Quantum states and intertwining phases in kagome materials

Interplay between magnetism and band topology in the kagome magnets 
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The pyrochlore magnet ${\mathrm{Ce}}_{2}{\mathrm{Zr}}_{2}{\mathrm{O}}_{7}$ has attracted much attention as a quantum spin ice candidate whose novelty derives in part from the dipolar-octupolar nature of the ${\mathrm{Ce}}^{3+}$ pseudospin-1/2 degrees of freedom it possesses. We report heat capacity measurements on single crystal samples of ${\mathrm{Ce}}_{2}{\mathrm{Zr}}_{2}{\mathrm{O}}_{7}$ down to $T\ensuremath{\sim}0.1\phantom{\rule{4pt}{0ex}}\mathrm{K}$ in a magnetic field along the $[1,\overline{1},0]$ direction. These measurements show that the broad hump in the zero-field heat capacity moves higher in temperature with increasing field strength and is split into two separate humps by the $[1,\overline{1},0]$ magnetic field at $\ensuremath{\sim}2\phantom{\rule{0.28em}{0ex}}\mathrm{T}$. These separate features are due to the decomposition of the pyrochlore lattice into effectively decoupled chains for fields in this direction: One set of chains ($\ensuremath{\alpha}$ chains) is polarized by the field while the other ($\ensuremath{\beta}$ chains) remains free. This situation is similar to that observed in the classical spin ices ${\mathrm{Ho}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ and ${\mathrm{Dy}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$, but with the twist that here the strong transverse exchange interactions produce substantial quantum effects. Our theoretical modeling suggests that the $\ensuremath{\beta}$ chains are close to a critical state, with nearly-gapless excitations. We also report elastic and inelastic neutron scattering measurements on single crystal ${\mathrm{Ce}}_{2}{\mathrm{Zr}}_{2}{\mathrm{O}}_{7}$ in $[1,\overline{1},0]$ and $[0,0,1]$ magnetic fields at temperatures down to $T=0.03\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. The elastic scattering behaves consistently with the formation of independent chains for a $[1,\overline{1},0]$ field, while the $[0,0,1]$ field produces a single field-induced elastic magnetic Bragg peak at $(0,2,0)$ and equivalent wavevectors, indicating a polarized spin ice state for fields above $\ensuremath{\sim}3\phantom{\rule{4pt}{0ex}}\mathrm{T}$. For both $[1,\overline{1},0]$ and $[0,0,1]$ magnetic fields, our inelastic neutron scattering results show an approximately-dispersionless continuum of scattering that increases in both energy and intensity with increasing field strength. By modeling the complete set of experimental data using numerical linked cluster and semiclassical molecular dynamics calculations, we demonstrate the dominantly multipolar nature of the exchange interactions in ${\mathrm{Ce}}_{2}{\mathrm{Zr}}_{2}{\mathrm{O}}_{7}$ and the smallness of the parameter $\ensuremath{\theta}$, which controls the mixing between dipolar and octupolar degrees of freedom. These results support previous estimates of the microscopic exchange parameters and place strong constraints on the theoretical description of this prominent spin ice candidate. 

Quantum spin ice response to a magnetic field in the dipole-octupole pyrochlore <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Ce</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Zr</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>7</mml:mn></mml:msub></mml:mrow></mml:math>

Kagome metals possess peculiar optical spectra consisting of contributions from free charge carriers in a Drude-type response, localized carriers seen as a strongly temperature-dependent localization peak, and, in some cases, phonons displaying strong anomalies. The rare-earth kagome metal series, $R{\mathrm{Mn}}_{6}{\mathrm{Sn}}_{6}$, provides a marvelous playground to study the electronic properties of kagome metals in the presence of variable magnetic order. Here, we report temperature-dependent reflectivity studies on two members of the $R{\mathrm{Mn}}_{6}{\mathrm{Sn}}_{6}$ family, ${\mathrm{GdMn}}_{6}{\mathrm{Sn}}_{6}$ (in-plane ferrimagnet) and ${\mathrm{TbMn}}_{6}{\mathrm{Sn}}_{6}$ (out-of-plane ferrimagnet), in a broad energy range (50--18 000 ${\mathrm{cm}}^{\ensuremath{-}1}$, equivalent to 6.2 meV--2.23 eV) down to 10 K. At high temperatures, a phonon mode at approximately 160 ${\mathrm{cm}}^{\ensuremath{-}1}$ is observed, which becomes screened out in ${\mathrm{TbMn}}_{6}{\mathrm{Sn}}_{6}$ below $\ensuremath{\sim}$150 K as the localization peak linearly passes through the mode. In ${\mathrm{GdMn}}_{6}{\mathrm{Sn}}_{6}$, the disappearance of the phonon is accompanied by the onset of saturation of the peak position, suggesting an unusual interplay between the two features. 

/pdf/effect-of-magnetism-and-phonons-on-localized-carriers-in-the-3q7w195o.pdf

Effect of magnetism and phonons on localized carriers in the ferrimagnetic kagome metals 
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Kagome magnet has been found to be a fertile ground for the search of exotic quantum states in condensed matter. Arising from the unusual geometry, the quantum interactions in the kagome lattice give rise to various quantum states, including the Chern-gapped Dirac fermion, Weyl fermion, flat band and van Hove singularity. Here we review recent advances in the study of the R166 kagome magnet (RT6E6, R = rare earths; T = transition metals; and E = Sn, Ge, etc) whose crystal structure highlights the transition-metal-based kagome lattice and rare-earth sublattice. Compared with other kagome magnets, the R166 family owns the particularly strong interplays between the d electrons on the kagome site and the localized f electrons on the rare-earth site. In the form of spin-orbital coupling, exchange interaction and many-body effect, the quantum interactions play an essential role in the Berry curvature in both the reciprocal and real spaces of R166 family. We discuss the spectroscopic and transport visualization of the topological electrons hosted in the Mn kagome layer of RMn6Sn6 and the various topological effects due to the quantum interactions, including the Chern-gap opening, the exchange-biased effect, the topological Hall effect and the emergent inductance. We hope this work serves as a guide for future explorations of quantum magnets.

pdf/quantum-interactions-in-topological-r166-kagome-magnet-52r6nvx5m0.pdf

Quantum interactions in topological R166 kagome magnet

Abstract Magnetic topological phases of quantum matter are an emerging frontier in physics and materials science, of which kagome magnets appear as a highly promising platform. Here, we explore magnetic correlations in the recently identified topological kagome system TbMn 6 Sn 6 using muon spin rotation, combined with local field analysis and neutron diffraction. Our studies identify an out-of-plane ferrimagnetic structure with slow magnetic fluctuations which exhibit a critical slowing down below $${T}_{{{{{{{{\rm{C1}}}}}}}}}^{* }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>C1</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup></mml:math> ≃ 120 K and finally freeze into static patches with ideal out-of-plane order below T C1 ≃ 20 K. We further show that hydrostatic pressure of 2.1 GPa stabilises the static out-of-plane topological ferrimagnetic ground state in the whole volume of the sample. Therefore the exciting perspective arises of a magnetically-induced topological system whose magnetism can be controlled through external parameters. The present results will stimulate theoretical investigations to obtain a microscopic understanding of the relation between the low-temperature volume-wise magnetic evolution of the static c -axis ferrimagnetic patches and the topological electronic properties in TbMn 6 Sn 6 . 

/pdf/low-temperature-magnetic-crossover-in-the-topological-kagome-2l9pqo7y.pdf

Low-temperature magnetic crossover in the topological kagome magnet TbMn6Sn6

We report the synthesis of powder and single-crystal samples of the cerium pyrohafnate and their characterization using neutron diﬀraction, thermogravimetry and X-ray absorption spectroscopy. We evaluate the amount of non-magnetic Ce 4+ defects and use this result to interpret the spectrum of crystal-electric ﬁeld transitions observed using inelastic neutron scattering. The analysis of these single-ion transitions indicates the dipole-octupole nature of the ground state doublet and a signif-icant degree of spin-lattice coupling. The single-ion properties calculated from the crystal-electric ﬁeld parameters obtained spectroscopically are in good agreement with bulk magnetic susceptibility data down to about 1 K. Below this temperature, the behavior of the magnetic susceptibility indicates a correlated regime without showing any sign of magnetic long-range order or freezing down to 0.08 K. We conclude that Ce 2 Hf 2 O 7 is another candidate to investigate exotic correlated states of quantum matter such as the octupolar quantum spin ice recently argued to exist in the isostructural compounds Ce 2 Sn 2 O 7 and Ce 2 Zr 2 O 7 .

Crystal-ﬁeld states and defect levels in candidate quantum spin ice Ce 2 Hf 2 O 7

We report the synthesis of powder and single-crystal samples of cerium pyrohafnate and their characterization using neutron diffraction, thermogravimetry and x-ray absorption spectroscopy. We evaluate the amount of nonmagnetic ${\mathrm{Ce}}^{4+}$ defects and use this result to interpret the spectrum of crystal-electric field transitions observed using inelastic neutron scattering. The analysis of these single-ion transitions indicates the dipole-octupole nature of the ground-state doublet and a significant degree of spin-lattice coupling. The single-ion properties calculated from the crystal-electric field parameters obtained spectroscopically are in good agreement with bulk magnetic susceptibility data down to about 1 K. Below this temperature, the behavior of the magnetic susceptibility indicates a correlated regime without showing any sign of magnetic long-range order or freezing down to 0.08 K. We conclude that ${\mathrm{Ce}}_{2}{\mathrm{Hf}}_{2}{\mathrm{O}}_{7}$ is another candidate to investigate exotic correlated states of quantum matter, such as the octupolar quantum spin ice recently argued to exist in the isostructural compounds ${\mathrm{Ce}}_{2}{\mathrm{Sn}}_{2}{\mathrm{O}}_{7}$ and ${\mathrm{Ce}}_{2}{\mathrm{Zr}}_{2}{\mathrm{O}}_{7}$. 

https://hal.science/hal-03644386/document

Crystal-field states and defect levels in candidate quantum spin ice 
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Low-temperature magnetic crossover in the topological kagome magnet TbMn6Sn6

Crystal-ﬁeld states and defect levels in candidate quantum spin ice Ce 2 Hf 2 O 7

Crystal-field states and defect levels in candidate quantum spin ice <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Ce</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Hf</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:m