Angular dependence of electron spin resonance for detecting the quadrupolar liquid state of frustrated spin chains

Spin nematic phase is a phase of frustrated quantum magnets with a quadrupolar order of electron spins. Since the spin nematic order is usually masked in experimentally accessible quantities, it is important to develop a methodology for detecting the spin nematic order experimentally. In this paper we propose a convenient method for detecting quasi-long-range spin nematic correlations of a quadrupolar Tomonaga-Luttinger liquid state of $S=1/2$ frustrated ferromagnetic spin chain compounds, using electron spin resonance (ESR). We focus on linewidth of a so-called paramagnetic resonance peak in ESR absorption spectrum. We show that a characteristic angular dependence of the linewidth on the direction of magnetic field arises in the spin nematic phase. Measurements of the angular dependence give a signature of the quadrupolar Tomonaga-Luttinger liquid state. In our method we change only the direction of the magnetic field, keeping the magnitude of the magnetic field and the temperature. Therefore, our method is advantageous for investigating the one-dimensional quadrupolar liquid phase that usually occupies only a narrow region of the phase diagram.

Figure 1

The angular dependence of the ESR linewidth of (a) the standard TLL and (b) the quadrupolar TLL induced by an intrachain exchange anisotropy. The angle $\theta$ specifies direction of magnetic field. At $\theta =0$, the magnetic field is parallel to direction of an anisotropic spin-spin interaction. The periodicity of the maximum linewidth against $\theta$ enables us to distinguish the quadrupolar TLL from the standard one.

Figure 2

The ground-state phase diagram of the $S=1/2$ frustrated ferromagnetic chain (2.1). The quadrupolar TLL phase is spread in a field range $H_{c1}<H<H_s$. For $H<H_{c1}$, the ground state belongs to the vector chiral phase. For $H>H_s$, the ground state is fully polarized. The ${\mathrm{SDW}}_2$ phase and the spin nematic phase are separated at $H=H^{*}$ where $K=1/2$.

Figure 3

Angular dependence of the resonance frequencies (D31) and (D32) of the split paramagnetic resonance peaks and their linewidth (D34) induced by the uniform DM interaction. Here we used a value $\gamma D/H=0.2$.