arXiv subjects

D. T. Adroja

Publications and source records attributed to D. T. Adroja.

At least 37 records · Page 2Linked to original sources

arXiv2025

Gapless spinon excitations emerging from a multipolar transverse field in the triangular-lattice Ising antiferromagnet NaTmSe2

The triangular-lattice quantum Ising antiferromagnet is a promising platform for realizing Anderson's quantum spin liquid, though finding suitable materials to realize it remains a challenge. Here, we present a comprehensive study of NaTmSe2 using magnetization, specific heat, neutron scattering, and muon spin relaxation, combined with theoretical calculations. We demonstrate that NaTmSe2 realizes the transverse field Ising model and quantitatively determine its exchange parameters. Our results reveal a multipolar spin-polarized state coexisting with a dipolar spin-disordered state. These states feature gapless spinon excitations mediated by the multipolar moments. The study shows how multiple types of magnetism can emerge in distinct magnetic channels (dipolar and multipolar) within a single magnet, advancing our understanding of spin-frustrated Ising physics and opening pathways for different quantum computing applications.

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arXiv2025

Spin dynamics and magnetic excitations of quasi-1D spin chain Ca$_3$ZnMnO$_6$

To reveal the structure-property relationship in quasi-one-dimensional (1D) spin-chain system Ca$_3$ZnMnO$_6$, we present comprehensive results, combining basic physical characterizations such as muon spin relaxation/rotation ($μ$SR), neutron powder diffraction (NPD), inelastic neutron scattering (INS), and theoretical calculations. Ca$_3$ZnMnO$_6$ features a dominant intrachain coupling $J_1$ and two distinct interchain interactions $J_2$ and $J_3$, and it undergoes antiferromagnetic ordering below $T_{\mathrm{N}}=25$~K, as revealed by dc magnetic susceptibility and specific-heat measurements. Zero-field $μ$SR shows persistent spin dynamics below $T_{\mathrm{N}}$, suggesting unconventional magnetic excitations in the ordered state. NPD results indicate a commensurate magnetic ground state with a propagation vector $\mathbf{k}=0$, where the Mn spins lie in the $ab$-plane. INS spectra display dispersive magnetic excitations extending up to about 5~meV, with an energy gap smaller than 0.5~meV. Notably, these spectra exhibit three-dimensional (3D) gapped features rather than the expected 1D behavior, yet spin-wave dispersion analysis confirms an underlying quasi-1D energy hierarchy. We discuss this apparent paradox of 3D-like magnetic excitations in a quasi-1D system in terms of the energy hierarchy modified by nonmagnetic-ion substitution and finite-temperature first-principles calculations. We also suggest that Ca$_3$ZnMnO$_6$ could be a potential candidate for an M-type altermagnet.

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arXiv2025

Incommensurate quantum magnet based on 4f-electron in a zigzag spin-1/2 chain of YbCuS$_2$

We performed high-resolution powder neutron diffraction experiments and discovered an elliptic helical incommensurate magnetic structure in the semiconducting rare-earth magnet YbCuS2, featuring effective spin-1/2 Yb$^{3+}$ ions that form a zigzag chain. Upon cooling the sample to 0.2 K, we observed very weak magnetic peaks indexed with an incommensurate propagation vector k = [0, 0.305, 0] along the zigzag chain. The magnitude of the magnetic moment is at least one-third smaller than the expected value for the Yb$^{3+}$ Kramers doublet ground state. In an applied magnetic field, up-up-down magnetic order was observed at 7.5 T, characterized by diffraction peaks indexed with k = [0, 1/3, 0] and substantial uniform magnetic components. These observations agree well with theoretical calculations based on the density matrix renormalization group for a zigzag spin-1/2 model with isotropic Heisenberg interactions and off-diagonal symmetric $Γ$-type exchange interactions derived from material parameters. The theory elucidates the quantum mechanical nature of the incommensurate magnetism as remnant off-diagonal spin correlations in a nematic dimer-singlet state.

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arXiv2024

Magnetic properties and field-induced phenomena in the Jeff = 1/2 distorted kagome antiferromagnet

The intertwining between competing degrees of freedom, anisotropy, and frustration-induced quantum fluctuations offers an ideal ground to realize exotic quantum phenomena in the rare-earth-based kagome lattice. The magnetic susceptibility reveals the presence of two energy scales in agreement with the INS results. The higher energy state is dominated by CEF excitations, where the lowest Kramers ground-state doublet is well separated from the excited state suggesting that the compound realizes a low-energy state at low temperatures. The second energy scale is witnessed via thermodynamic results that reveal an anomaly at 0.3 K typical of a phase transition, which is attributed to the presence of complex magnetic ordering phenomena. The broad maximum in the specific heat well above 0.3 K indicates the presence of short-range spin correlations that is corroborated by muon spin relaxation rate results. The isothermal magnetization reveals a field-induced 1/3 magnetization plateau at low temperatures. muSR relaxation rate experiments, on the other hand, neither show the signature of a phase transition nor spin-freezing down to 34 mK. The ZF muSR relaxation is governed by the Orbach process and reveals the presence of a fluctuating state owing to the depopulation of crystal field levels reflected as a constant value of relaxation rate in the temperature range 0.4-10 K. NMR results indicate the presence of fluctuating Nd3+ moments down to 1.8 K consistent with muSR experiments. Our comprehensive results reveal that a field-induced quantum critical phenomenon is at play in this frustrated kagome magnet and enable us to construct a phase diagram exemplifying the proximity effect of competing magnetic states. This sets the stage to investigate the broad RE3BWO9 family of rare-earth kagome magnets promising to host exotic quantum states driven by spin-orbit coupling and geometrical frustration.

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arXiv2024

Magnetic ground state and excitations in mixed 3$d$-4$d$ quasi-1D spin-chain oxide Sr$_3$NiRhO$_6$

Entanglement of spin and orbital degrees of freedom, via relativistic spin-orbit coupling, in 4$d$ transition metal oxides can give rise to a variety of novel quantum phases. A previous study of mixed 3$d$-4$d$ quasi-1D spin-chain oxide Sr$_3$NiRhO$_6$ using the magnetization measurements by Mohapatra et al. [Phys. Rev. B 75, 214422 (2007)] revealed a partially disordered antiferromagnetic (PDA) structure below 50 K [Mohapatra et al, Phys. Rev. B 75, 214422 (2007)]. We here report the magnetic ground state and spin-wave excitations in Sr$_3$NiRhO$_6$, using muon spin rotation and relaxation ($μ$SR), and neutron (elastic and inelastic) scattering techniques. Our neutron diffraction study reveals that in the magnetic structure of Sr$_3$NiRhO$_6$, Rh$^{4+}$ and Ni$^{2+}$ spins are aligned ferromagnetically in a spin-chain, with moments along the crystallographic $c$-axis. However, spin-chains are coupled antiferromanetically in the $ab$-plane. $μ$SR reveals the presence of oscillations in the asymmetry-time spectra below 50 K, supporting the long-range magnetically ordered ground state. Our inelastic neutron scattering study reveals gapped quasi-1D magnetic excitations with a large ratio of gap to exchange interaction. The observed spin-wave spectrum could be well fitted with a ferromagnetic isotropic exchange model (with $J = 3.7 $ meV) and single ion anisotropy ($D=10$ meV) on the Ni$^{2+}$ site. The magnetic excitations survive up to 85 K, well above the magnetic ordering temperature of $\sim 50$ K, also indicating a quasi-1D nature of the magnetic interactions in Sr$_3$NiRhO$_6$.

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arXiv2024

Magnetic structure and crystal field states of antiferromagnetic CeNiGe$_3$: Neutron scattering and $μ$SR investigations

We present the results of microscopic investigations of antiferromagnetic CeNiGe$_3$, using neutron powder diffraction (NPD), inelastic neutron scattering (INS), and muon spin relaxation ($μ$SR) measurements. CeNiGe$_3$ crystallizes in a centrosymmetric orthorhombic crystal structure (space group: $Cmmm$) and undergoes antiferromagnetic (AFM) ordering. The occurrence of long-range AFM ordering at $T_{\rm N} \approx 5.2$~K is confirmed by magnetic susceptibility, heat capacity, neutron diffraction, and $μ$SR measurements. The NPD data characterize the AFM state with an incommensurate helical magnetic structure having a propagation vector $k$ = (0, 0.41, 1/2). In addition, INS measurements at 10~K identified two crystal electric field (CEF) excitations at 9.17~meV and 18.42~meV. We analyzed the INS data using a CEF model for an orthorhombic environment of Ce$^{3+}$ ($J=5/2$) and determined the CEF parameters and ground state wavefunctions of CeNiGe$_3$. Moreover, zero-field $μ$SR data for CeNiGe$_3$ at $T< T_{\rm N}$ show long-range AFM ordering with three distinct oscillation frequencies corresponding to three different internal fields at the muon sites. The internal fields at the muon-stopping sites have been further investigated using density functional theory calculations.

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arXiv2024

Probing the superconducting gap structure of ScRuSi via $μ$SR and first-principles calculations

In this study, we present a thorough investigation into the superconducting state of the ruthenium-based ternary equiatomic compound ScRuSi. Our analysis combines experimental techniques, including muon spin rotation/relaxation ($μ$SR) and low-temperature resistivity measurements, with theoretical insights derived from first-principles calculations. The low-temperature resistivity measurements reveal a distinct superconducting phase transition in the orthorhombic structure of ScRuSi at a critical temperature ($T_\text{C}$) of $2.5$ K. Further, the TF-$μ$SR analysis yields a gap-to-critical-temperature ratio of $2Δ/k_\mathrm{B}T_\mathrm{C} = 2.71$, a value consistent with results obtained from previous heat capacity measurements. The temperature dependence of the superconducting normalized depolarization rate is fully described by the isotropic $s$-wave gap model. Additionally, zero-field $μ$SR measurements indicate that the relaxation rate remains nearly identical below and above $T_\text{C}$. This observation strongly suggests the preservation of time-reversal symmetry within the superconducting state. By employing the McMillan-Allen-Dynes equation, we calculate a $T_\text{C}$ of $2.11$ K from first-principles calculations within the density functional theory framework. This calculated value aligns closely with the experimentally determined critical temperature. The coupling between the low-frequency phonon modes and the transition metal d-orbital states play an important role in governing the superconducting pairing in ScRuSi. The combination of experimental and theoretical approaches provides a comprehensive microscopic understanding of the superconducting nature of ScRuSi, offering insights into its critical temperature, pairing symmetry, and the underlying electron-phonon coupling mechanism.

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arXiv2024

Origin of spin-driven ferroelectricity and effect of external pressure on the complex magnetism of 6H-perovskite Ba3HoRu2O9

The compound Ba3HoRu2O9 magnetically orders at 50 K (TN1) followed by another complex magnetic ordering at 10.2 K (TN2). The 2nd magnetic phase transition was characterized by the co-existence of two competing magnetic ground states associated with two different magnetic wave vectors (K1=1/2 0 0 and K2=1/4 1/4 0). Here, we have discussed the origin of spin-driven ferroelectricity, which is not known yet. We demonstrate through time-of-flight Neutron diffraction and theoretical calculation that the non-collinear structure involving two different magnetic ions, Ru(4d) and Ho(4f), break the spatial inversion symmetry via inverse Dzyaloshinskii-Moriya (D-M) interaction through strong 4d-4f magnetic correlation, which shifts the oxygen atoms and results in non-zero polarization. Such an observation of inverse D-M interaction from two different magnetic ions which caused ferroelectricity is rarely observed. We have systematically studied the spin and dipolar dynamics, which exhibit intriguing behavior with shorter coherence lengths of 2nd magnetic phase associated with the k2-wave vector. The results manifest the development of finite-size magnetoelectric domains instead of true long-range ordering which justifies the experimentally obtained low value of ferroelectric polarization. The synchrotron XRD analysis predicts a non-centrosymmetric space group P-62c. Furthermore, we have investigated the effect of external pressure on this complex magnetism. The result reveals an enhancement of ordering temperature by the application of external pressure (1.6 K/GPa). The external pressure might favor stabilizing the magnetic ground state associated with 2nd magnetic phase. Our study shows an unconventional mechanism of spin-driven ferroelectricity.

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arXiv2024

Inelastic neutron scattering and muon spin relaxation investigations of the deuterated Kondo lattices CeNiSnD$ _x $

CeNiSn is a Kondo semimetal where a gap opens at low temperatures due to hybridization between 4$f$ and conduction electrons, but a full insulating state fails to develop. Upon the insertion of hydrogen, long range magnetic order is induced. Here we report zero-field muon-spin relaxation and inelastic neutron scattering measurements of polycrystalline samples of the deuterides CeNiSnD$_x$ ($x$=1.0, 1.8). The muon-spin relaxation results confirm magnetic ordering in the whole sample of CeNiSnD below around 4.7 K, while inelastic neutron scattering reveals two well-defined crystalline-electric field (CEF) excitations at around 13 meV and 34 meV in CeNiSnD, and 5 meV and 27 meV for CeNiSnD$_{1.8}$. These results suggest that hydrogenation leads to the localization of the Ce-4$f$ electrons, giving rise to long-range magnetic order. We propose CEF level schemes for both systems, which predict a ground state moment of 0.96$μ_{\rm B}$/Ce within the $ab$-plane for CeNiSnD$_{1.8}$ and a saturated moment of 1.26$μ_{\rm B}$/Ce along the easy $c$ axis for CeNiSnD, that account for the observed magnetic properties.

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arXiv2024

Novel quantum spin liquid ground state in the trimer rhodate Ba$_4$NbRh$_3$O$_{12}$

Frustrated magnets offer a plethora of exotic magnetic ground states, including quantum spin liquids (QSLs), in which enhanced quantum fluctuations prevent a long-range magnetic ordering of the strongly correlated spins down to lowest temperature. Here we have investigated the trimer based mixed valence hexagonal rhodate Ba$_4$NbRh$_3$O$_{12}$ using a combination of dc and ac magnetization, electrical resistivity, specific heat, and muon spin rotation/relaxation ($μ$SR) measurements. Despite the substantial antiferromagnetic exchange interactions, as evident from the Weiss temperature ($θ_{\mathrm{W}}\sim -35$ to -45 K), among the Rh-local moments, neither long-range magnetic ordering nor spin-freezing is observed down to at least 50 mK, in ac-susceptibility, specific heat and ZF-$μ$SR measurements (down to 0.26 K). We ascribe the absence of any magnetic transition to enhanced quantum fluctuations as a result of geometrical frustration arising out of the edge-sharing equilateral Rh-triangular network in the structure. Our longitudinal-field $μ$SR result evidences persistent spin fluctuations down to 0.26~K, thus stabilizing a dynamic QSL ground state in Ba$_4$NbRh$_3$O$_{12}$. Furthermore, the magnetic specific heat ($C_{\mathrm{m}}$) data at low-$T$ reveal a significant $T$-linear contribution plus a quadratic $T$-dependence. A $T$-linear behavior is evocative of gapless spin excitations, while the $T^2$-term of $C_{\mathrm{m}}$ may indicate the Dirac QSL phenomenology of the spinon excitations with a linear dispersion.

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arXiv2023

Role of crystal field ground state in the classical spin-liquid behavior of a quasi-one dimensional spin-chain system Sr3NiPtO6

The spin-chain compound Sr3NiPtO6 is known to have a nonmagnetic ground state. We have investigated the nature of ground state of Sr3NiPtO6 using magnetic susceptibility $χ(T)$, heat capacity $C_{\rm p}(T)$, muon spin relaxation ($μ$SR) and inelastic neutron scattering (INS) measurements. The $χ(T)$ and $C_{\rm p}(T)$ do not exhibit any pronounced anomaly that can be associated with a phase transition to a magnetically ordered state. Our $μ$SR data confirm the absence of long-range magnetic ordering down to 0.04 K. Furthermore, the muon spin relaxation rate increases below 20 K and exhibits temperature independent behavior at low temperature, very similar to that observed in a quantum spin-liquid system. The INS data show a large excitation near 8~meV, and the analysis of the INS data reveals a singlet CEF ground state with a first excited CEF doublet state at $Δ_{\rm CEF}$ = 7.7 meV. The estimated CEF parameters reveal a strong planar anisotropy in the calculated $χ(T)$, consistent with the reported behavior of the $χ(T)$ of single crystal Sr3NiPtO6. We propose that the nonmagnetic singlet ground state and a large $Δ_{\rm CEF}$ (much larger than the exchange interaction $\mathcal{J}_{\rm ex}$) are responsible for the absence of long-range magnetic ordering and can mimic a classical spin-liquid behavior in this quasi-1D spin chain system Sr3NiPtO6. The classical spin-liquid ground state observed in Sr3NiPtO6 is due to the single-ion property, which is different from the quantum spin-liquid ground state observed in geometrically frustrated systems, where two-ion exchanges play an important role.

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arXiv2023

Superconducting Gap Structure of Filled Skutterudite LaOs$_4$As$_{12}$ Compound through $μ$SR Investigations

Filled skutterudite compounds have gained attention recently as an innovative platforms for studying intriguing low-temperature superconducting properties. Regarding the symmetry of the superconducting gap, contradicting findings from several experiments have been made for LaRu$_{4}$As$_{12}$ and its isoelectronic counterpart, LaOs$_{4}$As$_{12}$. In this vein, we report comprehensive bulk and microscopic results on LaOs$_{4}$As$_{12}$ utilizing specific heat analysis and muon-spin rotation/relaxation ($μ$SR) measurements. Bulk superconductivity with $T_C$ = 3.2 K was confirmed by heat capacity. The superconducting ground state of the filled-skutterudite LaOs$_{4}$As$_{12}$ compound is found to have two key characteristics: superfluid density exhibits saturation type behavior at low temperature, which points to a fully gapped superconductivity with gap value of $2Δ/k_BT_C$ = 3.26; additionally, the superconducting state does not show any sign of spontaneous magnetic field, supporting the preservation of time-reversal symmetry. These results open the door for the development of La-based skutterudites as special probes for examining the interplay of single- and multiband superconductivity in classical electron-phonon systems.

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arXiv2023

Quantum Griffiths singularity in the stoichiometric heavy-fermion system CeRh$_4$Al$_{15}$

We present a detailed investigation of the stoichiometric CeRh$_4$Al$_{15}$ single crystal compound using the temperature dependence of the heat capacity [$C_{\text{P}}$($T$)], electrical resistivity [$ρ$($T$)], magnetic susceptibility [$χ$($T$)], and magnetization [$M$($H$)] measurements for a magnetic field ($H$) applied in the basal plane and along the $c$-axis. The low temperature power-law behavior of $C$/$T$ $\propto$ $χ$ $\propto$ $T^{-1+α}$, the isotherm magnetization, $M \sim H^α$ with the exponent $α$ = 0.45 - 0.55, and the $T$-linear resistivity $Δρ$ $\sim$ $T^ε$ with $ε\sim$ 1 are found to be consistent with the formation of quantum Griffiths singularities in the non-Fermi-liquid (NFL) regime. We further investigated the spin dynamics of a polycrystalline sample of CeRh$_4$Al$_{15}$, using zero-field (ZF) and longitudinal-field (LF) muon spin relaxation ($μ$SR) measurements. ZF-$μ$SR measurements do not reveal any sign of long-range magnetic ordering down to 70~mK. The electronic relaxation rate ($λ$) below 0.5~K increases rapidly and shows a thermal activation-like characteristic [$T$log($λ$)$\sim$ $T$] over the entire measured temperature range between 70~mK to 4~K, indicating the presence of low energy spin fluctuations in CeRh$_4$Al$_{15}$. LF-$μ$SR measurements show a time-field ($t/H^η$) scaling of the $μ$SR asymmetry indicating a quantum critical behavior of this compound. Furthermore, inelastic neutron scattering study on the polycrystalline sample reveals two crystal field excitations near 19 and 33~meV. These features collectively provide strong evidence of NFL behavior in CeRh$_4$Al$_{15}$ due to the formation of Griffiths phase close to a $T$ $\rightarrow$ 0~K quantum critical point.

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arXiv2023

Muon spin relaxation and emergence of disorder-induced unconventional dynamic magnetic fluctuations in Dy$_{2}$Zr$_{2}$O$_{7}$

The disordered pyrochlore oxide Dy$_{2}$Zr$_{2}$O$_{7}$ shows the signatures of field-induced spin freezing with remnant zero-point spin-ice entropy at 5 kOe magnetic field. We have performed zero-field and longitudinal field Muon spin relaxation ($μ$SR) studies on Dy$_{2}$Zr$_{2}$O$_{7}$. Our zero field studies reveal the absence of both long-range ordering and spin freezing down to 62 mK. The $μ$SR relaxation rate exhibits a temperature-independent plateau below 4 K, indicating a dynamic ground state of fluctuating spins similar to the well-known spin ice system Dy$_{2}$Ti$_{2}$O$_{7}$. The low-temperature spin fluctuations persist in the longitudinal field of 20 kOe as well and show unusual field dependence of the relaxation rate, which is uncommon for a spin-liquid system. Our results, combined with the previous studies do not show any evidence of spin ice or spin glass ground state, rather point to a disorder-induced dynamic magnetic ground state in the Dy$_{2}$Zr$_{2}$O$_{7}$ material.

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arXiv2023

Nodeless superconductivity in noncentrosymmetric LaRhSn

The superconducting order parameter of the noncentrosymmetric superconductor LaRhSn is investigated by means of low temperature measurements of the specific heat, muon-spin relaxation/rotation ($μ$SR) and the tunnel-diode oscillator (TDO) based method. The specific heat and magnetic penetration depth [$λ(T)$] show an exponentially activated temperature dependence, demonstrating fully gapped superconductivity in LaRhSn. The temperature dependence of $λ^{-2}(T)$ deduced from the TDO based method and $μ$SR show nearly identical behavior, which can be well described by a single-gap $s$-wave model, with a zero temperature gap value of $Δ(0)=1.77(4)k_BT_c$. The zero-field $μ$SR spectra do not show detectable changes upon cooling below $T_c$, and therefore there is no evidence for time-reversal-symmetry breaking in the superconducting state.

cond-mat.supr-con↗

arXiv2022

Multigap Superconductivity in the Filled-Skutterudite Compound LaRu$_4$As$_{12}$ probed by muon spin rotation

Muon spin rotation ($μ$SR) and inelastic X-ray scattering (IXS) were used to investigate the superconducting properties of the filled-skutterudite compound LaRu$_{4}$As$_{12}$. A two-gap isotropic ($s+s$)-wave model can explain the temperature dependence of the superfluid density. Zero field $μ$SR measurements confirm that the time-reversal symmetry does not break upon entering the superconducting state. The measurements of lattice dynamics at 2, 20 and 300 K revealed temperature dependencies of the phonon modes that do not follow strictly a hardening of phonon frequencies upon cooling as expected within the quasi-harmonic picture. The 20~K data rather mark a turning point for the majority of the phonon frequencies. Indeed a hardening is observed approaching 20~K from above, while for a few branches a weak softening is visible upon further cooling to 2~K. The observed dispersion relations of phonon modes throughout the Brillouin zone matches with the DFT prediction quite closely. Our results point out that cubic LaRu$_{4}$As$_{12}$ is a good reference material for studying multiband superconductivity, including those with lower crystallographic symmetries such as iron arsenide-based superconductors.

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arXiv2022

Low-energy Spin Dynamics of Quantum Spin Liquid Candidate $NaYbSe_{2}$

The family of rare earth chalcogenides $ARECh_{2}$ (A = alkali or monovalent ions, RE = rare earth, and Ch = O, S, Se, and Te) appears as an inspiring playground for studying quantum spin liquids (QSL). The crucial low-energy spin dynamics remain to be uncovered. By employing muon spin relaxation ($μ$SR) and zero-field (ZF) AC susceptibility down to 50 mK, we are able to identify the gapless QSL in $NaYbSe_{2}$, a representative member with an effective spin-1/2, and explore its unusual spin dynamics. The ZF $μ$SR experiments unambiguously rule out spin ordering or freezing in $NaYbSe_{2}$ down to 50 mK, two orders of magnitude smaller than the exchange coupling energies. The spin relaxation rate, $λ$, approaches a constant below 0.3 K, indicating finite spin excitations featured by a gapless QSL ground state. This is consistently supported by our AC susceptibility measurements. The careful analysis of the longitudinal field (LF) $μ$SR spectra reveals a strong spatial correlation and a temporal correlation in the spin-disordered ground state, highlighting the unique feature of spin entanglement in the QSL state. The observations allow us to establish an experimental H-T phase diagram. The study offers insight into the rich and exotic magnetism of the rare earth family.

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arXiv2022

Quantum critical spin-liquid-like behavior in S = 1/2 quasikagome lattice CeRh1-xPdxSn investigated using muon spin relaxation and neutron scattering

We present the results of muon spin relaxation ($μ$SR) and neutron scattering on the Ce-based quasikagome lattice CeRh$_{1-x}$Pd$_{x}$Sn ($x=0.1$ to 0.75). Our ZF-$μ$SR results reveal the absence of static long-range magnetic order down to 0.05~K in $x = 0.1$ single crystals. The weak temperature-dependent plateaus of the dynamic spin fluctuations below 0.2~K in ZF-$μ$SR together with its longitudinal-field (LF) dependence between 0 and 3~kG indicate the presence of dynamic spin fluctuations persisting even at $T$ = 0.05~K without static magnetic order. On the other hand, $C_{\text{4f}}$/$T$ increases as --log $T$ on cooling below 0.9~K, passes through a broad maximum at 0.13~K and slightly decreases on further cooling. The ac-susceptibility also exhibits a frequency independent broad peak at 0.16~K, which is prominent with an applied field $H$ along $c$-direction. We, therefore, argue that such a behavior for $x=0.1$ (namely, a plateau in spin relaxation rate ($λ$) below 0.2~K and a linear $T$ dependence in $C_{\text{4f}}$ below 0.13~K) can be attributed to a metallic spin-liquid (SL) ground state near the quantum critical point in the frustrated Kondo lattice. The LF-$μ$SR study suggests that the out of kagome plane spin fluctuations are responsible for the SL behavior. Low energy inelastic neutron scattering (INS) of $x$ = 0.1 reveals gapless magnetic excitations, which are also supported by the behavior of $C_{\text{4f}}$ proportional to $T^{1.1}$ down to 0.06~K.

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