Electroresistance (ER) is a change in electrical resistance with applied voltage or applied current. A material that obeys Ohm's law has zero ER. So to say a material exhibits ER is equivalent to saying it is non-ohmic. A third way of saying the same thing is by referring to the voltage-current (V-I) characteristic. An ohmic material shows a linear relationship between voltage and current. In an electroresistive material the V-I relationship is non-linear.

The term "electroresistance" has sprung into vogue on the back of the cognate term "magnetoresistance", which refers to a change of electrical resistance with magnetic field. Magnetoresistance (MR) is defined by

MR = R ( B ) − R ( 0 ) R ( 0 ) = Δ R R , MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=MipeYlH8Hipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciaacaGaaeqabaqabeGadaaakeaacqqGnbqtcqqGsbGucqGH9aqpjuaGdaWcaaqaaiabdkfasjabcIcaOiabdkeacjabcMcaPiabgkHiTiabdkfasjabcIcaOiabicdaWiabcMcaPaqaaiabdkfasjabcIcaOiabicdaWiabcMcaPaaakiabg2da9KqbaoaalaaabaGaeuiLdqKaemOuaifabaGaemOuaifaaOGaeiilaWcaaa@410F@

where R(B) is the electrical resistance measured in applied magnetic field B. MR has broad implications both for fundamental physics and for technological applications, the latter particularly in relation to memory devices. Substantial magnitudes of MR have lead to the coining of the terms "giant magnetoresistance" (GMR), now mainly associated with metallic layer systems, and "colossal magnetoresistance" (CMR), now mainly associated with perovskite oxides. As the magnetic field typically reduces the electrical resistance, MR as defined in Eqn. 1 is typically negative; for this reason the opposite definition is sometimes employed. Sometimes the resistance at field is used as the denominator, usually with the effect of making the magnitude of the ratio larger than one (sometimes, much larger).

In analogy to Eqn. 1, ER may be defined in terms of the resistance at the applied electric field E,

ER ( E , 0 ) = R ( E ) − R ( 0 ) R ( 0 ) = Δ R R . MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=MipeYlH8Hipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciaacaGaaeqabaqabeGadaaakeaacqqGfbqrcqqGsbGucqGGOaakcqWGfbqrcqGGSaalcqaIWaamcqGGPaqkcqGH9aqpjuaGdaWcaaqaaiabdkfasjabcIcaOiabdweafjabcMcaPiabgkHiTiabdkfasjabcIcaOiabicdaWiabcMcaPaqaaiabdkfasjabcIcaOiabicdaWiabcMcaPaaakiabg2da9KqbaoaalaaabaGaeuiLdqKaemOuaifabaGaemOuaifaaOGaeiOla4caaa@459C@

This formulation is appropriate for experiments conducted in a field-effect (FE) configuration, in which the applied bias is provided by a gate, separate to the voltage drop between source and drain used to measure the sample resistance 12. A more common arrangement is to use the standard four-probe configuration to measure the sample resistance. The current is applied across two outer terminals and the voltage measured between two inner terminals. In this configuration it is not possible to obtain data at zero current so the resistance at a reference current is employed in the definition of ER. Consider measurements made at the two currents I_low and I_high. Each of four separate combinations to define electroresistance have been used in the literature.

ER = R ( I high ) − R ( I low ) R ( I low ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=MipeYlH8Hipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciaacaGaaeqabaqabeGadaaakeaacqqGfbqrcqqGsbGucqGH9aqpjuaGdaWcaaqaaiabdkfasjabcIcaOiabdMeajnaaBaaabaGaeeiAaGMaeeyAaKMaee4zaCMaeeiAaGgabeaacqGGPaqkcqGHsislcqWGsbGucqGGOaakcqWGjbqsdaWgaaqaaiabbYgaSjabb+gaVjabbEha3bqabaGaeiykaKcabaGaemOuaiLaeiikaGIaemysaK0aaSbaaeaacqqGSbaBcqqGVbWBcqqG3bWDaeqaaiabcMcaPaaaaaa@4940@

is used by Refs. 3456. Refs. 78 use the opposite ("ER-bar"):

ER ¯ = R ( I low ) − R ( I high ) R ( I low ) . MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=MipeYlH8Hipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciaacaGaaeqabaqabeGadaaakeaadaqdaaqaaiabbweafjabbkfasbaacqGH9aqpjuaGdaWcaaqaaiabdkfasjabcIcaOiabdMeajnaaBaaabaGaeeiBaWMaee4Ba8Maee4DaChabeaacqGGPaqkcqGHsislcqWGsbGucqGGOaakcqWGjbqsdaWgaaqaaiabbIgaOjabbMgaPjabbEgaNjabbIgaObqabaGaeiykaKcabaGaemOuaiLaeiikaGIaemysaK0aaSbaaeaacqqGSbaBcqqGVbWBcqqG3bWDaeqaaiabcMcaPaaacqGGUaGlaaa@4A35@

Alternatively, Refs. 910 use

ER ∗ = R ( I low ) − R ( I high ) R ( I high ) , MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=MipeYlH8Hipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciaacaGaaeqabaqabeGadaaakeaacqqGfbqrcqqGsbGudaahaaWcbeqaaiabgEHiQaaakiabg2da9KqbaoaalaaabaGaemOuaiLaeiikaGIaemysaK0aaSbaaeaacqqGSbaBcqqGVbWBcqqG3bWDaeqaaiabcMcaPiabgkHiTiabdkfasjabcIcaOiabdMeajnaaBaaabaGaeeiAaGMaeeyAaKMaee4zaCMaeeiAaGgabeaacqGGPaqkaeaacqWGsbGucqGGOaakcqWGjbqsdaWgaaqaaiabbIgaOjabbMgaPjabbEgaNjabbIgaObqabaGaeiykaKcaaiabcYcaSaaa@4C69@

("ER-star") while Refs. 1112 use

ER ¯ ∗ = R ( I high ) − R ( I low ) R ( I high ) , MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=MipeYlH8Hipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciaacaGaaeqabaqabeGadaaakeaadaqdaaqaaiabbweafjabbkfasbaadaahaaWcbeqaaiabgEHiQaaakiabg2da9KqbaoaalaaabaGaemOuaiLaeiikaGIaemysaK0aaSbaaeaacqqGObaAcqqGPbqAcqqGNbWzcqqGObaAaeqaaiabcMcaPiabgkHiTiabdkfasjabcIcaOiabdMeajnaaBaaabaGaeeiBaWMaee4Ba8Maee4DaChabeaacqGGPaqkaeaacqWGsbGucqGGOaakcqWGjbqsdaWgaaqaaiabbIgaOjabbMgaPjabbEgaNjabbIgaObqabaGaeiykaKcaaiabcYcaSaaa@4C7A@

("ER-star-bar"), and other definitions still are possible based on the maximum resistance 13 or dV/dI 14. Often the definition chosen is the one in which the result turns out to be large and positive. The measurements we report here are taken using the four-terminal method. We will use Eqn. 3 to define ER, as that seems most closely connected to the field-effect configuration definition, Eqn. 2, and the definition of magnetoresistance, Eqn. 1. As with magnetoresistance, the more emphatic terms "giant" ER (GER) 46141516 and "colossal" ER (CER) 237810111213171819202122 have been adopted, although no specific criteria appear to have been articulated as to when ER becomes GER or CER.

A prosaic origin of ER is joule heating. Consider a typical metal. Its resistance increases with temperature. If a large bias is applied, a large current will flow, leading to a large amount of joule heating, leading to an increase in temperature, leading to increase in resistance, and hence positive ER. On the other hand, a semiconductor, having a negative temperature coefficient of electrical resistance, will show negative ER as a consequence of joule heating. While joule heating is a legitimate way to induce ER, and the basis of the technical application of the ER effect 23, it is generally to be avoided where more subtle mechanisms of ER are to be identified 2425. This is the case in the present experiments.

In the last paragraph it was noted that electrical conductors and insulators may be differentiated depending on whether the temperature coefficient of resistance is positive (conductors) or negative (insulators). This is a fundamental way to distinguish whether a material is a conductor or an insulator – rather than on the basis of the magnitude of the resistivity – and the criteria used, for example, in attempting to determine if the ground state of a two-dimensional electron gas is metallic or not. It turns out that many materials that exhibit MR, and ER, undergo a change on increasing temperature from a metallic state to an insulating state, evidenced by a change in the sign of dR/dT. This is a temperature-induced metal-insulator transition (MIT). The experiments we report here detect the MIT through presenting resistance as a function of temperature.

ER has been reported in a variety of distinct physical systems. (a) Non-linear I-V characteristics are commonplace in electronic systems based on semiconductors, either conventional or low-dimensional, but are not generally referred to in terms of ER. (b) ER has been described in metal-ferroelectric-metal junctions (ferroelectric tunnel junctions), such as Pt/BaTiO₃/Pt 26, and has as its origin direct quantum tunnelling 15. (c) ER has been obtained above a temperature-dependent threshold in amorphous carbon film on a silicon substrate 13. (d) A strong ER, which is well-suited to switching operations, has been found in systems involving a metal electrode or electrodes and an oxide perovskite. Various metals (Pt, Au, Ag, Al, Ti, Mg) in conjunction with La_1-xSr_1+xMnO₄ crystals give the maximum effect for x ~0.5 21. SrRuO₃/SrTi_1-xNb_xO₃ Schottky junctions also have useful switching characteristics 20, as do films of Pr_0.63Ca_0.37MnO₃ 27 and Pr_0.7Ca_0.3MnO₃ between metallic electrodes 319; the proposed mechanism is a Mott transition 17 or electrochemical migration 28.

Much work on ER has been reported for thin films and single crystals of manganites. The most extensively-studied composition is La_0.7Ca_0.3MnO₃ 12452529. This composition is the member of the La_1-xCa_xMnO₃ series with the highest temperature of the MIT 30; it changes from paramagnetic insulator (PMI) to ferromagnetic metal (FMM) at about 250 K when in the bulk form. ER in this compound is generally attributed to a percolative phase separation (PS) 1. Formed into a p-n junction with a suitable substrate, a diodic behaviour is observed 1231. The ER has been attributed to current shunting 12. A p-i-n diode structure has also been fabricated 32. The composition La_0.8Ca_0.2MnO₃ shows similar behaviour 33, with the mechanism again taken to be related to PS 1834. ER has also been observed in the related compounds La_0.7Ce_0.3MnO₃ 10, which is electron doped, La_0.67Sr_0.33MnO₃ 6914, Nd_0.65Ca_0.35MnO₃ 23, La_0.9Ba_0.1MnO₃ 35, R_0.67Ca_xMnO₃ 24, Ca_0.9Ce_0.1MnO₃ 16, as well as the bi-layered manganite La_1.2Sr_1.8Mn₂O₇ 11. As the fraction x in La_1-xCa_xMnO₃ decreases below ~0.2 the low-temperature state is a ferromagnetic insulator (FMI). In La_0.82Ca_0.18MnO₃ 8 and other FMI materials Nd_0.7Pr_0.3MnO₃ 7 and La_0.9Sr_0.1MnO₃ 223336 it is observed that the ER and MR effects are decoupled. In ultrathin films 25 the non-linear characteristics are not intrinsic; extrinsic factors include contact resistance and joule heating. effects observed in thicker films are thought to arise due to grain structure and disorder 4.

The aim of the research to be reported here is to give a comprehensive experimental description of ER and MIT in lanthanum/calcium manganites by measuring V-I curves at many temperatures and so present the voltage (and hence resistance) data as a function of both current and temperature. Three aspects distinguish this work from previous studies. First, the work deals exclusively with bulk materials. Most previous studies have concentrated solely on thin films, in which the ER (and MR) effects are more pronounced. The present work is more fundamental in that the complications of lattice strain and anisotropy do not enter into the interpretation of the results. Second, this work is a systematic study of the series La_1-xCa_xMnO₃ for x = 0–0.5. Many previous reports on ER concentrate on a single composition. The wider view here gives a more complete picture of the ER phenomenon. Third, the work reported here is comprehensive in that a large number of V-I curves are presented at many temperatures; put another way, a large number of R(esistance)-T sets are presented at different currents. To give an idea of the scale of the difference, an earlier reports gives V-I curves at 6 temperatures 11; we use dozens of temperatures. Other reports give R-T curves at 3 or 6 voltages 12 or 3, 4 or 12 currents 4910; we use hundreds of currents. In short, others give curves, we give surfaces. This larger data set assists in visualization, and confirms which behaviour is systematic and does not depend on specific choice of experimental conditions.

The samples were synthesized by a partial melting technique as described previously 37. High-purity starting materials were weighed, mixed, pelletised and sintered at 1100°C for 24 hours then ground, pelletised, and partially melted at 1500°C for 10 minutes before rapid cooling to 900°C. X-ray diffraction peaks were well-indexed by a rhombohedral structure. Only a single phase was evident. We did not specifically examine oxygen deficiency in the samples but the systematic data to be presented below suggests it does not play an important role in these measurements. Variable temperature measurements were made using a Janis CCS350R closed-cycle cooler. Electrical contacts were made using Ag paint. The current was supplied and the voltage measured with a Keithley SourceMeter 2400.

Our experimental results appear in Figs. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, which give voltage and resistance surfaces for La_1-xCa_xMnO₃ for x = 0, 0.1, 0.2, 0.3, 0.4 and 0.5. In the voltage (odd-numbered) figures, the voltage drop across the sample is shown on the vertical axis as a function of the temperature of the sample and the current applied to the sample. The vertical panes perpendicular to the current axis give the temperature dependence of the voltage, or, within a multiplicative factor, the temperature dependence of the resistance or of the resistivity. The temperature-induced MIT may be observed with reference to data in these planes. The vertical planes perpendicular to the temperature axis give the V-I characteristic. If the cross-section of the data with one of these planes is not a straight line, then the sample exhibits ER. In the resistance (even-numbered) figures, the resistance of the sample (simply obtained by dividing V by I; not the differential resistance, dV/dI) is shown on the vertical axis. The vertical panes perpendicular to the current axis give the R-T curves and directly allow observation of the MIT. The vertical planes perpendicular to the temperature axis give the R-I characteristic; if these are not cut horizontally by the data, the sample exhibits ER. A detailed discussion of each of the data sets is now given, with reference to the phase diagram of La_1-xCa_xMnO₃ 30383940. At room temperature, each sample is a PMI.

Our results give a comprehensive picture of resistance as a function of both current and temperature in an important series of compounds La_1-xCa_xMnO₃ (x = 0–0.5). They illustrate a further aspect of the rich variety of physical phenomena in this family. ER is seen to be small in the compounds with x = 0, 0.1, and 0.2. It becomes pronounced in the compounds x = 0.3 and 0.4. It is generally strongest around T_p but – especially in the 0.3 compound – is observed at all temperatures. Taken as a whole, the present data are consistent with the explanation of ER being due to PS. According to that picture, in materials where there is no phase coexistence, only a single insulating state, ER is small. Our result confirm that this explanation, first postulated for thin films 15, also holds in the bulk.