Cyclotron Resonance in the Hidden-Order Phase of ${\mathrm{URu}}_2{\mathrm{Si}}_2$

We report the first observation of cyclotron resonance in the hidden-order phase of ultraclean ${\mathrm{URu}}_2{\mathrm{Si}}_2$ crystals, which allows the full determination of angle-dependent electron-mass structure of the main Fermi-surface sheets. We find an anomalous splitting of the sharpest resonance line under in-plane magnetic-field rotation. This is most naturally explained by the domain formation, which breaks the fourfold rotational symmetry of the underlying tetragonal lattice. The results reveal the emergence of an in-plane mass anisotropy with hot spots along the [110] direction, which can account for the anisotropic in-plane magnetic susceptibility reported recently. This is consistent with the “nematic” Fermi liquid state, in which itinerant electrons have unidirectional correlations.

Figure 1

Observation of cyclotron resonance in the hidden-order phase of ${\mathrm{URu}}_2{\mathrm{Si}}_2$. (a) Field dependence of the change in $1/Q$ at several temperatures for $\mathit{H}\parallel [100]$. Each resonance field corresponds to the cyclotron mass of each extremal orbit as labeled in unit of the free electron mass $m_0$. Each curve is shifted vertically for clarity. (b) Resonance fields at different frequencies for $\mathit{H}\parallel [100]$ show the linear relation (dotted lines). Inset shows a schematic configuration of the microwave measurements. The dc field $\mathit{H}$ is applied parallel to the microwave field component ${\mathit{H}}_{\omega }$, which excites the microwave current ${\mathit{J}}_{\omega }$ near the sample surface in the region characterized by the skin depth $\delta$ (red shades).

Figure 2

Cyclotron resonance under in-plane field rotation. (a) Microwave dissipation as a function of field measured at 28 GHz. A smooth polynomial background field dependence $1/Q_{\mathrm{bg}}$ has been subtracted and the two-peak fitting analysis is used (lines) to extract the resonance fields $A$ and $A^{\prime }$. Inset shows schematic U atom arrangements in the tetragonal crystal structure and the definition of magnetic-field angle $\varphi$ in the $ab$ plane. (b) The same plot for 60 GHz. The arrows indicate the resonance fields. Each curve is shifted vertically for clarity.

Figure 3

Structure of the cyclotron masses $m_{\mathrm{CR}}^{*}$ for each Fermi surface sheet in ${\mathrm{URu}}_2{\mathrm{Si}}_2$. (a) Cyclotron masses as a function of field angle for the $ac$-plane (left) and $ab$-plane (right) rotations. The solid (open) symbols are for the resonance lines with large (small) intensities. The dashed lines are guides to the eyes for the main three bands. (b) Schematic cross sectional view of FS in the $a$ plane including $\Gamma$ (the center), $X$, and $M$ points, obtained by the density functional band-structure calculations assuming the antiferromagnetic order [33]. The color indicates the inverse of Fermi velocity $1/v_F$ on the FS sheets. The extremal orbits relevant to the cyclotron resonance are indicated for the main $\alpha$, $\beta$, and $\kappa$ bands by yellow (pink) arrows for $\mathit{H}\parallel [110]$ ([100]). The dashed arrow depicts the incommensurate wave vector ${\mathit{Q}}_{\mathrm{IC}}$. (c) Cyclotron mass $m_{\mathrm{CR}}^{*}$ of the $\alpha$ band as a function of the in-plane field angle $\varphi$ expected for each domain (solid (open) symbols for the $[\overline{1}10]$ ([110]) domain). The lines are the guides to the eyes. Insets show schematic mass distribution revealed by the CR data for the quasispherical $\alpha$ pocket viewed along the $c$ axis for the two domains. The red color represents the hot (heavy) spots.