ESR study of the frustrated $S=\frac{1}{2}$ chain magnet ${\mathrm{LiCuVO}}_4$ in spiral and spin-modulated phases

We report on the electron spin resonance (ESR) study of ${\mathrm{LiCuVO}}_4$ in spiral and spin-modulated phases ($0<{\mu }_{0}H<10$ T). The measurements have been made on high quality samples that allowed getting rid of absorption lines arising from defects. In the field range of spiral phase ($0<{\mu }_{0}H<7.5$ T) all observed branches of the spectrum can be ascribed to uniform oscillations of planar spin structure. The ESR spectrum observed in spin-modulated phase (${\mu }_{0}H>7.5$ T) has two branches. One of them can be explained by uniform oscillations of spin structure, whereas the second branch, surprisingly demonstrates only a weak dependence on field orientation, which indicates the exchange nature of this mode. Allegedly this mode can be associated with soliton excitations.

Figure 1

The frequency-field diagram of ESR measured at $H\parallel \mathbf{a}$ (red circles) and $H\parallel \mathbf{b}$ (black squares) at $T=1.3$ K. The dashed line marks the field boundary between the spiral and SM phases. The solid lines I, III and II, IV show computed branches of the ESR for planar spiral structure before and after spin-flop reorientation. The dash-dotted line shows the ESR mode in the paramagnetic state ($T=4.2$ K) with $g_{a,b}=2.08$. The dotted line is the fitting result of branch V with dependency: $\nu =(g_{ab}{\mu }_B/h)(H-H_c^{*})$.

Figure 2

The frequency-field diagram of the ESR measured at $H\parallel \mathbf{c}$ at $T=1.3$ K. The dashed line marks the field boundary between the spiral and SM phases. The solid lines III and IV show computed branches of the ESR for planar spiral structure. The dash-dotted line shows the ESR mode in the paramagnetic state ($T=4.2$ K) with $g_c=2.46$. The dotted line is the fitting result of branch V with dependency: $\nu =(g_c{\mu }_B/h)(H-H_c^{*})$.

Figure 3

The examples of ESR lines measured at $H\parallel \mathbf{b}$ and $T=1.3$ K. The absorption lines are marked with symbols I–V in accordance with the designation of Figs. 1 and 2. Red lines represent the same spectra given in the expanded scale shown to the right.

Figure 4

Examples of ESR lines measured at $H\parallel \mathbf{c}$ and $T=1.3$ K. The absorption lines are marked with symbols III, IV, and V in accordance with the designation of Figs. 1 and 2. Crosses mark weak paramagnetic absorption lines from Diphenylpicrylhydrazyl (DPPH) used for field calibration and cavity background. Red lines represent the same spectra given in the expanded scale shown to the right.

Figure 5

The temperature evolution of ESR lines measured at $H\parallel \mathbf{a}$ and at excitation frequency: $\nu =26.2$ GHz. Colored dotted lines represent the same spectra given in the expanded scale shown to the right. The absorption lines are marked with symbols I, IV, and V in accordance with the designation of Figs. 1 and 2. Dashed lines mark the field boundaries between magnetic phases at $T=1.3$ K.

Figure 6

Examples of the ESR lines measured at $H\parallel \mathbf{b}$ and $T=1.3$ K and different polarization conditions: $h\parallel H$ and $h\perp H$. The absorption lines are marked with symbols in accordance with the designation of Figs. 1 and 2.

Figure 7

Black lines show the temperature evolution of the ESR lines at $H\parallel \mathbf{c}$ and $\nu =53.1$ GHz. All lines are normalized to 1 for high fields (see spectrum measured at $T=1.3$ K). The spectra measured at higher temperatures are shifted along the $y$ axis for better representation. Red lines demonstrate the results of fitting by combination of the Lorentz single line and steplike Fermi function.

Figure 8

The black line shows the ESR line measured at $H\parallel \mathbf{c}, T=2.42$ K and $\nu =53.1$ GHz. The red line shows the result of fitting with sum of Lorentz line (green dash-dotted line) and steplike Fermi function (blue dashed line).

Figure 9

Temperature dependencies of resonance field $H_R$ (black squares), linewidth $\mathrm{\Delta }H$ (open squares), and integral intensity $I$ (green triangles) of the Lorentz-like part of the absorption and integral intensity of nonresonance steplike absorption $I_n$ (red circles).