No Arabic abstract
Competing orders is a general concept to describe various quantum phases and transitions in various materials. One efficient way to investigate competing orders is to first classify different class of excitations in a given quantum phase, then study their competing responses under various external probes. This strategy may not only lead to deep understanding of the quantum phase itself, but also its deep connections to various other quantum phases nearby. We implement this approach by studying the Rotated Ferromagnetic Heisenberg model (RFHM) in two different transverse fields $h_x$ and $h_z$ which can be intuitively visualized as studying spin-orbit couplings (SOC) effects in 2d Ising or anisotropic XY model in a transverse field. At a special SOC class, it was known that the RFHM at a zero field owns an exact ground state called Y-x state. It supports non only the commensurate C-C$_0$ and C-C$_{pi} $ magnons, but also the in-commensurate C-IC magnons. These magnons are non-relativistic, not contained in the exact ground state, so need to be thermally excited. Their dramatic response under the longitudinal $ h_y $ field was recently worked out by the authors. Here we find they respond very differently under the two transverse fields. Any $h_x$ ($h_z$) changes the collinear Y-x state to a canted co-planar YX-x (YZ-x) state which suffers quantum fluctuations. The C-C$_0$, C-C$_{pi} $ and C-IC magnons sneak into the quantum ground state, become relativistic and play leading roles even at $ T=0 $. We map out the boundaries among the C-C$_0$, C-C$_{pi} $ and C-IC magnons, especially the detailed evolution of the C-IC magnons inside the canted phases. As $h_x$ ($h_z$) increases further, the C-C$_0$ magnons always win the competition and emerge as the seeds to drive a transition from the YX-x (YZ-x) to the X-FM ( Z-FM ) which is shown to be in the 3d Ising universality class.
In this work, we investigate the possible dramatic effects of Rashba or Dresselhaus spin-orbit coupling (SOC) on fermionic Hubbard model in a 2d square lattice. In the strong coupling limit, it leads to the Rotated Anti-ferromagnetic Heisenberg model which is a new class of quantum spin model. For a special equivalent class, we identify a new spin-orbital entangled commensurate ground ( Y-y ) state subject to strong quantum fluctuations at $T=0$. We evaluate the quantum fluctuations by the spin wave expansion up to order $ 1/S^2 $. In some SOC parameter regime, the Y-y state supports a massive relativistic in-commensurate magnon ( C-IC ) with its two gap minima positions continuously tuned by the SOC parameters. The C-IC magnons dominate all the low temperature thermodynamic quantities and also lead to the separation of the peak positions between the longitudinal and the transverse spin structure factors. In the weak coupling limit, any weak repulsive interaction also leads to a weak Y-y state. There is only a crossover from the weak to the strong coupling. High temperature expansions of the specific heats in both weak and strong coupling are presented. The dramatic roles to be played by these C-IC magnons at generic SOC parameters or under various external probes are hinted. Experimental applications to both layered noncentrosymmetric materials and cold atom are discussed.
Ferromagnetic (FM) manganites, a group of likely half-metallic oxides, are of special interest not only because they are a testing ground of the classical doubleexchange interaction mechanism for the colossal magnetoresistance, but also because they exhibit an extraordinary arena of emergent phenomena. These emergent phenomena are related to the complexity associated with strong interplay between charge, spin, orbital, and lattice. In this review, we focus on the use of inelastic neutron scattering to study the spin dynamics, mainly the magnon excitations in this class of FM metallic materials. In particular, we discussed the unusual magnon softening and damping near the Brillouin zone boundary in relatively narrow band compounds with strong Jahn-Teller lattice distortion and charge/orbital correlations. The anomalous behaviors of magnons in these compounds indicate the likelihood of cooperative excitations involving spin, lattice, as well as orbital degrees of freedom.
With the advancement in synthesizing and analyzing Kitaev materials, the Kitaev-Heisenberg model on the honeycomb lattice has attracted a lot of attention in the last few years. Several variations, which include additional anisotropic interactions as well as response to external magnetic field, have been investigated and many exotic ordered phases have been discussed. On the other hand, quantum spin systems are proving to be a fertile ground to realize and study bosonic analogues of fermionic topological states of matter. Using the spin-wave theory we show that the ferromagnetic phase of the extended Kitaev-Heisenberg model hosts topological excitations. Along the zig-zag edge of the honeycomb lattice we find chiral edge states, which are protected by a non-zero Chern number topological invariant. We discuss two different scenarios for the direction of the spin polarization namely $[001]$ and $[111]$, which are motivated by possible directions of applied field. Dynamic structure factor, accessible in scattering experiments, is shown to exhibit signatures of these topological edge excitations. Furthermore, we show that in case of spin polarization in $[001]$ direction, a topological phase transition occurs once the Kitaev couplings are made anisotropic.
We have performed 59Co NMR experiments on the ferromagnetic superconductor UCoGe under magnetic fields (H) along the a- and b- axes to investigate the relationship between ferromagnetic properties and superconductivity. The ferromagnetic ordering temperature TCurie is suppressed and the nuclear spin-lattice relaxation rate 1/T1 at 2 K is enhanced in H || b, although TCurie and 1/T1 are unchanged in H || a, indicating that the ferromagnetic criticality is induced only when H is applied along the b axis. We show the close relationship between the magnetic anisotropies and the superconducting ones reported by Aoki et al.: the superconductivity is gradually suppressed in H || a, but enhanced in H || b above 5 T. We strongly suggest that the enhancement of the superconductivity observed in H || b originates from the field induced ferromagnetic criticality, as pointed out by Aoki et al and Mineev.
The specific heat and thermal conductivity of the insulating ferrimagnet Y$_3$Fe$_5$O$_{12}$ (Yttrium Iron Garnet, YIG) single crystal were measured down to 50 mK. The ferromagnetic magnon specific heat $C$$_m$ shows a characteristic $T^{1.5}$ dependence down to 0.77 K. Below 0.77 K, a downward deviation is observed, which is attributed to the magnetic dipole-dipole interaction with typical magnitude of 10$^{-4}$ eV. The ferromagnetic magnon thermal conductivity $kappa_m$ does not show the characteristic $T^2$ dependence below 0.8 K. To fit the $kappa_m$ data, both magnetic defect scattering effect and dipole-dipole interaction are taken into account. These results complete our understanding of the thermodynamic and thermal transport properties of the low-lying ferromagnetic magnons.