Current-induced strong diamagnetism in the Mott insulator Ca2RuO4

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Science  24 Nov 2017:
Vol. 358, Issue 6366, pp. 1084-1087
DOI: 10.1126/science.aah4297

Tuning diamagnetism with current

Properties of materials can be tuned by various means, such as chemical doping, magnetic field, or pressure. Sow et al. used electrical currents of modest density to turn the Mott insulator Ca2RuO4 into a semimetal. Concurrently, its diamagnetic response—the ability to counter an externally applied magnetic field—rose to levels higher than in any other nonsuperconducting material. The use of electrical current as a powerful experimental knob may be applicable to other similar materials.

Science, this issue p. 1084


Mott insulators can host a surprisingly diverse set of quantum phenomena when their frozen electrons are perturbed by various stimuli. Superconductivity, metal-insulator transition, and colossal magnetoresistance induced by element substitution, pressure, and magnetic field are prominent examples. Here we report strong diamagnetism in the Mott insulator calcium ruthenate (Ca2RuO4) induced by dc electric current. The application of a current density of merely 1 ampere per centimeter squared induces diamagnetism stronger than that in other nonsuperconducting materials. This change is coincident with changes in the transport properties as the system becomes semimetallic. These findings suggest that dc current may be a means to control the properties of materials in the vicinity of a Mott insulating transition.

In response to an external magnetic field, conduction electrons in a material exhibit cyclotron motion, resulting in an orbital magnetic moment. Such orbital motion leads to quantized (discrete) energy levels, known as the Landau levels. In a simple system, the resultant increase in the total energy is proportional to the square of the applied magnetic field. This increase in energy results in a negative magnetic susceptibility, which does not depend on the field strength. This effect is known as the Landau diamagnetism, or orbital diamagnetism (1). Another source of diamagnetism, ubiquitously present irrespective of the metallicity of a material, is the circulation of inner-shell electrons. In most materials, both types of diamagnetism are rather weak and are often hindered by paramagnetic contributions. However, pyrolytic graphite and bismuth are well known to exhibit exceptionally large diamagnetism (Fig. 1A), owing to strong Landau diamagnetism originating from light-mass electrons with gapped Dirac dispersions as well as multi-orbital effects (24). Recently, relatively large diamagnetism was observed in some topological semimetals such as TaAs, ascribable to the Weyl electrons in the bulk electronic state (5), again with Dirac-cone dispersion.

Fig. 1 Strong diamagnetism is observed in Ca2RuO4.

(A) Diamagnetism in Ca2RuO4 (under current) compared with that in other diamagnets and superconductors, demonstrating that Ca2RuO4 under current exhibits a diamagnetism stronger than that of other nonsuperconducting materials at similar temperatures. Here, −M is plotted as a function of applied magnetic field [μ0H] for: Ca2RuO4 at 1.5 A/cm2 and 20 K, highly ordered pyrolytic graphite (HOPG) at 20 K, bismuth (Bi) at 14 K (30), TaAs at 5 K (5), Pb (type I superconductor) at 4.7 K (31), Nb (type II superconductor) at 4.7 K (31), and YBa2Cu3O7−δ (type II superconductor) at 4.2 K (31). We obtained the data for Ca2RuO4 and HOPG ourselves. emu, electromagnetic units. (B) Crystal structure of Ca2RuO4. The primitive vectors ao, bo, and co are defined in the orthorhombic notation. The magnetic structure in the antiferromagnetic state under zero current is illustrated by arrows. (C) Various characteristic temperatures of Ca2RuO4 versus current density. The Mott insulating state evolves into a state with semimetallic behavior under current, exhibiting diamagnetism above 1.3 A/cm2 and below TDM = 50 K.

Here we show that the Mott insulator Ca2RuO4 under dc electric current exhibits diamagnetism stronger than other known nonsuperconducting materials (Fig. 1A). Notably, the diamagnetism of Ca2RuO4 at 7 T is comparable to that of high-temperature superconductor YBa2Cu3O7−δ. Negative magnetization stemming from local magnetic moments is found in certain ferrimagnets, such as YVO3, which contain two or more magnetic sublattices (6). However, such negative magnetization is associated with the flipping of spontaneously ordered moments; the differential magnetic susceptibility dM/dH is always positive (7), where M is magnetization and H is applied magnetic field. By contrast, diamagnetism is defined as negative M induced gradually by an external magnetic field, characterized by negative dM/dH.

The Mott insulator Ca2RuO4 (8) is an end member of the system Ca2−xSrxRuO4, which exhibits a rich variety of magnetic, transport, and structural properties (913), including the spin-triplet superconductivity in Sr2RuO4, the other end member (14). Ca2RuO4 exhibits a metal-to-insulator transition at TMI = 357 K accompanied by a first-order structural transition characterized by the flattening of the RuO6 octahedra below TMI (1517). Below TMI, the fourth electron of the Ru4+(4d4) ion predominantly occupies the dxy orbital (18). On further cooling, Ca2RuO4 undergoes an antiferromagnetic ordering at the Neel temperature TN = 113 K, with the Ru spins aligning along the orthorhombic b axis [Fig. 1B, (17)]. Resonant x-ray diffraction reveals another order, known as orbital ordering (OO), at TOO ~ 260 K (19). Ca2RuO4 can be made metallic by pressure (12), chemical substitution (9), or an electric field (20), accompanied by a first-order structural transition to stretch the RuO6 octahedra along the c direction. However, diamagnetism in the normal state has never been reported in Ca2−xSrxRuO4.

Here we investigated the transport and magnetic properties of Ca2RuO4 single crystals under dc current, as summarized in Fig. 1C. Figure 2A shows the temperature dependence of the resistivity ρ(T) under various applied currents for a sample with a cross section of about 2.9 × 10−3 cm2. Typical insulating behavior in ρ(T) is observed at 10 nA. It is technically difficult to pass moderate current (e.g., 10 nA to 3 mA) down to low temperatures owing to the high resistivity of the material (Fig. 1C and fig. S6). However, with increasing current, it becomes possible to flow current down to 20 K because the resistivity drops by more than five orders of magnitude with a current as small as 4 mA. The shape of the ρ(T) curve changes from that expected for thermal activation to a curve shape characteristic of semimetallic behavior with increasing current, consistent with the observed partial closing of the Mott gap (21).

Fig. 2 Diamagnetic semimetal behavior in Ca2RuO4.

(A) Temperature dependence of the resistivity under various applied currents. The inset shows a photo of a Ca2RuO4 crystal (sample #1, dimensions about 3 mm by 0.9 mm by 0.3 mm) with the two-probe setting. Ω, ohm. (B) Temperature dependence of the magnetization under various applied currents. The strong diamagnetism is observed for currents larger than 4 mA. Such behavior is consistently reproducible in all of the samples (fig. S7). (C) The temperature dependence of the magnetoresistance ratio [ρ(H) − ρ(0)]/ρ(0) at 7 T. The inset shows ρ(H)/ρ(0) as a function of applied magnetic field at 20 and 300 K. (D) Hall coefficient (RH) as a function of temperature for three samples. RH is derived from the linear fitting of the Rxy-H data with magnetic field up to 7 T. The upper inset shows the Hall resistance as a function of magnetic field measured at various temperatures. The lower inset shows a photo of sample #5 (about 2.7 mm by 0.7 mm by 0.5 mm) with the six-probe setting. I, current leads; V, voltage leads.

The magnetization also exhibits substantial change. As shown in Fig. 2B, the behavior of M(T) under a current of 10 nA is identical to its behavior at zero current (8). However, with increasing current, M decreases gradually, and the antiferromagnetic transition is suppressed before 2 mA is reached. We speculate that by reducing the many-body correlation effect, carriers injected by current promote the itinerant nature of 4d electrons so effectively that the local moments readily vanish, melting the antiferromagnetic order. With higher current (4.0 to 5.5 mA), M(T) exhibits a decrease below ~150 K and eventually becomes negative below 50 K. We carefully checked that this negative signal is not an experimental artifact (fig. S3 to S5). The direction of the magnetization is always antiparallel to the applied field, regardless of the field and/or current directions (fig. S4); thus, the local magnetic field induced by external current does not play a role. This invariance also excludes magnetoelectric effects observed in multiferroic systems (22) as a possible origin. We emphasize that joule heating, which certainly raises the actual sample temperature, cannot explain the diamagnetism (fig. S5), because Ca2RuO4 under ambient conditions exhibits positive magnetic susceptibility at all temperatures (fig. S12). Therefore, we conclude that the observed negative magnetization in Ca2RuO4 originates from diamagnetism of conduction carriers. Interestingly, the observed diamagnetism exhibits a peculiar anisotropy with respect to the applied magnetic field directions (fig. S10).

Next, we focus on magnetotransport properties. The longitudinal magnetoresistance (MR) at 7 T under a current of 5 mA exhibits sign reversal at around 70 K (Fig. 2C). Such negative MR without apparent ferromagnetic spin fluctuations is unusual. The Hall coefficient (RH) under currents of 5 to 9 mA (Fig. 2D) also exhibits sign change below 70 to 80 K, indicating the presence of multiple types of carriers in the current-induced state with semimetallic behavior.

We summarize the present findings in Fig. 1C, where various characteristic temperatures are plotted as functions of the current density J. Above 0.4 A/cm2, the Mott insulating state gradually evolves into a state with semimetallic behavior, with suppression of the antiferromagnetic ordering. Above 1.3 A/cm2, strong diamagnetism emerges at temperatures below TDM = 50 K (DM, diamagnetism). TDM stays nearly constant with increasing current up to 2 A/cm2. We emphasize that the current used in this study is lower than the current required to induce the insulator to metal transition at room temperature (5 A/cm2) (20).

To understand the observed transport properties, as well as the strong diamagnetism, we introduce a phenomenological model of a semimetal originating from the Mott-Hubbard bands. In this state, electron and hole pockets with light quasiparticle masses emerge from the upper and lower Hubbard bands, respectively. The pockets appear in the parts of momentum space where the band hybridization is most prominent (Fig. 3, A to J). Although this model is somewhat speculative, it is consistent with the experimental findings, as explained below. For the modeling, we use a tight-binding approach and start with the band structure of a hypothetical two-band metallic state for Ca2RuO4 [Fig. 3, A and F, and (23), section 5] without electron correlations. We assume the ferro-orbital ordered states (18): Two electrons per Ru4+ ion fully occupy the quasi–two dimensional (2D) orbitals and the other two partially occupy the quasi-1D orbitals. Thus, the electronic states close to the Fermi level consist of two half-filled bands originating from the dxz and dyz orbitals with dispersions in the kx and ky directions (fig. S14). The two bands hybridize to form two rounded square–shaped Fermi surfaces called α (hole band) and β (electron band) (Fig. 3A). Note that the orbital mixing caused by octahedral distortion is neglected.

Fig. 3 Electronic structure and diamagnetism of Ca2RuO4 induced by electric current.

(A to E) 2D projection of the Fermi surface at various bare Mott gaps 2Δ, starting from the tight-binding model for Ca2RuO4. π, the size of the first Brillouin zone in the unit of 1/at; at, the lattice primitive vector in the tetragonal notation; ao*, reciprocal primitive vector in the orthorhombic notation; at*, reciprocal primitive vector in the tetragonal notation. (F to J) Correlated band structures (zero points of the Green function) corresponding to the cases (A) to (E). Red and blue lines in (A) to (K) indicate the α and β bands, and the brightness of the color corresponds to the spectral weight at each point. (A) and (F) represent a two-band metal without correlations; (B) to (D) and (G) to (I) correspond to a semimetal; and (E) and (J) represent a Mott insulator. Increasing current corresponds to the change from (E) to (D). (K) Magnified plot of (I) near the Fermi energy. The upper and lower Hubbard bands (UHB and LHB) serve as the electron and hole pockets of the semimetal. (L) Momentum-resolved diamagnetic susceptibility Λ(k) (at T = 12 K) for Δ = 24 meV. (M) Integrated (sum over k) orbital magnetic susceptibility as a function of temperature. Large diamagnetic susceptibility emerges in the vicinity of the insulator-semimetal transition (Δ = 24 meV). The results qualitatively agree with the observed emergence of diamagnetism, including its temperature dependence. However, the calculated diamagnetism is an order of magnitude smaller than that observed.

To account for the electronic correlation and the Mott insulating nature, we next use a phenomenological approach proposed in (24, 25). When the effect of electron correlation represented by the self-energy Σ = Δ2/[ω + ϵ1D(k)] is turned on [where ϵ1D(k) is uncorrelated 1D dispersion and Δ is the gap parameter.], a Mott gap immediately opens up in the Brillouin zone (BZ) where the 1D nature is strongly preserved on the Γ-M and M-X lines (Fig. 3B). The hybridization forces the two 1D bands to repel each other, pushing one downward and the other upward, as shown in the magnified band dispersion in Fig. 3K. In the middle of the Γ-X line, where the hybridization is strongest, the Hubbard bands form a structure reminiscent of electron-hole pockets in an indirect-gap semiconductor or semimetal. The bottom of the upper Hubbard band (UHB) with α character is given by ±Δ − 2g and the top of the lower Hubbard band (LHB) with β character by ±Δ + 2g, where g is the hybridization parameter [see (23), section 5(b)]. For a small correlation (Δ < 2g), the bottom of the α-UHB and the top of the β-LHB form a Fermi arc–like structure (Fig. 3, B and C). These Fermi arcs shrink as the electron correlation is increased, resulting in a pair of small electron-hole pockets on the Γ-X line (Fig. 3D) at Δ ∼ 2g (Fig. 3K). As correlations are increased further, the gap fully opens, and the formation of the UHB and LHB is completed (Fig. 3J). In our experimental system, the tuning of the electronic correlations is achieved by varying the current (21); the possible mechanisms for this tuning are discussed below.

When the system approaches the insulator-to-semimetal transition (i.e., for Δ = 24 meV), the effective band mass m* becomes light for both the UHB and LHB (Fig. 3K). According to the Landau picture, diamagnetism is inversely proportional to m*. Thus, we expect large diamagnetism. The associated momentum-resolved contribution of the orbital susceptibility Λ(k) [see (23), section 5(b)] indeed exhibits sharp peaks at the band edges (Fig. 3L). The total orbital magnetic susceptibility is obtained by integrating Λ(k) over the BZ (Fig. 3M). In the vicinity of the full gap opening (Δ = 24 meV), a large diamagnetism with a sharp drop in susceptibility below a certain temperature is derived. With this value of Δ, the sign change of the calculated magnetic susceptibility occurs at 32 K, agreeing reasonably with the experimental observation of the negative susceptibility below TDM = 50 K. In spite of such qualitative agreements in the temperature dependence, the size of the calculated diamagnetism is an order of magnitude smaller than that observed. Section 5(c) of (23) gives an intuitive explanation of the negative susceptibility and its temperature dependence: The UHB and LHB of the Mott insulator act as the conduction and valence bands. With the gap closing, they form tiny electron and hole pockets; the strong diamagnetism originates from the orbital motions of thermally excited quasiparticles on these pockets.

One of the remaining issues to be resolved is the mechanism by which the Mott gap is closed by a dc electric current; although experimentally, such an occurrence has been established (21). One possible mechanism is the increase in the effective electron temperature in the nonequilibrium state under dc current. This mechanism has been considered to explain the suppression of ferromagnetic ordering (26) and melting of charge density waves (27) in strongly correlated electron systems. As an additional mechanism, we speculate that the enhanced screening by the mobile quasiparticles reduces the effect of electron correlations. In Ca2RuO4, weakening of the lattice deformation, known to occur by Sr substitution (28) and pressure (29), may take place under current and further assist the reduction of the effective correlation through the enhancement of the hopping energy. To elucidate the relative relevance of these scenarios, it would be useful to further probe the properties of this material under dc current, such as by using photoemission to probe the thermal distribution of electrons and Raman spectroscopy to probe the softening of phonons. Local electronic properties can be investigated with various scanning probes.

This work demonstrates that the Mott insulator can be driven to a distinct electronic state under nonequilibrium steady-state conditions induced by a simple dc electric current. Our work demonstrates that dc current is a powerful tuning parameter that can be used to explore phases emerging around the Mott insulating state.

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S16

References (3241)

References and Notes

  1. See supplementary materials.
Acknowledgments: We acknowledge discussions with J. G. Bednorz. We also acknowledge technical support from M. P. Jimenez-Segura. This work was supported by Japan Society for the Promotion of Science (JSPS) Grants-in-Aid for Scientific Research (KAKENHI) (nos. JP26247060, JP15H05852, JP15K21717, and JP17H06136), the JSPS Core-to-Core program, and the Impulsing Paradigm Change through Disruptive Technologies Program (ImPACT) from Japan Science and Technology Agency (JST) (grant no. 2015-PM12-05-01). C.S. acknowledges the support of the JSPS International Research Fellowship (grant no. JP17F17027). S.K. acknowledges the support of the Advanced Leading Graduate Course for Photon Science (ALPS). All the relevant data are available upon request from the authors.
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