Questioning Antiferromagnetic Ordering in the Expanded Metal, Li

Sep 14, 2015 - We present the results of a muon spin relaxation study of the solid phases of the expanded metal, Li(NH3)4. No discernible change in mu...
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Questioning Antiferromagnetic Ordering in the Expanded Metal, Li(NH3)4: A Lack of Evidence from μSR Andrew G. Seel,*,†,‡ Peter J. Baker,† Stephen P. Cottrell,† Christopher A. Howard,∥ Neal T. Skipper,∥,⊥ and Peter P. Edwards‡ †

ISIS Spallation Neutron and Muon Source, Chilton, Didcot, Oxfordshire OX11 0QX, United Kingdom Inorganic Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QR, United Kingdom ∥ Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom ⊥ London Centre for Nanotechnology, 19 Gordon Street, London WC1H 0AH, United Kingdom ‡

ABSTRACT: We present the results of a muon spin relaxation study of the solid phases of the expanded metal, Li(NH3)4. No discernible change in muon depolarization dynamics is witnessed in the lowest temperature phase (≤25 K) of Li(NH3)4, thus suggesting that the prevailing view of antiferromagnetic ordering is incorrect. This is consistent with the most recent neutron diffraction data. Discernible differences in muon behavior are reported for the highest temperature phase of Li(NH3)4 (82−89 K), attributed to the onset of structural dynamics prior to melting.

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phase) with both NH3 rotation and full-body tetrahedral motions.10 Phase II, previously thought to be hexagonal with a distortion of the tetrahedral units,11,12 has been shown to remain cubic, with no distortion, and crystallize in space group I43d.6 Phase II is less conductive than phase I,13 there is a concomitant drop in carrier concentration at this transition is shown in Hall effect data,4 and the available magnetic susceptibility measurements demonstrated a reduction in magnitude.8,14 Interestingly, the indication of a broad, weak maximum in the magnetic susceptibility between 10 and 25 K (just before the phase II−phase III transition) has led to the interpretation of antiferromagnetic ordering,8,14 which initially seemed to be verified by additional, unindexed reflections in the neutron diffraction data.7 These additional reflections have subsequently been reevaluated in a recent neutron diffraction study,6 without the need of magnetic scattering, precluded by their persistence to large Q values. Structurally, phase II and phase III are now known to be very similar, each with a complex unit cell comprising two interpenetrating “nets” of Li(NH3)4 units, as shown in Figure 1. The Li−Li distance is lower between units in the same net (∼5.2 Å) than between nets (∼6.2 Å). The Li(NH3)4 tetrahedra are orientated such that the Internet direction lies along the vertex (Li−N bond) of one tetrahedra toward the face of the next, whereas the intranet

olutions of alkali metals in anhydrous ammonia are wellknown examples of electronic systems undergoing a concentration-dependent insulator−metal transition,1,2 with a dramatic shift from blue electrolytic solutions to golden liquid metals. The concentration limit for lithium is 20 mol percent metal (MPM), yielding Li(NH3)4,3 a metallic compound with an electrical conductivity in the liquid state approximately twice that of liquid mercury.4 Remarkably, this liquid metal does not solidify upon cooling until a temperature of 89 K, making Li(NH3)4 the lowest melting point metal yet discovered. It must also be noted that despite its conductivity the electron density of Li(NH3) is low, conventionally quantified through the Wigner−Seitz radius, which for Li(NH3)4 is 7.2 a0 (compared with 3.25 and 5.62 for Li and Cs, respectively). This has led to the expanded metal appellative and interest in the possibility of electron−electron correlations in these systems.2,5 Upon solidification, Li(NH3)4 is known to form three crystalline, metallic phases: phase I (82−89 K), phase II (25− 82 K), and phase III (≤25 K) .6 These phases exhibit some unusual and still contested properties.4,6−8 The crystal structures of these phases have only recently been determined, in all cases consisting of an arrangement of close to ideal Li(NH3)4 tetrahedra. Phase I adopts a body-centered-cubic (BCC) structure and interestingly does not exist for the deuterated analogue, demonstrating a strong nuclear isotope effect.9 A quasielastic neutron scattering (QENS) study indicates that this phase is dynamically disordered (a plastic © XXXX American Chemical Society

Received: June 29, 2015 Accepted: September 14, 2015

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DOI: 10.1021/acs.jpclett.5b01380 J. Phys. Chem. Lett. 2015, 6, 3966−3970

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Figure 1. Structural schematic of Li(NH3)4 phase II/phase III, adapted from Zurek et al.3 Spheres represent the Li(NH3)4 tetrahedral centers, with colors and linkages denoting the connectivity of interpenetrating nets. Views are taken down the [001] (left) and [111] (center) directions. Right: Tetrahedral orientations.

Examples of zero-field (ZF) μSR measurements are given in Figure 2 for each of the solid phase of Li(NH3)4. Observation

direction is a displaced face−face orientation. The transition to phase III involves only very slight displacements of the Li atoms from their ideal, phase II positions, principally along the [111] direction.6 This axis consists of vertex-face orientations between tetrahedra of alternating nets. phase III crystallizes in the P213 space group. The electronic structure of Li(NH3)4 remains poorly understood. Calculation of the electronic densities of states for solid phases I and II has recently been performed within the framework density functional theory,3 but an optimized picture of the phase II/III transition is yet to appear. Interestingly, calculation of phase II showed that a pseudogap may exist at the Fermi level, which is presumably more pronounced in the lower symmetry phase III. This would be concordant with its lower (but still metallic) conductivity.13 The electron density in the vicinity of the Fermi level exhibits maxima at the nitrogen atoms of the Li(NH3)4 tetrahedra, with secondary maxima in the cavities between tetrahedra.3 It is difficult to envisage from the structure of phase II/phase III alone, what form any antiferromagnetic ordering in Li(NH3)4, if present, would take. Magnetization data from Sienko et al. suggests that approximately 11 to 12% of spins in the conduction band of phase II may be polarized,8 equating to approximately two spins per unit cell/16 Li(NH3)4 tetrahedra. These were posited to order at low temperature, although it should be noted that the change in susceptibility across the phase II/phase III boundary is not pronounced and exhibits only a weak maximum. To confirm unambiguously the existence of antiferromagnetism or spin-localization in Li(NH3)4 we have conducted muon spin relaxation (μSR) across each of the solid phases. Positive muons (μ+) act as a microscopic spin probe in condensed matter, being implanted with full polarization within the system and uniquely sampling the local magnetic environment through their depolarization dynamics. By probing the magnetic fields within a sample, muons are particularly sensitive to the presence of weak magnetism in both crystal and polycrystalline materials, with the ability to detect magnetic moments as small as ∼10−4 μB.15 μSR has been utilized in the characterization of magnetic ground states in molecular systems containing dissolved alkali metals, including the alkali metal fullerides and alkali-ammonia fullerides, which may possess ordered16 or disordered17 magnetic ground states or nonmagnetic ground states.18 Expanded metals such as Li(NH3)4 are distinct from these in that there is no anionic moiety, with the conduction band arising from spatially extended valence orbitals of the Li(NH3)4 molecules.3

Figure 2. Top: Example ZF μSR measurements of the crystalline phases of Li(NH3)4 where solid lines represent a fit to eq 1. Middle: The effect of an applied LF on muon depolarization at 5 K. Bottom: TF field measurement at 15 K where the solid line represents a fit to eq 2. Note the differing axis scales.

of the form of muon depolarization shows that while a discernible difference can be seen in phase I, those of phases II and III are similar. The polarization, Az(t), is fitted to the following relaxation form ⎤ ⎡1 2 ⎛ −Δ2 t 2 ⎞ 2 2 Az (t ) = ⎢ + exp⎜ ⎟(1 − Δ t )⎥exp(−λt ) + BG 3 ⎝ 2 ⎠ ⎦ ⎣3 (1)

being a Kubo-Toyabe (KT) relaxation accounting for the a nuclear field distribution, and an exponential decay incorporating additional contribution from electronic moments. The background, BG, term is a decaying exponential representing muons implanted in the TiZr sample container, and is 3967

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Figure 3. (A) Variation of Δ and λ from a fit of eq 1 to ZF measurements. (B) Variation of λ and ωμ from fit of eq 2 to TF measurements. Vertical dashed lines denote the temperatures of phase transitions, with phases given in red.

determined and fixed through measurement of the empty container. The Δ parameter of the KT function denotes the width of the field distribution sampled by the muon, and λ is the modifying exponential decay rate. A purely KT form of eq 1 would be true for muons depolarizing in an isotropic field of frozen nuclear moments. The inclusion of an exponential term was necessary to fit the experimental ZF data, demonstrating that an additional contribution to muon depolarization is present. Measurements were also performed with an applied longitudinal field, that is, one parallel to the initial muon spin polarization. These are presented in the middle panel of eq 2, where it can be seen that full depolarization is achieved with as little as 50 G LF. Also shown in Figure 2 is the evolution of muon asymmetry under an applied transverse field, where the field is perpendicular to the initial muon spin polarization. The depolarization function in this case is given by Ax (t ) = A cos(ωμt + ϕ) exp( −λt )

combination of NH3 rotation and Li(NH3)4 spherical diffusion (full body rotation) .10 NH3 rotational dynamics were shown to be present at 40 K (i.e., into phase II) on a picosecond time scale, shorter than muon decay dynamics. This may account for the (much reduced) temperature dependence of Δ in this phase, but we note that the susceptibility of phase II has also demonstrated a slight temperature dependence,8 which suggests an electronic origin to the muon relaxation. Importantly, Figure 3A demonstrates the similarity between phases II and III for both Δ and λ, which is not consistent with a discernible ordering of spin density influencing the muon depolarization. It can be seen in Figure 3B that the values for λ in the transverse-field (TF) measurements mimic those of Δ in the ZF measurements, reflecting the differing depolarization dynamics across the solid phases of Li(NH3)4. Once again, it is clear that while a stark difference occurs across the phase II/I boundary, no discernible difference in λ is seen in phase III. There is an slight increase in ωμ values crossing from phase II to phase III, but the magnitude of this change (9.4 × 10−4 MHz) corresponds to an increased local field experienced by the muon of 6.9 × 10−2 G (6.9 × 10−3 mT), which is at the very edge of the detection limit. The lack of difference in Figure 3 across the phase II/phase III boundary is significant in our understanding of possible ordering of electronic moments in Li(NH3)4. It is interesting to speculate on the limits these results place on an ordered moment, considering the high sensitivity of μSR,15−17 possible probe sites, and magnetic ground states. We can estimate an upper bound for the magnitude of a localized moment, under the assumption that the muon is situated within a given Li(NH3) unit, whereby the muon is associated within the Li−N tetrahedra. A limiting case in a model of a magnetic ordering

(2)

In this expression, ωμ is the precession frequency of the muon, proportional to the magnetic field strength, ωμ = γμH, where γμ is the muon magnetogyric ratio. A gives the initial muon asymmetry and ϕ is the phase factor, with relaxation dynamics given by the exponential term. The variation of fit parameters with temperature across the solid phases of Li(NH3)4 is given in Figure 3A. It can be seen that there is a discernible phase dependence for both Δ and λ across the phase II/I boundary. The sharp decrease in Δ with increasing temperature across phase I indicates a marked increase in the structural dynamics of the system as the melting point of Li(NH3)4 is approached. This confirms the dynamic nature of phase I, as first determined by the interpretation of QENS data at 85 K as a 3968

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data across the crystalline regime of the expanded metal, Li(NH3)4.

transition at the phase II/phase III boundary is the localization of spin density at a distinct crystallographic site within the phase III, P213 unit cell. The “worst-case” scenario for this isolated spin locale would be in the center of the intertetrahedra cavity, that is, at a maximized muon-moment distance. This would be a distance of approximately 3 to 4 Å, resulting in an increase in the field experienced by the muon of ∼14.5 mTμ−1 B . If we assume a conservative sensitivity limit of 0.01 mT for our measurements, to account for a lack of response in Figure 3 across the phase II/phase III boundary, we must place an upper bound of 690× 10−6(≃ 1 × 10−3)μB on the moment. Such a moment would be far below the limit of neutron diffraction to detect any discernible ordering. A more likely scenario is one whereby the electron spin density is associated with and distributed across the Li(NH3)4 units, with the question then becoming one of “which units and how many”. As previously mentioned, we can presume that any moment, arising as it does from electronic states near the Fermi level of the system, will be appreciably associated around the nitrogen atoms of the Li(NH3)4 units and to a lesser extent within the cavity regions. Recent calculations of phase II of the system give a density of at least 0.0087 electrons/Å3 from states around the Fermi level to be associated with both nitrogen atoms and cavity regions.3 This is an underestimation of the electron probability density around the nitrogen atoms alone. Were some percentage of this density to transition to ordered moments in phase III (remembering the similarity in structure to phase II), we can make a crude estimate as to the sensitivity of the muon, accepting that the muon−nitrogen distance is within 1 Å. A hypothetical, fully localized moment of 0.0087 μB would give rise to a field of 8.07 mT. Thus, assuming a limit of 0.01 mT, an upper bound for our detection limit would be for 0.12% of valence electrons to localize. We have presented μSR data for the solid phases of the expanded metal, Li(NH3)4 to determine the existence or extent of antiferromagnetism. The proposed existence of a pseudogap close to the Fermi level in phases II and III has been used to suggest an ordering of spin density around 10−25 K in Li(NH3)4. Importantly, we find no compelling evidence of the existence of such in the form of spin relaxation of implanted muons in either ZF or TF measurements, evidenced by the absence of a discernible transition in the muon data across the phase II/phase III boundary. This has allowed us to rule out spin ordering to the sensitivity of the muon technique; for a spin-density distributed across the Li(NH3)4 unit cell we can put an upper bound of 0.12% of the valence electron density, giving rise to a detectable moment. In this limit the detection of any discernible antiferromagnetic ordering would be rendered moot, even for the case of a disordered spin localization. This places a further limit on the interpretation of the literature magnetization data, suggesting that the prevailing model of the lowest temperature phase of Li(NH3)4 being antiferromagnetically ordered is incorrect. Clearly this low-temperature region of the Li(NH3)4 phase diagram exhibits a far more subtle change in the magnetic (and electronic) behavior of this expanded metal than previously thought. In contrast, we have also demonstrated a stark difference in muon response between the cubic phases (II/III) and plastic phase (I) of the Li(NH3)4. The increased relaxation in phase I is concordant with the system being dynamically disordered on the time scale of the muon depolarization. Our findings are thus in agreement with both neutron diffraction and quasielastic neutron scattering

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EXPERIMENTAL SECTION μSR measurements were conducted on the EMU spectrometer at the ISIS pulsed neutron and muon source, Chilton, U.K.19 A sample of Li(NH3)4 was prepared in situ following the same methods as used previously for neutron studies of this system.10,20,21 Anhydrous ammonia was condensed at 200 K onto clean lithium metal within a titanium−zirconium alloy, TiZr, sample container. This material has been demonstrated to not catalyze the decomposition of Li(NH3)4, and to give a slowly relaxing muon response.20,21 The system pressure was monitored throughout, and no evolution of H2 was observed, which would indicate sample decomposition. Both ZF and TF μSR measurements were performed across all solid phases in the range 5−90 K. TF measurements were also taken into the liquid state.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the ISIS Spallation Neutron and Muon Source for beamtime on the EMU instrument. We would also like to extend our thanks to Mark Kibble and Chris Goodway of the experimental support team for rigorous testing and modification of the vacuum and gas-handling setup and to Anton Orszulik for aid in sample cell design.

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REFERENCES

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