Introduction

The electronic properties of quasi-two-dimensional LnMAsO (Fig. 1a; Ln = lanthanide, M = transition metal) pnictides can be transformed with a small degree of electron doping. High-temperature superconductivity is observed with just 5% F doping in LaFeAsO0.95F0.051. In stark contrast to the LnFeAsO oxypnictides, which have a metallic ground state, LnMnPnO (Ln = lanthanide; Pn = As, P) are Mott insulators2,3,4. These phases have drawn interest due to their magnetoresistance (MR) properties. MR is defined as a change in resistivity upon the application of a magnetic field, H, such that MR = ((ρH − ρ0)/ρ0), where ρ0 and ρH are the resistivities in zero and applied field, respectively. Magnetoresistant materials find technological application in sensing and spintronics devices. Discovering and employing new magnetoresistant materials with enhanced properties thus represents an ongoing goal. For NdMnAsO, exchanging just 5% of the oxygen site for fluorine induces colossal magnetoresistance (CMR) such that MR9T (3 K) = −95%5,6. In contrast, PrMnAsO0.95F0.05 exhibits a structural phase transition at 34 K, driven by the Pr 4f electrons degrees of freedom which also results in a sizeable MR7T (12 K) = −13.4%7.

Fig. 1: The crystal structure and DC electronic properties of CeMnAsO1-xFx.
figure 1

a The tetragonal unit cell of CeMnAsO1-xFx, which crystallises in the P4/nmm space group. Insulating CeO1-xFx layers are situated between tetrahedral layers of MnAs. b The temperature-dependent resistivity (ρ) of CeMnAsO1-xFx, showing an insulator-insulator transition for x > 0.03. The data are normalised so that the transitions are apparent. The inset shows the variation of log(resistivity) versus inverse temperature where the insulator-insulator transition is observed for x = 0.035, 0.050 and 0.075.

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In order to further investigate the electronic properties of Mn oxypnictides, we have now synthesised CeMnAsO1-xFx (x = 0–0.075). Here we show that upon electron doping CeMnAsO1-xFx, a transition from the Mott insulating phase to a distinct quantum insulating phase is observed below a critical temperature TII. The transition has no thermodynamic signature and is a purely dynamical quantum criticality.

Results and discussion

CeMnAsO1-xFx (x = 0–0.075) phases have been synthesised and the chemical characterisation is described in the Supplementary Information (Supplementary Figs. 1 and 2 and Supplementary Tables 1–3). The parent compound, CeMnAsO, is a Mott insulator (ρ290 K = 1.76 × 104 Ω cm) as previously reported3,8. Figure 1b and Supplementary Fig. 3 show the temperature variation of the resistivity, ρ, for CeMnAsO1-xFx. For all x, between ∼300 ∼ 100 K the electron transport is dominated by thermally activated charge carriers across a band gap (Eg). Below ∼100 K a transition from Arrhenius behaviour to Mott three-dimensional variable-range hopping (VRH) is observed in CeMnAsO1-xFx for x > 0 so that the electrons are localised (Supplementary Fig. 4 and Supplementary Table 4). Below this temperature, transport can be described by phonon-assisted tunnelling of electrons between localised states. Surprisingly, upon further cooling, an insulator-insulator transition is observed for x > 0.03 where the resistivity increases by more than two orders of magnitude over a narrow temperature interval below a distinct temperature, TII (Fig. 1b). The samples rapidly become too resistive to measure for temperatures <TII. The insulator-insulator transition is also apparent from Hall resistivity measurements, where a sharp and significant drop in the Hall mobility occurs at TII (Fig. 2a and Supplementary Fig. 5). This significant reduction in electron mobility further triggers a colossal Seebeck effect at TII (Supplementary Fig. 6)9. Such a quantum insulating phase emerging from a Mott insulator is surprising. The transition is also distinct from Efros-Shklovskii (ES) variable range hopping where a subtle electronic transition is observed as a soft Coulomb gap pinned at the Fermi level opens up at low temperature as a result of enhanced Coulomb correlations, as reported for NdMnAsO1-xFx5 (Supplementary Fig. 7).

Fig. 2: Hall mobility and resistivity of Ce0.97MnAsO0.95F0.05 and electronic phase diagram of CeyMnAsO1-xFx.
figure 2

a The temperature dependence of the Hall mobility of Ce0.97MnAsO0.95F0.05 (defined as |RH(T)|/ρ(T), where RH(T) is the Hall coefficient recorded in H = 5000 Oe and ρ is the resistivity). A small drop in the Hall mobility is detected at the transition to variable range hopping (100 K) followed by a dramatic reduction in the mobility of the electrons at TII. The resistivity is shown in the inset and becomes too high to measure below 48.5 K. b The phase diagram shows the boundary of the Mott insulating phase and the quantum insulating phase for x = 0.00–0.075. The filled circles show TII for Ce stoichiometric phases and the filled squares shows TII for CeyMnAsO0.95F0.05 (y = 0.96 and 0.97).

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The electronic phase diagram of CeMnAsO1-xFx is shown in Fig. 2b. The transition temperature from the Mott insulator to the quantum insulating phase can be tuned by varying x. It is also possible to control TII by manipulating the composition, as the transition appears to be highly sensitive to chemical non-stoichiometry (Supplementary Table 4). Two Ce-deficient samples exhibit TIIs of 104 K and 50 K. The Ce occupancies were determined from Rietveld refinement using high-resolution X-ray diffraction data and the stoichiometries refined to Ce0.96MnAsO0.95F0.05 and Ce0.97MnAsO0.95F0.05 respectively. Although it is not possible to fully elucidate the exact Ce and F stoichiometry through X-ray diffraction and/or EDX, the results strongly suggest that cerium deficiency significantly enhances TII (Supplementary Figs. 8 and 9), and that further study of Ce deficient samples is warranted. For more details see the Supplementary Information.

Resistivity changes of several orders of magnitude, within a narrow temperature range, have attracted technological interest for a range of practical applications in functional devices. Notable examples include VO2, which exhibits a change of lattice structure and a Mott metal-insulator transition10, and magnetite, where the transition to insulating behaviour is driven by charge ordering involving three-site distortions called trimerons11. Such temperature-driven metal-insulator and insulator-insulator transitions are generally caused by subtle changes in the crystal lattice and/or magnetic structure. However, magnetic susceptibility measurements show TII is not coupled to any magnetic transition (Supplementary Figs. 11 and 12). Variable temperature powder neutron diffraction data recorded for Ce0.96MnAsO0.95F0.05 with TII = 104 K confirm there is no change in the nuclear or magnetic structure at TII (Supplementary Figs. 12–14 and Supplementary Tables 5 and 6). Heat capacity measurements on the same sample also show no evidence of any transition at TII (Supplementary Fig. 15). Furthermore, high-resolution neutron diffraction data recorded for CeMnAsO1-xFx (x = 0.00, 0.035, 0.050 and 0.075) at 300 K and 10 K also show that there is no change in crystal symmetry upon cooling (Supplementary Figs. 16 and 17). These results rule out other possible mechanisms for the insulator-insulator transition such as charge ordering, a spin state transition, a magnetic or structural transition, or orbital ordering, all of which would show a signature in either the magnetic or neutron diffraction or heat capacity data. The presence of an insulator-insulator transition with no change in the crystal or magnetic structure is highly unusual and suggests a more exotic phenomenon drives the significant increase in resistivity at TII.

Electron doping of several Mott-insulating Mn oxypnictides (LnMnAsO1-xXx) (Ln = La, Pr, Nd, Sm; X = F−, H− or a vacancy) has been performed previously2,5,7,12. The transition from insulating to metallic behaviour is normally observed at x ≈ 0.2. The conductivity observed in materials with x < 0.2 comes from charge carriers in the gap states that remain localised so that variable range hopping of the electrons is observed below ∼100 K. Typically reported values of T0 (T0 quantifies the degree of electronic disorder) are 4–7 × 105 K for LnMnAsO1-xFx (x = 0.05–0.08) (Ln = Nd, Pr)5,7. For CeMnAsO1-xFx and CeyMnAsO0.95F0.05, T0 ranges from 1.88 × 106 K–1.89 × 107 K (Supplementary Table 4), which suggests that a much greater degree of Anderson electronic disorder is present in this series (see Supplementary Information for more details on the electronic properties).

The lack of a peak in the heat capacity at TII (Supplementary Fig. 15) suggests that the transition has no thermodynamic signature and is a purely dynamical quantum criticality. To further explore the origin of the transition, variable-temperature and variable-frequency AC transport measurements were recorded for Ce0.97MnAsO0.95F0.05, Ce0.96MnAsO0.95F0.05 and CeMnAsO0.0965F0.035. The dissipative part of the AC conductivity is shown in Fig. 3 and Supplementary Figs. 18 and 19, respectively. A broad peak is observed at T* which is slightly higher than TII (T* = 53 K for Ce0.97MnAsO0.95F0.05 (TII = 50 K), 112 K for Ce0.96MnAsO0.95F0.05 (TII = 104 K) and 26 K for CeMnAsO0.0965F0.035 (TII = 18 K)). The peak exhibits a clear frequency response, typical of a dynamical system, and is reminiscent of the variable-frequency properties of other materials which exhibit dynamic phenomena such as spin and dipole glasses. The frequency dependence of the peak temperature (T*) is well modelled by the power law (Fig. 3 and Supplementary Fig. 18) with relaxation time constants of 4.2(2) × 10−5 s, 7.2(3) × 10−5 s and 3.2(2) × 10−5 s and zv = 1.4(1), 1.1(2) and 1.3(2) for Ce0.97MnAsO0.95F0.05, Ce0.96MnAsO0.95F0.05 and CeMnAsO0.0965F0.035 respectively. The fit to the power law demonstrates that there is a critical slowing of dynamics at T*.

Fig. 3: The AC transport of Ce0.97MnAsO0.95F0.05 with TII = 50 K.
figure 3

The inset shows the temperature variation of the dissipative part of the AC resistivity of Ce0.97MnAsO0.95F0.05 at selected frequencies between 1 Hz and 1000 Hz. A peak is observed at TII and moves to higher temperature with increasing frequency. The frequency dependence of the peak obeys the power law for Ce0.97MnAsO0.95F0.05. The power law states: \({\tau}={{\tau}}^{*}{\left[\frac{{T}_{{{{{{\rm{p}}}}}}}}{({T}_{{{{{{\rm{p}}}}}}}-{T}^{*})}\right]}^{ZV}\) where τ is a characteristic time describing the dynamical fluctuation time scale, τ* is the relaxation time constant, Tp is the temperature of the peak maximum temperature at a given frequency, T* is the critical temperature, z is the dynamical critical exponent and v is the correlation length exponent.

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The electronic behaviour at TII is distinct from an electron glass. The transition reported here is sensitive to the applied AC frequency so that a very low frequency is required to modify the transition (Fig. 3 and Supplementary Figs. 18 and 19). Exotic electron glasses such as the marginal Fermi glass observed in phosphorus-doped silicon (Si:P)13 and the electron glass indium oxide14 only show anomalous behaviour at much higher frequencies (MHz–THz). In these materials, it has been proposed the glassy behaviour only emerges when the applied AC frequency is similar to the phonon-electron relaxation time, as the presence of an AC frequency similar to the phonon relaxation time disrupts the ability for the electrons to interact with the phonons. For the CeyMnAsO1-xFx phases, slow dynamics are observed at much lower frequencies of ~1 Hz, which indicates the electrons are much more poorly coupled to thermal reservoirs such as phonons than they are in established electron glasses. The relaxation times we extracted from the AC resistivity data (~10–5 s) are also significantly slower than the typical phonon or electron-phonon relaxation times. Variable frequency AC transport measurements such as those reported here are therefore ideal to distinguish the quantum insulating phase observed in CeyMnAsO1-xFx from a glassy system.

The results from the AC transport measurements would suggest that the observed slowing of dynamics in CeyMnAsO1-xFx is due to a gradual decoupling between the electrons and phonons. This is highly unusual and shows that there is a transition from an open to a closed system upon cooling. It has previously been reported that it is possible for electrons and phonons to decouple, if the interacting electrons are not equilibrated with the crystal lattice, which can arise due to electron overheating in strongly disordered systems15,16. Further research is needed to fully elucidate the mechanism behind the electron-phonon decoupling in CeyMnAsO1-xFx.

To gain further insight into the origin of the insulator-insulator transition in CeyMnAsO1-xFx phases, density functional theory (DFT) calculations including non-local electron exchange were performed. The electronic band structures of CeMnAsO and CeMnAsO0.94F0.06 are presented in Fig. 4a, b, respectively. The narrow band at the valence band maximum in Fig. 4a, which originates from the Ce-4f state, is clearly absent in Fig. 4b. This suggests that, surprisingly, upon electron doping by substitution of F− for O2−, the Ce 4f band is destabilised in the vicinity of the F− anions and Ce3+ is oxidised to Ce4+. In CeMnAsO, Ce3+ has a formal 4f1 electronic configuration and upon electron doping the system reverts to a stable Ce4+ 4f0 configuration as found in CeO2. This suggests that in CeMnAsO, the 4f0 and 4f1 electronic configurations are competing with initial preference for the 4f1 state and that this subtle balance is broken by the substitution of F−. Charge neutrality is preserved as the excess electrons, upon oxidation of Ce3+ to Ce4+, move from the insulating CeO/F charge transfer layer to the As-Mn-As block as itinerant electrons.

Fig. 4: Calculated electronic properties of CeMnAsO and CeMnAsO0.94F0.06.
figure 4

a The electronic band structure and density of states of stoichiometric CeMnAsO. The partial density of states calculated with respect to Ce 4f and Mn 3d projections are shaded in blue and yellow, respectively. The energy was shifted so that 0.0 eV corresponds to the Fermi energy. b The unfolded electronic band structure and density of states of CeMnAsO0.94F0.06. The unfolding was done to match the reciprocal space path of the stoichiometric system. The energy was shifted so that 0.0 eV corresponds to the valence band maximum (Fermi energy at 2.0 eV). Both results are for the majority spin channel (the minority spin channel is shown in Supplementary Figs. 20 and 21).

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The results from the quantum mechanical calculations are confirmed by neutron diffraction data recorded at 4 K for CeMnAsO1-xFx which show a significant reduction in the ordered Ce moment with F− doping, as would be expected upon oxidation of Ce3+ to Ce4+ (Supplementary Fig. 22). However, the reduction in the Ce moment upon increasing the F− concentration from 0–0.05 is 16%, which would suggest that while there is some oxidation of Ce3+ to Ce4+, it is not uniform throughout the whole sample. It is therefore likely that domains of Ce3+ and Ce4+ coexist within the structure.

Chemical doping of Mott-insulators leads to chemical disorder which then results in electronic inhomogeneity and hence electronic disorder17. The Anderson-Hubbard model is used to describe doped transition metal oxides or oxypnictides such as CeyMnAsO1−xFx, where the electronic properties arise due to doping-related disorder and strong local Coulomb potential18. The electronic disorder and inhomogeneity that arises upon doping Mott insulators can also lead to exotic states inside the Mott gap19. For CeyMnAsO1-xFx, the electronic disorder is amplified as it is likely that the phases will contain insulating regions of localised correlated electrons and metallic regions of itinerant electrons from the 5% F− doping and subsequent oxidation of Ce3+ in the vicinity of the F- ion. Such mixed electronic states can lead to exotic properties and is most likely the origin of the quantum insulating state in CeyMnAsO1-xFx. It is surprising that such a large increase in TII is observed upon decreasing the Ce stoichiometry from y = 1–0.96 (TII increases from 34 K–104 K). The presence of Ce non-stoichiometry could further enhance the oxidation of Ce3+ to Ce4+ and hence increase the electronic disorder which would explain why there is such a significant increase in TII with very small changes in Ce stoichiometry.

Given that TII is an entirely dynamical transition, observed in an electronically disordered phase, and that AC transport measurements show that there is a change from an open to a closed system upon cooling, a potential origin of the localisation transition observed in CeyMnAsO1-xFx at TII is many body localisation (MBL). MBL has previously been described by theoretical and numerical studies of isolated quantum systems20,21,22, and transiently probed with ultra-cold atoms within isolated small systems on finite times23,24. MBL arises within a disordered system of interacting particles when quantum interference effects restrict transport to prevent the system from attaining thermal equilibrium under its own internal dynamics21,22. The transition to the MBL state is also characterised by singularities only in dynamical quantities25, so it does not require a breaking of symmetry. MBL systems have been proposed to serve as a form of quantum memory, in which information may be preserved in local observables across arbitrarily long timescales21,26. Furthermore, MBL systems may also be exploited as a promising platform to access alternative exotic quantum phases26, including the recently discovered discrete time crystal27.

Signatures of MBL have previously been detected in a handful of materials. Thin films of amorphous indium oxide exhibit vanishing conductivity in proximity to a magnetic-field-induced superconductor-insulator transition, which was attributed to the onset of a finite-temperature insulating state28. However, this was not accompanied by the characteristic slowing of dynamics that should precede the emergence of MBL29, so it most likely has an alternative physical origin. Nuclear magnetic resonance experiments on fluorapatite single crystals have revealed that the correlation length of the quasi-1D chains of spin-1/2 19F nuclei exhibits a similar evolution with time to the expected growth of entanglement entropy in the MBL regime30. However, while this resembles the theoretically expected response for MBL, further experimental signatures have yet to be reported in this material. AC magnetic susceptibility measurements on a single crystal of the disordered cluster magnet LiHo0.045Y0.955F4, revealed that interactions between spin clusters and residual free spins within the wider system can be tuned by a magnetic field such that magnetic dipole excitations can become localised31. This suggests that the residual spins can no longer act as a bath with respect to the spin clusters, and the system appears to become dissipationless. In this sense, LiHo0.045Y0.955F4 shows promise for studying how fragile non-equilibrium phenomena interact with a thermal reservoir, but ultimately no other behaviour consistent with MBL has been detected in this material.

The transition to the quantum insulating phase in CeyMnAsO1-xFx (x > 0.03) does not arise due to a change in the crystal or magnetic structure. Upon cooling, a critical slowing of dynamics is observed as the electrons and phonons decouple. An insulator-insulator transition is then observed at TII. This transition is not accompanied by a thermodynamic signature and below TII there is vanishing conductivity, a rapid change in the charge mobility and a colossal Seebeck effect as the electrons become localised. The CeyMnAsO1-xFx phases are electronically inhomogeneous and likely contain insulating regions of localised correlated electrons and metallic regions of itinerant electrons. Given the dynamical nature of the electron localisation transition at TII, we hypothesise that the transition could be a result of MBL. However, the electronic structure of CeyMnAsO1-xFx is pseudo two-dimensional and it is not yet clear whether MBL is possible in two-dimensional electronic phases32,33,34,35,36. Further experimental and theoretical studies are warranted to corroborate MBL in CeyMnAsO1-xFx. If confirmed, the discovery of this novel MBL phase emerging from a Mott insulator will inspire further understanding of non-equilibrium quantum statistical mechanics and could revolutionise next-generation technological applications involving quantum computing. Further studies of the electronic phase diagram of CeyMnAsO1-xFx are also clearly warranted to explore the boundaries between existing quantum and classical models.

Methods

Synthesis

Polycrystalline samples of CeMnAsO1-xFx (x = 0.00, 0.030, 0.035, 0.050 and 0.075) and CeyMnAsO0.95F0.05 were synthesised via a two-step solid-state reaction method. Initially, the CeAs precursor was obtained by the reaction of Ce pieces (Aldrich 99.9%) and As (Alfa Aesar 99.999%) at 980 °C for 33 h in an evacuated, sealed quartz tube. The resulting precursor was then reacted with stoichiometric amounts of MnO2, Mn and MnF2 (Aldrich 99.99%), all powders were ground in an inert atmosphere and pressed into pellets of 10 mm diameter. The pellets were placed into a Ta crucible and sintered at 1150 °C for 48 h, again in a quartz tube sealed under vacuum.

Diffraction

Room temperature powder X-ray diffraction patterns suitable for Rietveld refinement were recorded on a PANalytical Empyrean diffractometer using a Cu Kα1 source (λ = 1.54059 Å) between 10 < 2θ < 120° with a step size of 0.013°. Powder neutron diffraction patterns were recorded on the high intensity diffractometer D20 at the Institute Laue Langevin (ILL, Grenoble, France) with a wavelength of 2.4188 Å. A 1 g sample of Ce0.96MnAsO0.95F0.05 was inserted into an 8 mm vanadium can contained in a cryofurnace and data were recorded between 5 and 400 K, with a collection time of ~20 min at each temperature. Data were also recorded on the high-resolution, two-axis diffractometer, D2B between 3.5 and 290 K in an 8 mm vanadium can with a collection time of ~3 h at each temperature.

Rietveld refinements37 of the structural model were carried out using the GSAS program38. The scale factor, background (shifted Chebyschev polynomial function), pseudo-Voigt profile function, lattice parameters, atomic positions, zero shift and atomic displacement parameters were all refined. The atomic displacement U-factors were refined isotropically.

EDS analysis

EDS analysis was performed using a field emission gun Carl Zeiss Gemini SEM 300 equipped with an AZtec Energy EDS analysis system with an XMax 80 detector and an AZtecHKL EBSD analysis system with a Nordlys Nano EBSD camera (Oxford Instruments Ltd.). Energy dispersive spectroscopy (EDS) analysis was performed on CeMnAsO1-xFx (x = 0, 0.035, 0.05 and 0.075) and Ce0.97MnAsO0.95F0.05. For each sample, data were collected on 15 randomly selected crystallites.

Physical property measurements

The temperature dependence of the DC electrical resistance, Seebeck coefficient and Hall resistivity of the CeyMnAsO1-xFx phases were recorded using a Quantum Design physical property measurement system (PPMS) between 4 and 300 K. The measurements were performed with both the 2-probe and 4-probe methods to ensure the transitions were not a result of instrumental error. From ∼20 K above TII, data were also recorded every 0.25 K in order to obtain high quality and reliable data around the transition and to fully map out the transition. The temperature and frequency dependence of the AC transport of Ce0.96MnAsO0.95F0.05, Ce0.97MnAsO0.95F0.05 and CeMnAsO0.0965F0.035 were also recorded between 4 K and 300 K on the PPMS with selected frequencies between 1 Hz and 1000 Hz. Magnetisation measurements of all samples were recorded on a Quantum Design SQUID Magnetometer in an applied field of 100 Oe after zero field cooling (ZFC) and field cooling (FC) at temperatures between 2–400 K.

First-principles calculations

The electronic structure was calculated using plane-wave density functional theory within projector-augmented wave scheme as implemented in VASP. A cut-off energy of 600 eV and reciprocal space sampling of 6 × 6 × 3 and 3 × 3 × 3 were used for CeMnAsO and CeMnAsO0.94F0.06, respectively39,40,41. For CeMnAsO0.94F0.06, the supercell size was expanded into a size of 3 × 3 × 1 (18 formula units) and one O was replaced by F. For all the calculations, the HSE06 exchange-correlation functional within collinear spin representation was used42,43. The lattice constants were taken from the experimental structural refinement and the internal atomic coordinates were fully relaxed. To compare the band structure between CeMnAsO and CeMnAsO0.94F0.06, which have a different cell size, the band structure in CeMnAsO0.94F0.06 was unfolded onto the Brillouin zone path in CeMnAsO using the VASPBandUnfolding package44 .The density of states was analysed and plotted with the sumo package45.