Thermodynamic evidence of fractionalized excitations in α−RuCl3

Abstract

Fractionalized excitations are of considerable interest in recent condensed-matter physics. Fractionalization of the spin degrees of freedom into localized and itinerant Majorana fermions are predicted for the Kitaev spin liquid, an exactly solvable model with bond-dependent interactions on a two-dimensional honeycomb lattice. As function of temperature, theory predicts a characteristic two-peak structure of the heat capacity as fingerprint of these excitations. Here we report on detailed heat-capacity experiments as function of temperature and magnetic field in high-quality single crystals of α-RuCl 3 and undertook considerable efforts to determine the exact phonon background. We measured single-crystalline RhCl 3 as non-magnetic reference and performed ab-initio calculations of the phonon density of states for both compounds. These ab-initio calculations document that the intrinsic phonon contribution to the heat capacity cannot be obtained by a simple rescaling of the nonmagnetic reference using differences in the atomic masses. Sizable renormalization is required even for non-magnetic RhCl 3 with its minute difference from the title compound. In α-RuCl 3 in zero magnetic field, excess heat capacity exists at temperatures well above the onset of magnetic order. In external magnetic fields far beyond quantum criticality, when long-range magnetic order is fully suppressed, the excess heat capacity exhibits the characteristic two-peak structure. In zero field, the lower peak just appears at temperatures around the onset of magnetic order and seems to be connected with canonical spin degrees of freedom. At higher fields, beyond the critical field, this peak is shifted to 10 K. The high-temperature peak located around 50 K is hardly influenced by external magnetic fields, carries the predicted amount of entropy, R/2 ln2, and may resemble remnants of Kitaev physics.

Dynamical and thermal magnetic properties of the Kitaev spin liquid candidate α-RuCl3

“…A similar two-peak structure has been found in α-RuCl 3 experiments, using both RhCl 3 [34] and ScCl 3 [25,64,65] as nonmagnetic analogue compounds. In clean samples, a sharp low-T peak representing the magnetic ordering occurs at T l ≈ 6.5K [30,34], and then a broader peak occurs at a higher temperature T h , followed by a (non-magnetic) structural transition of α-RuCl 3 near 165 − 170K [25,34] [65] find a broad maximum around 80 − 100K), but it appears to be an order of magnitude larger than T l . Whether or not the T h peak can be attributed to fractionalized excitations due to a proximate Kitaev QSL, the feature appears to be real and ought to be captured by a realistic spin Hamiltonian.…”

Terahertz excitations in α−RuCl3 : Majorana fermions and rigid-plane shear and compression modes

“…In α-RuCl3 these modes are located close to 2.5 and 6 meV. Strictly speaking, these are acoustic modes and according to ab-inito phonon calculations [42] these values correspond to eigenfrequencies at the zone boundary along the crystallographic c direction. In THz spectroscopy, these modes probably can be observed via disorder of the stacking or via backfolding of zoneboundary intensities due to the ABC stacking sequences of the rhombohedral phase.…”

“…The two phonon modes at 2.5 and 6 meV correspond to rigid-plane shear and breathing modes of molecular layers, respectively. Support for the latter notion comes from recent ab-initio phonon calculations, which predict these excitations close to 3 and 7 meV [42].…”

“…In Raman experiments the continuum extends to significantly higher frequencies ( 30 meV) and survives almost up to room temperature [14,23,24]. Fractionalization of spin degrees of freedom in α-RuCl3 was also derived from heat-capacity experiments [21,42]. Widmann et al, utilizing a phonon correction based on ab-initio calculations, identified a heat capacity anomaly close to 70 K extending up to 150 K [38].…”

Universal thermodynamics in the Kitaev fractional liquid

“…Thermodynamic features, including the double-peaked specific-heat curve, the linear-T behavior, and the fractional thermal entropy S integrated from C V /T , have been exploited in detecting finite-T fractionalization in the Kitaev materials [18,24,[57][58][59]. However, the magnetic response to external fields, the susceptibility χ , has been much less analyzed, except for the high-T behaviors in the Kitaev materials.…”