Anomalous high-magnetic field electronic state of the nematic superconductors FeSe$_{1-x}$S$_x$

TL;DR

This study reveals that the nematic electronic state in FeSe$_{1-x}$S$_x$ superconductors exhibits anomalous non-Fermi liquid behavior with unusual resistivity and magnetoresistance, influenced by magnetic fields, disorder, and electronic structure changes.

Contribution

It provides detailed high-field transport measurements showing the non-Fermi liquid nature and anomalous scattering in the nematic phase of FeSe$_{1-x}$S$_x$, highlighting new insights into its electronic state.

Findings

Nematic state shows linear resistivity at low temperatures.

Resistivity exhibits a $T^{1.5}$ dependence near the nematic end point.

Magnetoresistance follows an $H^{1.55}$ dependence with an unusual low-temperature peak.

Abstract

Understanding superconductivity requires detailed knowledge of the normal electronic state from which it emerges. A nematic electronic state that breaks the rotational symmetry of the lattice can potentially promote unique scattering relevant for superconductivity. Here, we investigate the normal transport of superconducting FeSe$_{1-x}$S$_x$ across a nematic phase transition using high magnetic fields up to 69 T to establish the temperature and field-dependencies. We find that the nematic state is an anomalous non-Fermi liquid, dominated by a linear resistivity at low temperatures that can transform into a Fermi liquid, depending on the composition $x$ and the impurity level. Near the nematic end point, we find an extended temperature regime with $T^{1.5}$ resistivity. The transverse magnetoresistance inside the nematic phase has as a $H^{1.55}$ dependence over a large magnetic field range and it displays an unusual peak at low temperatures inside the nematic phase. Our study reveals anomalous transport inside the nematic phase, driven by the subtle interplay between the changes in the electronic structure of a multi-band system and the unusual scattering processes affected by large magnetic fields and disorder

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Anomalous high-magnetic field electronic state of the nematic superconductors Fe(Se1-xSx)

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Magnetic field is a unique tuning parameter that can suppress superconductivity to reveal the normal low-temperature electronic behavior of many unconventional superconductors Ramshaw et al. (2015); Boebinger et al. (1996). High-magnetic fields can also induce new phases of matter, probe Fermi surfaces and determine the quasi-particle masses from quantum oscillations in the proximity of quantum critical points Ramshaw et al. (2015); Coldea et al. (2019). In unconventional superconductors, close to antiferromagnetic critical regions, an unusual scaling between a linear resistivity in temperature and magnetic fields was found Hayes et al. (2016); Giraldo-Gallo et al. (2018). Magnetic fields can also induce metal-to-insulator transitions, as in hole-doped cuprates, where superconductivity emerges from an exotic electronic ground state Boebinger et al. (1996).

FeSe is a unique bulk superconductor with $T_{c}\sim 9$ K which displays a variety of complex and competing electronic phases Coldea and Watson (2018). FeSe is a bad metal at room temperature and it enters a nematic electronic state below $T_{s}\sim 87$ K. This nematic phase is characterized by multi-band shifts driven by orbital ordering that lead to Fermi surface distortions Coldea and Watson (2018); Watson et al. (2015a). Furthermore, the electronic ground state is that of a strongly correlated system and the quasiparticle masses display orbital-dependent enhancements Watson et al. (2017, 2015a). FeSe shows no long-range magnetic order at ambient pressure, but complex magnetic fluctuations are present at high energies over a large temperature range Wang et al. (2016). Below $T_{s}$, the spin-lattice relaxation rate from NMR experiments is enhanced as it captures the low-energy tail of the stripe spin-fluctuations Kasahara et al. (2016); Shi et al. (2018). Furthermore, recent $\mu$SR studies invoke the close proximity of FeSe to a magnetic quantum critical point as the muon relaxation rate shows unusual temperature dependence inside the nematic state Grinenko et al. (2018).

The changes in the electronic structure and magnetic fluctuations of FeSe can have profound implication on its transport and superconducting properties. STM reveals a highly anisotropic superconducting gap driven by orbital-selective Cooper pairing Sprau et al. (2016). Due to the the presence of the small inner bands, whose Fermi energies are comparable to the superconducting gap, FeSe was placed inside the BCS-BEC crossover regime Kasahara et al. (2014). In large magnetic fields, when the Zeeman energy is comparable to the gap and Fermi energies, a peculiar highly-polarized superconducting state may occur Kasahara et al. (2014).

To establish the role played by different competing interactions on nematicity and superconductivity, an ideal route is provided by the isoelectronic substitution of selenium by sulphur ions in FeSe1-xSx Watson et al. (2015b). This tuning parameter suppresses nematicity and it leads to changes in the electronic structure, similar to the temperature effects, with the Fermi surface becoming isotropic in the tetragonal phase and the electronic correlations becoming weaker Watson et al. (2015b); Coldea and Watson (2018); Coldea et al. (2019); Reiss et al. (2017). As nematicity is suppressed, it creates ideal conditions to explore a potential nematic critical point Hosoi et al. (2016) in the absence of magnetism. The superconducting dome extends outside the nematic state but anisotropic pairing remains robust Sato et al. (2018) and a different superconducting state was suggested to be stabilized in the tetragonal phase Hanaguri et al. (2018).

In this paper we study the normal electronic state across the nematic transition in FeSe1-xSx using magnetotransport studies in high-magnetic fields up to 69 T. We find that the nematic state has a non-Fermi-liquid behaviour with an unusual transverse magnetoresistance ($\sim H^{1.55}$), reflecting an unconventional scattering mechanism. Just outside the nematic phase, resistivity is dominated by a $\sim T^{1.5}$ dependence, similar to studies under pressure Reiss et al. (2019). The transverse magnetoresistance is significant inside the nematic phase and it shows an unusual change in slope at low temperatures. Inside the nematic phase at low temperatures, we find linear resistivity followed by Fermi-liquid behaviour for certain $x$ and impurity levels. Our study reveals anomalous transport in the nematic state due to the subtle changes in the electronic structure and/or scattering, which are also influenced by impurity levels.

I Results and Discussion

Figs. 1a-e show the transverse magnetoresistance, $\rho_{xx}$, of different single crystals of Fe(Se1-xSx) up to 35 T at various fixed temperatures inside the nematic phase and up to 69 T for $x\sim 0.25$ in the tetragonal phase. From these constant temperature runs, we can extract the magnetoresistance at fixed fields for each composition $x$, as shown in Fig. 1f-j, which reveals several striking features. Firstly, the magnetoresistance increases significantly once a system enters the nematic state at $T_{s}$, and its magnitude dependents on the concentration $x$, being largest for FeSe, just above $T_{c}$.

Secondly, in the vicinity of $T_{c}$ in magnetic fields much larger than the upper critical field, the magnetoresistance shows an unusual temperature dependence that varies strongly with $x$ across the phase diagram, as shown in Fig. 1(f-g). The resistivity slope $d\rho_{xx}/dT$ in 34 T of FeSe changes sign around a crossover temperature, $T^{*}\sim$ 14 K, as shown in Fig.1f (also in the colour plot of the slope in Fig. 3d). With increasing sulphur substitution from FeSe towards $x\sim 0.07$ (defined as the nematic A region), the position of $T^{*}$ shifts to a slightly higher temperature of $\sim 20$ K, and the peak in magnetoresistance is much smaller than for FeSe. For higher concentrations, approaching the nematic phase boundary, ($x\sim 0.11-0.17$ defined as the nematic B region), there is a small peak at $T^{*}$ but the negative slope $d\rho_{xx}/dT$ in 34 T is strongly enhanced at low temperatures, different from the nematic A phase (see Fig. 1(h,i) and Fig. 3(d)). Lastly, in the tetragonal phase, the magnetoresistance shows a conventional behaviour and increases quadratically in magnetic fields (Fig. 1(e) and (j)).

The unusual downturn in resistivity in high-field fields below $T^{*}$ inside the nematic A phase was previously assigned to large superconducting fluctuations in FeSe in magnetic fields up to 16 T Kasahara et al. (2016); Shi et al. (2018). We find that this behaviour remains robust in magnetic fields at least a factor of 2 higher than the upper critical field of $\sim$16 T for $H||c$ Kasahara et al. (2016). Furthermore, it also manifests in $x\sim 0.07$ inside the nematic A phase but it disappears for higher $x\gtrsim 0.1$. As $T_{c}$ and the upper critical field inside the nematic phase for different $x$ remain close to that of FeSe Coldea et al. (2019); Bristow et al. (2019), the changes in the resistivity slope in high magnetic fields are likely driven by field-induced effects that influence scattering and/or the electronic structure.

The Hall coefficient, $R_{H}=\rho_{xy}/\mu_{0}H$, extrapolated in the low-field limit (below 1 T) for FeSe1-xSx has an unusual temperature dependence, as shown in Fig.2b. For a compensated metal, the sign of the Hall coefficient depends on the difference between the hole and electron mobilities Watson et al. (2015c). In the tetragonal phase above $T_{s}$ and for $x\gtrsim 0.18$, $R_{H}$ is close to zero (Fig.2b), as expected for a two-band compensated metal. On the other hand, in the low-temperature nematic A phase the sign of $R_{H}$ is negative suggesting that transport is dominated by a highly mobile electron band Watson et al. (2015b); Sun et al. (2016). It becomes positive inside the nematic B phase, dominated by a hole-like band (Fig. 2(a)). It is worth mentioning that inside the nematic B phase the quantum oscillations are dominated by a low-frequency pocket with light-mass that disappears at the nematic end point Coldea et al. (2019). Thus, the behaviour of $R_{H}$ is linked to the disappearance of a small 3D hole pocket center at the $Z$-point in FeSe below $T_{s}$ and its re-emergence in the nematic B phase with $x$ substitution around $x\sim 0.11$, as found in ARPES studies Watson et al. (2015b) and sketched in Fig.1(m). Interestingly, the subtle changes in the electronic structure in FeSe1-xSx seem to correlate with the different features observed both in magnetoresistance (Fig.1(f-i)) and in the Hall coefficient $|R_{H}|$ that shows a maximum near $T^{*}$ (Fig.2(b)). In a high magnetic field, the Hall component of FeSe is complex, changing sign and being non-linear Watson et al. (2015b); Bristow et al. (2019). A magnetic field can induce changes in scattering and/or field-induced Fermi-surface effects in the limit when the cyclotron energy is close to the Zeeman energy. The smallest inner bands of FeSe1-xSx shift in energy as a function of composition $x$ (and temperature Coldea et al. (2019)), as shown in Figs.1(k-o). Furthermore, Hall effect in iron-based superconductors can be affected by the spin fluctuations that induce mixing of the electron and hole currents Fanfarillo et al. (2012).

Next, we attempt to quantify the magnetoresistance across the phase diagram and in the vicinity of the nematic end point in FeSe1-xSx, as shown in Fig.1(a-e). At the lowest temperature, inside the nematic phase, the transverse magnetoresistance of most samples is dominated by quantum oscillations Coldea et al. (2019) making difficult to quantify its dependence. A near-linear magnetoresistance is detected for $x\sim 0.07$ in Fig. 1b and for a dirty sample (with low residual resistivity ratio $\sim 8.5$) in Fig. S9. The quasi-linear field magnetoresistance at low temperature can arise from squeezed trajectories of carriers in semiclassically large magnetic fields in case of small Fermi surfaces ($\omega_{c}\tau\gg 1$) Pippard (1989); Du et al. (2005). Another explanation for an almost linear magnetoresistance is the presence of mobility fluctuations caused by spatial inhomogeneities, as found in low carrier density systems Narayanan et al. (2015); Du et al. (2005); Singleton (2018).

Classical magnetoresistance in systems with a single dominant scattering time is expected to follow a $H^{2}$ dependence Pippard (1989). This results in Kohler’s rule, which is violated in FeSe1-xSx suggesting that the magnetoresistance is not dominated by a single scattering time, as shown in Fig. S2(a-c). Magnetoresistance is quadratic in magnetic fields up to 69 T in the tetragonal phase ($x\geq 0.19$) (see Fig.1e and Fig.S4(e-f)) but not inside the nematic phase. FeSe1-xSx are compensated multi-band systems Coldea and Watson (2018) where the high-field magnetoresistance is expected to be very large and dependent on scattering times of electron and hole bands Watson et al. (2015c). Magnetoresistance has a complex form and instead simpler scaling have been sought to reveal its importance, in particular in the vicinity of critical points Hayes et al. (2016); Giraldo-Gallo et al. (2018). For example, in BaFe2(As1-xPx) for $x\sim 0.33$ at the antiferromagnetic critical point, a universal $H-T$ scaling was empirically found between the linear resistivity in temperature and magnetic field Hayes et al. (2016). For FeSe1-xSx near the nematic end point at $x\sim 0.17$ we find that a $H-T$ dependence collapses onto a single curve, as shown in Fig. S2(e). Despite this, the energy scaling of magnetoresistance used to described the antiferromagnetic critical point in Ref. Hayes et al. (2016) is not obeyed in the vicinity of the nematic end point in FeSe1-xSx, as detailed in Fig. S2(g-i). This could be due to additional constrains to be included either to account for the nematoelastic coupling Paul and Garst (2017) and/or the effect of impurities. For example, a very dirty sample of FeSe1-xSx close to $x_{nom}\sim 0.18$ was recently suggested to obey $H-T$ scaling Licciardello et al. (2019).

For reasons described above, we propose a different approach to model the magnetoresistance data in the nematic state of FeSe1-xSx, using a power law in magnetic fields given by $\rho_{xx}(H)=\rho_{0}(H)+bH^{\delta}$. Strikingly, we find that all the magnetoresistance data inside the nematic phase can be described by a unique exponent $\delta\sim 1.55(5)$ over a large field window, as shown by the colour plot in Fig.3(c) as well as in Figs.2(c) and S4(a-d). A detailed method of the extraction of $\delta$ and its stability over a large temperature and field window is shown in Fig.S3. Furthermore, this gives $\delta\sim 2$ for samples in the tetragonal phase (see Fig.3(c)). Inside the nematic phase, the Fermi surface of FeSe1-xSx distorts anisotropically Watson et al. (2015a); Coldea and Watson (2018) and an unusual type of scattering could become operational due to presence of hot and cold spots along certain directions Wang and Berg (2019).

In the absence of magnetic field the transport behaviour can also be described by a power law, $\rho(T)=\rho_{0}+AT^{\gamma}$. Fig. 3a shows a colour plot of the exponent $\gamma$, which is close to unity at low temperatures inside the nematic phase and becomes sublinear close to the nematic phase boundary, indicating a significant deviation from Fermi-liquid behaviour (a value of $\gamma$=1.1(2) was previously reported for FeSe Kasahara et al. (2010)). Outside the nematic phase a $T^{1.5}$ dependence of resistivity describes the data well over a large temperature range up to 120 K (see Fig. 2(a) and Fig.3(a)), in agreement with previous studies of FeSe1-xSx under pressure Reiss et al. (2019). Using the high-magnetic field data below $T_{c}$, we extract the low-temperature resistivity in the absence of superconductivity, $\rho_{H\rightarrow 0}$(T). Fig. 2(d-f) shows resistivity against temperature for different values of $x$, together with the extrapolated high-field points, using longitudinal magnetoresistance when $H||(ab)$ plane, shown in Fig.S5. We also use transverse magnetoresistance data to extract the zero-field resistivity, using the established power law $H^{1.55}$, as shown in Fig. S7. From both measurements, we find strong evidence for a linear resistivity in the low temperature regime, below $T^{*}$, inside the nematic phase. Linear resistivity was also detected from the 35 T temperature dependence of the longitudinal magnetoresistance in Ref.Licciardello et al. (2019), however, it was assumed to occur near the nematic critical point defined as $x_{nom}\sim 0.16$, which corresponds to $x\sim 0.13$ in our phase diagrams in Fig.3 and Fig.S1(b) (as the resistivity derivative in Ref.Licciardello et al. (2019) show a $T_{s}\sim$ 51 K). At low temperatures, we observe that Fermi-liquid behaviour recovers in the tetragonal phase (see also Refs. Urata et al. (2016); Licciardello et al. (2019)) and inside the nematic phase, below $T_{FL}$ (see Figs. 2(d-f) and 3(b)). This is strongly dependent on composition and impurity level, even in the vicinity of the nematic end point (see Figs. S8 and S9). We find that $T_{FL}$ is highest for the samples with the largest residual resistivity ratio (above $\sim 16$) (see Figs.S1(c) and S6). Theoretical models suggest that the temperature exponent, $\gamma$, in vicinity of critical points is highly dependent on the presence of cold spots on different Fermi surfaces, due to the symmetry of the nematic order parameter Wang and Berg (2019); Maslov et al. (2011). On the other hand, near a antiferromagnetic critical point in the presence of spin fluctuations the impurity level also affects the temperature exponent Rosch (1999). Furthermore, the scale at which the crossover to Fermi liquid behavior occurs at $T_{FL}$ in nematic critical systems could depend on the strength of the coupling to the lattice Paul and Garst (2017).

An overall representation of the resistivity slope $d\rho_{xx}{\rm(34~{}T)}/dT$ in 34 T for FeSe1-xSx as a function of temperature is shown in the phase diagram in Fig. 3d. The low-temperature manifestation of the nematic A and B phases is clearly different below $T^{*}$. In order to identify possible sources of scattering responsible for these changes, we consider the role of spin fluctuations. Recent NMR data found that anti-ferromagnetic spin fluctuations are present inside the nematic phase of FeSe1-xSx, being strongest around $x\sim 0.1$ Wiecki et al. (2018). In FeSe, spin fluctuations are rather anisotropic Cao et al. (2018); Wiecki et al. (2018) and strongly field-dependent below 15 K Shi et al. (2018). Interestingly, the spin-fluctuations relaxation rate is enhanced below $T^{*}$ (Fig. 3(d)), suggesting a correlation between spin-dependent scattering, the high-field magnetoresistance and the low-temperature transport inside the nematic state. High-magnetic fields are expected to align magnetic spins and could affect the energy dispersion of low-energy spin excitations and spin-dependent scattering in magnetic fields. In FeSe, the spin-relaxation rate in different magnetic fields up to 19 T deviates at $T^{*}$ Shi et al. (2018) but it remains relatively constant in 19 T at the lowest temperatures. This may suggest the variation in magnetoresistance in high magnetic fields at low temperatures in FeSe1-xSx is more sensitive to the changes in the electronic behaviour rather to the spin fluctuations across the nematic phase.

The low-temperature regime below $T^{*}$ displays linear resistivity, which is a potential manifestation of scattering induced by critical spin-fluctuations in clean systems Rosch (1999). $\mu$SR studies place FeSe near an itinerant antiferromagnetic quantum critical point at very low temperatures Grinenko et al. (2018) and spin-fluctuations are only found inside the nematic state Wiecki et al. (2018); Shi et al. (2018). On the other hand, close to the nematic end point in FeSe1-xSx we find that resistivity is not linear in temperature but is dominated by a $T^{1.5}$ dependence. This is contrast to the linear resistivity found near a antiferromagnetic critical point in BaFe2(As1-xPx) Kasahara et al. (2010). Theoretically, $\gamma=3/2$ could describe the resistivity caused by strong antiferromagnetic critical fluctuations in the dirty limit Rosch (1999); Moriya (1985). However, in FeSe1-xSx the spin fluctuations are suppressed and a Lifshitz transition was detected at the nematic end point Coldea et al. (2019). At a nematic critical point the divergent fluctuations for different Fermi surfaces could display unusual power laws in resistivity, as discussed in Refs. Wang and Berg (2019); Dell’Anna and Metzner (2007); Maslov et al. (2011). To asses the critical behaviour, it is worth emphasizing that the effective masses associated to the outer hole bands do not show any divergence close to the nematic end point $x\sim 0.18$ Coldea et al. (2019). This agrees with the variation of the $A^{1/2}$ coefficient (see Fig. S11) and previous studies under pressure Reiss et al. (2019), suggesting the critical nematic fluctuations could be quenched by the coupling to the lattice along certain directions in FeSe1-xSx.

The striking difference in magnetotransport behaviour between the nematic and tetragonal phase in FeSe1-xSx can have significant implications on what kind of superconductivity is stabilized inside and outside the nematic phase as different pairing channels may be dominant in different regions, as found experimentally Sato et al. (2018); Hanaguri et al. (2018). Linear resistivity found at low temperatures inside the nematic state is present in the region where spin-fluctuations are likely to be present. Furthermore, the absence of superconductivity enhancement at the nematic end point in FeSe1-xSx is supported by the lack of divergent critical fluctuations, found both with chemical pressure Coldea et al. (2019) and applied pressure Reiss et al. (2019). It is expected that the coupling to the relevant lattice strain restricts criticality in nematic systems only to certain high symmetry directions Labat and Paul (2017); Paul and Garst (2017).

In conclusion, we have studied the evolution of the low-temperature magnetotransport behaviour in FeSe1-xSx in high-magnetic fields up to 69 T. We find that the nematic state has non-Fermi liquid behaviour and displays unconventional power laws in magnetic field, reflecting the dominant anomalous scattering inside the nematic phase. In high magnetic fields, well-above the upper critical fields, the transverse magnetoresistance shows a change in slope that reflects the changes in the spin-fluctuations and/or the electronic structure. In the low-temperature limit, high magnetic field suppresses superconductivity and it reveals an extended linear resistivity in temperature followed by a Fermi-liquid like dependence, highly dependent on the composition and impurity level. Our study reveals the anomalous transport behaviour of the nematic state, strikingly different from the tetragonal phase, that influences how superconductivity is stabilized in different phases.

II Materials and Methods

Single crystals of FeSe1-xSx were grown by the KCl/AlCl3 chemical vapor transport method Böhmer et al. (2013). The composition for samples from the same batch were checked using EDX as reported previously in Ref. Coldea et al. (2019). Note that in Refs.Licciardello et al. (2019, 2019) the nominal, $x_{nom}$ were can be at least 80% less than the real $x$ (see also Ref. Hosoi et al. (2016); Wiecki et al. (2018); Coldea et al. (2019)). The structural transition at $T_{s}$ also provides useful information about the expected $x$ value, as shown in Fig.S1. More than 30 samples were screened for high magnetic field studies to test their physical properties. Residual resistivity ratio varies between 15-44, as shown in Fig.S1c. We observed the variation within the same batch due to the inhomogeneous distribution of sulfur with increasing $x$ (see Figs.S1 and S8). We estimate that the nematic end point is located close to $x\sim 0.180(5)$ (see Figs.S1) and S11).

In-plane transport measurements ($I||$(ab)) were performed in a variable temperature cryostat in dc fields up to 38 T at HFML, Nijmegen and up to 70 T at LNCMI, Toulouse with the magnetic field applied mainly along the $c$-axis (transverse magnetoresistance) but also in the ($ab$) conducting plane (longitudinal magnetoresistance) at constant temperatures. Low-field measurements were performed in a 16 T Quantum Design PPMS. The resistivity $\rho_{xx}$ and Hall $\rho_{xy}$ components were measured using a low-frequency five-probe technique and were separated by (anti)symmetrizing data measured in positive and negative magnetic fields. Good electrical contacts were achieved by In soldering along the long edge of the single crystals and electrical currents up to 3 mA were used to avoid heating. Magnetic fields along the $c$-axis suppress superconductivity in fields higher than 20 T for all $x$ values Coldea et al. (2019).

III Acknowledgments

We thank Lara Befatto, Dmitrii Maslov, Rafael Fernandes, Erez Berg, Shigeru Kasahara, Steve Simon, Siddharth Parameswaran and Stephen Blundell for useful comments and discussions. We thank and acknowledge previous contributions from Matthew Watson, Mara Bruma, Samuel Blake, Abhinav Naga and Nathaniel Davies. This work was mainly supported by EPSRC (EP/L001772/1, EP/I004475/1, EP/I017836/1). A.A.H. acknowledges the financial support of the Oxford Quantum Materials Platform Grant (EP/M020517/1). A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by National Science Foundation Cooperative Agreement No. DMR-1157490 and the State of Florida. Part of this work was supported supported by HFML-RU/FOM and LNCMI-CNRS, members of the European Magnetic Field Laboratory (EMFL) and by EPSRC (UK) via its membership to the EMFL (grant no. EP/N01085X/1). Part of this work was supported by Programme Investissements d’ Avenir under the programme ANR-11-IDEX-0002-02, reference ANR-10-LABX-0037-NEXT We also acknowledge the Oxford Centre for Applied Superconductivity and the Oxford John Fell Fund. A.I.C. acknowledges an EPSRC Career Acceleration Fellowship (EP/I004475/1).

IV Footnotes

To whom correspondence may be addressed: amalia.coldea@physics.ox.ac.uk

Author contributions: A.I.C designed, planned and supervised the research. M.B., P.R., Z.Z. and A.I.C. performed experiments in Nijmegen with support from A.M.; P.R. and A.I.C. performed experiments in Tallahassee with support from D.G.; M.B., P.R., and A.I.C. performed experiments in Toulouse with support from W.K.; A.A.H., T.W. and S.S grew single crystals. M.B. and A.I.C. performed data analysis. A.I.C and M.B. wrote the paper with contributions and comments from all the authors.