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Angle-dependent thermodynamics of $alpha$-RuCl$_3$

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 Added by Alexander Tsirlin
 Publication date 2021
  fields Physics
and research's language is English




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Thermodynamics of the Kitaev honeycomb magnet $alpha$-RuCl$_3$ is studied for different directions of in-plane magnetic field using measurements of the magnetic Gruneisen parameter $Gamma_B$ and specific heat $C$. We identify two critical fields $B_c^{rm AF1}$ and $B_c^{rm AF2}$ corresponding, respectively, to a transition between two magnetically ordered states and the loss of magnetic order toward a quantum paramagnetic state. The $B_c^{AF2}$ phase boundary reveals a narrow region of magnetic fields where inverse melting of the ordered phase may occur. No additional transitions are detected above $B_c^{rm AF2}$ for any direction of the in-plane field, although a shoulder anomaly in $Gamma_B$ is observed systematically at $8-10$ T. Large field-induced entropy effects imply additional low-energy excitations at low fields and/or strongly field-dependent phonon entropies. Our results establish universal features of $alpha$-RuCl$_3$ in high magnetic fields and challenge the presence of a field-induced Kitaev spin liquid in this material.



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Measurements of the magnetic Gruneisen parameter ($Gamma_B$) and specific heat on the Kitaev material candidate $alpha$-RuCl$_3$ are used to access in-plane field- and temperature-dependence of the entropy up to 12 T and down to 1 K. No signatures corresponding to phase transitions are detected beyond the boundary of the magnetically ordered region, but only a shoulder-like anomaly in $Gamma_B$, involving an entropy increment as small as $10^{-5} Rlog 2$. These observations put into question the presence of a thermodynamic phase transition between the purported quantum spin liquid and the field-polarized state of $alpha$-RuCl$_3$. We show theoretically that at low temperatures $Gamma_B$ is sensitive to crossings in the lowest excitations within gapped phases, and identify the measured shoulder-like anomaly as being of such origin. Exact diagonalization calculations demonstrate that the shoulder-like anomaly can be reproduced in extended Kitaev models that gain proximity to an additional phase at finite field without entering it. We discuss manifestations of this proximity in other measurements.
An external magnetic field can induce a transition in $alpha$-RuCl$_3$ from an ordered zigzag state to a disordered state that is possibly related to the Kitaev quantum spin liquid. Here we present new field dependent inelastic neutron scattering and magnetocaloric effect measurements implying the existence of an additional transition out of the quantum spin liquid phase at an upper field limit $B_u$. The neutron scattering shows three distinct regimes of magnetic response. In the low field ordered state the response shows magnon peaks; the intermediate field regime shows only continuum scattering, and above $B_u$ the response shows sharp magnon peaks at the lower bound of a strong continuum. Measurable dispersion of magnon modes along the $(0,0,L)$ direction implies non-negligible inter-plane interactions. Combining the magnetocaloric effect measurements with other data a $T-B$ phase diagram is constructed. The results constrain the range where one might expect to observe quantum spin liquid behavior in $alpha$-RuCl$_3$.
The frustrated magnet $alpha$-RuCl$_3$ constitutes a fascinating quantum material platform that harbors the intriguing Kitaev physics. However, a consensus on its intricate spin interactions and field-induced quantum phases has not been reached yet. Here we exploit multiple state-of-the-art many-body methods and determine the microscopic spin model that quantitatively explains major observations in $alpha$-RuCl$_3$, including the zigzag order, double-peak specific heat, magnetic anisotropy, and the characteristic M-star dynamical spin structure, etc. According to our model simulations, the in-plane field drives the system into the polarized phase at about 7 T and a thermal fractionalization occurs at finite temperature, reconciling observations in different experiments. Under out-of-plane fields, the zigzag order is suppressed at 35 T, above which, and below a polarization field of 100 T level, there emerges a field-induced quantum spin liquid. The fractional entropy and algebraic low-temperature specific heat unveil the nature of a gapless spin liquid, which can be explored in high-field measurements on $alpha$-RuCl$_3$.
We study on transport and magnetic properties of hydrated and lithium-intercalated $alpha$-RuCl$_3$, Li$_x$RuCl$_3 cdot y$H$_2$O, for investigating the effect on mobile-carrier doping into candidate materials for a realization of a Kitaev model. From thermogravitometoric and one-dimensional electron map analyses, we find two crystal structures of this system, that is, mono-layer hydrated Li$_x$RuCl$_3 cdot y$H$_2$O~$(xapprox0.56, yapprox1.3)$ and bi-layer hydrated Li$_x$RuCl$_3 cdot y$H$_2$O~$(xapprox0.56, yapprox3.9)$. The temperature dependence of the electrical resistivity shows a temperature hysteresis at 200-270 K, which is considered to relate with a formation of a charge order. The antiferromagnetic order at 7-13 K in pristine $alpha$-RuCl$_3$~ is successfully suppressed down to 2 K in bi-layer hydrated Li$_x$RuCl$_3 cdot y$H$_2$O, which is sensitive to not only an electronic state of Ru but also an interlayer distance between Ru-Cl planes.
We perform Raman spectroscopy studies on $alpha$-RuCl$_3$ at room temperature to explore its phase transitions of magnetism and chemical bonding under pressures. The Raman measurements resolve two critical pressures, about $p_1=1.1$~GPa and $p_2=1.7$~GPa, involving very different intertwining behaviors between the structural and magnetic excitations. With increasing pressures, a stacking order phase transition of $alpha$-RuCl$_3$ layers develops at $p_1=1.1$~GPa, indicated by the new Raman phonon modes and the modest Raman magnetic susceptibility adjustment. The abnormal softening and splitting of the Ru in-plane Raman mode provide direct evidence of the in-plane dimerization of the Ru-Ru bonds at $p_2=1.7$~GPa. The Raman susceptibility is greatly enhanced with pressure increasing and sharply suppressed after the dimerization. We propose that the system undergoes Mott collapse at $p_2=1.7$~GPa and turns into a dimerized correlated band insulator. Our studies demonstrate competitions between Kitaev physics, magnetism, and chemical bondings in Kitaev compounds.
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