lattice. Interestingly, we find that the DzD_zDz​ term removes the local spin spiral structure in z-direction, while developing a spiral order in the XY plane.
We report a combined analytical and density matrix renormalized group study of the antiferromagnetic XXZXXZXXZ spin-1/21/21/2 Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya (DM) interaction and a transverse magnetic field. The numerically determined phase diagram of this model, which features two ordered Ising phases and a critical Luttinger liquid, one with fully broken spin-rotational symmetry, agrees well with the predictions of Garate and Affleck [I. Garate and I. Affleck, Phys. Rev. B 81, 144419 (2010)]. We also confirm the prevalence of the Nz{N}^{z}Nz N\'eel Ising order in the regime of comparable DM and magnetic field magnitudes.
We study the interplay of electric and magnetic order in the one-dimensional Heisenberg spin-12\frac{1}{2}21​ XXZ chain with large Ising anisotropy in the presence of the Dzyaloshinskii-Moriya (DM) interaction and with longitudinal and transverse magnetic fields, interpreting the DM interaction as a coupling between the local electric polarization and an external electric field. We obtain the ground state phase diagram using the density matrix renormalization group method and compute various ground state quantities like the magnetization, staggered magnetization, electric polarization and spin correlation functions, etc. In the presence of both longitudinal and transverse magnetic fields, there are three different phases corresponding to a gapped N\'eel phase with antiferromagnetic (AF) order, gapped saturated phase, and a critical incommensurate gapless phase. The external electric field modifies the phase boundaries but does not lead to any new phases. Both external magnetic fields and electric fields can be used to tune between the phases. We also show that the transverse magnetic field induces a vector chiral order in the N\'eel phase (even in the absence of an electric field) which can be interpreted as an electric polarization in a direction parallel to the AF order.