Electrically-driven phase transition in magnetite nanostructures
Sungbae Lee, Alexandra Fursina, John T. Mayo, Cafer T. Yavuz, Vicki L. Colvin, R. G. Sumesh Sofin, Igor V. Shvets, Douglas Natelson
aa r X i v : . [ c ond - m a t . m t r l - s c i ] N ov Electrically-driven phase transition in magnetite nanostructures
Sungbae Lee , Alexandra Fursina , John T. Mayo , Cafer T. Yavuz , VickiL. Colvin , R. G. Sumesh Sofin , Igor V. Shvets , Douglas Natelson , Department of Physics and Astronomy,Rice University, 6100 Main St., Houston, TX 77005, Department of Chemistry, Rice University,6100 Main St., Houston, TX 77005, CRANN,School of Physics, Trinity College, Dublin 2, Ireland, Department of Electrical and Computer Engineering,Rice University, 6100 Main St., Houston, TX 77005
Abstract
Magnetite (Fe O ), an archetypal transition metal oxide, has been used for thousands of years,from lodestones in primitive compasses[1] to a candidate material for magnetoelectronic devices.[2]In 1939 Verwey[3] found that bulk magnetite undergoes a transition at T V ≈ K from a hightemperature “bad metal” conducting phase to a low-temperature insulating phase. He suggested[4]that high temperature conduction is via the fluctuating and correlated valences of the octahedral ironatoms, and that the transition is the onset of charge ordering upon cooling. The Verwey transitionmechanism and the question of charge ordering remain highly controversial.[5, 6, 7, 8, 9, 10, 11]Here we show that magnetite nanocrystals and single-crystal thin films exhibit an electrically drivenphase transition below the Verwey temperature. The signature of this transition is the onset of sharpconductance switching in high electric fields, hysteretic in voltage. We demonstrate that this transitionis not due to local heating, but instead is due to the breakdown of the correlated insulating state whendriven out of equilibrium by electrical bias. We anticipate that further studies of this newly observedtransition and its low-temperature conducting phase will shed light on how charge ordering andvibrational degrees of freedom determine the ground state of this important compound. e.g. , hightemperature superconductivity, metal-insulator transitions, and charge ordering) not present insimple systems with weaker electron-electron interactions. Such rich electronic phenomenologycan result when electron-electron interactions, electron-phonon interactions, and electronic band-width are all of similar magnitude, as in magnetite.[12] Verwey[3] found nearly seven decades agothat bulk magnetite, while moderately conductive at room temperature, undergoes a transition toa more insulating state below what is now called the Verwey temperature, T V ≈ K. Similartransitions are known in a number of materials.[13, 14] Above T V , Fe O has an inverse-spinelstructure of the form AB O , with tetrahedrally coordinated A sites occupied by Fe and oc-trahedrally coordinated B sites of mixed valence, equally occupied by irons with formal +3 and +2 charges. Conduction at high temperatures has long been thought to be through fluctuatingvalences of the B sites, with the transition corresponding to some kind of B site charge orderingas T decreases; concurrent is a first-order structural phase transition to an orthorhombic unit cell.This explanation remains controversial,[5, 6] with experiments showing some charge dispropor-tion or charge order (CO),[7, 8] and others implying that the structural degrees of freedom drivethe change in conductivity.[9, 10] Recent theoretical progress has been made in understanding thecomplex interplay of charge and structural degrees of freedom[15, 16], including a complete pic-ture of the transition mechanism [11] with strongly correlated 3 d Fe electrons acting to amplifyelectron-phonon couplings. Testing these ideas experimentally is of much interest.In this Letter we report electronic transport measurements in magnetite at the nanoscale onboth nanocrystals and single-crystal epitaxial thin films. Both types of devices exhibit strikingelectrically-driven hysteretic switching of the electronic conductance once sample temperaturesare reduced below T V . The data clearly show that the transition is not the result of local heat-ing above T V , but instead is an electrically-driven breakdown of the insulating state. We dis-cuss possible explanations for this switching in the context of the general Verwey transition prob-lem. While qualitatively similar resistive switching has been observed in other correlated oxidesystems[17, 18], the phenomenon in Fe O is a bulk effect with a mechanism distinct from these.Two-terminal devices for applying voltages and measuring conduction at the nanoscale havebeen fabricated (see Methods) incorporating both Fe O nanocrystals[19] (10-20 nm in diam-eter with oleic acid coating) and single-crystal thin films (40-60 nm thick).[20] Devices weremeasured in both a variable temperature vacuum probe station and a He cryostat with magnet.Current-voltage characteristics have been measured with both a semiconductor parameter analyzer2
150 30010 R [] T [K] -1 0 1-303 -2 -1 0 1 2-2-1012
60K 120K 70K 150K 80K 200K 100K R [] L CH [um] (a)(b) I D [ m A ] V DS [V] FIG. 1: Hysteretic conductance switching below T V . (a) Current-voltage characteristics at various temper-atures for a device based on 10 nm magnetite nanocrystals. Arrows indicate the direction of the hysteresis.Inset: Zero-bias resistance, R ( T ) . (b) Analogous data for a device based on a 50 nm-thick MBE-grownmagnetite film. The nominal interelectrode gap was planned to be 100 nm, but at its narrowest was ap-proximately 10 nm. Inset: Two-terminal resistance as function of channel length for another set of devicesfabricated on another piece of the same film. and directly using voltage sources and current amplifiers, with differential conductance computednumerically.Figure 1a shows I − V characteristics of a nanocrystal device at selected temperatures. Whencooling, zero-bias conductance decreases monotonically until T → T V . Below T V , the I − V characteristics show sharp switching between a low bias insulating state and a high bias state withmuch higher differential conductance dI/dV ( V ) (close to dI/dV ( V = 0 , T = 300 K)) , withdramatic hysteresis as a function of voltage sweep direction. The switching threshold voltages3 -5 -3 -1 -2 -1 0 1 210 -9 -7 -5 -3
60K 120K 70K 150K 80K 200K 100K (a)(b) d I D / d V D S [ S ] V DS [V] FIG. 2: Differential conductance plots of the switching. (a) dI/dV vs. V for the nanocrystal device fromFig. 1a at the same temperatures. (b) dI/dV vs. V for the thin film device from Fig. 1b. Both plots havelogarithmic dI/dV axes to better show the lowest temperature data. increase in magnitude as T is decreased.Dozens of nanocrystal devices were measured and only those with 300 K resistances below10 k Ω showed the switching, with higher resistance devices having higher switching thresholdvoltages. Resistances decrease by some three orders of magnitude with vacuum annealing at673 K, likely because of oleic acid decomposition.[21, 22] The temperature dependence (Fig. 1a,inset) of the zero-bias resistance, R ( T ) , has no step at T V , showing that R ( T ) remains dominatedby contact effects.Qualitatively identical conduction is apparent in the thin film devices, as shown in Fig. 1b.Contact resistances are also important in these structures, as demonstrated by examining R at lowbias ( < mV) as a function of channel length, L , as shown in the inset for one set of devices.Extrapolating back to L → , the contact resistance, R c , at 300 K is 390 Ω , while the 50 nm4hick channel of width 20 µ m contributes 27.2 Ω /micron, implying (based on channel geometry) amagnetite resistivity of 2.9 m Ω -cm, somewhat below bulk expectations. Further investigations areseeking to understand and minimize R c . Analysis of R ( L ) at lower temperatures shows that R c increases significantly as T is decreased, exceeding 80 k Ω by 80 K. This complicates the analysisof the switching, since some of the total V is dropped across R c rather than directly within theFe O ; further, the contacts may not be Ohmic near the switching threshold. We return to thisissue later.The transitions in all devices are extremely sharp, with widths less than 50 µ V, though inrepeated sweeps at a fixed temperature, there is sweep-to-sweep variability of a few mV in switch-ing thresholds. Using the substrate as a gate electrode, no discernable gate modulation was seenin nanocrystal devices for gate biases between -80 V and +80 V; this suggests that nanocrystalcharging effects do not dominate. Switching characteristics were independent of magnetic fieldperpendicular to the sample surface up to 9 T, showing no large coupling between magnetizationand the transition.Differential conductance traces (Figure 2) show the transition even more dramatically. In thehigh conductance state, dI/dV is relatively temperature independent. As T is decreased, a clearzero-bias suppression develops, deepening into a hard gap when T < T V . In the nanocrystaldata there are indications (in d I/dV ( V ) ) of gap formation even at 150 K. We note that T V innanocrystals could be elevated, since nanocrystals have large surface-to-volume ratios and thetransition temperature of the magnetite surface is known to be higher than in the bulk.[23]Several lines of evidence indicate that these sharp conductance transitions are not the result oflocal Joule heating (as in macroscopic samples of Fe O [24, 25] and in the Mott insulator VO [26, 27]), but rather are electrically driven. In the worst-case scenario, all of the I × V Joule heat-ing power is dissipated within the magnetite, and inhomogeneous dissipation ( e.g. , filamentaryconduction through a locally heated path) can complicate the analysis. The local steady-state tem-perature is determined by the power dissipated and the thermal path. Thermally driven switchingwould then correspond to raising the local temperature above T V . At a fixed cryostat temperaturean improved thermal path would imply that more power dissipation would be required for a givenlocal temperature rise. Similarly, for a fixed thermal path, the necessary dissipated power for ther-mal switching would approach zero as T → T V . Furthermore, at a given cryostat temperaturethermally-driven switching would imply that the power dissipated at the low-to-high conductancetransition (needed to raise the local temperature to T V ) should be close to that at the high-to-low5
20 40 60 80 10001020304050 T r a n s iti on P o w e r [ W ] Temperature [K] I D [ A ] V DS [V] FIG. 3: Power required to switch from the insulating into the more conducting state as a function of tem-perature, for a device based on ∼
20 nm diameter nanocrystals. Inset: Hysteresis loop in the conduction ofthe same device at 80 K, showing essentially no change in switching characteristics as the voltage sweeprate is varied over two orders of magnitude. conductance transition.The thermal conductivity, κ , of magnetite is dominated by phonons in this temperature range,and limited by phonon-electron scattering,[28] even when T > T V . As a result, κ increases as T is decreased through and below T V , and the material’s thermal coupling to the cryostat improves as T is reduced. In all devices showing switching, the electrical power required to switch from low tohigh conductance decreases with decreasing T , with Fig. 3 showing one example. This is preciselythe opposite of what one would expect from thermally-driven switching. Similarly, in all devicesthe power dissipated at switching does not approach zero as T → T V , again inconsistent withthermally-driven switching. Furthermore, at a given T the power dissipated just before V is sweptback down through the high-to-low conductance threshold significantly exceeds that dissipatedat the low-to-high point in many devices, including those in Fig. 1, inconsistent with thermalswitching expectations. Finally, nanocrystal and thin film devices show quantitatively similarswitching properties and trends with temperature, despite what would be expected to be verydifferent thermal paths. These switching characteristics are also qualitatively very different fromthose in known inhomogeneous Joule heating.[24, 25]. These facts rule out local heating throughthe Verwey transition as the cause of the conductance switching.Figure 3 (inset) shows details of hysteresis loops on a nanocrystal device comparing different6
500 1000051015 S w it c h O n V o lt a g e [ V ] Channel Length L [nm]
60K 80K 100K
FIG. 4: Switching voltages in a series of film devices as a function of channel length at several temperatures.The linear variation with L strongly implies that for each temperature there is a characteristic electric fieldrequired for switching. The non-zero intercepts of the trend lines indicate that some device-dependentthreshold voltage must be exceeded for switching even when L = 0 , suggestive of contact effects. voltage sweep rates. The loop shape and switching voltages are unchanged to within the precisionof the data collection as voltage sweep rates are varied from around 0.7 V/s up to 70 V/s. Thisindicates that the switching process is relatively rapid. Further studies will examine the intrinsicswitching speed.The observed conductance transition appears to be driven electrically . Figure 4 is a plot ofthe low-to-high conductance switching voltage as a function of L in a series of film devices forseveral temperatures. The linear dependence implies that the transition is driven by electric fielditself, rather than by the absolute magnitude of the voltage or the current density. The fact that thevoltage extrapolates to a nonzero value at L = 0 is likely a contact resistance effect. Minimizingand better understanding the contact resistance will allow the determination of the electric fielddistribution within the channel.The length scaling of the transition voltage also demonstrates that this is a bulk effect. Thecontacts in all of these devices are identical, so any change in switching properties must result fromthe magnetite channel. This is in contrast to the resistive switching in Pr . Ca . MnO (PCMO)that is ascribed to a change in contact resistance due to occupation of interfacial states[18].The field-driven conductance transition may give insights into the equilibrium Verwey tran-sition. This switching may be useful in testing recent calculations[11, 15, 16] about the role of7trongly correlated B-site Fe 3 d electrons and their coupling to phonons in the Verwey transitionmechanism. It is interesting to ask, to what degree is the field-driven electronic transition coupledto the local structure? It is greatly desirable to perform local probes of the magnetite structure(via x-ray or electron-diffraction techniques or scanned probe microscopy) in situ in the channelof biased devices, to see if the coherence between structural symmetry changes and the formationof a gap in the electronic spectrum is broken under these noequilibrium conditions. This is a sig-nificant experimental challenge. Similarly, local Raman spectroscopy of devices under bias couldreveal field-induced changes in phonon modes and electron-phonon couplings, and single-crystalthin films permit the application of bias along well-defined crystallographic directions relevant tostructural symmetry changes at T V . We do note that qualitatively identical switching occurs innanocrystal devices as in strained thin films strongly coupled to rigid MgO substrates. This sug-gests that elastic constraints on scales much larger than the unit cell have relatively little influenceon the observed switching.It is also possible that the nonequilibrium carrier distribution contributes to destabilizing theinsulating state. In the presence of a strong electric field a carrier can gain significant energy evenin a single hopping step, even though carrier relaxation times are very short. A rough estimate ofthe average critical E -field for switching at 80 K is V/m, from the slope of the line in Fig. 4.The high temperature cubic unit cell is 0.84 nm on a side, meaning that a carrier traversing onecell would gain approximately 8.4 meV, comparable to k B T V ≈ . METHODS Magnetite nanocrystals were prepared via solution-phase decomposition of iron carboxylatesalts.[19] The nanocrystals have been characterized by transmission electron microscopy (TEM),x-ray diffraction, and infrared and Raman spectroscopy, as discussed in Supplemental Material.As synthesized the nanocrystals are protected by weakly bound oleic acid ligands; these ligandsallow the suspension of the nanocrystals in organic solvents, but act as electrically insulating layersthat must be largely removed for effective electronic transport measurements.Two-step electron beam lithography and e-beam evaporation (1 nm Ti, 15 nm Au) were usedto pattern closely spaced source and drain electrode pairs onto degenerately n -doped silicon sub-strates coated with 200 nm of thermally grown SiO . Interelectrode gaps (channel lengths) rangedfrom zero to tens of nm, with a 10 µ m wide channel region. Nanocrystals were spin-coated fromhexane solutions to form slightly more than one densely packed monolayer of nanocrystals overthe channel region. Samples were then baked at 673 K in vacuum for 1 hr to remove as much ofthe oleic acid as possible. In one set of samples, a second layer of particles was added followedby a second round of baking.The other class of devices are based on epitaxial magnetite films 50 nm thick grown by oxygen-plasma-assisted molecular beam epitaxy (MBE) on h i MgO single-crystal substrates. Detailsof the growth process have been reported elsewhere.[20] Single-step e-beam lithography and e-beam evaporation were used to pattern Au (no Ti adhesion layer) source and drain electrodesdefining a channel length ranging from tens of nm to hundreds of nm, and a channel width of20 µ m. The interelectrode conduction is dominated by the channel region due to this geometry.No annealing was performed following electrode deposition. [1] Mills, A. A. 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Supplementary Information is linked to the online version of the paper.
Acknowledgements . This work was supported by the US Department of Energy grant DE-FG02-06ER46337. DN also acknowledges the David and Lucille Packard Foundation and theResearch Corporation. VLC acknowledges the NSF Center for Biological and EnvironmentalNanotechnology (EEC-0647452), Office of Naval Research (N00014-04-1-0003), and the USEnvironmental Protection Agency Star Program (RD-83253601-0). CTY acknowledges a RobertA. Welch Foundation (C-1349) graduate fellowship. RGSS and IVS acknowledge the ScienceFoundation Ireland grant 06/IN.1/I91.
Author Contributions . SL fabricated and measured the devices in this work and analyzed thedata. AF fabricated devices and performed XRD characterization of the nanocrystal materials.DN and SL wrote the paper. JTM and CYZ made the nanocrystals in VLC’s laboratory, andVLC contributed expertise in nanomaterials chemistry and characterization. RGSS and IVS grew11he magnetite films, and IVS contributed expertise on magnetite physical properties. All authorsdiscussed the results and commented on the manuscript.
Competing Interests . The authors declare that they have no competing financial interests.