Complex electronic states in double layered ruthenates (Sr1-xCax)3Ru2O7
Zhe Qu, Jin Peng, Tijiang Liu, David Fobes, Leonard Spinu, Zhiqiang Mao
aa r X i v : . [ c ond - m a t . s t r- e l ] S e p Complex electronic states in double layered ruthenates(Sr − x Ca x ) Ru O Zhe Qu , Jin Peng , Tijiang Liu , David Fobes , Leonard Spinu , and Zhiqiang Mao ∗
1. Department of Physics and Engineering Physics,Tulane University, New Orleans, Louisiana 70118, USA.2. Advanced Material Research Institute and Physics Department,University of New Orleans, Louisiana 70148, USA. (Dated: November 11, 2018)
Abstract
The magnetic ground state of (Sr − x Ca x ) Ru O (0 ≤ x ≤
1) is complex, ranging from anitinerant metamagnetic state (0 ≤ x < < x < ≤ x ≤ x = 1.0, to an Anderson localized state for0 . ≤ x < . . ≤ x < .
4, and then to a magnetic metallic state with the in-planeresistivity ρ ab ∝ T α ( α >
2) for 0 . < x < .
25. The system eventually transforms into a Fermiliquid ground state when the magnetic ground state enters the itinerant metamagnetic state for x < .
08. When x approaches the critical composition ( x ∼ PACS numbers: 71.30.+h,72.15.Rn,71.27.+a . INTRODUCTION The Ruddlesden-Popper series of perovskite ruthenates (Sr,Ca) n +1 Ru n O n +1 have at-tracted significant attention since they exhibit a wide range of unique electronic and mag-netic states. The richness of states in ruthenates is epitomized by unconventional spin-tripletsuperconductivity , antiferromagnetic (AFM) Mott insulating behavior , an electronicnematic phase , itinerant magnetism , and orbital ordered states . These states alloccur in close proximity and provide a rare opportunity to tune the system between var-ious states using non-thermal control parameters such as chemical composition, pressure,and magnetic field. Tuning of non-thermal parameters often results in interesting exoticproperties.The double layered ruthenates (Sr − x Ca x ) Ru O provide a typical example. The prop-erties of the end members in this series are dramatically different. The x = 0 member,Sr Ru O , is an enhanced paramagnet showing an itinerant metamagnetic transition . Itselectronic properties under magnetic fields remarkably depend on field orientation .Magnetic field applied along the c -axis induces an electronic nematic phase near a meta-magnetic quantum critical end point . In contrast, Ca Ru O ( x = 1) is AFM withN´eel temperature T N = 56 K and exhibits giant magnetoresistance attributed to a bulkspin-valve effect . Recent studies on floating-zone grown high quality single crystalsof (Sr − x Ca x ) Ru O revealed rich exotic magnetic properties . With Ca substitution forSr, the system evolves from an itinerant metamagnetic state (0 ≤ x < R w (0.08 < x < R w is ∼
10 for Sr Ru O ; it increases to a maximum of ∼
700 near x = 0 . .The nearly FM state does not develop a long-range FM order despite considerably strongFM correlations manifested by the large Wilson ratio, but instead freezes in a cluster-spin-glass (CSG) phase at low temperatures . The system eventually switches to a long rangeAFM state for 0 . ≤ x ≤ , in which the magnetic easy axis changes continuously fromthe c -axis to the ab -plane with increasing Ca content .To better understand these complex magnetic phase transitions, information on the elec-tronic states involved in these transitions is needed. The end members of (Sr − x Ca x ) Ru O have been shown to exhibit distinctly different electronic states; while Sr Ru O exhibitsFermi liquid behavior , Ca Ru O undergoes a metal-insulator transition (MIT) at 482 , which has been suggested to be caused by the opening of a pseudogap associatedwith a density wave instability , and enters a quasi-two-dimensional (2D) metallic groundstate at low temperatures . It is particularly interesting to investigate the evolution of theelectronic states between these two end members and how the states are coupled to themagnetic states.Here, we report a systematic study on the electronic states of the (Sr − x Ca x ) Ru O solidsolution by means of transport and specific heat measurements. We find that the electronicstates are complex and strongly coupled with the magnetic states in this system. In theAFM state with 0.4 ≤ x < . ≤ x < . ρ ∝ T α ( α > . < x < .
25. When the nearly FM state transforms to a metamagneticstate for x < x approaches the critical value 0.08.Non-Fermi liquid behavior is also observed in thermodynamic properties near this criticalcomposition. II. EXPERIMENT
We have succeeded in growing high quality single crystal samples of (Sr − x Ca x ) Ru O inthe whole range of x using the floating-zone technique . All crystals selected for measure-ments were characterized carefully by x-ray diffraction and SQUID magnetometer. SinceSQUID has an extremely high sensitivity to ferromagnetic materials, it guarantees that theselected samples do not contain any FM impurity phases such as (Sr,Ca) Ru O and(Sr,Ca)RuO . SQUID was also used for magnetization measurements on selected samples.Specific heat measurements were performed using a thermal relaxation method in a Quan-tum Design PPMS. The electrical transport measurements were carried out in a He cryostatwith a base temperature of 0.3 K, using a standard four-probe technique. The crystallo-graphic axes of the samples selected for transport measurements were identified using X-rayLaue diffraction. The electrical current was applied along in-plane Ru-O-Ru bond directionfor in-plane resistivity ρ ab measurements and along the c-axis for out-of-plane resistivity ρ c III. RESULTS
Figure 1 shows the temperature dependence of resistivity, ρ ab ( T ) and ρ c ( T ), for typicalcompositions of the (Sr − x Ca x ) Ru O solid solution series. Like other layered ruthenateswith cylindrical Fermi Surfaces (FS) , (Sr − x Ca x ) Ru O displays remarkableanisotropy between ρ ab and ρ c . ρ c is much higher than ρ ab throughout the entire series. ForCa Ru O ( x = 1 . ρ ab and ρ c exhibit anomalies at temperatures corresponding to T N and T MIT ; they show metallic behavior immediately below T N = 56 K, but a discontinuousincrease at T MIT = 48 K. Below T MIT , ρ ab first increases with decreasing temperature, thenexhibits metallic behavior once again at low temperatures. These characteristics are con-sistent with previous results obtained using floating-zone grown crystals . Recent studiesdemonstrate that the low temperature metallic behavior originates from small FS pocketswhich survive below T MIT24 . With Sr substitution for Ca, T N and T MIT , as determinedfrom ρ ab , systematically shift to lower temperatures for 0.4 ≤ x < . The system still remains anAFM metallic state between T N and T MIT in this composition range. However in contrastto the first-order-like MIT observed in Ca Ru O , the MIT in doped samples occurs in acontinuous fashion. Below T MIT , both ρ ab and ρ c exhibit non-metallic behavior down to 2K( dρ/dT < et al. , . We also note that ρ c show anomalies at T N and T MIT for 0.6 < x ≤
1, but only at T MIT for 0.4 ≤ x ≤ . ≤ x <
1) leads the electronic groundstate to transform from a quasi 2D metallic state in Ca Ru O to a non-metallic state. Thisnon-metallic state can be ascribed to Anderson localization as discussed below.When x < .
4, a magnetic phase transition from the AFM to the heavy-mass, nearlyFM state occurs . This transition is also probed in magnetoresistivity measurements,as shown in Fig. 2. For x ≥ .
4, a metamagnetic transition with clear hysteresis occurs,ascribed to the spin flip/flop transition of the AFM state. The metamagnetic transitionfield increases with increasing x and exceeds 6 T for x ≥ i.e. the (110) direction inthe Bb m space group, which is not the easy axis of magnetization . For x = 0 . . Accompanied with the magnetic phasetransition, the electronic state changes drastically. As seen in Fig. 1, the resistivity of thenearly FM state in 0.08 < x < ≤ x < ≤ x < ρ ab exhibitsa small upturn at low temperature (see Fig. 3b), suggesting a weakly localized state, whilefor 0 . < x < . ρ ab shows metallic behavior in the whole temperature range and canbe fitted to ρ ∝ T α ( α >
2) at low temperatures ( e.g. α = 2 . x = 0 . . ≤ x < x = 0 .
08, the system transforms into a metam-agnetic Fermi liquid ground state. As shown in the upper panel of the Fig. 6, the metamag-netic transition can be identified in both resistivity and magnetization for this compositionrange. In contrast to the spin flip/flop induced metamagnetic transition seen in the sampleswith x ≥ .
4, the metamagnetic transition observed here is reversible between upward anddownward field sweeps and this transition is generally interpreted as a field-induced Stonertransition . The metamagnetic transition field B IM depends sensitively on the Ca content;for x = 0, B IM ∼ ; B IM decreases rapidly as x increases, down to zero as x approaching the critical value 0.08 (see the inset to the lowerpanel of Fig. 6). Occurring along with the metamagnetism, as shown in Fig. 7, the resis-tivity exhibits a quadratic temperature dependence below a characteristic temperature T FL ,indicating a Fermi liquid ground state. The Fermi liquid temperature T FL is ∼
10 K for x = 0; it decreases rapidly to ∼ .
95 K for x = 0 .
02, and is eventually suppressed to zeronear x = 0 . − x Ca x ) Ru O , and plotted it together with the magnetic phase dia-gram we obtained earlier , as shown in the upper panel of Fig. 8. To summarize, Ca Ru O shows an AFM metallic state below T N = 56 K and then experiences a metal-insulator tran-sition at T MIT = 48 K, eventually evolving into a quasi two-dimensional metallic ground5tate at low temperatures. With Sr substitution for Ca, the metallic state remains between T N and T MIT (0 . ≤ x <
1, Region I) and yields to an Anderson localized state caused by dis-orders as the temperature is decreased below T MIT (0 . ≤ x <
1, Region II). When x < . . Accompanying this magnetic phase transition is anelectronic ground state transition from the Anderson localized state to a weakly localizedstate induced by magnetic scattering (0 . ≤ x < .
4, Region III). Further decrease of x leads to the presence of a magnetic metallic state (0 . < x < .
25, Region IV). When x < .
08, the system enters an itinerant metamagnetic Fermi liquid ground state (RegionV).
IV. DISCUSSION
First we will discuss the mechanism behind the MIT between Region I and II. In astrongly correlated electron system, MITs can generally be separated into two categoriesaccording to their driving forces , i.e. a Mott transition due to the correlation effect ofelectrons , and an Anderson transition due to disorder. In a typical Mott transition, on-siteCoulomb interactions create strongly renormalized quasiparticle states and open a gap atthe Fermi level . Therefore, there should be no density of states at Fermi level, resulting inan electronic specific heat equal to zero for a Mott-type insulator. This is well known andhas been observed in many materials, e.g. single layered ruthenate Ca RuO .However, the MIT observed in (Sr − x Ca x ) Ru O for 0 . ≤ x ≤ . Ru O was initially thought to be a Mott-likesystem with a small charge gap ∼ . . But later, an angle-resolved photoemis-sion spectroscopy (ARPES) study revealed that small, non-nesting Fermi pockets surviveeven at lowest achievable temperatures , leading to a small, but nevertheless, non-zero elec-tronic specific heat coefficient ( γ e =1.7 mJ/Rumol K ) and a quasi-2D metallic transportbehavior . In order to examine how γ e changes with Sr substitution for Ca, we measuredthe specific heat of (Sr − x Ca x ) Ru O ; the data is shown in Fig. 9. Since the phonon termis proportional to T , the phonon contribution can be evaluated by a linear fitting of C/T vs. T . The electronic specific heat is obtained by subtracting the phonon contributionfrom the total specific heat. From these analyses, we obtained γ e for most of our samples,6s shown in Fig. 8(b). We find that γ e is indeed small for Ca Ru O , consistent with theprevious result ; the Sr substitution for Ca gradually increases γ e , suggesting that the sizeof FS increases. These results are clearly not expected for a typical Mott insulator, thereforethe non-metallic state observed in Region II cannot be attributed to a Mott insulating state.Since Sr substitution for Ca introduces disorders to the system, disorder-driven Andersonlocalization effect should be considered. In general, in the presence of Anderson localization,there exists a finite density of state near the Fermi level, which is localized and does notcontribute to conduction. In this scenario, electronic specific heat remains finite despite thesystem showing non-metallic behavior. This is precisely in agreement with our observationin Region II. Therefore, the non-metallic behavior below T MIT should primarily be ascribedto Anderson localization.As the magnetic state switches from the AFM state to the nearly FM state near x =0.4, the electronic state changes to a weakly localized state. Our analyses show that itresults from magnetic scattering. As shown in Fig. 3a, the small upturn of resistivity at lowtemperature for the x = 0 . x = 0 .
38 sample isalso observed (see the inset to Fig. 3a). These results strongly support the assertion that theweak localization behavior observed for Region III is due to magnetic scattering. In addition,we note that the minimum resistivity occurs close to the CSG phase freezing temperature T f . Similar behavior has been observed in many other d - and f - electron spin glasses, suchas NiMn , NiMnPt , FeAl and U PdSi , and it is considered to be associated withthe formation of remanent FM domains. For our case, FM correlations are progressivelyenhanced with lowering temperature, eventually freezing into a CSG phase . In the CSGphase the FM clusters are randomly frozen, resulting in strong magnetic scattering amongFM clusters. Under the application of magnetic field such magnetic scattering is suppressed,thus suppressing the small upturn of resistivity at low temperatures.With decreasing Ca content, T f decreases and FM magnetic correlations becomeweaker , thus reducing magnetic scattering. Consequently, the weakly localized behaviorgradually disappears, eventually yielding to a fully metallic state in Region IV. The tem-perature dependence of resistivity in this metallic state can be fit to ρ = ρ + AT α at lowtemperatures with α > α is 2 . x = 0 . x . When x = 0 . α is decreased to 2.2, suggesting that the magnetic scatteringis still involved in the transport process in this sample. Thus, the electronic state in RegionIV can be viewed as a magnetic metallic state. When x is decreased below 0.08, the systementers a metamagnetic state and its electronic state behaves as a Fermi liquid ground state.As seen in Fig. 7, starting from x = 0, the Fermi liquid temperature T FL gradually decreaseswith increasing x , from 10 K for x = 0 down to zero for x ≈ .
08. We observed a non-Fermiliquid behavior in the temperature dependence of the electronic specific heat near the criti-cal composition ( x ≈ .
08) in our early work . Such a non-Fermi liquid behavior could beattributed to the system approaching a magnetic instability near x ∼ . x < . Ax (1 − x ) with A = 378 µ Ω · cm, implying that the randomness intrinsic to the Sr/Casubstitution alone can account for the variation of residual resistivity with the Ca content.Only when the electronic state transitions to the Anderson localized state for x ≥ .
4, showthe residual resistivity (taken as the resistivity at 0.3 K), significant deviation from thisformula. Another reason for this deviation is that the spin-valve effect sets in for x ≥ . .Comparing the double layered ruthenates (Sr − x Ca x ) Ru O to their single layered ana-logue Ca − x Sr x RuO we note that while they undergo a similar nearly FM-to-AFM tran-sition, distinct differences exist between their electronic states. First, we have shown thatthe electronic ground state near the Ca side in the double layered ruthenates is an Andersonlocalized state, whereas the insulating state near the Ca side in single layered ruthenates isa Mott insulating state . Second, while both solid solutions show CSG phases , theelectronic ground state differs significantly between them: a Fermi liquid ground state isobserved in the CSG phase of Ca − x Sr x RuO , but in the CSG phase of (Sr − x Ca x ) Ru O the magnetic scattering plays a critical role, resulting in a weakly localized state.Variations of electronic and magnetic properties in (Sr − x Ca x ) Ru O can all be at-tributed to structure changes caused by Ca substitution for Sr. Since Ca is smaller thanSr in ionic radius, Ca substitution for Sr should increase structural distortion as in8a − x Sr x RuO . Consistent with this expectation, Iwata et al. observed discontinuouschanges in lattice parameters near the boundary between the AFM and the nearly FMphases, and bifurcation of the a -axis lattice parameter for 0.6 < x <
1. From our X-raydiffraction measurements, we observed similar results. Furthermore, we recently performedstructure refinement of X-ray diffraction spectra for most of the samples presented in thephase diagram in Fig. 8. We found that the structure distortion caused by the substitutionoccurs via rotation and tilting of RuO octahedra . Rotation angle gradually increaseswith Ca substitution for Sr and approaches saturation for x > .
6, whereas the tilting doesnot occur until the Ca content x is increased above 0.4, and it enhances significantly for x > .
6. These results explain the magnetic phase transitions observed in this system ,the enhanced in-plane magnetic anisotropy for x > . , as well as the lattice parameterchanges observed by Iwata et al. . This, together with our observation of complex electronicstates described above, suggests strong interplay between charge, spin, and lattice degreesof freedom in double-layered ruthenates. V. CONCLUSION
In summary, we have established an electronic phase diagram for double layered ruthen-ates (Sr − x Ca x ) Ru O . Our results show that the electronic states of this system arecomplex and strongly coupled with the magnetic states. Disorder has a remarkable effect onelectronic transport properties. The electronic ground state in Ca Ru O is quasi-2D metal,but transforms into an Anderson localized state in the AFM region with 0.4 ≤ x < x = 0.4, the electronic state changes toa weakly localized state induced by magnetic scattering for 0.25 ≤ x < < x < x is decreased below 0.08, thesystem enters a metamagnetic Fermi liquid ground state. The Fermi liquid temperature issuppressed to zero near the critical composition with x ∼ cknowledgments We would like to acknowledge valuable discussions with Dr. I. Vekhter and Dr. V. Do-brosavljevic. 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50 100 1500.00.51.01.52.02.5 T N T MIT T N T MIT T (K) r a b ( mW c m ) T N x = 0.6 (a) T MIT x = 10.380.10.6 r c ( T ) / r c ( K ) T (K) x = 0.8 (b) r c ( W c m ) T (K) FIG. 1: (color online) (a) Temperature dependence of in-plane resistivity ρ ab ( T ) for double layeredruthenates (Sr − x Ca x ) Ru O . The downward arrow denotes the N´eel temperature T N and theupward arrow marks the metal-insulator transition temperature T MIT . (b) Temperature depen-dence of out-of-plane resistivity ρ c ( T ) (normalized to its 300 K value) for typical compositions.Inset shows ρ c as a function of temperature for Ca Ru O ( x = 1). .91.0 ρ a b ( B ) / ρ a b ( T ) x = 0.6 -6 -4 -2 0 2 4 60.960.981.00 B (T) x = 0.4 2
13 4 5213 4 5 -6 -4 -2 0 2 4 60.960.981.00 B (T) x = 0.38 x = 0.3 ρ a b ( B ) / ρ a b ( T ) FIG. 2: In-plane resistivity (normalized to its 0 T values) at 0.3 K versus field for(Sr − x Ca x ) Ru O . The magnetic field is applied parallel to the electrical current. r a b ( T ) / r a b ( K ) T (K) x = 0.30 20 40 60 80 1000.920.940.96 0.5T1T r a b ( T ) / r a b ( K ) T (K )
0T 2T3T4T x = 0.3 (a) T (K ) r a b ( T ) / r a b ( K ) x = 0.38 0.991.00 FIG. 3: (color online) (a) In-plane resistivity (normalized to its 15 K value) plotted versus T under a range of applied fields, for the x = 0 . T under zero field and 6 T for the x = 0 .
38 sample. (b)Temperaturedependence of the in-plane resistivity for several samples with 0 . ≤ x ≤ .
3, normalized to theirvalues at 5 K.
10 20 30 x = 0.2(a) r a b ( T ) / r a b ( . K ) T (K ) B = 0T B = 6T // ab r a b ( T ) / r a b ( . K ) T (K )(b) x = 0.2 FIG. 4: (color online) (a) In-plane resistivity (normalized to its value at 0.3 K) plotted versus T . under zero field for the x = 0 . T under 6 T for the x = 0 . r a b ( T ) / r a b ( K ) T (K)6T0T x = 0.6 B // (110) FIG. 5: Temperature dependence of the in-plane resistivity (normalized to its 15K value) underzero field and 6 T for the x = 0 . M ( m B R u - ) B (T) x = 0.080.05 B // ab B I M ( T ) Ca content x B // ab r a b ( mW c m ) r ab d M / d B ( m B R u - T - ) x = 0.05d M /d B FIG. 6: Upper panel: in-plane resistivity and the first derivative of the magnetization dM/dB as a function of magnetic field at T = 2 K for the x = 0 .
05 sample. The dash line marks themetamagnetic transition field B IM . Lower panel: magnetization as a function of magnetic fieldat 2 K for the samples with x = 0 . , . , .
02 and 0. Inset: the evolution of the metamagnetictransition field as a function of the Ca content. x = 0 0.05 r a b ( T ) / r a b ( . K ) T (K ) x = 0.08 T (K ) r a b ( T ) / r a b ( . K ) FIG. 7: (color online) In-plane resistivity (normalized to its 0.3 K value) plotted versus T forseveral samples with various Ca contents. Arrows indicate the temperature where the curve deviatesfrom linearity, i.e. the Fermi liquid temperature T FL . Inset shows the data for the x = 0.08 sample. T FL (Sr x Ca x ) Ru O II T ( K ) T MIT T N PM metalCSG T f T IM I M e t a m a g . (a)1.0 0.8 0.6 0.4 0.2 0.00.00.10.2 (b) g e ( J R u m o l - K - ) Ca content x FIG. 8: (color online) (a) The electronic phase diagram of the double layered ruthenates(Sr − x Ca x ) Ru O . T N : N´eel temperature; T MIT : metal-insulator transition temperature. Theopen squares (cid:3) and open circles (cid:13) represent T N and T MIT determined from magnetizationmeasurements , and the filled upward and downward triangles ( N and H ) represent those de-termined from ρ ab measurements. T f is the freezing temperature for the cluster spin glass (CSG)phase . The filled diamond (cid:7) is the temperature below which the electronic state becomes weaklylocalized due to magnetic scattering. T IM : the characteristic temperature below which an itinerantmetamagnetic phase transition occurs . T FL is the Fermi liquid temperature. Region I: the AFMmetallic state. Region II: the AFM Anderson localized state. Region III: the weakly localized stateinduced by magnetic scattering. Region IV: the magnetic metallic state (see text). Region V: themetamagnetic Fermi liquid state. (b) The electronic specific heat coefficient γ e as a function of Cacontent x .
200 400 600 C p / T ( J R u m o l - K - ) T (K ) x = 0.3 FIG. 9: (color online) Specific heat divided by temperature
C/T plotted versus T for typicalsamples. r a b , ( mW c m ) Ca content x FIG. 10: (color online) Residual in-plane resistivity as a function of the Ca content x . For thosesamples which show localized behaviors at low temperatures, ρ ab at 0.3 K is taken as the residualin-plane resistivity. The solid curve represents a fit to the Nordheim law Ax (1 − x ).).