Emergent ferromagnetism with Fermi-liquid behavior in proton intercalated CaRuO3

The evolution between Fermi liquid and non-Fermi-liquid states in correlated electron systems has been a central subject in condensed matter physics because of the coupled intriguing magnetic and electronic states. An effective pathway to explore the nature of non-Fermi liquid behavior is to approach its phase boundary. Here we report a crossover from non-Fermi liquid to Fermi-liquid state in metallic CaRuO3 through ionic liquid gating induced protonation with electric field. This electronic transition subsequently triggers a reversible magnetic transition with the emergence of an exotic ferromagnetic state from this paramagnetic compound. Our theoretical analysis reveals that hydrogen incorporation plays a critical role in both the electronic and magnetic phase transitions via structural distortion and electron doping. These observations not only help understand the correlated magnetic and electronic transitions in perovskite ruthenate systems, but also provide novel pathways to design electronic phases in correlated materials.

I. INTRODUCTION Landau Fermi liquid (FL) theory has been a successful model for describing the lowtemperature electronic properties of metals [1]. However, recently there have appeared an increasing number of systems that challenge the concept of FL by showing anomalous properties with non-Fermi liquid (NFL) behavior [2][3][4][5][6][7][8]. How to understand the NFL behavior forms an essential topic in the study of strongly correlated systems.
Among these systems, transition metal oxides have attracted particular interest due to their vastly unusual properties with notable NFL behavior [9][10][11][12][13][14], and the corresponding investigation is an important factor toward understanding of their fascinating properties. For instance, near a magnetic transition, the associated order parameter fluctuations may lead to the breakdown of FL and emergence of NFL behavior [4,5,15]. Although extensive investigations have been carried out in heavy fermion compounds and metallic alloys [4][5][6], the correlation of NFL and magnetic phase transition in transition metal oxides remains rare [11,12,16], which is likely due to the lack of effective pathways to obtain delicate manipulation of their magnetic and electronic states across these transitions.
Ruthenates represent an important family of complex oxides with rich spectrum of properties, ranging from unconventional superconductivity to ferromagnetism [12,[17][18][19]. Among this family, CaRuO3 has been extensively studied due to its unique nonmagnetic metallic state, as well as notable NFL behavior [16,[20][21][22]. Interestingly, its isoelectronic SrRuO3 shows an ferromagnetic ground state with FL behavior [19], and such distinct magnetic states were recognized due to the change of crystalline structure [23,24]. The contrasting magnetic and electronic properties between SrRuO3 and CaRuO3 suggest an intimate correlation between the Fermi-liquid behavior and ferromagnetic state in those systems. Hence, CaRuO3 provides a great playground to explore the correlation between NFL behavior and magnetic phase transition if one can introduce the ferromagnetic state into this system. Chemical substitution with B site isovalent chemical ions was widely employed to manipulate the magnetic state in CaRuO3 in the last several decades with the aim to probe the magnetic and electronic transition simultaneously [25][26][27][28][29][30][31], which however generally leads to electron localization rather than itinerant ferromagnetism, and the resulted magnetism was likely attributed to the suppressed long range magnetic ordering with local cluster [32][33][34].
While Sr1-xCaxRuO3 system undergoes a transition from ferromagnetic metal with FL behavior (FM-FL) to paramagnetic metal with NFL behavior (PM-NFL) with the increase of Ca concentration, the details close to the phase boundary differ substantially among previous reports limited by sample-to-sample variation [35][36][37][38]. Besides, previous theoretical work suggested that an itinerant ferromagnetic state can be potentially obtained from CaRuO3 through the epitaxial tensile strain [39], while the experimental results are controversial [36,40]. Therefore, it remains elusive whether a ferromagnetic FL metallic state could be obtained from CaRuO3, and if achievable how its FL behavior is correlated with the ferromagnetic state near the transition.
It is interesting to note that a recent study revealed a convenient method to control the magnetic state of SrRuO3 through the ionic liquid gating (ILG) induced proton intercalation (protonation) with the associated electron doping and structural deformation, which leads to a ferromagnetic to paramagnetic transition, while maintaining its robust FL behavior at low temperatures [41]. This study evokes immediately a series of interesting questions: whether the protonation process can lead to a novel magnetic state in CaRuO3, and how it would be coupled with the NFL behavior? In this letter, we demonstrate a reversible protonation of pristine CaRuO3 thin films through ILG. As a consequence, we observe an emergent ferromagnetic state as evidenced by the anomalous hall effect. Through careful analysis of the temperaturedependent transport data, we reveal an interesting NFL to FL crossover as the precursor of the magnetic transition. We attribute this distinct PM-NFL to FM-FL transition to the protonation induced band structural modulation as well as suppressed electronic correlation.

A. Proton intercalation in CaRuO3 film
High quality thin films of CaRuO3 were grown on (001) (LaAlO3)0.3-(SrAl0.5Ta0.5O3)0.7 (LSAT) substrates by a pulsed laser deposition system. Our samples show fully coherent epitaxial nature due to the relatively small lattice mismatch between sample and substrate. Figure 1(a) shows a schematic drawing of the ILG induced proton intercalation into the sample, in which protons are produced through the electrolysis of residual water within the ionic liquid (DEME-TFSI) and then inserted into the sample with the application of positive voltage across the gating electrode and sample [41][42][43].
To maintain charge neutrality, electrons are injected from the counter electrode into sample, completing the protonation process. With this setup, we first carried out in-situ X-ray diffraction (XRD) measurements during the ILG of CaRuO3 thin films. As shown in Fig. 1(b), with increasing gate voltage (VG), we observe a clear shift of the CaRuO3 (001) diffraction peak toward lower angles when VG is larger than 1.5 V, and such a critical voltage is consistent with the previous study of SrRuO3, and is attributed to the water electrolysis process [41]. The c lattice constant changes gradually from the pristine state and is eventually saturated with expansion of ~4.1%, providing the opportunity to manipulate continuously the electronic state of CaRuO3. It is important to note that the in-plane epitaxial strain remains unchanged throughout the phase transformation as evidenced by in-situ RSM measurements (Fig. S1 [44]). Similar to the previous study of SrRuO3, the structural transformation is also volatile, i.e., the crystal structure returns back to its pristine state when the gate voltage is turned off.
The slight offset of the XRD peak (as shown in Fig. S1(a) [44]) is attributed to small amount of residual hydrogen within the sample, as supported by our ex-situ SIMS measurements on gated samples ( Fig. 1(c)), in which about 10% hydrogen is observed in the post-gated HxCaRuO3.

B. Proton intercalation induced magnetic phase transition
To trace the evolution of magnetic and electronic states in CaRuO3 thin films through protonation, we performed in-situ transport measurements during ILG (see methods in Supplementary Information [44]). Figure 2(a) shows the temperature dependent resistivity ρxx(T) at different VG. At lower VG, the resistivity remains almost unchanged, while when VG is above 1.5 V, the resistivity is slightly enhanced, which is attributed to the local lattice distortion induced by the protonation. With the observation of robust metallic state, we then study its magnetic state through the anomalous Hall effect (AHE) measurements [45]. For pristine CaRuO3 film, the Hall resistivity shows a linear dependence on the magnetic field ( Fig. 2(b)), indicating a non-magnetic state.
Surprisingly, the gated samples (e.g. VG = 2.5 V) exhibits a distinct AHE hysteresis loop with nonzero remnant Hall resistivity at zero magnetic field, which signals an emergent ferromagnetic state through the ILG. Besides, the magnetic field angle dependence of Hall resistance and longitudinal resistance suggests the magnetic easy axis in ferromagnetic HxCaRuO3 is along out-of-plane direction (Fig. S3). It is important to note that the emergence of ferromagnetism by the protonation is exactly opposite to that of SrRuO3, in which the AHE, i.e. ferromagnetism, is totally suppressed through the protonation [41]. Furthermore, although the well-defined AHE hysteresis signal an emergent remnant ferromagnetization in proton intercalated CaRuO3, its actual spin configuration remains undetermined and left for future investigations.
To trace the evolution of the ferromagnetic state in HxCaRuO3, we then systematically measured the temperature dependent Hall resistivity as a function of VG (  More importantly, the VG dependence of AHE is nonmonotonic, exhibiting a dome shape with increasing VG (Fig. 2(d)). Furthermore, the extracted carrier concentration (hole type) increases by almost one order of magnitude at initial stage of ILG and then decreases gradually for higher VG (Fig. 2(d)). The notable similarity between the VG dependent carrier concentration and anomalous Hall resistivity suggests the emergence of ferromagnetism in HxCaRuO3 is correlated with the electronic state. The discrepancy between the increase of hole concentration and hydrogen intercalation induced electron doping indicates that the Fermi surface of sample is composed of both electron-like and hole-like pockets.

C. Proton intercalation induced NFL to FL transition
With this established magnetic phase diagram, we then further investigate the evolution of NFL through the ILG. Generally, NFL manifests itself into different power-law behavior of physical quantities from those of a FL. For instance, the temperature dependent resistivity can be fitted with ~, where α = 2 for FL and typically α < 2 for NFL [2,3,5,16,20]. To explore the potential variance in electronic behavior of the ILG sample, we quantitatively analyze the diagonal resistivity ρxx(T) by fitting the curves with the empirical relation ~ at low temperatures ( Fig. S4 [44]).
Intriguingly, the exponent clearly shows two regimes. As shown in Fig. 3(a), the pristine film and gated samples with VG of 0.5 and 1.0 V show an obvious power law behavior with ~3/2 at low temperatures, and such a NFL behavior is typically attributed to the diffusive electron motion induced by strong interactions between itinerant electrons and the critically damped long-wavelength magnons in quantum critical point systems [20,46]. With increasing VG at 1.5 V and above, changes from ~3/2 to ~2 ( Fig. 3(b)), indicating an electronic transition from a NFL to a FL.
Noteworthily, the Hall measurements reveal that the ferromagnetic state (with ≠ 0) emerges only at VG > 1.5 V (Figs. 3(c) and S2 [44]), which clearly indicates that the ferromagnetism emerges subsequently after the FL, rather than emerging simultaneously. This further suggests that the FL appears as a precursor of the ferromagnetism in CaRuO3 system, which is consistent with the fact that the FL is robust through the magnetic transition in SrRuO3. 39 Furthermore, it is also found that this magnetic and electronic transition can be induced reversibly with the application of gating voltage, showing an exotic magnetoelectric coupling. More specifically, when VG is cycled between 0 V and 3.5 V, the ON/OFF switching of ferromagnetic states can be realized, and the electronic behavior translates between NFL and FL as well, as shown in Figs. 3(d) and S5 [44].

D. Mechanism of proton intercalation induced phase transitions
To gain insight into the emergent ferromagnetism and FL behavior in HxCaRuO3, we carried out density functional theory (DFT) calculations, and then integrated them with dynamical mean-field theory (DMFT) calculations, i.e., DFT+DMFT. The details are presented in Supplementary Information [44]. The optimized crystalline structure of HxCaRuO3 (x = 0.5) is shown in the Fig. 1(a) respectively [44]. The pristine CaRuO3 shows suppressed spectral weights at Fermi level (E = 0) ( Fig. S7(a) and S8(a) [44]), which is consistent with earlier theoretical study [23] and account for the paramagnetic ground state following the Stoner criteria.
By contrast, the proton intercalation process leads to a pronounced enhancement of DOSs in the van Hove singularity around the Fermi level (Figs. S7(b-d) and S8(b-d) [44]). Such peaked DOS could potentially have the Stoner instability, leading to ferromagnetic ordering in itinerant electron system [47,48]. As expected, ferromagnetism is found to be stabilized in DFT+DMFT for some HxCaRuO3 cases, e.g., H0.5CaRuO3 in Fig.4a (Fig. S9 [44]). Relatively small difference between the minority spin and majority spin DOS suggests that H0.5CaRuO3 is a weak ferromagnet, which is consistent with our experimental observations of low Curie temperature and small AHE. In addition, the electronic behavior also changes with proton intercalation, as indicated by the imaginary part of the self-energy (Figs. 4(b) and S8 [44]). For pristine CaRuO3, it behaves as (ωn) 1/2 , which indicates a non-Fermi-liquid behavior due to the spin freezing ( Fig. 4(b)) [22]. For H0.5CaRuO3, the frequency range of this (ωn) 1/2 behavior becomes narrower and the absolute value of the self-energy becomes much smaller than that of CaRuO3, suggesting it is more Fermi liquid like ( Fig. 4(b)). In accordance with our experimental observations, DFT+DMFT calculations also manifest that proton intercalation induces a magnetic phase transition following the evolution from NFL to FL behavior. qualitatively consistent with the dome-shape AHE signal we observed. It is interesting to note that the largest M is found at Ne = 4 with the fully proton intercalated HCaRuO3 structure (Fig. S10 [44]). This suggests that stronger ferromagnetism could be achieved by doping holes into the fully proton intercalated HCaRuO3 or by inducing the similar structural distortion as HCaRuO3 without changing the nominal Ru valence by, for example, He implantation [49].

III. DISCUSSION
Due to the fact that the 4d transition metal ions typical process more extended d-orbitals,  Electrical transport measurements. The transport measurements were performed in a PPMS setup (Quantum Design DynaCool system, 9 T) equipped with lock-in amplifiers (Model LI 5640, NF Corporation). To carry out the in-situ transport studies, a 60 μm × 220 μm Hall bar was fabricated through standard lithography from thin films and the electrodes were capped with sputtered Ti/Au. Subsequently, the sample was placed in a quartz bowl cover entirely with ionic liquid and a slice of Pt was used as the gate electrode. For each state, VG was changed and then held up to 20 minutes at 290 K before cooling down toward lower temperature (<240 K) to freeze the ionic liquid.

First-principles calculations:
In density function theory (DFT) calculations, we first considered CaRuO3 with its pristine orthorhombic structure (Pnma), which contains 8 Ru sites per structural unit cell. Then we fixed the in-plane lattice constants with those of LSAT substrate, while optimizing the out-of-plane lattice constant and atomic coordinates. We used a supercell consisting of eight chemical formula unites of CaRuO3, and varied the number of hydrogen atom per cell as 0 (distorted CaRuO3, x=0), 2 (protonated H0.25CaRuO3), 4 (protonated H0.5CaRuO3), and 8 (protonated HCaRuO3).
It is important to note that in proton intercalated samples, all Ru sites were distorted from their original orthorhombic coordinates, and therefore when calculating the partial density of states, we averaged over "symmetry-related" d orbitals in the basis which diagonalizes the local crystal field 1 . These local orbitals can then be labeled using the . The band part is expressed in the Wannier basis, and the interaction part , is given by