Abstract
LiCrSe2 constitutes a recent valuable addition to the ensemble of two-dimensional triangular lattice antiferromagnets. In this work, we present a comprehensive study of the low temperature nuclear and magnetic structure established in this material. Being subject to a strong magnetoelastic coupling, LiCrSe2 was found to undergo a first order structural transition from a trigonal crystal system (\(P\bar{3}m1\)) to a monoclinic one (C2/m) at Ts = 30 K. Such restructuring of the lattice is accompanied by a magnetic transition at TN = 30 K. Refinement of the magnetic structure with neutron diffraction data and complementary muon spin rotation analysis reveal the presence of a complex incommensurate magnetic structure with a up-up-down-down arrangement of the chromium moments with ferromagnetic double chains coupled antiferromagnetically. The spin axial vector is also modulated both in direction and modulus, resulting in a spin density wave-like order with periodic suppression of the chromium moment along the chains. This behavior is believed to appear as a result of strong competition between direct exchange antiferromagnetic and superexchange ferromagnetic couplings established between both nearest neighbor and next nearest neighbor Cr3+ ions. We finally conjecture that the resulting magnetic order is stabilized via subtle vacancy/charge order within the lithium layers, potentially causing a mix of two co-existing magnetic phases within the sample.
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Introduction
In periodic crystalline lattices containing magnetic atoms, long-range ordering of their electronic magnetic moments can be stabilized by the exchange couplings among them at low temperatures. In some systems however, due to peculiar structural properties, not all these interactions can be satisfied simultaneously. Examples of such systems are provided by geometrically frustrated triangular lattice antiferromagnets (TLA), whose crystal structure consists of two-dimensional triangular lattice (2D-TL) layers, in which each corner of the triangular lattice is occupied by a magnetic atom, with nearest neighbor antiferromagnetic (AFM) interactions that cannot be stabilized1. Some prominent representative cases of 2D-TLA are found amid transition metal oxides (TMO), such as NaCoO22,3,4,5,6,7 or Li/Na/KCrO28,9. The highly degenerate spin states established in these materials, owing to their inherent geometrical frustration, may result in diverse exotic magnetic ground states and electronic properties. Indeed, due to subtle differences between one system and another, as well as to the strong interplay established between their lattice geometry and correlated electrons, these materials can host anomalous orbital states10,11,12, unconventional superconductivity13,14, rare magnetic ground states15,16,17, and distinctive spin-lattice dynamics18,19,20. The latter two aspects will be the main focus of this work. Among the currently available 2D-TLA, chromium-based compounds of the type ACrX2, where A is a monovalent atom and X is a chalcogen element, have been extensively investigated as geometrically frustrated S = 3/2 Heisenberg spin systems. The interest around these materials lies in the fact that they manifest a smörgåsbord of complex magnetic ground states19,21,22,23,24,25,26,27 and attractive technological properties (e.g. multiferroicity)28,29,30. These systems entail higher energy spin configurations, therefore, in the low-temperature regime, often a compromise between spin and lattice degrees of freedom has to be reached. The compromise can be realized through a first-order energetically beneficial distortion of the lattice leading to a new symmetry of the crystal, in which new interaction paths are realized and a magnetic order can be stabilized. When such an interplay between strongly correlated spins and geometrical degrees of freedom is realized, it is said that the system manifests magnetoelastic coupling. The appeal for materials undergoing these kinds of phenomena is twofold, as they constitute a unique playground for fundamental scientific research19,21,22,23,24,25,26,27,31, but also lend themselves to potential future technical applications32,33. Here it is worth mentioning that, in the context of quantum magnetism and magnetic frustration, S = 1/2 is often considered the theoretically ideal spin configuration, being the smallest non-integer spin value allowing for non-trivial quantum behavior. S = 3/2 systems involve larger spin values compared to S = 1/2, which can lead to a richer and more complex physics due to stronger magnetic interactions and quantum fluctuations, but also to a more challenging theoretical landscape to explore. Therefore, while theoretical modeling remains beneficial for guiding experimental investigations and providing qualitative insights, experimental studies on existing materials are crucial to ultimately clarify the physics of S = 3/2 systems.
The recent synthesis of LiCrSe2, via Li intercalation in CrSe2 by Kobayashi et al. 34,35, constitutes a valuable addition to the ensemble of TLAs that manifest magnetoelastic coupling since, probably due to the difficulty in manufacturing alkali chromium selenides, the most of the studies in this framework are performed on oxides and sulfides. Beyond the fundamental physics interest surrounding LiCrSe2, recent theoretical works foresee remarkable electronic properties, such as the presence of tunable field-free topological spin textures, which make this material appealing for applications in spintronics circuitry36,37,38. The room-temperature crystal structure of LiCrSe2 was identified as trigonal by synchrotron X-ray diffraction, with space group \(P\bar{3}m1\). Here, the Cr3+ ions create 2DTL layers, stacked along the c axis, by the connection of edge-sharing CrSe6 octahedra in the ab-plane39. Indications of a first-order structural transition towards a lower symmetry crystal system were observed around T = 30 K with in-house X-ray diffraction35; here it is suggested that such transition leads to a low temperature monoclinic structure. From bulk magnetic characterization methods, LiCrSe2 was found to undergo a first order-like magnetic transition, with an AFM character, also around TN = 30 K, which is a hint of magnetoelastic coupling. This behavior is similar to the one observed in the magnetoelastic TLA-Cr sulfides AuCrS2 and AgCrS222,26. However, remarkable qualitative differences in the structural distortions and magnetic properties between LiCrSe2 and the sulfides, indicate that LiCrSe2 would select a different magnetic ground state with respect to the one realized in AuCrS2 and AgCrS2. Indeed, the small negative value of the LiCrSe2 Curie-Weiss temperature Θ = −28 K and the small frustration index \(f=\frac{| {{\Theta }}| }{{T}_{{{{{{{{\rm{N}}}}}}}}}}\approx 1\) estimated in reference35, are suggestive of a weak nearest neighbor magnetic interaction (weaker than the one found in the sulfides) in favor of a strong further neighbor magnetic interaction (stronger than the one found in the sulfides). These results indicate that further neighbor interactions have a leading role in the determination of the magnetic ground state in LiCrSe2, making it a promising candidate for the realization of unconventional magnetic structures.
In this work, we investigated the temperature evolution of the crystal and magnetic structure of polycrystalline LiCrSe2 by means of neutron diffraction (ND), synchrotron X-ray diffraction (XRD) and muon spin rotation (μ+SR). Our observations confirm the conjectures of Kobayashi and coworkers35, as a clear structural transition from trigonal to monoclinic crystal system is observed and a complex incommensurate magnetic structure seems to be established in the sample, with periodic modulation in direction and modulus of the Cr3+ spin axial vector. Here we identified a main magnetic structure and a possible magnetic superstructure which contribute differently to the neutron diffraction pattern, suggesting that one is larger than the other, as also indicated by the μ+SR analysis. A solution for the main and secondary magnetic structures is proposed, together with a possible interpretation of such a spin ordering in terms of the magnetic exchange interactions for the main phase.
Results
Muon spin rotation experiment
A zero-field (ZF) and weak transverse field (wTF) bulk μ+SR experiment has been performed for different temperatures, in order to observe the evolution of the sample’s internal magnetic field distribution. In the wTF mode an external magnetic field of weak magnitude is applied (here, wTF = 30 G), with its flux lines perpendicular to the initial direction of the muon spin polarization. In this set-up, it is possible to follow the magnetic phase transition, while lowering the temperature of the system, as the muon spin precession (Larmor precession) is more and more affected by the sample’s strong internal field, induced by long-range magnetic ordering, at the expense of the externally applied weak field (for more details about the μ+SR experimental technique refer to ref. 40).
The wTF time spectra are well fitted using the following function:
were A0 is the initial asymmetry at time zero, PTF(t) is the muon spin polarization function, ATF is the oscillating asymmetry while Atail is the asymmetry of a slow relaxing exponential term due to the components of the internal field which are parallel to the initial polarization direction of the muons spins. This “tail" component, is also sometimes called the “powder average" signal when measuring polycrystalline (powder) samples, which ideally constitute 1/3 of the total asymmetry (in our case Atail ~ 0.08 ~ 0.22/3 where the total asymmetry is equal to 0.22). Further, νTF is the muon spin precession frequency having the phase ϕ (which in this case has a value of ≈ 12∘ in the entire temperature range), and finally λTF and λtail are the depolarization rates for the respective polarization components. wTF μ+SR time spectra at selected temperatures are shown in Fig. 1a with best fits Eq. (1) as solid lines. Further fitting of the full wTF temperature dependence and extracting the wTF asymmetry as a function of temperature (ATF(T)), allow us to estimate the magnetic transition temperature of LiCrSe2. The result is shown in Fig. 1b where ATF(T) is fitted to a sigmoid function. Such a curve is commonly used in the μ+SR related research to follow the temperature dependence of magnetic transitions in magnetically ordered systems. Here the transition temperature TN can be identified in correspondence with the inflection point of the s-shaped function, giving TN = 29.11 ± 0.06 K, which is in very good agreement with previously published bulk characterizations35. From the wTF data, it is also possible to deduce that more or less 100% of the sample enters the magnetically ordered state. Further, and contrary to our previous μ+SR studies of the related LiCrTe2 compound41, we do not seem to have any clear missing asymmetry fraction above TN, i.e. absence of any evident FM impurities in the current LiCrSe2 sample.
In the ZF configuration, the muon spin only senses the local internal magnetic field of the sample and if long-range magnetic order is established, a clear precession signal (i.e., oscillation) will appear. The ZF μ+SR time spectrum at base temperature (T = 2 K) in LiCrSe2 is displayed in Fig. 1c, d.
At first look, the ZF signal in the short-time domain [Fig. 1d] presents very clear oscillations, indicating the occurrence of AFM spin order. However, initial fitting attempts, using two simple exponentially relaxing cosine functions, gave poor results. Several problems were found, e.g., the full asymmetry could not be recovered, the fit could only work if the phase of the cosine functions would be left free and acquire very large un-physical values, and the chosen model could not fully capture the features of the Fast Fourier transformed (FFT) signal [Fig. 1e]. After testing several combinations of different oscillatory functions, the best fit to the data was achieved with a combination of two spherical Bessel functions j0:
Here A0 is the initial asymmetry, PTF(t) is the muon spin polarization function, ABess1 and ABess2 are the asymmetries of the oscillating part of the signal, ABG is a small background component possibly coming from muons stopping in the sample holder, and Atail is the asymmetry of the tail component. The frequency of the Larmor precession is given by 2π ⋅ νBess, and ϕ is the relative phase of the oscillating signals. Here ϕ ≈ 0 for both the Bessel functions in the entire temperature range. Finally, λBess, λBG, and λtail = 0 are the depolarization rates for the respective polarization components. Figure 1d, f shows the ZF raw data in the short time domain, for different temperatures, with the fitting curves as solid lines. As seen from these results, as well as the accurate fit to the FFT at T = 2 K in a large frequency range in Fig. 1e, Eq. (2) provides a good model for the experimental data.
The temperature dependence of the relevant ZF fitting parameters is shown in Fig. 1g, h. For both the relaxation rates (λ) as well as oscillation frequencies (νBess) it is clear that an abrupt, first-order like, transition occurs for TN ≈ 30 K. In more detail, the depolarization rate, and especially λBess2 display a very typical and strong increase just below TN, indicating the onset of spin dynamics/fluctuations as the magnetic phase transition approaches. The trend for λBess1 is similar, however, the absolute values are much smaller. Here it is also important to emphasize that ABess2 ≈ 12 ⋅ ABess1, i.e. the oscillating component Bess2 has more than an order of magnitude larger volume fraction with respect to Bess1. What such differences mean is hard to rigorously deduce using the μ+SR data alone. Nevertheless, it indicates that the two oscillating components originate from muons experiencing two rather different local magnetic environments42,43,44. Finally, the temperature dependence of the oscillation frequencies is shown in Fig. 1h, which reflect the magnetic order parameter of the phase transition. The behavior of the two components is in fact very similar, the oscillation frequencies have similar values, and follow the same temperature dependence. The latter shows an approximately constant trend below TN, with a slow downturn of both νBess1 and νBess1. This is then abruptly interrupted at TN ≈ 30 K which, we know from previous studies35, coincides with a structural phase transition at Ts.
The presence of large non-zero phases (ϕ) for cosine functions and replacement with a damped j0 Bessel is commonly used in the μ+SR community to model incommensurate magnetic structures. This solution is well established and proven, both theoretically and experimentally, to describe incommensurate spin density waves associated with single q − vectors45,46,47. The presence of two distinct Bessel functions with two frequencies of similar value in LiCrSe2 could be due to the presence of two different muon-stopping sites in the lattice, thereby probing the same incommensurate magnetic structure in a different fashion. Another option would be that we have two slightly different incommensurate magnetic phases present in the sample. Additional discussions on this matter will follow below.
Structural refinement from X-ray and neutron powder diffraction
The high- and low-temperature crystal structure of LiCrSe2, was determined from high-resolution neutron powder diffraction (NPD) studies [see Fig. 2a–f and Fig. 3c–f] along with complementary synchrotron X-ray diffraction (XRD) data [see Fig. 3a, b]. The refinement of the diffraction patterns was carried out by means of the Rietveld refinement method. Here we adopted a global refinement routine, which simultaneously included the three detector banks BS, SE, and LA35 covering the high-, intermediate-, and low-Q regions, respectively. The atomic positions, the cell parameters, and the basis vectors of the magnetic moment were refined as common parameters among the 3 data files. The calculated NPD/XRD pattern consists of a majority LiCrSe2 phase plus a small Li2Se non-mangetic impurity phase (the Li2Se impurity weight fraction in the diffraction pattern is 1.5%, consistently with the μ+SR data). For the XRD an additional Al phase is included to account for the sample holder/capillary. Further, for NPD the magnetic phase is present below TN in the low Q-range, while disregarded for large Q due to the magnetic form factor48 (by means of the command MDLIM in FullProf).
The room temperature crystal structure [see Fig. 3g] was found to be well modeled by the trigonal \(P\bar{3}m1\) space group (no. 164), with lattice parameters a = b = 3.65425(3) Å, c = 6.28911(4) Å, α = β = 90∘, γ = 120∘, in which Cr3+ ions occupy the vertices of the hexagonal unit cell, hereby creating the 2D-TLA. Below T ≈ 30 K (corresponding to both the structural and magnetic transition temperatures Ts = TN), the diffraction pattern undergoes a dramatic change, as clearly displayed in Fig. 2. Several nuclear Bragg peaks split into double peaks [Fig. 2(a–d] and, at the same time, the magnetic Bragg peaks appear [Fig. 2e, f]. Concerning the structural change, the increased number of Bragg reflections in the diffraction pattern, due to the peak splitting, is suggestive of a symmetry loss in the system, possibly owing to the disappearance of the 3-fold symmetry axis of the high-temperature parent space group. Moreover, no clear super-lattice reflection peaks seem to appear in the experimental data. Under the light of these observations, and from a group/subgroup relationship argument, the most probable final space group for such a structural transition would be the monoclinic C2/m (no. 12). This is because C2/m is the only monoclinic maximal subgroup of the parent space group \(P\bar{3}m1\) with a single step in its symmetry reduction path (see Bärnighausen tree for \(P\bar{3}m1\) from the Bilbao Crystallographic Server49). Indeed, Rietveld refinement of the low-temperature diffraction pattern with C2/m provided a good agreement with the experimental data, as it was able to correctly index all the additional new peaks [Fig. 3b, d, f]. Nevertheless, in light of the first-order nature of the structural transition, the possibility that the group subgroup relationship might not hold in this particular case must be considered. Several other monoclinic space groups were tested with a trial an error approach; among them Cm (no. 8) provided the best matching between the calculated and the observed pattern, which was however comparable to C2/m. The fact that the loss of the 2-fold symmetry axis from C2/m to Cm did not improve the refinement, made C2/m a more reasonable choice. This space group was also suggested from previous in-house XRD measurements35, and we have now confirmed such suggestion with high-resolution experimental methods. The base temperature (T = 2 K) crystal structure was therefore modeled with the monoclinic C2/m space group, with lattice parameters a = 6.32904(8) Å, b = 3.64287(5) Å, c = 6.25345(7) Å, α = γ = 90∘, and β = 90.08(13)∘ (see also the crystallographic information file provided as Supplementary Data 1–3). Here the Cr3+ ions occupy the vertices of a unit cell, which is nearly rectangular in the ab-plane, with one additional Cr atom in the central point of coordinates (0.5, 0.5, z) [see Fig. 3g]. The detailed result of the refinement is displayed in Fig. 3(e, f), with a plot of the observed and calculated diffraction patterns at high and low temperature, in the high-resolution high-Q BS detector bank. It is important to emphasize that in this bank (and Q-range) any potential low-temperature magnetic peak is virtually invisible, and does not interfere with the structural refinement. The complementary XRD patterns are also shown [Fig. 3a, b], and the structural refinement for XRD/NPD measurements is fully consistent, further allowing us to effectively discern between nuclear and magnetic contributions. It should also be noted that refinement of fractional occupancies did not improve the goodness of the fit, which allows us to conclude that the LiCrSe2 sample has a stoichiometric composition very close to the ideal one.
The temperature evolution of the lattice parameters, resulting from the structural refinement, is displayed in Fig. 3h. Table 1 further summarizes the refined structural parameter along with the Bragg agreement R factors, whose low values highlight the goodness of the refinement model. Since the Cr atoms sit at the vertices of the unit cell, the evolution of the lattice parameters reflects directly the evolution of the in-plane Cr–Cr distances. This is a factor of major importance in the determination of the magnetic structure for 2D-TLAs50. On cooling, the size of the crystallographic axes is reduced, due to thermal contraction, down to the magnetic transition temperature TN. As seen in Fig. 3h, the contraction of the c-axis occurs at a much higher rate with respect to the a- and b-axes, which is phenomenologically compatible with the 2D-TLA nature of the compound. At TN = Ts the first-order structural transition is clearly visible as a sharp change in the temperature dependence of the axes, with the major effect observed in the ab-plane. The synchronized nuclear and magnetic phase transition appearing at T = 30 K indicated a strong spin-lattice coupling. Here, the ordering of the Cr magnetic moments seems to be the driving mechanism for such a modification of the crystal lattice, aimed at stabilizing the competing coupling mechanisms simultaneously established among them. To further clarify such synergic effect, a detailed understanding of the spin structure is required. A dedicated discussion around the structural evolution of the system in concomitance with the evolution of the magnetic structure will be presented in the next subsection.
Magnetic refinement from neutron powder diffraction
Several temperature-dependent magnetic Bragg peaks appear below 30 K, as clearly seen in Fig. 2e, f. These peaks are assumed to be magnetic. Such transition is presented in higher detail in Fig. 4a, b, which displays a comparison between NPD patterns (intermediate-Q SE → 90∘ and low-Q LA35 → 35∘ detector banks) acquired at T = 35 K (just above TN) and at base temperature (T = 2 K). The square root of the integrated intensity of the large magnetic peak in the lower Q-region (Q = 0.66 Å−1) is also plotted as a function of temperature [see Fig. 4c]. The latter quantity reflects the order parameter of the magnetic transition which, as clearly seen from the plot in Fig. 4c, has a first-order character. The fit of the plot to a sigmoid function [solid line in Fig. 4c], well follows the sharp profile of the data and provides the magnetic transition temperature TN = 29.94 ± 0.09 K (defined as the midpoint of the sigmoid curve). The inset of Fig. 4c shows the normalized integrated intensities of the large magnetic peak together with the two neighboring small satellites, which all clearly manifest the same temperature-dependent behavior. Nevertheless, as discussed further below, these peaks do not belong to the same magnetic phase. Here a distinction is necessary between a main and a secondary magnetic phase. In the immediate following, we will describe the main magnetic phase.
The magnetic propagation vector qmain was determined by a very extensive trial and error procedure with the software K-Search. As expected from our μ+SR data, it was found to be incommensurate: qmain = (0.045, \(\approx \frac{1}{4},\approx \frac{1}{2}\)), see also Table 2 for the exact values. Such propagation vector can successfully index the high-intensity magnetic peak and most of the lower intensity ones as well. The origin of the remaining un-indexed weak peaks [e.g. at Q = 0.74 Å−1, orange arrow in Fig. 4a] will be discussed in the next section.
The Rietveld Method was used to refine the LiCrSe2 magnetic (qmain) phase. This phase includes a single magnetic Cr atom in the crystallographic site Cr(0 0 0). To ensure an accurate estimation of the Cr magnetic moment μCr, the scale factor and structural parameters were constrained to match their counterparts in the nuclear LiCrSe2 phase. The software BasIreps provided only one possible irreducible representation of the propagation vector group Gk for qmain, compatible with the space group C2/m (IRrep Γ1), consisting of three basis vectors BsV, with no imaginary components, parallel to the main crystallographic axes:
-
BsV(1): Re (1 0 0),
-
BsV(2): Re (0 1 0),
-
BsV(3): Re (0 0 1).
The refinement of the coefficients of the basis vectors C1, C2 and C3, representing here the weights of the basis vectors in the decomposition of the projections of the spin axial vector along the main crystallographic axes51, provided a large component along the a direction and a negligibly small component along the b direction [Fig. 5a–g].
Using IRrep Γ1 in the magnetic structure refinement [shown in Fig. 5a–d], it was possible to capture the temperature-dependent magnetic peaks of the diffraction pattern indexed by the q-vector qmain. The resulting magnetic structure presents a very large magnetic unit cell, with AFM coupled layers stacked along the c-axis with a peculiar “breathing" arrangement of the moments within the ab-plane [Fig. 5e–g]. Such arrangement of the spins resembles a spin-density wave-like structure, but without angular modulation of the Cr spin axial vector and with a very long periodicity. The intra-layer orientation of the Cr moments along the b-axis is reminiscent of an alternate up-up-down-down sequence [see dashed magenta ellipses in Fig. 5g], built up by double FM-coupled Cr spin chains running along the a-axis. This peculiar arrangement of the Cr moments is very similar to what was found for AuCrS222. However, in this case the orientation of the spins in the FM-coupled chains undergoes a change of direction, accompanied by a size modulation of the magnetic moment while moving along the a-axis [see plot (e) and bottom of panel (g) in Fig. 5]. As a result, a periodic suppression of the magnetic moment appears along the chain. The modulation interval between two consecutive spin flips along the a-axis is 11 unit cells. Figure 5e, f displays the calculated value of the Cr moment μCr as a function of the atomic coordinate xCr. This is obtained as the modulus of the refined spin axial vector expressed in units of Bohr magneton. The periodic “breathing" feature of the magnetic moment modulation is clearly visible. The simple 22-cell periodicity displayed in Fig. 5 is referred to a single one-dimensional Cr chain running along the a-axis for clarity of display. Given the incommensurate three-dimensional propagation vector of this magnetic structure, no simple periodicity for the orientation of the Cr spins can be identified in three dimensions.
The highest value for μCr in the chain is 2.25(3)μB, lower than the value previously estimated from bulk magnetic measurements ≈ 4 μB35, which is closer to the ideal spin-only value μ3/2 = 2\(\sqrt{S(S+1)}\) = 3.87 μB for an isolated Cr3+ ion in the spin state S = 3/2. This discrepancy is likely due to the differences between the two investigation methods. For a transition metal element in a covalently bonded system, a lower value of its magnetic moment with respect to the ideal value is expected, due to the competition between covalency and magnetism52. This reduction would occur at low temperature, where the system is in the ordered state. On the other hand, effective moments at high temperature, in the paramagnetic region, are not necessarily reduced53, hence the value estimated in reference35. Further, when geometric frustration is present, the appearance of staggered magnetic moments and a following reduction of μCr is very common8,22,26,54,55,56. Therefore, frustration might also be a contributor to the low-temperature reduction of the effective Cr moment in LiCrSe2. As also mentioned above, the frustration index in LiCrSe2 was also estimated in reference35 as \(f=\frac{| {{\Theta }}| }{{T}_{{{{{{{{\rm{N}}}}}}}}}}\approx 1\). Such value would imply the absence of frustration in this system. However, in the presence of simultaneously co-existing FM and AFM intralayer interactions such as in this case, the Weiss temperature does not directly reflect the magnitude of antiferromagnetic interactions, which may lead to an underestimation of the frustration index. Such behavior was recently observed also in AgCrSe257, a compound that manifests in many aspects a phenomenology similar to LiCrSe2. Therefore, in agreement with systems analogous to LiCrSe222, the value μCr = 2.25(3)μB estimated by NPD in the current work can be considered reliable, and consistent with a S = 3/2 spin system scenario. The resulting parameters obtained from the refinement of the magnetic unit cell for the LiCrSe2 magnetic phase are reported in Table 2. The very good agreement between the observed profiles and the calculated models can be clearly seen in Fig. 5(a-d). The goodness of the model is confirmed by the low value of the reliability R-factor for the magnetic phase, also reported in Table 2, not exceeding a few percent. All the values reported in Tables 1 and 2 are obtained from the global, simultaneous Rietveld refinement of diffraction patterns from the 3 detector banks BS, SE and LA35 covering the high-, intermediate-, and low-Q regions respectively. Although in powder diffraction studies possible ambiguities in the indexing of the magnetic peaks can eventuate, the analysis method used here (i.e., extremely high-resolution high-Q diffraction patterns are refined in a global routine together with the low-Q diffraction patterns, where the peaks from the magnetic structures can be clearly detected) ensures the reliability of our solution.
High-temperature properties
Concerning the high-temperature structural and dynamic properties of LiCrSe2, the refined isotropic thermal displacement parameters Biso up to 400 K are shown in Fig. 6a. Here, the structural transition at TN = 30 K is clearly visible. It can be seen that Biso for all atoms actually deviate from the general trend already above the transition. The first detectable temperature point where the refined Debye–Waller factors for all the atoms in the lattice abruptly move away from their trend at higher temperatures is regarded as the temperature point indicating the onset of a structural instability (si): Tsi ≈ 45 K. This would also explain the broad transition found in the wTF μ+SR data [Fig. 1(b)], just above the first-order downturn. It is also clear that the Li atoms undergo the largest thermal displacement (cf. Cr and Se). At high temperature BLi display an almost linear temperature dependence, however, below approximately 180 K a clear deviation from this trend appears. If we consider the similarity of LiCrSe2 with several other well-known layered TMO compounds (e.g. LiCoO258), and their utilization in rechargeable batteries59, we should consider the possibility of, and effects from, Li-ion dynamics. In fact, our team has developed and pioneered an experimental method to investigate ion dynamics by μ+SR. A detailed description of the method and selected examples can be found in refs. 60,61,62. Briefly, the muon spin is so sensitive to internal fields that it is capable of even probing static and dynamic changes in the nuclear moment. When implanted in these compounds in their higher temperature paramagnetic (PM) phase, the muon will mainly ‘feel’ the nuclear moment of the alkali metal (here Li), measured in both ZF and applied magnetic field parallel to the initial direction of the muon spin polarization (LF-μ + +SR). If the Li-ion is static, only a static nuclear field distribution (Δ) is probed. However, if Li-ion dynamics sets in, an additional field fluctuation rate (ν) component will be present. In the simplest interpretation, ν would translate into a Li-ion hopping rate that can be directly probed as a function of, e.g. temperature. In fact, our team recently conducted initial test measurements (still to be completed) of Li-ion dynamics in LiCrSe2 at the instrument S1 in J-PARC (see the Methods section for further experimental details) and ν(T) was successfully extracted at a few selected temperatures. As shown in Fig. 6(b), ν(T) displays a clear exponential trend, typical for a thermally activated diffusion process, where the exponential curve starts to move away from its horizontal asymptote around TD ≈ 180 K. This means that the Li-ions are fully mobile at least down to TD ≈ 180 K, which would indicate the possibility for Li order to appear during cool-down of the sample. This would also explain the change of trend found for BLi at TD. In fact, a smaller kink is also visible in BSe, which is reasonable considering that the Se sits next to the Li layers in the LiCrSe2 structure [see inset of Fig. 6b]. Interestingly, this behavior is different with respect to the one observed in the directly related compound LiCrO2, which was proven to be electrochemically inactive up to 480 K, despite its striking structural similarity with LiCrSe2. Therefore, the diffusion properties of this material could provide a hint on how to increment the Li-ion mobility in layered structures.
Discussion
The low-temperature incommensurate magnetic order, with itinerant frustration of the Cr moment63,64, found in LiCrSe2 is rather peculiar. While the inter-planar magnetic ordering along the c-axis can be explained with an AFM coupling mediated by super-exchange interactions through the path Cr-Se-Se-Cr, to explain the complex intra-planar magnetic structure the coexistence of competing magnetic interactions must be considered. In ternary chromium chalcogenide compounds, the magnetic interactions between two neighboring Cr3+ ions can be of two types, as for the Goodenough–Kanamori–Anderson rules65,66,67. Either a FM super-exchange interaction is established, by hybridization of the p orbitals of an anion with the d orbitals of the Cr ions (specifically with the half-filled t2g orbital of one Cr ion and the empty eg orbital of the other one) forming a 90∘ bond of the type Cr–Anion–Cr; or an AFM direct exchange interaction is established between the half-filled t2g orbitals of two adjacent Cr3+ ions. In the FM coupling, the Cr–Cr distance d(Cr–Cr) is unimportant as long as the angle in the bond Cr–Anion–Cr is close to 90∘. On the other hand, for the AFM coupling, d(Cr–Cr) has a major relevance. Rosenberg and coworkers identified a cutoff nearest neighbor (NN) Cr–Cr distance of ≈3.6 Å in the Cr layers of ternary chromium chalcogenides, for one mechanism to be dominant over the other50. In particular, for d(Cr–Cr) < 3.6 Å the AFM interaction would be preferred, while for d(Cr–Cr) > 3.6 Å the FM interaction would be preferred. In LiCrSe2 a dramatic structural change is observed, in concomitance to the magnetic transition at TN, leading to a modification of the Cr–Cr distances and of the angles \(\widehat{{{{{{\rm{Cr}}}}}}-{{{{{\rm{Se}}}}}}-{{{{{\rm{Cr}}}}}}}\), which are summarized in Table 3. In the trigonal phase just above the magnetic transition, the distance NN-d(Cr−Cr)a−b is very close to the critical value 3.6 Å and the angle \(\widehat{{{{{{\rm{Cr}}}}}}-{{{{{\rm{Se}}}}}}-{{{{{\rm{Cr}}}}}}}\) is very close to 90∘. In these conditions, the AFM and FM couplings are equally likely to be established between NN Cr3+ ions. As a consequence, the system is subjected to a geometrical frustration, which is removed through the energetically beneficial structural transition. This results in two non-equivalent NN and two non-equivalent next nearest neighbor (NNN) Cr3+ distances, d1(Cr−Cr)a−b and d2(Cr−Cr)a−b. In the low-temperature monoclinic phase small distortions of the lattice occur, indeed both the NN distances are still very close to the critical value 3.6 Å (see Table 3), and the angles \(\widehat{{{{{{\rm{Cr}}}}}}-{{{{{\rm{Se}}}}}}-{{{{{\rm{Cr}}}}}}}\) are still very close to 90∘. Nevertheless, as usually happens in frustration-driven structural transitions, this distortion is enough to lift the degeneracy of the magnetic ground state. Here, a strong competition between AFM and FM interactions is established, which leads to an overall weakening of the exchange mechanism between NN Cr3+ ions. At this point, the NNN Cr3+ interactions must come into play to stabilize the magnetic structure. The alignment of the Cr moments, resulting from our magnetic refinement [Fig. 5], and the aforementioned structural considerations on the Cr bonds, are consistent with the presence of both in-plane FM and AFM interactions simultaneously established across NN (J1) and NNN (J2) Cr bonds. Based on these assumptions, a potential arrangement of the magnetic couplings in this system is proposed in Supplementary Fig. 1. In addition, exchange interaction established among further than NNN Cr ions might be relevant in the determination of the ground state of LiCrSe2. Indeed, it was found that in delafossite structures with S as chalcogenide ligand (e.g., AuCrS2 and AgCrS2), the NNN exchange interaction J2 is typically comparable with the 3rd neighbor AFM exchange interaction J368. Such mechanism of super-super-exchange, realized via two p-orbitals of the S ligands, seems to drive the magnetic transition and determine the magnetic ground state in these materials68. The third neighbor interaction was recently found to be relevant also for the determination of the magnetic ground state in the triangular Cr-oxide PdCrO269. The p-orbitals of the Se element have a a larger spatial extension with respect to the ones in S and O. Therefore, in qualitative agreement with the aforementioned systems68,69, J3 could be expected to be even larger than J2 in LiCrSe2. However, first principles calculations would be needed to ultimately ascertain the roles of J1, J2 and J3 in the determination of the magnetic order on this material.
The resulting magnetic structure presents ferromagnetic double chains running along the a-axis, which are AFM coupled along the b-axis, similarly to AuCrS2 and AgCrS222,26. The only difference is that for LiCrSe2 the orientation of the Cr moment along the chains overturns periodically with a consequent modulation of its modulus. The possible coexistence of alternating AFM-FM interactions between NN Cr3+ atoms might be responsible for this peculiar behavior. The proposed magnetic structure is consistent with the observation that magnetic correlations in compounds similar to LiCrSe2 display significant further neighbor interactions involving Cr–Cr distances of 6–7 Å22,26. Additionally, our results are in very good agreement with the findings of Kobayashi etal. 35, who observed an AFM character of the signal in magnetic susceptibility measurements. This suggested that further neighbor exchange interactions in LiCrSe2 are in fact stronger than the nearest neighbor ones and of utmost importance in the determination of the magnetic ground state of LiCrSe2. In reference35 it was also hypothesized that LiCrSe2 is likely to possess a magnetic ground state different from other triangular lattice Cr chalcogenides with a similar structure and behavior21,22,26. The results of our work confirm this conjecture and provide a qualitative explanation for the difference between LiCrSe2 and the other systems: in AuCrS2 and AgCrS2 and CuCrS2 the in-plane Cr–Cr distances are always 3–4% different from the critical value found by Rosenberg. On the other hand, for LiCrSe2 the in-plane Cr–Cr distances are just ≈1% different from the critical value 3.6 Å. The Cr–Anion–Cr angles are very close to 90∘ in all cases. Therefore, in LiCrSe2 distinctive geometric conditions are realized, which lead to a configuration of the overlapping electronic orbitals that might allow the conflictual coexistence of FM and AFM exchange interactions over the same crystallographic sites, making this material unique in the 2D-TLA family. Future modeling efforts would be needed to systematically understand the complex spin interactions and order in LiCrSe2. The detailed information presented in this work, concerning the atomic/spin arrangement across the transition, will most likely be a valuable input for such modeling efforts.
Going back to the un-indexed weak Bragg peaks found in the low-temperature C2/m phase, it is important to emphasize that we clearly do not believe that these peaks are from an impurity phase. This is because there is no trace of magnetic impurities in the room temperature diffraction patterns, there is no sign of phase separation in the wTF μ+SR data, and the additional peaks appear exactly at the same structural/magnetic transition temperature of the LiCrSe2 main phase (Ts = TN = 30 K). In our refinement efforts, a huge number of different magnetic propagation vectors in combination with different crystal structures and super-cells, including higher-order harmonics of the parent cell, were attempted for the purpose of simultaneous indexing of all the peaks in the diffraction pattern. Attempts of indexing the magnetic peaks with a single 2q structure have been made and, although the peak position could be retrieved in the refinement, the intensity of the calculated magnetic peaks could not match the intensity of the measured peaks. In order to identify a possible lower than C2/m symmetry for the nuclear structure, many attempts of indexing the nuclear peaks together with the small satellites have been made. Such attempts provided no solution. Attempts to refine the small satellites alone as an independent nuclear structure could not provide any solution either.
Therefore, these efforts did not produce any outcome and, even if the C2/m nuclear structure combined with magnetic propagation vector qmain gives a very nice result, a few weak Bragg peaks were still left un-indexed [e.g. Q = 0.74 Å−1 being the strongest un-indexed peak, see Fig. 4a and Fig. 5b]. Considering the coinciding structural and magnetic phase transition occuring at T ≈ 30 K, it is indeed challenging to identify whether new Bragg peaks appearing at low temperature have nuclear or magnetic origin. In this work, we therefore combined NPD with synchrotron XRD experiments in order to improve the identification process. Indeed, the low-temperature peak at Q = 0.74 Å−1 is not visible in the T = 11 K XRD data. This fact, together with the ZF μ+SR results indicating the presence of two slightly different magnetic phases, and with the low-Q position and temperature-dependent behavior of the satellites in the ND pattern, seems to point toward a magnetic nature for these peaks. For this reason, we decided to try to index the few weak remaining low-temperature satellites with a secondary magnetic phase. Considering the fact that the ZF asymmetry of the the first Bessel component, ABess1, was so much smaller than ABess2, it seems reasonable to assume that the weak un-indexed magnetic Bragg peaks could be associated with ABess1.
To deduce the possible secondary magnetic phase (consistent with the presence of a magnetic supercell) we utilized a similar procedure as for the identification of the main magnetic structure. The refinement [Fig. 7a, b], carried out with a global routine taking into account all the detector banks, successfully provided a good match for both position and intensity of most of the minority satellites [orange tick-marks in Fig. 7a, b]. The resulting secondary magnetic structure, characterized by an incommensurate propagation vector qsecondary = (0.7249(5), −0.0885(3), −0.1292(9)), appears similar yet complementary to the main structure, although in this case the spin axial vector forms a canting angle of about 20∘ with the c-axis. Here the canted modulated FM chains run along the c-axis while the up-up-down-down arrangement of the Cr spins develops along the a-axis [Fig. 7c]. A more detailed description of this refinement can be found in the Supplementary Information.
A magnetic nature for the minority satellites would be consistent with the results of the ZF μ+SR, also considering the ratio between the two phases. Moreover, the clear canting angle found in the secondary magnetic phase is suggestive of the presence of asymmetric magnetic couplings, possibly due to the presence of Dzyaloshinskii–Moriya interaction (DMI). This would be consistent with a recent theoretical work36, which indeed predicts the occurrence of large DMI in LiCrSe2. However, the reliability R-factor for the refinement of the secondary magnetic phase has a rather large value (\({R}_{{{{{{{{\rm{B(mag)}}}}}}}}}^{{{{{{{{\rm{secondary}}}}}}}}}=25.7 \%\)), implying a relatively poor agreement between the experimental data and the calculated model for this phase. The large value for the R-factor, although it could simply be due to the scarcity and weak intensity of the refined satellites, makes this interpretation for the nature of the minority satellites not fully unambiguous. Therefore, another option might be that the small un-indexed low-temperature Bragg peaks are in fact not magnetic but have nuclear origin related to charge ordering. Indeed, we could consider the appearance of a superstructure induced by e.g. Li(-vacancy) ordering. In principle such superstructure peaks should be visible also in the XRD, however, if they are indeed originating from the light Li atoms (low Z) the peaks might be difficult to discern (or even invisible) for X-rays. Possible indications of the validity of this option could be found in the high-temperature properties of LiCrSe2 [Fig. 6].
The dynamic phenomenology manifested by LiCrSe2 is reminiscent of the behavior of the rather well-known and strongly related NaxCoO2 (NCO) compound2,3,4,5,6. From very extensive studies of NCO it has been shown that Na-ions (vacancies) can order in many different types of configurations70,71,72. It was also clearly shown that the Na-ion are in fact mobile even below room temperature and that the dynamics allow the Na-ions to arrange themselves in different patterns at lower temperatures5,73,74. Even in the case of NCO with the heavier Na-ions, it was not straightforward to identify the superstructure ordering. Several of the successful studies were performed using neutron scattering and, in more or less all cases, the superstructures could only be identified using single crystalline samples rather than powder. It was also in single crystals where the most recent study of the in-plane as well as out-of-plane Na ordering was studied, this time using XRD75. Therefore, in qualitative agreement with NCO, it is not improbable that the small satellites found in NPD on LiCrSe2 could be nuclear superstructures and still not visible in the XRD pattern. However, NCO and LiCrSe2 present some differences: in NCO there are two Na sites and neither of them is fully occupied, while in LiCrSe2 there is only one Li site, which results fully occupied from our refinement (i.e. no vacancies). On the other hand, the refined magnetic (main) phase has a very long periodicity (large unit cell), which would fit well with a Li-vacancy order based on very few existing vacancies that we did not discern in our refinement. It is of course possible to have Li order without vacancies, e.g. in the form of a charge-density-wave (CDW), but future more detailed studies of Li-ion ordering and dynamics in LiCrSe2 coupled to the magnetic properties would be needed to clarify this aspect.
Finally, we speculate about the electronic origins of the magnetic peaks and the very unusual spin arrangement realized in LiCrSe2. The spin density modulation along the FM chains and the incommensurate positions of the magnetic peaks might be originated by a combination of localized and itinerant moments, with a phenomenology similar to both the NaxCoO2 compound76 as well as the intermetallic material ErPd2Si2. The latter in fact also manifests two distinct incommensurate spin states77. Looking at the size of the magnetic peaks belonging to the two structures, it can be argued that the moments for qmain have mostly a localized character, while qsecondary are mainly itinerant. Although being consistent with the experimental observations, single crystal magnetic field-dependent studies would be necessary to confirm or deny such hypothesis. On the other hand, the comparison with NCO actually opens up an even more interesting possibility. Considering that both LiCrSe2 and NCO have their magnetic ions sitting on the triangular (frustrated) lattice with competing magnetic interactions, the spins are highly susceptible to any additional perturbation. In the case of NCO it was clearly shown that the Na-ion ordering actually creates a periodic coulomb potential (charge) landscape that is able to tune the electronic states and magnetic properties within the TMO layers76. It has even been proved that, by controlling the cooling rate of the sample, thereby gaining control of dynamics and vacancy order, different magnetic ground states could be achieved for the NCO compound4,75. Further, by electrochemical cycling of NCO inside a battery cell (i.e. changing the Na content x for NaxCoO2), very detailed studies could be performed on the nuclear structure78 as well as how this strongly affects the magnetic phase diagram6,79. The conditions for such phenomenology could in fact be verified also for LiCrSe2. We could imagine that if Li-ions organize themselves in an ordered pattern, their periodic potential could affect the spin order within the triangular lattice Cr planes. Such effect could be the origin for the peculiar main magnetic phase (qmain) firmly established in LiCrSe2, as well as for the potential secondary magnetic cell (qsecondary).
In summary, we discuss a few possible scenarios attempting to explain the un-indexed Bragg peaks found in our NPD data. Here it is important to underline that, although neutron powder diffraction is a powerful technique for studying crystal and magnetic structures, it does have some limitations, especially when dealing with complex systems. NPD provides average structural information from a polycrystalline sample, but not detailed information about single crystal domains or orientation-dependent properties. In complex systems, there may be significant peak overlap in the diffraction pattern, making it difficult to assign individual reflections to specific structural or magnetic components. Indeed, neutron powder diffraction typically has lower resolution compared to single crystal diffraction techniques, which can limit the precise determination of complex structural features. Symmetry-equivalent reflections will have the same d-spacing, therefore, especially in case of coexistence of multiple phases, the resulting powder diffraction pattern can be challenging to interpret accurately. This difficulty applies also to the determination of complex magnetic structures involving multiple magnetic substructures. Background signals and sample absorption can also interfere with weak diffraction peaks, especially in magnetic systems with low scattering strength.
These limitations can be mitigated in several ways, such as the ones adopted in this work. High-resolution TOF powder diffraction instruments and carefully optimized experimental conditions can help reduce peak overlap, resolve fine structural details, and capture the system’s behavior in a broad Q-range at all relevant conditions. Additionally, by combining data from multiple techniques like synchrotron X-ray diffraction and muon spin rotation, peak assignment can be improved leading to an enhanced accuracy of the solution. The analysis of the secondary phases can be conducted separately, which allows to disentangle their respective contributions to the diffraction pattern. Also in this case, the combination of neutron powder diffraction with other characterization techniques aids in resolving phase separation issues. Using high-quality samples can also significantly improve the reliability and accuracy of the structural determination and help overcome some of the challenges associated with this technique. A high-quality sample with a well-defined crystallinity, homogeneity and purity ensures a better signal-to-noise ratio, a more reliable average representation of the entire sample, as well as sharper and well resolved diffraction peaks in the pattern, facilitating peak assignment.
For these reasons, despite the inherent limitations of NPD, our solution for the magnetic phase in LiCrSe2 is overall a reasonably good representation of the magnetic ordering in this material. The uncertainty about the nature of the minority satellites can be removed by complementing the powder diffraction data with single crystal diffraction data, which can help resolve possible structural and magnetic ambiguities in the powder pattern.
In this regard, to ultimately discern if the additional satellites are of nuclear or magnetic origin, single crystal polarized neutron diffraction would be the optimal approach. However, although single crystal synthesis of the related compound LiCrTe2 has been very recently successfully achieved80, to the best of our knowledge no large enough LiCrSe2 single crystals are presently available.
Conclusions
The magnetic and crystal structure of the triangular antiferromanget LiCrSe2 has been solved at high and low temperature by means of neutron diffraction, synchrotron X-ray diffraction and muon spin rotation experimental techniques. The unique arrangement of the Cr atoms in this material is consistent with the simultaneous presence of competing nearest-neighbor ferromagnetic and antiferromagnetic exchange couplings over the same crystallographic sites, with a predominance of the next nearest neighbor interactions in the determination of the magnetic ground state in LiCrSe2. As a result, a structural transition from trigonal \(P\bar{3}m1\) to monoclinic C2/m crystal system induced by a strong magnetoelastic coupling occurs, accompanied by the formation of two up-up-down-down magnetic structures (a main one and a secondary one) with itinerant modulation of the Cr spin axial vector, in direction and modulus, and incommensurate q − vectors qmain = (0.045, \(\approx \frac{1}{4},\approx \frac{1}{2}\)) and qsecondary = (0.7249(5), −0.0885(3), −0.1292(9)). Such arrangement of the Cr spins is reminiscent of the magnetic ordering established in the Cr sulfide triangular antiferromagnets AuCrS2 and AgCrS2 which also manifest strong magnetoelastic coupling. However, the seemingly unprecedented geometric conditions realized in LiCrSe2 provide access to a unique combination of the competing magnetic mechanisms, resulting in a much more complex magnetic ground state in which the magnetic moment is periodically suppressed and changes direction. This peculiar behavior might be originated from a dual itinerant/localized nature of the electrons in this system. From the results of this work LiCrSe2 was proven to be an extremely fascinating study case, which lends itself to very promising future single crystal investigations, and constitutes an important step forward in understanding the spin-lattice relationship in strongly correlated spin systems.
Methods
Polycrystalline LiCrSe2 was prepared by direct reaction of the Li, Cr, and Se elements. The sample preparation is described in higher detail in reference35.
Bulk μ +SR Experiment
The temperature-dependent bulk-μ+SR spectra have been acquired at the multi purpose muon beam-line M20 of Canada’s particle accelerator center TRIUMF. ~ 200 mg of LiCrSe2 in powder was packed in a 1 × 1 cm2 area Aluminum-coated Mylar tape (0.05 mm thickness), in order to reduce the background signal. This envelope was attached to a low background sample holder inserted in a helium exchange gas cryostat (temperature range: 2 K to 300 K).
LF-μ +SR experiment
The high-temperature LF-μ+SR data were obtained using the surface muon beamline S1 at the high-intensity proton accelerator facility J-PARC, in Japan. The LiCrSe2 powder was pressed into a pellet introduced into hermetically sealed non-magnetic titanium cells. The surface of the pellet facing the muon beam was covered using a very thin (50 μm) titanium window. By using a closed-cycle refrigerator (CCR), data were collected in the temperature range T = 50 − 375 K. A more detailed description of the sample cell and experimental setup can be found in ref. 56.
Synchrotron XRD experiment
The XRD measurements were collected at the instrument I11 of the Diamond Light Source in Didcot (UK). The sample was mounted by filling and sealing an Al capillary with internal diameter 0.7 mm, which was in turn attached to a phoenix cryostat, with a 10∘ sample rocking stage, which allows measurements in a temperature range from 11 K to 300 K.
Neutron diffraction experiment
The time-of-flight (ToF) neutron diffraction measurements were performed at the powder diffractometer iMATERIA81, at J-PARC, in Japan. The powder samples (~500 mg) were mounted into cylindrical vanadium cells with diameters and 5 mm and sealed with an aluminum cap, aluminum screws and indium wire. The cell was mounted on a closed cycle refrigerator to reach temperatures between 2 K and 300 K. iMATERIA allows for the simultaneous adoption of different detector banks for wide d-range (Q-range) coverage. The backscattering bank (BS), suitable for detailed structural characterization, has a resolution Δd/d = 0.16% and covers a d-range from 0.181 Å up to 5.09 Å. The 90-degree detector bank (SE) has a resolution Δd/d = 0.5% and covers a d-range from 0.255 Å up to 7.2 Å. The low angle bank (LA35), ideal for the detection of low Q-range magnetic Bragg peaks, has a d-range from 0.25 Å up to 40 Å.
The sample preparations for all the measurements were carried out in a controlled environment using Ar and/or He glove-boxes, to avoid degradation of the highly air- and moisture-sensitive LiCrSe2 samples.
Softwares
The crystal and magnetic structure determination was carried out with the help of the Bilbao crystallographic server82,83, and the FullProf software suite84 was employed for the data refinement. All images involving crystal structure were made with the VESTA software85, the parameter plots and fitting are produced with the software Igorpro86 and the μ+SR data were fitted using the software package musrfit87.
Data availability
All the data of this work are available from the corresponding authors on request. The data are also publicly available on request from the repositories of the respective large-scale facilities where the experiments were performed upon providing the experimental beam time proposal number (see acknowledgements).
Change history
24 November 2023
A Correction to this paper has been published: https://doi.org/10.1038/s43246-023-00426-8
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Acknowledgements
The μ+SR measurements were performed at the instrument M20 of the muon source TRIUMF (beam time proposal: M1673) as well as at the S1 beam line of J-PARC (beam time proposal: 2019A0327). The XRD measurements were performed at the instrument I11 of the synchrotron facility Diamond (beam time proposal: CY23840). The NPD measurements were performed at the instrument iMATERIA of the neutron spallation source J-PARC (beam time proposal: 20180056A). The authors wish to thank Hiroshi Nozaki for his support during the μ+SR experiment, and Juan Rodriguez-Carvajal for the assistance he provided on the neutron diffraction data refinement, along with the staff of TRIUMF, Diamond and J-PARC for the help in the experimental measurements. This research is funded by the Swedish Foundation for Strategic Research (SSF) within the Swedish national graduate school in neutron scattering (SwedNess), as well as the Swedish Research Council VR (Dnr. 2022-03936, Dnr. 2021-06157, and Dnr. 2017-05078), and the Carl Tryggers Foundation for Scientific Research (CTS-22:2374). J.S. is supported by the Japan Society for the Promotion Science (JSPS) KAKENHI Grant No. JP18H01863 and JP20K21149. Y.S. and O.K.F. acknowledge funding from the Swedish Research Council (VR) through a Starting Grant (Dnr. 2017-05078) and Area of Advances-Material Sciences from Chalmers University of Technology. Y.S. is also supported by Wallenberg Young Fellow through the grant KAW 2021.0150. S.K. and K.Y. are supported by JSPS KAKENHI Grant No.18KK0150. The work at the University of Zürich and the University of Geneva was supported by the Swiss National Science Foundation under Grant No. PCEFP2-194183.
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E.N., J.S., and M.M. conceived the experiments. E.N., O.K.F., N.M., C.T., T.M., A.H., A.K., I.U., Y.S., J.S., and M.M. conducted the experiments. E.N, J.S., N.M., O.K.F., J.H.B., V.P., and M.M. analyzed the results. The samples were synthesized by S.K. and K.Y., as well as by C.W. and F.O.v.R.; they also conducted the initial sample characterizations. E.N and M.M. made all the figures. E.N. created the first draft, and all co-authors reviewed and revised the manuscript.
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Nocerino, E., Kobayashi, S., Witteveen, C. et al. Competition between magnetic interactions and structural instabilities leading to itinerant frustration in the triangular lattice antiferromagnet LiCrSe2. Commun Mater 4, 81 (2023). https://doi.org/10.1038/s43246-023-00407-x
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DOI: https://doi.org/10.1038/s43246-023-00407-x
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