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Register a new userAntiferromagnetic magnons and local anisotropy: dynamical mean-field study
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We present a dynamical mean-field study of antiferromagnetic magnons in one-, two- and three-orbital Hubbard model of square and bcc cubic lattice at intermediate coupling strength. Weinvestigate the effect of anisotropy introduced by an external magnetic field or single-ion anisotropy.For the latter we tune continuously between the easy-axis and easy-plane models. We also analyzea model with spin-orbit coupling in cubic site-symmetry setting. The ordered states as well as themagnetic excitations are sensitive to even a small breaking ofSU(2)symmetry of the model andfollow the expectations of spin-wave theory as well as general symmetry considerations.
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We consider nonlinear magnon interactions in collinear antiferromagnetic (AF) insulators at finite temperatures. In AF systems with biaxial magnetocrystalline anisotropy, we implement a self-consistent Hartree-Fock mean-field approximation to explore the nonlinear interactions. The resulting nonlinear magnon interactions separate into two-magnon intra- and interband scattering processes. Furthermore, we compute the temperature dependence of the magnon spectrum due to nonlinear magnon interactions for square and hexagonal lattices. Measurements of the predicted AF resonance at different temperatures can probe nonlinear interactions close to the magnetic phase transitions. Our findings establish a framework for exploring magnonic phenomena where interactions are essential, e.g., magnon transport and Bose-Einstein condensation of magnons.
The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the foundations of the DMFT, derive the underlying self-consistency equations, and present several applications which have provided important insights into the properties of correlated matter.
We develop an approach to describe antiferromagnetic magnons on a bipartite lattice supporting the N{e}el state using fractionalized degrees of freedom typically inherent to quantum spin liquids. In particular we consider a long-range magnetically ordered state of interacting two-dimensional quantum spin$-1/2$ models using the Chern-Simons (CS) fermion representation of interacting spins. The interaction leads to Cooper instability and pairing of CS fermions, and to CS superconductivity which spontaneously violates the continuous $mathrm{U}(1)$ symmetry generating a linearly-dispersing gapless Nambu-Goldstone mode due to phase fluctuations. We evaluate this mode and show that it is in high-precision agreement with magnons of the corresponding N{e}el antiferromagnet irrespective to the lattice symmetry. Using the fermion formulation of a system with competing interactions, we show that the frustration gives raise to nontrivial long-range four, six, and higher-leg interaction vertices mediated by the CS gauge field, which are responsible for restoring of the continuous symmetry at sufficiently strong frustration. We identify these new interaction vertices and discuss their implications to unconventional phase transitions. We also apply the proposed theory to a model of anyons that can be tuned continuously from fermions to bosons.
Low-energy magnon excitations in magnetoelectric LiFePO$_4$ have been investigated by high-frequency high-field electron spin resonance spectroscopy in magnetic fields up to B = 58 T and frequencies up to f = 745 GHz. For magnetic fields applied along the easy magnetic axis, the excitation gap softens and vanishes at the spin-flop field of BSF = 32 T before hardening again at higher fields. In addition, for B smaller than BSF we observe a resonance mode assigned to excitations due to Dzyaloshinskii-Moriya (DM)-interactions, thereby evidencing sizable DM interaction of approx 150 micro eV in LiFePO4. Both the magnetisation and the excitations up to high magnetic fields are described in terms of a mean-field theory model which extends recent zero field inelastic neutron scattering results. Our results imply that magnetic interactions as well as magnetic anisotropy have a sizable quadratic field dependence which we attribute to significant magnetostriction.
A technique allowing for a perturbative treatment of nonlocal corrections to the single-site dynamical mean-field theory (DMFT) in finite dimensions is developed. It is based on the observation that in the case of strong electron correlation the one-electron Greens function is strongly spatially damped so that its intersite matrix elements may be considered as small perturbations. Because the non-local corrections are at least quadratic in these matrix elements, DMFT in such cases may be a very accurate approximation in dimensions d = 1-3. This observation provides a rigorous justification for the application of DMFT to physical systems. Furthermore, the technique allows for a systematic evaluation of the nonlocal corrections. This is illustrated with the calculation of the magnetic short range order parameter for nearest neighbor spins in the half filled Hubbard model on the square lattice in its insulating phase which exhibits an excellent agreement with the results of a recent cluster approach.As a second example we study the lowest order correction to the DMFT self-energy and its influence on the local density of states.
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