Excitations and quasi-one-dimensionality in field-induced nematic and spin density wave states

Oleg A. Starykh and Leon Balents

Phys. Rev. B 89, 104407 – Published 10 March 2014

Abstract

We study the excitation spectrum and dynamical response functions for several quasi-one-dimensional spin systems in magnetic fields without dipolar spin order transverse to the field. This includes both nematic phases, which harbor “hidden” breaking of spin-rotation symmetry about the field and have been argued to occur in high fields in certain frustrated chain systems with competing ferromagnetic and antiferromagnetic interactions, and spin density wave states, in which spin-rotation symmetry is truly unbroken. Using bosonization, field theory, and exact results on the integrable sine-Gordon model, we establish the collective mode structure of these states, and show how they can be distinguished experimentally.

Received 16 December 2013

DOI:https://doi.org/10.1103/PhysRevB.89.104407

Authors & Affiliations

Oleg A. Starykh¹ and Leon Balents²

¹Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA
²Kavli Institute of Theoretical Physics, University of California, Santa Barbara, Santa Barbara, California, 93106, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 89, Iss. 10 — 1 March 2014

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Schematic view of the excitation spectrum in the collinear SDW state (see Sec. 3), i.e., the inelastic structure factor, in momentum (parallel to the chain direction defined by strong bonds) and energy space. Solid (black) lines show the results of chain mean-field theory, i.e., excitations on single chains, and dashed (blue) lines give the two-dimensional results corrected for collective interchain effects (by the RPA approximation). The symbols $s$ (soliton), $\bar{s}$ (antisoliton), and $B_{1}$ (breather) on top of solid lines indicate their origin in the excitations of the single chain sine-Gordon model. The excitations shown here at momenta $k_{x} = π (1 \pm 2 M)$ and $k_{x} = 0$ occur in the longitudinal ( $S^{z}$ ) channel, while those at $k_{x} = π$ and $k_{x} = \pm 2 π M$ occur in the transverse ( $S^{\pm}$ ) one. Note that while all excitations are gapped at the sine-Gordon level (solid lines), the longitudinal excitations become gapless, reflecting the phason mode, once two-dimensional effects are included. The shaded gray area indicates a multi-particle continuum composed of solitons, antisolitons $(s, \bar{s})$ and breathers $B_{1}$ . The figure is drawn for the situation $M < 1 / 4$ , for which $π (1 - 2 M)$ is larger than $2 π M$ . For $M > 1 / 4$ , the corresponding features exchange places in the sketch.
Reuse & Permissions
Figure 2
Schematic structure factor, analogous to Fig. 1, for the two-dimensional spin nematic state (see Sec. 4). In contrast to the SDW case, only qualitative shifts of the excitations away from $k_{x} = 0$ occur, so we draw only solid (black) lines there. Excitations at momenta $k_{x} = π (1 \pm 2 M)$ and $k_{x} = 0$ are longitudinal, and those at $k_{x} = π$ are transverse (a gapped transverse mode at $2 π M$ is also present, but not shown in the figure). Note the absence of low-energy transverse excitations. Indeed, as indicated by the break in vertical scale, excitations at $k_{x} = π$ exhibit a much larger gap in the spin nematic case, owing to the formation of this gap already at the decoupled chain level. The gapless Goldstone mode of the spin nematic, shown as a dashed (blue) line, contributes only in the vicinity of $k_{x} = 0$ . Vertical axes labels and energy separations refer to symbols from the treatment in Sec. 4.
Reuse & Permissions
Figure 3
Lattice geometries considered in the paper. (a) Rectangular geometry, relevant for Ising-like coupled chains, discussed in Sec. 2b1, and also for nematic chains, considered in Sec. 2b2. In the latter case, $J_{1} < 0$ and $J_{2} > 0$ . (b) Equivalent representation of coupled nematic chains as a system of coupled zigzag ladders. (c) Spatially anisotropic triangular lattice, discussed in Sec. 2b3.
Reuse & Permissions
Figure 4
Plot of $ξ$ [solid (magenta) line] and breather masses $m_{1} / m_{s}$ [dashed (red) line] and $m_{2} / m_{s}$ [dotted (blue) line] as a function of magnetization $M$ . Horizontal $y = 0.5$ line is used to highlight “high magnetization” region with $[1 / ξ] = 1$ : note that the second breather is absent there.
Reuse & Permissions
Figure 5
Plot of soliton mass $m_{s} / v$ as a function of magnetization $M$ for $J^{'} = 0.5 J$ . “Old $m_{s}$ ” (blue curve) is obtained using $F_{standard}$ , without correcting for $ξ \to 1$ divergence. “New $m_{s}$ ” (red curve) is the corrected result (28), which is obtained using $F_{new}$ from the Appendix pp1. For the spatially anisotropic triangular lattice, the SDW phase, for which $m_{s}$ is calculated here, is the ground state of the 2d problem in the interval $0 < M ≲ 0.3$ . At higher $M$ , the SDW is replaced by the cone phase. Note that, in the limit $J^{'} / J \to 0$ , at fixed $M$ , the two curves converge to one another (in fact the ratio of $m_{s}$ calculated in both fashions converges to one).
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics