arXiv subjects

Siân E. Dutton

Publications and source records attributed to Siân E. Dutton.

At least 19 recordsLinked to original sources

arXiv2026

Incommensurate structural and magnetic modulations in potassium-rich cryptomelane, K$_x$Mn$_8$O$_{16}$ ($x\approx1.45$)

Cryptomelane is a hollandite-like material consisting of K$^+$ cations in an $α$-MnO$_2$ tunnel-like crystallographic motif. Cryptomelane with stoichiometry K$_x$Mn$_8$O$_{16}$ ($x\approx1.45$) has been synthesized and its magnetic properties investigated using variable-temperature magnetic susceptibility, heat capacity, and neutron powder diffraction. Three distinct transitions at $T_1=184$\,K, $T_2=54.5$\,K, and $T_3=24$\,K are observed. At $T_1$ there is a subtle tetragonal$\rightarrow$monoclinic transition associated with emergence of a set of non-magnetic superstructure peaks indexable to a $\vec{k}_\mathrm{struc}\approx0.74\vec{c^*}$ incommensurate modulation parallel to the $α$-MnO$_2$ tunnels. Our findings are consistent with a relation previously reported in titanate hollandites, that $x\approx2|\vec{k}_\mathrm{struc}|$. Magnetic Bragg peaks emerge below $T_2=54.5$\,K, and their positions indicate an incommensurate modulated magnetic structure. The model consistent with the data is a dual-$\vec{k}_\mathrm{mag}$ structure with a ferromagnetic $|\vec{k}_\mathrm{mag}|=0$ component and an incommensurate $\vec{k}_\mathrm{mag}\approx0.37\vec{c^*}$, with the latter most likely to be helical. The period of oscillation of the incommensurate magnetic component is in line with predictions based on a Heisenberg spin Hamiltonian [Mandal \textit{et al}. Phys. Rev. B 90, 104420 (2014)]. Below $T_3=24$\,K, there is a magnetic transition, which gives rise to a different set of magnetic Bragg peaks indicative of a highly complex magnetic structure.

cond-mat.mtrl-sci↗

arXiv2026

Revisiting Jahn--Teller Transitions in Correlated Oxides with Monte Carlo Modeling

Jahn--Teller (JT) distortions are a key driver of physical properties in many correlated oxide materials. Cooperative JT distortions, in which long-range orbital order reduces the symmetry of the average structure macroscopically, are common in JT-distorted materials at low temperatures. This long-range order will often melt on heating, \textit{via} a transition to a high-temperature state without long-range orbital order. The nature of this transition has been observed to vary with different materials depending on crystal structure; in LaMnO$_3$ the transition has generally been interpreted as order-disorder, whereas in layered nickelates $A$NiO$_2$ ($A$=Li,Na) there is a displacive transition. Alternatively, recent theoretical work has suggested that previous attributions of order-disorder may in fact be a consequence of phonon anharmonicity, rather than persistence of JT distortions, which would suggest that the displacive transition may be more common than currently believed. In this work, we run Monte Carlo simulations with a simple Hamiltonian which is modified to include terms dependent on the JT amplitude $ρ$, which is allowed to vary within the simulation \textit{via} the Metropolis algorithm. Our simulations yield distributions of JT amplitudes consistent with displacive rather than order-disorder behaviour for both perovskites and layered nickelates, suggesting that displacive-like JT transitions may be more common than previously assumed in both perovskites and layered nickelates. We also find significant differences between the transition observed for perovskites compared with layered nickelates, which we attribute to differing extensivity of configurational entropy on the two lattices, showing the crucial role of lattice geometry in determining behaviour.

cond-mat.str-el↗

arXiv2026

Bulk magnetic properties of distorted square lattice compounds M'-LnTaO4 (Ln = Tb, Dy, Ho, Er)

We report bulk magnetic properties of the monoclinic lanthanide tantalates, M'-LnTaO4 (Ln = Tb, Dy, Ho, Er), where the magnetic Ln3+ ions are arranged on a distorted 2D square lattice. The heavier analogue M'-YbTaO4 has been investigated as a spin-orbit-coupled, quasi-two-dimensional frustrated magnet, and the properties of the other M'-LnTaO4 are expected to vary depending on the electronic configuration of the Ln ion, namely Kramers vs non-Kramers behaviour and different crystal electric field parameters. In this work, powder neutron diffraction is used to confirm the crystal structure for Ln = Tb, Ho, Er, and to determine the magnetic structure of M'-TbTaO4, which displays long-range antiferromagnetic (AFM) order below T_N = 2.1 K. The Tb3+ moments are aligned primarily along the c-axis with AFM nearest-neighbour interactions. Susceptibility data suggest that M'-DyTaO4 may display short-range ordering around 2.7 K, while M'-HoTaO4 and M'-ErTaO4 show AFM correlations but do not order above 1.8 K. Measurements of the magnetic specific heat provide evidence for a Kramers doublet ground state in M'-ErTaO4, similar to its heavier analogue M'-YbTaO4.

cond-mat.str-el↗

arXiv2026

High-pressure synthesis of quantum magnet M-YbTaO4 with a stretched diamond lattice

We report bulk magnetic properties of ytterbium tantalate in its monoclinic fergusonite modification, M-YbTaO4. The spin-1/2 Yb3+ ions in this phase are arranged on a geometrically frustrated "stretched diamond" lattice. M-YbTaO4 cannot be prepared at ambient pressure and was instead prepared in a belt-type apparatus at 6 GPa and 1800 C. Susceptibility and specific heat data show no long-range ordering down to 1.8 K and are consistent with a Jeff = 1/2 Kramers doublet which splits in an applied field. Furthermore, under high-pressure synthesis the entire solid solution YbNbxTa1-xO4 (0 < x < 1) can be stabilised in the M phase, in contrast to ambient-pressure synthesis which favours the competing M' phase for Ta-rich compositions. Subsequent annealing of the Nb-Ta mixed samples resulted in colour changes, suggesting oxygen deficiency in some of the as-prepared high pressure samples. There was little variation in the bulk magnetic properties upon varying either the Nb/Ta ratio or the annealing conditions.

cond-mat.mtrl-sci↗

arXiv2025

Magnetic Properties of the Quasi-1D Magnesium Lanthanide Borates Mg$Ln$B$_5$O$_{10}$

Lanthanide borates are widely studied for their optical and magnetic properties. A wide variety of structures are known with 3, 2, 1 and 0 dimensional connectivity of lanthanide ions. Here, we explore Mg$Ln$B$_5$O$_{10}$, with a quasi-1D arrangement of the $Ln$ ions. Polycrystalline samples of Mg$Ln$B$_5$O$_{10}$ ($Ln$ = La, Pr, Nd, Sm--Er) were synthesised with high purity via a sol-gel method. Powder X-ray diffraction data confirmed the reported monoclinic space group ($P2_1/c$). The magnetic $Ln^{3+}$ ions in Mg$Ln$B$_5$O$_{10}$ form relatively isolated zig-zag chains parallel to the $b$ axis. Magnetic susceptibility and isothermal magnetisation were measured: all samples except $Ln=$ (Eu, Sm) fit the Curie-Weiss Law in isothermal magnetisation at high temperatures, in broad agreement with theoretical expectations. $Ln =$ (Nd, Tb, Dy, Ho) exhibit signatures characteristic of Ising spin saturation, implying single ion anisotropy, while Gd exhibits characteristics of Heisenberg spins. Estimation of magnetic interactions suggests that Mg$Ln$B$_5$O$_{10}$ are candidate materials for quasi-1D magnetism. The magnetocaloric entropy change was also calculated, with MgGdB$_5$O$_{10}$ showing promise for application to solid-state refrigeration at liquid helium temperatures.

cond-mat.mtrl-sci↗

arXiv2024

Displacive Jahn--Teller transition in NaNiO$_2$

Below its Jahn--Teller transition temperature, $T_\mathrm{JT}$, NaNiO$_2$ has a monoclinic layered structure consisting of alternating layers of edge-sharing NaO$_6$ and Jahn-Teller-distorted NiO$_6$ octahedra. Above $T_\mathrm{JT}$ where NaNiO$_2$ is rhombohedral, diffraction measurements show the absence of a cooperative Jahn-Teller distortion, accompanied by an increase in the unit cell volume. Using neutron total scattering, solid-state Nuclear Magnetic Resonance (NMR), and extended X-ray absorption fine structure (EXAFS) experiments as local probes of the structure we find direct evidence for a displacive, as opposed to order-disorder Jahn-Teller transition at $T_\mathrm{JT}$. This is supported by \textit{ab initio} molecular dynamics (AIMD) simulations. To our knowledge this study is the first to show a displacive Jahn-Teller transition in any material using direct observations with local probe techniques.

cond-mat.mtrl-sci↗

arXiv2023

Van Vleck Analysis of Angularly Distorted Octahedra using VanVleckCalculator

Van Vleck modes describe all possible displacements of octahedrally-coordinated ligands about a core atom. They are a useful analytical tool for analysing the distortion of octahedra, particularly for the first-order Jahn-Teller distortion. Determination of Van Vleck modes of an octahedron is complicated by the presence of angular distortion of octahedra however. This problem is most commonly resolved by calculating the bond distortion modes ($Q_2$, $Q_3$) along the bond axes of the octahedron, disregarding the angular distortion and losing information on the octahedral shear modes ($Q_4$, $Q_5$, and $Q_6$) in the process. In this paper, the validity of assuming bond lengths to be orthogonal in order to calculate the van Vleck modes is discussed, and a method is described for calculating Van Vleck modes without disregarding the angular distortion. A Python code for doing this, VanVleckCalculator, is introduced, and some examples of its use are given. Finally, we show that octahedral shear and angular distortion are often, but not always, correlated, and propose a parameter as the shear fraction, $η$. We demonstrate that $η$ can be used to predict whether the values will be correlated when varying a tuning parameter such as temperature or pressure.

cond-mat.mtrl-sci↗

arXiv2023

Comparative study of magnetocaloric properties for Gd$^{3+}$ compounds with different frustrated lattice geometries

As materials with suppressed ordering temperatures and enhanced ground state entropies, frustrated magnetic oxides are ideal candidates for cryogenic magnetocaloric refrigeration. While previous materials design has focused on tuning the magnetic moments, their interactions, and density of moments on the lattice, there has been relatively little attention to frustrated lattices. Prior theoretical work has shown that the magnetocaloric cooling rate at the saturation field is proportional to a macroscopic number of soft mode excitations that arise due to the classical ground state degeneracy. The number of these modes is directly determined by the geometry of the frustrating lattice. For corner-sharing geometries, the pyrochlore has 50\% more modes than the garnet and kagome lattices, whereas the edge-sharing \emph{fcc} has only a subextensive number of soft modes. Here, we study the role of soft modes in the magnetocaloric effect of four large-spin Gd$^{3+}$ ($L=0$, $J=S=7/2$) Heisenberg antiferromagnets on a kagome, garnet, pyrochlore, and \emph{fcc} lattice. By comparing measurements of the magnetic entropy change $ΔS_m$ of these materials at fields up to $9$~T with predictions using mean-field theory and Monte Carlo simulations, we are able to understand the relative importance of spin correlations and quantization effects. We observe that tuning the value of the nearest neighbor coupling has a more dominant contribution to the magnetocaloric entropy change in the liquid-He cooling regime ($2$-$20$~K), rather than tuning the number of soft mode excitations. Our results inform future materials design in terms of dimensionality, degree of magnetic frustration, and lattice geometry.

cond-mat.str-el↗

arXiv2022

Magnetism on the stretched diamond lattice in lanthanide orthotantalates

The magnetic Ln$^{3+}$ ions in the fergusonite and scheelite crystal structures form a distorted or stretched diamond lattice which is predicted to host exotic magnetic ground states. In this study, polycrystalline samples of the fergusonite orthotantalates $M$-LnTaO$_4$ (Ln = Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er) are synthesized and then characterized using powder diffraction and bulk magnetometry and heat capacity. TbTaO$_4$ orders antiferromagnetically at 2.25 K into a commensurate magnetic cell with $\vec{k}=0$, magnetic space group 14.77 ($P2_1$$'/c$) and Tb moments parallel to the $a$-axis. No magnetic order was observed in the other materials studied, leaving open the possibility of exotic magnetic states at $T<2$ K.

cond-mat.mtrl-sci↗

arXiv2021

Site-selective $d^{10}$/$d^0$ substitution in a $S = 1/2$ spin ladder Ba$_2$CuTe$_{1-x}$W$_x$O$_6$ ($0 \leq x \leq 0.3$)

Remarkably, doping isovalent $d^{10}$ and $d^0$ cations onto the $B$'' site in $A_2B$'$B$''O$_6$ double perovskites has the power to direct the magnetic interactions between magnetic $B$' cations. This is due to changes in orbital hybridization, which favors different superexchange pathways, and leads to the formation of alternative magnetic structures depending on whether $B$'' is $d^{10}$ or $d^0$. Furthermore, the competition generated by introducing mixtures of $d^{10}$ and $d^0$ cations can drive the material into the realms of exotic quantum magnetism. Here, a W$^{6+}$ $d^0$ dopant was introduced to a $d^{10}$ hexagonal perovskite Ba$_2$CuTeO$_6$, which possesses a spin ladder geometry of Cu$^{2+}$ cations, creating a Ba$_2$CuTe$_{1-x}$W$_x$O$_6$ solid solution ($x$ = 0 - 0.3). Neutron and synchrotron X-ray diffraction show that W$^{6+}$ is almost exclusively substituted for Te$^{6+}$ on the corner-sharing site within the spin ladder, in preference to the face-sharing site between ladders. This means the intra-ladder interactions are selectively tuned by the $d^0$ cations. Bulk magnetic measurements suggest this suppresses magnetic ordering in a similar manner to that observed for the spin-liquid like material Sr$_2$CuTe$_{1-x}$W$_x$O$_6$. This further demonstrates the utility of $d^{10}$ and $d^0$ dopants as a tool for tuning magnetic ground states in a wide range of perovskites and perovskite-derived structures.

cond-mat.str-el↗

arXiv2020

Strengthening the magnetic interactions in pseudobinary first-row transition metal thiocyanates, $\it{M}$(NCS)$_{2}$

Understanding the effect of chemical composition on the strength of magnetic interactions is key to the design of magnets with stronger exchange interactions. The magnetic divalent first-row transition metal (TM) thiocyanates are a class of chemically simple layered molecular frameworks. Here, we report two new members of the family, manganese (II) thiocyanate, Mn(NCS)$_{2}$, and iron (II) thiocyanate, Fe(NCS)$_{2}$. Using magnetic susceptibility measurements on these materials and on cobalt (II) thiocyanate and nickel (II) thiocyanate, Co(NCS)$_{2}$ and Ni(NCS)$_{2}$, respectively, we identify significantly stronger net antiferromagnetic interactions between the earlier TM ions-a decrease in the Weiss constant, θ, from 29 K for Ni(NCS)$_{2}$ to -115 K for Mn(NCS)$_{2}$-a consequence of more diffuse 3d orbitals, increased orbital overlap and increasing numbers of unpaired $\it{t}$$_{2g}$ electrons. We elucidate the magnetic structures of these materials: Mn(NCS)$_{2}$, Fe(NCS)$_{2}$ and Co(NCS)$_{2}$ order into the same antiferromagnetic commensurate ground state, whilst Ni(NCS)$_{2}$ adopts a ground state structure consisting of ferromagnetically ordered layers stacked antiferromagnetically. We show that magnetic molecular frameworks with significantly stronger net exchange interactions can be constructed by using earlier TMs.

cond-mat.mtrl-sci↗

arXiv2020

Magnetic properties of quasi-one-dimensional lanthanide calcium oxyborates Ca$_4$LnO(BO$_3$)$_3$

This study examines the lanthanide calcium oxyborates Ca$_4$LnO(BO$_3$)$_3$ (Ln = La, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Y, Er, Yb). The reported monoclinic structure (space group $Cm$) was confirmed using powder X-ray diffraction. The magnetic Ln$^{3+}$ ions are situated in well-separated chains parallel to the c axis in a quasi-one-dimensional array. Here we report the first bulk magnetic characterisation of Ca$_4$LnO(BO$_3$)$_3$ using magnetic susceptibility $χ$(T) and isothermal magnetisation M(H) measurements at T $\geq$ 2 K. With the sole exception of Ca$_4$TbO(BO$_3$)$_3$, which displays a transition at T = 3.6 K, no magnetic transitions occur above 2 K, and Curie-Weiss analysis indicates antiferromagnetic nearest-neighbour interactions for all samples. Calculation of the magnetic entropy change $ΔS_m$ indicates that Ca$_4$GdO(BO$_3$)$_3$ and Ca$_4$HoO(BO$_3$)$_3$ are viable magnetocaloric materials at liquid helium temperatures in the high-field and low-field regimes respectively.

cond-mat.str-el↗

arXiv2019

Modeling Spin Dynamics in the Singlet Ground State Garnet Ho3Ga5O12

Materials containing non-Kramers magnetic ions can show unusual quantum excitations because of the exact mapping of the two-singlet crystal-field ground state to a quantum model of Ising spins in a transverse magnetic field. Here, we model the magnetic excitation spectrum of garnet-structured Ho3Ga5O12, which has a two-singlet crystal-field ground state. We use a reaction-field approximation to explain published inelastic neutron-scattering data [Zhou et al., Phys. Rev. B 78, 140406(R) (2008)] using a three-parameter model containing the magnetic dipolar interaction, the two-singlet crystal-field splitting, and the nuclear hyperfine coupling. Our study clarifies the magnetic Hamiltonian of Ho3Ga5O12, reveals that the nuclear hyperfine interaction drives magnetic ordering in this system, and provides a framework for quantitative analysis of magnetic excitation spectra of materials with singlet crystal-field ground states.

cond-mat.str-el↗

arXiv2018

The role of ionic liquid breakdown in the electrochemical metallization of VO2: An NMR study of gating mechanisms and VO2 reduction

Metallization of initially insulating VO2 via ionic liquid electrolytes (electrolyte gating) has recently been a topic of much interest. It is clear that the metallization takes place electrochemically and there has previously been extensive evidence for the removal of small amounts of oxygen during ionic liquid gating. Hydrogen intercalation has also been proposed, but the source of the hydrogen has remained unclear. In this work, solid-state magic angle spinning NMR spectroscopy is used to investigate the thermal metal-insulator transition in VO2, before progressing to catalytically hydrogenated and electrochemically metallized VO2. Electrochemical metallization of bulk VO2 particles is shown to be associated with intercalation of hydrogen, the degree of which can be measured with quantitative 1H NMR spectroscopy. Possible sources of the hydrogen are explored, and by using a selectively deuterated ionic liquid, it is revealed that the hydrogenation is due to deprotonation of the ionic liquid; specifically, for the commonly used dialkylimidazolium based ionic liquids, it is the "carbene" proton that is responsible. Increasing the temperature of the electrochemistry is shown to increase the degree of hydrogenation, forming first a less hydrogenated metallic phase then a more hydrogenated insulating Curie-Weiss paramagnetic phase, both of which were also observed for catalytically hydrogenated VO2. The NMR results are supported by magnetic susceptibility measurements, which corroborate the degree of Pauli and Curie-Weiss paramagnetism. NMR spectroscopy is used to identify the presence of hydrogen in an electrolyte gated thin film of VO2, suggesting that electrolyte breakdown, proton intercalation and reactions with decomposition products within the electrolyte should not be ignored when interpreting the electronic and structural changes observed in electrochemical gating experiments.

cond-mat.str-el↗

arXiv2018

Low-dimensional quantum magnetism in Cu(NCS)$_2$: A molecular framework material

Low-dimensional magnetic materials with spin-$\frac{1}{2}$ moments can host a range of exotic magnetic phenomena due to the intrinsic importance of quantum fluctuations to their behavior. Here, we report the structure, magnetic structure and magnetic properties of copper(II) thiocyanate, Cu(NCS)$_2$, a one-dimensional coordination polymer which displays low-dimensional quantum magnetism. Magnetic susceptibility, electron paramagnetic resonance (EPR) spectroscopy, $^{13}$C magic-angle spinning nuclear magnetic resonance (MASNMR) spectroscopy, and density functional theory (DFT) investigations indicate that Cu(NCS)$_2$ behaves as a two-dimensional array of weakly coupled antiferromagnetic spin chains ($J_2 = 133(1)$ K, $α= J_1/J_2 = 0.08$). Powder neutron-diffraction measurements confirm that Cu(NCS)$_2$ orders as a commensurate antiferromagnet below $T_\mathrm{N} = 12$ K, with a strongly reduced ordered moment (0.3 $μ_\mathrm{B}$) due to quantum fluctuations.

cond-mat.str-el↗

arXiv2018

Quantum Critical Points in Ferroelectric Relaxors: Stuffed Tungsten Bronze K3Li2Ta5O15 and Lead Pyrochlore (Pb2Nb2O7)

We have synthesised ceramic specimens of the tetragonal tungsten bronze K3Li2Ta5O15 (KLT) and characterized its phase transition via X-ray, dielectric permittivity, ultrasonic spectroscopy and heat capacity measurements. The space group of KLT is reported as both P4/mbm or Cmmm with the orthorhombic distortion occurring when there are higher partial pressures of volatile K and Li used within the closed crucibles for the solid state synthesis. The data show strong relaxor behaviour, with the temperature at which the two dielectric relative permittivity peaks decreasing with 104 K $\geqslant$ Tm1 $\geqslant$ 69 K and 69 K $\geqslant$ Tm2 $\geqslant$ 46 K as probe frequency f is reduced from 1 MHz to 316 Hz. The data satisfy a Vogel-Fulcher model with an extrapolated freezing temperature for ε' and ε" of Tf1 = + 15.8 and - 11.8 K and Tf2 = - 5.0 and - 15.0 K for f $\rightarrow$ 0 (tending to dc). Therefore by tuning frequency, the transition could be shifted to absolute zero suggesting KLT has a relaxor-type quantum critical point. In addition, we have reanalysed the conflicting literature for Pb2Nb2O7 pyrochlore which suggests that this is also a relaxor-type quantum critical point as the freezing temperature from Vogel-Fulcher fitting is below absolute zero. Since the transition temperature evidenced in the dielectric data at ca. 100 kHz shifts below zero Kelvin for very low frequencies, heat capacity data collected in the zero-frequency (dc) limit, should not indicate a transition. Both of these materials show promise as possible new relaxor-type quantum critical points within non-perovskite based structures as multiple compounds are reported with low-temperature transitions.

cond-mat.mtrl-sci↗

arXiv2018

Spin-specific heat determination of the ratio of competing first- and second-neighbor exchange interactions in frustrated spin-$\frac{1}{2}$ chains

The magnetic susceptibility $χ(T)$ of spin-1/2 chains is widely used to quantify exchange interactions, even though $χ(T)$ is similar for different combinations of ferromagnetic $J_1$ between first neighbors and antiferromagnetic $J_2$ between second neighbors. We point out that the spin specific heat $C(T)$ directly determines the ratio $α= J_2/|J_1|$ of competing interactions. The $J_1-J_2$ model is used to fit the isothermal magnetization $M(T,H)$ and $C(T,H)$ of spin-1/2 Cu(II) chains in LiCuSbO$_4$. By fixing $α$, $C(T)$ resolves the offsetting $J_1$, $α$ combinations obtained from $M(T,H)$ in cuprates with frustrated spin chains.

cond-mat.str-el↗

arXiv2017

Possible quadrupolar nematic phase in the frustrated spin chain LiCuSbO$_4$: an NMR investigation

The frustrated one-dimensional (1D) quantum magnet LiCuSbO$_4$ is one rare realization of the $J_1-J_2$ spin chain model with an easily accessible saturation field, formerly estimated to 12~T. Exotic multipolar nematic phases were theoretically predicted in such compounds just below the saturation field, but without unambiguous experimental observation so far. In this paper we present extensive experimental research of the compound in the wide temperature (30mK$-$300K) and field (0$-$13.3T) range by muon spin rotation ($μ$SR), $^7$Li nuclear magnetic resonance (NMR) and magnetic susceptibility (SQUID). $μ$SR experiments in zero magnetic field demonstrate the absence of long range 3D ordering down to 30mK. Together with former heat capacity data [S.E. Dutton \emph{et al}, Phys. Rev. Lett. 108, 187206 (2012)], magnetic susceptibility measurements suggest short range correlated vector chiral phase in the field range $0-4$T. In the intermediate field values (5$-$12T), the system enters in a 3D ordered spin density wave phase with 0.75$μ_B$ per copper site at lowest temperatures (125mK), estimated by NMR. At still higher field, the magnetization is found to be saturated above 13T where the spin lattice $T_1^{-1}$ relaxation reveals a spin gap estimated to 3.2(2)K. We narrow down the possibility of observing a multipolar nematic phase to the range 12.5$-$13T.

cond-mat.str-el↗