arXiv subjects

A. S. Sefat

Publications and source records attributed to A. S. Sefat.

At least 19 recordsLinked to original sources

arXiv2024

Magnetic field-temperature phase diagram of spin-1/2 triangular lattice antiferromagnet KYbSe$_2$

A quantum spin liquid (QSL) is a state of matter characterized by fractionalized quasiparticle excitations, quantum entanglement, and a lack of long-range magnetic order. However, QSLs have evaded definitive experimental observation. Several Yb$^{3+}$-based triangular lattice antiferromagnets with effective $S$ = $\frac{1}{2}$ have been suggested to stabilize the QSL state as the ground state. Here, we build a comprehensive magnetic temperature phase diagram of a high-quality single crystalline KYbSe$_2$ via heat capacity and magnetocaloric effect down to 30 mK with magnetic field applied along the $a$-axis. At zero magnetic field, we observe the magnetic long-range order at $T_N$ = 0.29 K entering 120 degrees ordered state in heat capacity, consistent with neutron scattering studies. Analysis of the low-temperature ($T$) specific heat ($C$) at zero magnetic field indicates linear $T$-dependence of $C/T$ and a broad hump of $C/T$ in the proximate QSL region above $T_N$. By applying magnetic field, we observe the up-up-down phase with 1/3 magnetization plateau and oblique phases, in addition to two new phases. These observations strongly indicate that while KYbSe$_2$ closely exhibits characteristics resembling an ideal triangular lattice, deviations may exist, such as the effect of the next-nearest-neighbor exchange interaction, calling for careful consideration for spin Hamiltonian modeling. Further investigations into tuning parameters, such as chemical pressure, could potentially induce an intriguing QSL phase in the material.

cond-mat.str-el↗

arXiv2023

Non-linear magnons and exchange Hamiltonians of delafossite proximate quantum spin liquids

Quantum spin liquids (QSL) are theoretical states of matter with long-range entanglement and exotic quasiparticles. However, they generally elude quantitative theory, rendering their underlying phases mysterious and hampering efforts to identify experimental QSL states. Here we study triangular lattice resonating valence bond QSL candidate materials KYbSe$_2$ and NaYbSe$_2$. We measure the magnon modes in their 1/3 plateau phase, where quantitative theory is tractable, using inelastic neutron scattering and fit them using nonlinear spin wave theory. We also fit the KYbSe$_2$ heat capacity using high temperature series expansion. Both KYbSe$_2$ fits yield the same magnetic Hamiltonian to within uncertainty, confirming previous estimates and showing the Heisenberg $J_2/J_1$ to be an accurate model for these materials. Most importantly, comparing KYbSe$_2$ and NaYbSe$_2$ shows that smaller $A$-site Na$^+$ ion has a larger $J_2/J_1$ ratio. However, hydrostatic pressure applied to KYbSe$_2$ increases the ordering temperature (a result consistent with density functional theory calculations), indicating that pressure decreases $J_2/J_1$. These results show how periodic table and hydrostatic pressure can tune the $A$YbSe$_2$ materials in a controlled way.

cond-mat.str-el↗

arXiv2023

Witnessing quantum criticality and entanglement in the triangular antiferromagnet KYbSe$_2$

The Heisenberg triangular lattice quantum spin liquid and the phase transitions to nearby magnetic orders have received much theoretical attention, but clear experimental manifestations of these states are rare. This work investigates a new spin-half Yb$^{3+}$ delafossite material, KYbSe$_2$, whose inelastic neutron scattering spectra reveal a diffuse continuum with a sharp lower bound. Applying entanglement witnesses to the data reveals significant multipartite entanglement spread between its neighbors, and analysis of its magnetic exchange couplings shows close proximity to the triangular lattice Heisenberg quantum spin liquid. Key features of the data are reproduced by Schwinger-boson theory and tensor network calculations with a significant second-neighbor coupling $J_2$. The strength of the dynamical structure factor at the $K$ point shows a scaling collapse in $\hbarω/k_\mathrm{B}T$ down to 0.3 K, indicating a second-order quantum phase transition. Comparing this to previous theoretical work suggests that the proximate phase at larger $J_2$ is a gapped $\mathbb{Z}_2$ spin liquid, resolving a long-debated issue. We thus show that KYbSe$_2$ is close to a spin liquid phase, which in turn sheds light on the theoretical phase diagram itself.

cond-mat.str-el↗

arXiv2022

Zig-Zag magnetic order and potential Kitaev interactions in the spin-1 honeycomb lattice KNiAsO$_4$

Despite the exciting implications of the Kitaev spin-Hamiltonian, finding and confirming the quantum spin liquid state has proven incredibly difficult. Recently the applicability of the model has been expanded through the development of a microscopic description of a spin-1 Kitaev interaction. Here we explore a candidate spin-1 honeycomb system, KNiAsO$_4$ , which meets many of the proposed criteria to generate such an interaction. Bulk measurements reveal an antiferromagnetic transition at $\sim$ 19 K which is generally robust to applied magnetic fields. Neutron diffraction measurements show magnetic order with a $\textbf{k}=(\frac{3}{2},0,0)$ ordering vector which results in the well-known ``zig-zag" magnetic structure thought to be adjacent to the spin-liquid ground state. Field dependent diffraction shows that while the structure is robust, the field can tune the direction of the ordered moment. Inelastic neutron scattering experiments show a well defined gapped spin-wave spectrum with no evidence of the continuum expected for fractionalized excitations. Modeling of the spin waves shows that the extended Kitaev spin-Hamiltonians is generally necessary to model the spectra and reproduce the observed magnetic order. First principles calculations suggest that the substitution of Pd on the Ni sublattice may strengthen the Kitaev interactions while simultaneously weakening the exchange interactions thus pushing KNiAsO$_4$ closer to the spin-liquid ground state.

cond-mat.str-el↗

arXiv2022

Single pair of Weyl nodes in the spin-canted structure of EuCd$_2$As$_2$

Time reversal symmetry breaking Weyl semimetals are unique among Weyl materials in allowing the minimal number of Weyl points thus offering the clearest signatures of the associated physics. Here we present neutron diffraction, density functional theory and transport measurement results which indicate that EuCd$_2$As$_2$ , under ambient field, strain and pressure, is such a material with a single pair of Weyl points. Our work reveals a magnetic structure (magnetic space group $C2'/m'$) with Eu moments pointing along the [210] direction in-plane and canted $\sim$ 30$^{\circ}$ out-of-plane. Density functional theory calculations using this structure show that the observed canting drastically alters the relevant electronic bands, relative to the in-plane order, leading to a single set of well defined Weyl points. Furthermore, we find the canting angle can tune the distance of the Weyl points above the Fermi level, with the smallest distance at low canting angles. Finally, transport measurements of the anomalous Hall Effect and longitudinal magnetoresistance exhibit properties indicative of a chiral anomaly, thus supporting the neutron scattering and DFT results suggesting EuCd$_2$As$_2$ is close to the ideal situation of the Weyl "Hydrogen atom".

cond-mat.str-el↗

arXiv2021

Field-Induced Spin Excitations in the Spin-1/2 Triangular-Lattice Antiferromagnet CsYbSe$_2$

A layered triangular lattice with spin-1/2 ions is an ideal platform to explore highly entangled exotic states like quantum spin liquid (QSL). Here, we report a systematic in-field neutron scattering study on a perfect two-dimensional triangular-lattice antiferromagnet, CsYbSe$_2$, a member of the large QSL candidate family rare-earth chalcogenides. The elastic neutron scattering measured down to 70 mK shows that there is a short-range 120$^{\circ}$ magnetic order at zero field. In the field-induced ordered states, the spin-spin correlation lengths along the $c$ axis are relatively short, although the heat capacity results indicate long-range magnetic orders at 3 T $-$ 5 T. The inelastic neutron scattering spectra evolve from highly damped continuum-like excitations at zero field to relatively sharp spin wave modes at the plateau phase. Our extensive large-cluster density-matrix renormalization group calculations with a Heisenberg triangular-lattice nearest-neighbor antiferromagnetic model reproduce the essential features of the experimental spectra, including continuum-like excitations at zero field, series of sharp magnons at the plateau phase as well as two-magnon excitations at high energy. This work presents comprehensive experimental and theoretical overview of the unconventional field-induced spin dynamics in triangular-lattice Heisenberg antiferromagnet and thus provides valuable insight into quantum many-body phenomena.

cond-mat.str-el↗

arXiv2021

Relationship between A-site Cation and Magnetic Structure in 3d-5d-4f Double Perovskite Iridates Ln2NiIrO6 (Ln=La, Pr, Nd)

We report a comprehensive investigation of Ln2NiIrO6 (Ln = La, Pr, Nd) using thermodynamic and transport properties, neutron powder diffraction, resonant inelastic x-ray scattering, and density functional theory (DFT) calculations to investigate the role of A-site cations on the magnetic interactions in this family of hybrid 3d-5d-4f compositions. Magnetic structure determination using neutron diffraction reveals antiferromagnetism for La2NiIrO6, a collinear ferrimagnetic Ni/Ir state that is driven to long range antiferromagnetism upon the onset of Nd ordering in Nd2NiIrO6, and a non-collinear ferrimagnetic Ni/Ir sublattice interpenetrated by a ferromagnetic Pr lattice for Pr2NiIrO6. For Pr2NiIrO6 heat capacity results reveal the presence of two independent magnetic sublattices and transport resistivity indicates insulating behavior and a conduction pathway that is thermally mediated. First principles DFT calculation elucidates the existence of the two independent magnetic sublattices within Pr2NiIrO6 and offers insight into the behavior in La2NiIrO6 and Nd2NiIrO6. Resonant inelastic x-ray scattering is consistent with spin-orbit coupling splitting the t2g manifold of octahedral Ir4+ into a Jeff = 1/2 and Jeff = 3/2 state for all members of the series considered.

cond-mat.str-el↗

arXiv2021

Multiband effects on the upper critical field angular dependence of 122-family iron pnictide superconductors

Detailed measurements of the in-plane resistivity were performed in a high-quality Ba(Fe$_{1-x}$Co$_{x}$)$_2$As$_2$ ($x=0.065$) single crystal, in magnetic fields up to 9 T and with different orientations $θ$ relative to the crystal $c$ axis. A significant $ρ(T)_{H,θ}$ rounding is observed just above the superconducting critical temperature $T_c$ due to Cooper pairs created by superconducting fluctuations. These data are analyzed in terms of a generalization of the Aslamazov-Larkin approach, that extends its applicability to high reduced-temperatures and magnetic fields. This method allows us to carry out a criterion-independent determination of the angular dependence of the upper critical field, $H_{c2}(θ)$. In spite of the relatively small anisotropy of this compound, it is found that $H_{c2}(θ)$ presents a significant deviation from the single-band 3D anisotropic Ginzburg-Landau (3D-aGL) approach, particularly for large $θ$ (typically above $\sim60^o$). These results are interpreted in terms of the multiband nature of these materials, in contrast with other proposals for similar $H_{c2}(θ)$ anomalies. Our results are also consistent with an effective anisotropy factor almost temperature independent near $T_c$, a result that differs from the ones obtained by using a single-band model.

cond-mat.supr-con↗

arXiv2020

Evidence of Ba substitution induced spin-canting in the magnetic Weyl semimetal EuCd$_2$As$_2$

Recently EuCd$_2$As$_2$ was predicted to be a magnetic Weyl semi-metal with a lone pair of Weyl nodes generated by A-type antiferromagnetism and protected by a rotational symmetry. However, it was soon discovered that the actual magnetic structure broke the rotational symmetry and internal pressure was later suggested as a route to stabilize the desired magnetic state. In this work we test this prediction by synthesizing a series of Eu$_{1-x}$Ba$_x$Cd$_2$As$_2$ single crystals and studying their structural, magnetic and transport properties via both experimental techniques and first-principles calculations. We find that small concentrations of Ba ($\sim 3-10\% $) lead to a small out-of-plane canting of the Eu moment. However, for higher concentrations this effect is suppressed and a nearly in-plane model is recovered. Studying the transport properties we find that all compositions show evidence of an Anomalous Hall Effect dominated by the intrinsic mechanism as well as large negative magnetoresistances in the longitudinal channel. A non-monotonic evolution of the transport properties is seen across the series which correlates to the proposed canting suggesting canting may enhance the topological effects. Careful density functional theory calculations using an all-electron approach revise prior predictions finding a purely ferromagnetic ground state with in-plane moments for both the EuCd$_2$As$_2$ and Eu$_{0.5}$Ba$_{0.5}$Cd$_2$As$_2$ compounds - corroborating our experimental findings. This work suggests that Ba substitution can tune the magnetic properties in unexpected ways which correlate to changes in measures of topological properties, encouraging future work to locate the ideal Ba concentration for Eu moment canting.

cond-mat.str-el↗

arXiv2020

Crystal field Hamiltonian and anisotropy in KErSe2 and CsErSe2

We use neutron scattering and bulk property measurements to determine the single-ion crystal-field Hamiltonians of delafossites $\rm KErSe_2$ and $\rm CsErSe_2$. These two systems contains planar equilateral triangular Er lattices arranged in two stacking variants: rhombohedral (for K) or hexagonal (Cs). Our analysis shows that regardless the stacking order both compound exhibit an easy-plane ground state doublet with large $J_z=1/2$ terms and the potential for significant quantum effects, making them candidates for quantum spin liquid or other exotic ground states.

cond-mat.str-el↗

arXiv2020

Superconductivity with Tc=7 K under pressure for Cu-, and Au-doped BaFe2As2

It is noteworthy that chemical substitution of BaFe2As2 (122) with the noble elements Cu and Au gives superconductivity with a maximum Tc=3 K, while Ag substitution (Ag-122) stays antiferromagnetic. For Ba(Fe1-xTMx)2As2, TM= Cu, Au, or Ag, and by doping an amount of x=0.04, a-lattice parameter slightly increases (0.4%) for all TM dopants, while c-lattice decreases (-0.2%) for TM=Cu, barely moves (0.05%) for Au, and increases (0.2%) for Ag. Despite the naive expectation that the noble elements of group 11 should affect the quantum properties of 122 similarly, they produce significant differences extending to the character of the ground state. For the Ag-122 crystal, evidence of only a filamentary superconductivity is noted with pressure. However, for Au and Cu doping (x=0.03) we find a substantial improvement in the superconductivity, with Tc increasing to 7 K and 7.5 K, respectively, under 20 kbar of pressure. As with the ambient pressure results, the identity of the dopant therefore has a substantial impact on the ground state properties. Density functional theory calculations corroborate these results and find evidence of strong electronic scattering for Au and Ag dopants, while Cu is comparatively less disruptive to the 122 electronic structure.

cond-mat.supr-con↗

arXiv2019

Tunable magnetic order in low-symmetry SeO$_3$ ligand linked $TM_3$(SeO$_3$)$_3$H$_2$O ($TM$ = Mn, Co and Ni) compounds

Generally, one has two strategies to achieve magnetic frustration: through geometric means or interactions with different length scales. As the former leads to much simpler theoretical treatments it is favored and so magnetic sublattices with geometric frustration are sought after. One approach to finding such lattices is to design them chemically by using non-magnetic linker ligands. Here we report on the magnetic properties of one such family of materials, the transition metal ($TM$) selenite hydrate compounds chemical formula $TM_3$(SeO$_3$)$_3$H$_2$O . These materials link highly distorted $TM$O$_6$ octahedra via non-magnetic [SeO$_3$]$^{2+}$ linkers. Using $TM$ = Mn, Co and Ni we report on the structural effects of changing the $TM$ site and how they may influence the magnetic structure. Using magnetic susceptibility and neutron powder diffraction we identify low temperature magnetic transitions for all three compounds characterized by the onset of long-range AFM order with moderate frustration indexes. Consideration of the magnetic structures reveal that the magnetic order is sensitive to the $TM$ site ion and is tunable as it is changed - especially from Mn to Co - with changes in both the moment direction and the ordering vector. Field dependent susceptibility and heat capacity measurements reveal metamagnetic transitions in both Mn$_3$(SeO$_3$)$_3$H$_2$O and Co$_3$(SeO$_3$)$_3$H$_2$O indicating nearby magnetic ground states accessible under relatively small applied fields. Density functional theory calculations broadly confirm these results, showing both a sensitivity of the magnetic structure to the $TM$ and its local environment. Although no spin liquid behavior is achieved, these results suggest the fruitfulness of such synthesis philosophies and encourage future work to engender higher frustration in these materials via doping, field, pressure or larger linker ligands.

cond-mat.str-el↗

arXiv2018

Unusual Effects of Be doping in the Iron Based Superconductor FeSe

Recent superconducting transition temperatures (Tc) over 100 K for monolayer FeSe on SrTiO3 have renewed interest in the bulk parent compound. In KCl:AlCl3 flux-transport-grown crystals of FeSe0.94Be0.06, FeSe0.97Be0.03 and, for comparison, FeSe, this work reports doping of FeSe using Be, among the smallest of possible dopants, corresponding to an effective chemical pressure. According to lattice parameter measurements, 6% Be doping shrank the tetragonal FeSe lattice equivalent to a physical pressure of 0.75 GPa. Using this flux-transport method of sample preparation, 6% of Be was the maximum amount of dopant achievable. At this maximal composition of FeSe0.94Be0.06, the lattice unit cell shrinks by 2.4%, Tc - measured in the bulk via specific heat - increases by almost 10%, the Tc vs pressure behavior shifts its peak Tconset downwards by ~1 GPa, the high temperature structural transition around TS = 89 K increases by 1.9 K (in contrast to other dopants in FeSe which uniformly depress TS), and the low temperature specific heat gamma increases by 10 % compared to pure FeSe. Also, upon doping by 6% Be the residual resistivity ratio, rho(300K)/rho(T->0), increases by almost a factor of four, while rho(300K)/rho(T=Tc+) increases by 50%.

cond-mat.supr-con↗

arXiv2018

Local-Ising type magnetic order and metamagnetism in the rare-earth pyrogermanate Er$_2$Ge$_2$O$_7$

The recent discoveries of proximate quantum spin-liquid compounds and their potential application in quantum computing informs the search for new candidate materials for quantum spin-ice and spin-liquid physics. While the majority of such work has centered on members of the pyrochlore family due to their inherently frustrated linked tetrahedral structure, the rare-earth pyrogermanates also show promise for possible frustrated magnetic behavior. With the familiar stoichiometry $RE_2$Ge$_2$O$_7$, these compounds generally have tetragonal symmetry with a rare-earth sublattice built of a spiral of alternating edge and corner sharing rare-earth site triangles. Studies on Dy$_2$Ge$_2$O$_7$ and Ho$_2$Ge$_2$O$_7$ have shown tunable low temperature antiferromagnetic order, a high frustration index and spin-ice like dynamics. Here we use neutron diffraction to study magnetic order in Er$_2$Ge$_2$O$_7$ (space group $P4_{1}2_{1}2$ ) and find the lowest yet Neél temperature in the pyrogermanates of 1.15 K. Using neutron powder diffraction we find the magnetic structure to order with $k = (0,0,0)$ ordering vector, magnetic space group symmetry $P4_{1}^{'}2_{1}2^{'}$ and a refined Er moment of $m = 8.1 μ_B$ - near the expected value for the Er$^{3+}$ free ion. Provocatively, the magnetic structure exhibits similar 'local-Ising' behavior to that seen in the pyrocholres where the Er moment points up or down along the short Er-Er bond. Upon applying a magnetic field we find a first order metamagnetic transition at $\sim$ 0.35 T to a lower symmetry $P2_{1}^{'}2_{1}^{'}2$ structure. This magnetic transition involves an inversion of Er moments aligned antiparallel to the applied field describing a class I spin-flip type transition, indicating a strong local anisotropy at the Er site - reminiscent of that seen in the spin-ice pyrochlores.

cond-mat.str-el↗

arXiv2018

Decoupled spin dynamics in the rare-earth orthoferrite YbFeO$_3$: Evolution of magnetic excitations through the spin-reorientation transition

In this paper we present a comprehensive study of magnetic dynamics in the rare-earth orthoferrite YbFeO$_3$ at temperatures below and above the spin-reorientation (SR) transition $T_{\mathrm{SR}}=7.6$ K, in magnetic fields applied along the $a, b$ and $c$ axes. Using single-crystal inelastic neutron scattering, we observed that the spectrum of magnetic excitations consists of two collective modes well separated in energy: 3D gapped magnons with a bandwidth of $\sim$60 meV, associated with the antiferromagnetically (AFM) ordered Fe subsystem, and quasi-1D AFM fluctuations of $\sim$1 meV within the Yb subsystem, with no hybridization of those modes. The spin dynamics of the Fe subsystem changes very little through the SR transition and could be well described in the frame of semiclassical linear spin-wave theory. On the other hand, the rotation of the net moment of the Fe subsystem at $T_{\mathrm{SR}}$ drastically changes the excitation spectrum of the Yb subsystem, inducing the transition between two regimes with magnon and spinon-like fluctuations. At $T < T_{\mathrm{SR}}$, the Yb spin chains have a well defined field-induced ferromagnetic (FM) ground state, and the spectrum consists of a sharp single-magnon mode, a two-magnon bound state, and a two-magnon continuum, whereas at $T > T_{\mathrm{SR}}$ only a gapped broad spinon-like continuum dominates the spectrum. In this work we show that a weak quasi-1D coupling within the Yb subsystem $J_\text{Yb-Yb}$, mainly neglected in previous studies, creates unusual quantum spin dynamics on the low energy scales. The results of our work may stimulate further experimental search for similar compounds with several magnetic subsystems and energy scales, where low-energy fluctuations and underlying physics could be "hidden" by a dominating interaction.

cond-mat.str-el↗

arXiv2018

Study of the second magnetization peak and the pinning behaviour in Ba(Fe$_{0.935}$Co$_{0.065}$)$_2$As$_2

Isothermal magnetic field dependence of magnetization and the magnetic relaxation measurements were performed for $H$$\parallel$c axis on single crystal of Ba(Fe$_{0.935}$Co$_{0.065}$)$_2$As$_2$ pnictide superconductor having $T_c$ = 21.7 K. The second magnetization peak (SMP) for each isothermal $M(H)$ was observed in a wide temperature range from $T_c$ to the lowest temperature of measurement (2 K). Magnetic field dependence of relaxation rate $R(H)$, shows a peak (H$_{spt}$) between H$_{on}$ (onset of SMP in $M(H)$) and H$_p$ (peak field of SMP in $M(H)$), which is likely to be related with a vortex-lattice structural phase transition, as suggested in literature for similar sample. In addition, the magnetic relaxation measured for magnetic fields near H$_{spt}$ show some noise which might be the signature of the structural phase transition of the vortex lattice. Analysis of the magnetic relaxation data using Maley's criterion and the collective pinning theory suggests that the second magnetization peak (SMP) in the sample is due to the collective (elastic) to plastic creep crossover, which is also accompanied with a rhombic to square vortex lattice phase transition. Analysis of the pinning force density suggests single dominating pinning mechanism in the sample and is not showing the usual $δ$l and $δT_c$ nature of pinning. The critical current density ($J_c$) estimated using the Bean's critical state model is found to be 5 $\times$ 10$^5$ A/cm$^2$ at 2 K in the zero magnetic field limit. Surprisingly, the maximum in the pinning force density is not responsible for the maximum value of the critical current density in the sample.

cond-mat.supr-con↗

arXiv2017

On the origin of critical nematic fluctuations in pnictide superconductors

We employ polarization-resolved Raman spectroscopy to study critical nematic fluctuations in Ba(Fe$_{1-x}$Au$_x$)$_2$As$_2$ superconductors above and across well separated tetragonal to orthorhombic phase transition at temperature $T_S(x)$ and the Néel transition at $T_N(x)$. The static Raman susceptibility in $XY$ symmetry channel increases upon cooling from room temperature following the Curie-Weiss law, with Weiss temperature $T_θ(x)$ several tens of degrees lower than $T_S(x)$. Data reveals a hidden nematic quantum critical point at $x_{c} = 0.031$ when the system becomes superconducting, indicating a direct connection between quantum critical nematic fluctuations and unconventional superconductivity. We attribute the origin of the nematicity to charge quadrupole fluctuations due to electron transfer between the nearly degenerate $d_{xz}/d_{yz}$ orbitals.

cond-mat.supr-con↗

arXiv2017

Anomalous magneto-elastic coupling in Au-doped BaFe2As2

We used polarization-resolved Raman scattering to study magneto-elastic coupling in Ba(Fe$_{1-x}$Au$_{x}$)$_2$As$_2$ crystals as a function of light Au-doping, materials for which temperatures of the structural transition ($T_S$) and of the magnetic ordering transition ($T_N$) split. We study the appearance of the $A_g$(As)phonon intensity in the $XY$ scattering geometry that is very weak just below $T_S$, but for which the intensity is significantly enhanced below $T_N$. In addition, the $A_g$(As) phonon shows an asymmetric line shape below $T_N$ and an anomalous linewidth broadening upon Au-doping in the magnetic phase. We demonstrate that the anomalous behavior of the $A_g$(As) phonon mode in the $XY$ scattering geometry can be consistently described by a Fano model involving the $A_g$(As) phonon mode interacting with the $B_{2g}$ symmetry-like magnetic continuum in which the magneto-elastic coupling constant is proportional to the magnetic order parameter.

cond-mat.supr-con↗