Spin nematic fluctuations near a spin-density-wave phase

TL;DR

This paper investigates spin nematic fluctuations near a spin-density-wave phase, revealing how the nematic instability develops with temperature and magnetic correlation length, and characterizing the spectral features associated with this transition.

Contribution

It provides a phenomenological analysis of spin nematic susceptibility and spectral functions near the SDW phase, highlighting the conditions for nematic instability and its spectral signatures.

Findings

Nematic instability occurs when the correlation length reaches a critical value.

Nematic spectral function shows a central peak at finite temperature and a soft mode at zero temperature.

The spectral function exhibits a diffusive peak around zero momentum and energy.

Abstract

We study an interacting electronic system exhibiting a spin nematic instability. Using a phenomenological form for the spin fluctuation spectrum near the spin-density-wave (SDW) phase, we compute the spin nematic susceptibility in energy and momentum space as a function of temperature and the magnetic correlation length xi. The spin nematic instability occurs when xi reaches a critical value xi_{cr}, i.e., its transition temperature T_{SN} is always higher than the SDW critical temperature T_{SDW}. In particular, xi_{cr} decreases monotonically with increasing T_{SN}. Concomitantly, low-energy nematic fluctuations are present in a wider temperature region as T_{SN} becomes higher. Approaching the spin nematic instability, the nematic spectral function at zero momentum exhibits a central peak as a function of energy for a finite temperature and a soft mode at zero temperature. These properties originate from the general feature that the imaginary part of the spin-fluctuation bubble has a term linear in energy and its coefficient is proportional to the square of temperature. Furthermore we find that the nematic spectral function exhibits a diffusive peak around zero momentum and zero energy without clear dispersive features. A possible phase diagram for the spin nematic and SDW transitions is also discussed.