Journal ArticleWe have performed a variety of experiments on switching phenomena in a metal oxide, magnetite. Our findings are consistent with Joule microheating which drives the Verwey transition occurring at 119 K. We conclude that considerations of band structure, direct electric-field-induced transitions, tunneling, injection, and space-charge phenomena are not required to explain any of our observations

Burch, T.

Mattis, Daniel C.

English

The University of Utah: J. Willard Marriott Digital Library

VOLUME 23, NUMBER 2S PHYSICAL REVIEW LETTERS 22 DECEMBER 1969 SWITCHING IN MAGNETITE: A THERMALLY DRIVEN MAGNETIC PHASE TRANSITION* T. Burch,t P. P. Craig, C. Hedrick,! and T. A. Kitchens Brookhaven National Laboratory, Upton, New York 11973 and J. 1. Budnick and J. A. Cannonll Fordham University, Bronx, New York 10458 and M. Lipsicas and D. Mattis§ Belfer Graduate School of Science, Yeshiva University, New York, New York 10033 (Received 19 September 1969) We have performed a variety of experiments on switching phenomena in a metal oxide, magnetite. Our findings are consistent with Joule microheating which drives the Ver-wey transition occurring at 119 K. We conclude that considerations of band structure, direct electric-field-induced transitions, tunneling, injection, and space-charge phe-nomena are not required to explain any of our observations. Nonlinear electrical transport properties, neg-ative resistance, and electrical switching have been observed in many different systems, includ-ing glasses, 1 -3 transition- metal oxides, and oth-er compounds. 4 -9 While a variety of mecha-nisms 10 -14 have been proposed to explain switch-ing, to date it has not proven possible to mar-shall sufficient evidence to permit an unambigu-ous determination of the principal mechanism. In this Letter we restrict ourselves to the low-frequency properties of a single system showing negative resistance: magnetite. We present a body of experimental and theoretical evidence which makes, we believe, a compelling case that for this material the gross features of the switch-ing mechanism are largely thermal in origin. High-frequency and dynamic characteristics will be discussed in a later paper. Magnetite (Fe30 4 ) undergoes a Verwey transi-tion at 119. 4°K. 15 ,16 It is ferrimagnetically or-dered both above and below the transition: At the transition a crystallographic modification oc-curs and the hyperfine magnetic-field distribu-tion alters appreciably.17,18 The most striking feature of the transition is the change in resistiv-ity p by about two orders of magnitude. 16 ,19 The low-temperature phase is semiconducting with an activation energy of 0.03 eV at low tempera-tures increasing to 0.15 eV at the transition tem-perature. 19 The thermal conductivity K 20 and the specific heat C p 21 are also anomalous at the transition. The transition is affected by impuri-ties, strain, and other defects which tend both to shift and to broaden it. However, pure mag-netite is sometimes considered4 the prototype of the Mott, or metal-insulator, transition. 22 Be-1444 cause of the lattice distortion which accompanies the phase change it remains uncertain whether lattice or electronic instability drives the transi-tion,22 or indeed, whether these effects are sepa-rable,14 For the purposes of the present paper, such questions are not important, and the exper-imentally observed properties will be used with-out regard for their causes. POSSibly the first discovery of switching in magnetite was made by Christopher et al., 5 who observed negative resistance at helium tempera-tures in tunneling junctions made with oxidized iron. No quantitative explanation for the phenom-enon has yet been proposed, although recently Mattis13 ,14 suggested a mechanism by which the Mott transition is driven by tunneling in an ap-plied electric field. Following this idea, Lipsi-cas et al. 6 observed switching and oscillation in magnetite powders held at 77 K. We now know that not only can magnetite powders be switched but also thin films and single-crystal samples, and that even lack of purity of the material does not quench the effect. In Fig. 1 we present an experimentally ob-served current through a cylinder of magnetite versus the applied voltage (solid curve). The thickness is 0.447 cm and the mean radius is about 0.375 cm. The sample is mounted in a special gas-flow cryostat in which cold gas flows continuously over the sample walls. The sample temperature is monitored with a thermocouple. The occurrence of a threshold voltage and nega-tive resistance is apparent in this dc character-istic. These and other observations on switching in magnetite can be semiquantitatively understood VOLUME 23, NUMBER 25 PHYSICAL REVIEW LETTERS 22 DECEMBER 1969 1.8 1.6 1.4 1.2 g "-(f) 1.0 w a:: w "-::E ~ HI~ 0.8 0.6 0.4 0.2 77 --78 \ \ \ \ \ \ \ \ NORMALIZED I-V CURVE FOR Fe 2 .995 CO.005 04 IN LIQUID N2 ----- THEORETICAL -- EXPERIMENTAL \ \133 \ \ \ 126', 119 ,--,\ \ \ \112 \ \ \ \ \103 I I I I 193 I I /'86 ...,../84 _--82 _---7'9- 80 10 15 !.::!... (VOLTS) ~ FIG. 1. The experimental I-V characteristic of the magnetite sample described in the text with a boundary temperature T b = 85 K (solid curve), and the I-V char-acteristic for magnetite calculated from published val-ues of the conductivities assuming a thickness of 0.447 cm and a diameter of 0.750 cm and T b = 90 K (dashed curve). Computed maximum temperatures within the sample are indicated at various points. The data are scaled according to the requirements of Eq. (1). in terms of a self-heating model, in which Joule heating provides local self-heating. For suffi-ciently high power input a threshold is passed, and the sample develops a negative resistance characteristic. The thermal diffusion equation is -j. E = -PCpClT /Clt + V· (KVT), (1) where j is the current density and E is the elec-tric field. This equation has been solved utiliz-ing published values of the thermal conductivity20 and the isothermal electrical conductivity of the sample measured in our laboratory. Equation (1) must be supplemented with equations govern-ing the external electronic circuit, when dynam-ic response is calculated. Because (1) is nonlinear, it is necessary to re-sort to numerical solutions. For simplicity we have restricted most of our attention to cylindri-cal geometry, with the current along the z axis and the cylinder walls maintained at a specified boundary temperature T bo Advantages of this geometry are that Eq. (1) is readily solved, and that it is possible to construct an experimental system approximating these boundary conditions. A major approximation in our calculation is the use of Ohm's law, since our measurements show magnetite to be highly non-Ohmic, especially in the low-temperature phase. The dashed curve in Fig. 1 presents a numeri-cal steady-state solution of Eq. (1) with T b = 77 K. No adjustable parameters are used. The agreement in the low- and high-current regimes is apparent. Further, in the low-current re-gime, the thermal calculation correctly predicts the experimental result I ex: V 3 / 2 without any con-sideration of space-charge effects. The doubling back of the theoretical curve results from the complicated temperature dependence of the input parameters. Owing to external circuit require-ments this intermediate structure is difficult to verify experimentally the steady state. However, using published values of a for pure Fe30 4, the calculations would predict more hystersis. This has been observed. In this particular sample ne-gative resistance sets in when the computed core temperature reaches 105 K. However, switching occurs when the core temperature reaches the Verwey transition temperature. The maximum temperature inSide the sample is indicated at various points on the calculated curve. Additional confirmation of the validity of calcu-lation may be obtained by varying the wall-tem-perature boundary condition. Figure 2(a) pre-sents computed and observed switching voltages for two natural magnetite samples of radii 0.030 and 0.036 in. and thicknesses 0.015 and 0.009 in. as a function of the wall temperature. Again, agreement is excellent, and there are no adjust-able parameters. The disagreement for T b -75 K results from excess conductivity of our sam-ple at low temperatures as compared with the published resistivity used in this computation. Figure 2(b) shows the calculated current density versus radial position for several points on the J- V characteristic and for T b = 77 K. The fila-mentary conduction mechanism is clearly indi-cated. However, there is no pronounced core in the temperature profiles at these points. Even for relatively large transport currents only a small fraction of the total cross section is actu-ally heated above the Verwey temperature. This prediction has been verified directly in Moss-1445 VOLUME 23, NUMBER 25 PHYSICAL REVIEW LETTERS 22 DECEMBER 1969 -100 ~ o .t'" 0.009 in., '" 0.036 in. 104 NATURAL MAGNETITE > ;:;:; 50 • J "0.015in.,,"0.030in. t"lmm,'"lmm <.!) N <t S § 10' ':J "-~~b%O 0- TeoRE"131 K ~ THEORY E <.!) .0 " z A~9 ;::102 TeOUNDARY" 77 K I 10 '. f-U 0 0 U) f-.00 z 3 ~IO' TeoRE "9SK If) 5 0 f-W Z N W ::J ~ 100 <t ::;; u TeORE" 79K cr: 0 (D) (b) z 10' SO 90 100 110 0.2 0.4 0.6 O.S 1.0 BOUNDARY TEMPERATURE (K) SAMPLE RADIUS (mm) FIG. 2. (a) The experimentally measured threshold voltages for two different samples and the calculated threshold voltage (solid curve). There are no adjust-able parameters in this calculation; the thickness and radius were taken to be those measured on the natural magnetite sample described in the text. For temper-atures below about 75 K the activation-controlled re-sistivity used in the calculation exceeds the observed sample resistivity, accounting for the increasing dis-crepancy in switching voltage. (b) The computed cur-rent distribution for three bias conditions. The forma-tion of a filamentary core at high current is apparent. bauer measurements discussed below. A scaling analysis of Eq. (1) applied to the cyl-indrical model indicates that the threshold volt-age should vary linearly with the sample length for a fixed boundary temperature and radius. We have observed this dependence in natural magnetite samples with lengths of 0.062 to 0.293 in. with radii - 00 095 in. immersed in liquid N2 • An analysis of Eq. (1) for flat plates cooled on the ends has also been made. This model yields little or no negative resistance but is consistent with some of our observations on thin films. We have also investigated the effect of magnetic field23 ,24 on the Verwey transition and on the switching characteristic. Our experiments show a 9% decrease in the switching voltage at 77 K in a field of 8 kOe with only 0.5 K change in T c for the same magnetic field, both independent of the orientation of the field to the current direction. Mossbauer experiments offer a useful tool for determining the proportion of a magnetite sam-ple in the high- and the low-temperature phas-es. 17 ,18 A 0.005-in.-thick sample was prepared by pressing magnetite powder in a Lucite holder. A thermocouple was embedded within the sample, which was then mounted in a cryostat and cooled to 77 K Current passing through the sample produced switching, but only a slight tempera-ture rise. Mossbauer hyperfine-field measure-1446 0.5>----0.0125 v (volts) FIG. 3. The single-pass I-V characteristic of a nat-ural magnetite sample, (l = 0.009 in., r= 00 036 in.) tak-en at the designated scan rates. Onset of negative re-sistance is an increasing function of scan rate. The curve is a tracing of an oscilloscope photograph, and the curves are vertically displaced between scans; the dashed portions of the curves are regions of rapid switching. ments showed that in the switched state at least 85 % of the material was in the low-temperature phase, while no more than 20% was in the high-temperature phase. (The hyperfine field shows a discrete change at the Verwey transition, so that the observed spectrum can be decomposed into contributions from the high- and low-tem-perature phases.) These results are in agree-ment with the heating theory. They show that no theory is tenable which requires that the entire sample is heated, nor in which the energy gap is changed throughout the entire sample so as to correspond to the high-temperature phase. Dynamic experiments provide independent evi-dence for the local-heating model. This type of experiment tests the role of the specific-heat term in Eq. (1). The J- V characteristic of the above-mentioned bulk magnetite sample im-mersed in liquid N2 was measured by rapid sin-gle voltage scans at various rates (Figo 3). At the highest scan rates used, the J- V characteris-tic is extended to voltages more than twice the threshold voltage observed in the constant-cur-rent (dc) experiments. This indicates that at 77 K switching from the low-conductivity state to the high-conductivity state is not controlled by the electric field in the manner assumed in Refs. 13 and 14. Rather, the specific heat of the ma-terial controls the rate of temperature rise and thus delays switching. 25 Devices having negative resistance are ob-served to oscillate spontaneously when properly VOLUME 23, NUMBER 25 PHYSICAL REVIEW LETTERS 22 DECEMBER 1969 biased or can be caused to oscillate by means of an external capacitoro Our study on magnetite film samples of the oscillation period versus ca-pacitance shows that relaxation oscillation can occur even in the absence of all electrical capac-itance (including stray internal capacitance). Analysis shows that the specific heat of the sam-ple plays the role of a (negative or positive) ca-pacitor and that spontaneous oscillation with no external electrical capacitance is expected for certain thermal boundary conditions, This mech-anism provides a simple explanation for the hith-erto unexplained observations by Walsh et a1,2 of a field-dependent negative capacitance in glass devices, and will be given in detail in a future paper. The variety of experimental data presented above together with the predictions of the ther-mal diffusion equation lead to a consistent pic-ture of switching effects in magnetite. An essen-tial feature of the switching is a geometry per-mitting the formation of a high-conductivity core or filament within the material. Many other sys-tems behave in a qualitatively similar manner. It remains to be shown whether the thermal mechanism is ubiquitous. In any event, it is now apparent that future investigations designed to demonstrate other mechanisms must show that thermal effects are insufficient to explain the ob-servations. We wish to acknowledge numerous conversa-tions concerning this topic with M. Blume, D. Cox, V. Emery, R. Gayley, E. Lord, and M. strong in. Many people provided technical assistance; we wish expecially to thank D. Burnstein, J. Crow, N. Garcia, J. Hurst, O. Kammerer, and I. Metal. *Work performed under the auspices of the U. S. Atomic Energy Commission. tPermanent address: St. Joseph's College, Philadel-phia, Pa. ~Permanent address: Haverford College, Haverford, Pa. Participant in Brookhaven Summer Program for undergraduates. II Permanent address: Pace College Westchester, Pleasantville, N. Y. §Work supported in part by AF 69-1642 and N00014-69-A-041l. IS. Ovshinsky, Phys. Rev, Letters 21, 1450 (1968). 2R. Vogel and P. J. Walsh, Feltma~esearch Labo-ratories, Picatinny Arsenal, Dover, N. J., Technical Report No. 3797,1968 (unpublished); P. J. Walsh, R. Vogel, and E. J. Evans, Feltman Research Labora-tories, Picatinny Arsenal, Dover, N. J., Technical Re-port No. 3765 (unpublished), and Phys. Rev. 178, 1274 (1969). -3M. H. Cohen, H. Fritzsche, and S. R. Ovshinsky, Phys. Rev. Letters 22, 1065 (1969). 4 -D. Adler, Rev. Mod. Phys. 40, 714 (1968), and Solid State Phys. 21, 1 (1968); K. W. Boer, Festkorperprob-Ierne 1, 38 (1962). 5J. E. Christopher, R. V. Coleman, A. Isin, and R. C. Morris, Phys. Rev. 172, 485 (1968); R. C. Mor-ris, J. E. Christopher, and R, V. Coleman, Phys. Rev. 184, 565 (1969). ~. Lipsicas, D. Mattis, A. Kornblit, and E. Lord, to be published. 7L. M. Falicovand J. C. Kimball, Phys. Rev. Letters 22, 997 (1969). 8 K. L. Chopra, J. Appl. Phys. 36, 184 (1965). 9L. Gildart, J. Appl. Phys. 36,335 (1965). lOR. G. Cope and H. J. Goldsmid, Brit. J. Appl. Phys. 16, 1501 (1965). 1tB. Yu. Lototskii and L. K. Chirkin, Fiz. Tverd. Tela 8, 1967 (1966) [translation: Soviet Phys.-Solid State 8, 1564 (1966)1. -12 N. F. Mott, Contemp. Phys. 10, 125 (1969). 13D• C. MattiS, Phys. Rev. Letters 22, 936 (1969). 14D. C. Mattis and L. Landovitz, to be published. 15E. J. W. Verwey and P. W. Haayman, Physica 8, 979 (1941). -16For a survey of the properties of magnetite, see K.-H. Hellwege and A. M. Hellwege, in Landolt-Born-stein Zahlenwerte und Funktionen, edited by K.-H. Hellwege and A. M. Hellwege (Springer-Verlag, Berlin, Germany, 1962), Vol. 2, Pt. 9, pp. 27 et seq. 17G. A. Sawatzky, J. M. D. Coey, and A. H. Morrish, J. Appl. Phys. 40, 1402 (1969); B. J. Evans and S. S. Hafner, J. Appl. Phys. 40, 1411 (1969). 18R. S. Hargrove and W-:-Kiindig, Bull. Am. Phys. Soc. 14, 837 (1969). 19p . A. Miles, W. B. Westphal, and A. von Hippel, Rev. Mod. Phys. 29, 279 (1957); B. Calhoun, Phys. Rev. 94, 1577 (1954). 20G• A. Slack, Phys. Rev. 126, 427 (1962). 21B. S. Ellefson and N. W. Taylor, J. Chern. Phys. ~, 58 (1934). 22N. F. Mott, Rev. Mod. Phys. 40, 677 (1968). 23Reviewed in S. Methfessel and]). C. Mattis, in Handbuch der Physik, edited by S. Fliigge (Springer-Verlag, Berlin, Germany, 1968), Vol. 18, Pt. l. 24A. Rosencwaig, Phys. Rev. 181, 946 (1969); W. J. Siemans, "Hall Mobility Meas~ments on Magnetite," IBM Symposium on Magnetic Semiconductors, York-town Heights, N. Y., 13-14 November 1969 (unpub-lished). 25It is of course possible to adduce other mechanisms which will delay and shift the switching point. 1447 

Switching in magnetite: a thermally driven magnetic phase transition

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Switching in magnetite: a thermally driven magnetic phase transition

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