APPLIED PHYSICS LETTERS 96, 082103 共2010兲
Variation in hopping conduction across the magnetic transition in spinel Mn1.56Co0.96Ni0.48O4 films Jing Wu, Zhiming Huang,a兲 Yun Hou, Yanqing Gao, and Junhao Chu National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, 500 Yu Tian Road, Shanghai 200083, People’s Republic of China
共Received 8 December 2009; accepted 24 January 2010; published online 23 February 2010兲 The temperature dependent dc resistivity of spinel Mn1.56Co0.96Ni0.48O4 共MCN兲 films is measured in the range of 130–304 K. The hopping exponent p of small polaron hopping conduction shows a clear variation from a value of 0.46 in the paramagnetic to 0.91 in the ferromagnetic phase. In order to explain such variation, a model is proposed where Gaussian distributed localized electron states gradually withdraw from the Hubbard band gap below the magnetic transition as a result of increased magnetic order. This correlation between hopping conduction and magnetic order in MCN films may provide a possible approach to fabricate the devices which couple magnetic and electronic properties in one unit. © 2010 American Institute of Physics. 关doi:10.1063/1.3318459兴 Transition metal oxides 共TMOs兲 are on focus and are challenges in modern condensed matter physics because of the existence of complex interaction among spin, charge, lattice, and orbit.1–3 Because of the rich physical phenomena, such as metal-insulator transition, spin glass, superconductivity, colossal magnetoresistance, and quantum Hall effect, TMOs are one of the major candidates on which the next generation electronics may be built.2 Recently, in order to push the applications of oxide electronics forward, many attentions were paid to the research on the correlations among structural, electrical, and magnetic properties of TMOs.3 Mn3−x−yCoxNiyO4 共0 ⱕ x , y ⱕ 1兲, developed basically from the prototype of Mn3O4, belong to strongly correlated electronic systems where the electrical and magnetic properties are closely linked with interactions among spin, orbit and lattice.4 Due to strong electron-phonon coupling, Mn3−x−yCoxNiyO4 serial materials are used as thermistors in temperature sensors and bolometers in infrared detection widely.5 In this kind of materials, the mixed valences of Mn3+ and Mn4+ arise from the displacement of bivalent cations 共Ni2+兲 from tetrahedral sites to octahedral sites. As a result, a corresponding proportion of Mn3+ cations on octahedral sites disproportionate to Mn2+ and Mn4+, and Mn2+ cations move to the tetrahedral sites to compensate Ni2+ vacancies.6 The electrical conduction is accomplished by small polaron hopping between localized Mn3+ and Mn4+ states under the assistance of thermal activation.6,7 In the view of energy space, the localized Mn3+ and Mn4+ states are broadened to form lower and upper Hubbard bands, respectively, and there is a Hubbard gap between them.6,8 Mn1.56Co0.96Ni0.48O4 共MCN兲 is a specifically important composition because it is very close to the resistivity minimum among these ternary oxides9,10 and has a high ferromagnetic transition temperature.11 So this material is very suitable to investigate the correlation between electrical and magnetic properties due to its high sensitivity to temperature and due to the high Curie temperature. In this letter, transitional behavior of hopping conduction at the Curie point is observed in MCN films. This behavior is expatiated as a variation in the hopping exponent p across the magnetic trana兲
Electronic mail:
[email protected].
0003-6951/2010/96共8兲/082103/3/$30.00
sition. A physical model concerned with the distribution of localized density of states 共LDOS兲 and magnetic order is proposed to explain the variation in p. The discovery of the correlation between electrical transport and magnetic order makes MCN films be promising for functional devices to integrate magnetic and electronic properties, such as magnetic sensor, spintronic devices, and so on. MCN films were prepared on Al2O3 substrate by chemical solution deposition. Sample preparation methods and characteristics of crystalline structure were described in detail elsewhere.5 Two stripe-shape Au electrodes were deposited onto edges of the films by evaporation. Ohmic behavior of the electrodes was confirmed in the range of 130–304 K. The dc current-voltage characteristics were measured using a computer-controlled source meter 共Keithley 2400兲. The temperature was controlled using cycling helium cryogenic equipment 共RGD210, Leybold兲 with temperature controller 共Lakeshore 330兲. The sample and temperature sensor were attached to each side of a copper bulk which was enwound by a heater to keep the samples and the sensor at the same temperature exactly. The data acquisition interval was 2 K. The time interval between two data acquisition was long enough in order to obtain stable and precise temperature readings. Magnetic measurements were made using a vibrating sample magnetometer 共PPMS-6000, Quantum Design兲. Figure 1共a兲 shows the temperature dependent resistivity of MCN films. The curve presents good linear relation between ln and 1 / T at lower temperature but diverge at ⬃200 K. For clarity, log is differentiated in Fig. 1共b兲. There is an obvious discontinuity at 200 K. The temperature dependent resistivity of hopping conduction can be expressed by the following:8
冉
共T兲 = 0 exp
冊
2r + , ␣ k BT
共1兲
where 0 depends on particular physical and material properties of the samples, r is the hopping distance, is the hopping energy, ␣ is the localization length related to the wave functions of acceptors and donors, and kB is the Boltzmann constant. The hopping distance and hopping energy obey a constraint condition
96, 082103-1
© 2010 American Institute of Physics
082103-2
Appl. Phys. Lett. 96, 082103 共2010兲
Wu et al.
FIG. 2. 共Color online兲 ln共W兲 vs ln共T兲 plots: 共a兲 experimental data and 共b兲 the calculated result.
FIG. 1. 共Color online兲 共a兲 Plot of ln vs 1000/ T. The solid 共red兲 line is the linear fitting to the data below 200 K. 共b兲 The derivative of log共兲 vs temperature.
冉 冊冕 4 3 r 3
g共⬘兲d⬘ = 1,
共2兲
0
where g共兲 is the LDOS. Under this condition, the most probable hopping distance and hopping energy are determined by minimizing the term 2r / ␣ + / kBT in Eq. 共1兲. The different distribution of LDOS will leads to different formula for the temperature-dependent resistivity. For example, 共1兲 a uniform LDOS near Fermi level corresponds to Mott’s variable range hopping 共VRH兲 model;12 共T兲 ⬀ exp共T0 / T兲0.25, where T0 is a characteristic temperature. 共2兲 Taking the electronic coulomb interaction into account, Efros and Shklovskii 共ES兲 deduced a parabolic distribution of LDOS near Fermi level and the LDOS vanishes at Fermi level.13 Using this parabolic distribution of LDOS, they obtained 共T兲 ⬀ exp共T0 / T兲0.5. In general, the temperature dependent resistivity of the system with hopping conduction can be described by the following:
冉 冊
共T兲 ⬀ exp
T0 T
p
共3兲
.
The linear relation between ln and 1 / T as shown in Fig. 1共a兲 indicates that p is close to unity below 200 K. While above 200 K, the curve does not keep the linear character. That is, the temperature dependent resistivity cannot be described by one uniform hopping exponent law for the whole temperature range. The discontinuity at 200 K as shown in Fig. 1共b兲 indicates transitional behavior related to the hopping conduction. By using the method proposed by Shklovskii and Efros,14 p can be determined from the slope of a plot of ln共W兲 versus ln共T兲 as follows: W=
冉 冊
1 d共ln 兲 T0 −1 ⬇ p T d共T 兲 T
der of the system.15,17 Spatial fluctuation of spin-dependent potentials is one kind of important disorder. The localization of electronic states induced by spatial fluctuation of spindependent potentials related to the magnetic order was reported in mixed-valence manganites with perovskite structure previously.18 The magnetic measurement in Fig. 3 shows that the magnetic transition point of MCN films is at ⬃200 K, which coincides with the temperature point where the discontinuity of p occurs. In MCN films the spindependent potential may vary across the magnetic transition, which causes the change of the distribution of LDOS, and then leads to the variation in the hopping exponent. To support the above scenario, Gaussian band-tails of localized states forming the Hubbard gap are employed to describe the effect of the disorder.15,17 The band-tails are given by the following: g0
g共兲 =
冑2 ␦
再 冋 再 冋
exp −
册 冋 册 冋
共 − Eg/2兲2 共Eg/2兲2 − exp − 2 2␦ 2␦2
共 + Eg/2兲2 共Eg/2兲2 exp − − exp − 2 冑2 ␦ 2␦ 2␦2 g0
册冎 册冎
ⱖ0 , ⱕ0 共5兲
where Eq. 共5兲 is the Gaussian function which satisfies g共兲 = 0 at = F = 0. The Hubbard band gap Eg is taken as 0.4 eV referring to the gap of NiMn2O4 which was determined to be 0.35–0.4 eV.8 Due to the gradual establishment of magnetic order beginning at the Curie temperature from high to low temperature, the Gaussian band-tails of localized states gradually narrow and withdraw from the Hubbard gap. The maximum of g共兲, i.e., gmax共兲 = g0 / 冑2␦, increases with magnetization as gmax共兲 ⬀ 1 / 关1 − 共M / M S兲2兴.19 Therefore, the withdrawal is described by the reduction in the Hubbard band width ␦ associated with the magnetization as follows:
p
.
共4兲
Figure 2共a兲 shows that p is divided into two different ranges at about 200 K. It is 0.91 below 200 K, while 0.46 above 200 K, close to the value of ES-VRH, which indicates a paraboliclike distribution of LDOS in the system. The variation in the hopping exponent is caused by a change of the distribution of LDOS near Fermi level.15,16 The distribution of localized electronic states closely links with the degree of disor-
FIG. 3. 共Color online兲 The temperature dependence of magnetic moment measured in FC mode. Inset: the solid 共green兲 line is the fitting curve to M = T / TC共1 − T / TC兲1/2,  is a fitting parameter.
082103-3
Appl. Phys. Lett. 96, 082103 共2010兲
Wu et al.
In conclusion, we have investigated the hopping conduction of MCN films in detail. The variation in hopping exponent p across the magnetic phase transition has been observed. A physical model of the gradual withdrawal of Gaussian distributed localized electronic states from the Hubbard gap due to the gradual establishment of magnetic order has been proposed to successfully explain this behavior. The calculated results based on this model are in excellent agreement with the experimental data. The discovery of a variation in hopping conduction across the magnetic transition is not only helpful for understanding the physical process of electrical transport in MCN but also instructive for future developments of functional devices which integrate magnetic and electronic properties in one unit.
FIG. 4. 共Color online兲 共a兲 The proposed distribution of LDOS. 共b兲 The calculated results of hopping distance and hopping energy.
冋 冉 冊册
M ␦ = ␦0 1 − MS
2
,
共6兲
冉 冊
1/2
T ⱕ TC ,
共7兲
where Tc = 200 K. And above Tc, M is set to zero. The temperature dependent distribution of the LDOS is obtained from Eqs. 共5兲–共7兲. Then 共T兲 is calculated by finding the minimal value of 2r / ␣ + / kBT under the constraint condition of Eq. 共2兲 and assuming that ␣ is 1 Å, a little longer than the radius of Mn3+ ion. g0 and ␦0 are obtained by fitting experimental data. The calculated resistivities consist very well with experimental data and the evolution of p is retrieved as shown in Fig. 2共b兲. It is reasonable that the theoretical and experimental values for p deviate at lower temperature because Eq. 共7兲 is invalid far below Tc. In the ferromagnetic phase, the calculated average hopping energy is ⬃0.21 eV as shown in Fig. 4共b兲, which coincides with the characteristic temperature 共2402.3 K兲 as shown in Fig. 1共a兲. These calculated results give a strong vindication to our proposed model.
Nos. No. No. and
E. Dagotto, Science 309, 257 共2005兲. A. P. Ramirez, Science 315, 1377 共2007兲. S. W. Cheong, Nature Mater. 6, 927 共2007兲. 4 N. Tsuda, K. Nasu, A. Fujimori, and K. Siratori, in Electronic Conduction in Oxides, Solid-State Sciences, edited by M. Cardona, P. Fulde, K. von Klitzing, R. Merlin, H. J. Queisser, and H. Störmer 共Springer, Berlin, 2002兲. 5 Y. Hou, Z. M. Huang, Y. Q. Gao, Y. J. Ge, J. Wu, and J. H. Chu, Appl. Phys. Lett. 92, 202115 共2008兲. 6 R. Schmidt, A. Basu, A. W. Brinkman, Z. Klusek, and P. K. Datta, Appl. Phys. Lett. 86, 073501 共2005兲. 7 R. Dannenberg, S. Baliga, R. J. Gambino, A. H. King, and A. P. Doctor, J. Appl. Phys. 86, 514 共1999兲. 8 R. Schmidt, A. Basu, and A. W. Brinkman, Phys. Rev. B 72, 115101 共2005兲. 9 I. T. Sheftel, A. I. Zaslavskii, E. V. Kurlina, and G. N. Tekster Provryakova, Sov. Phys. Solid State 3, 1978 共1962兲. 10 M. Vakiv, O. Shpotyuk, O. Mrooz, and I. Hadzaman, J. Eur. Ceram. Soc. 21, 1783 共2001兲. 11 O. Pena, Y. Ma, P. Barahona, M. Bahout, P. Duran, C. Moure, M. N. Baibich, and G. Martinez, J. Eur. Ceram. Soc. 25, 3051 共2005兲. 12 N. F. Mott, Conduction in Non-Crystalline Materials, 2nd ed. 共Clarendon, Oxford, 1993兲. 13 A. L. Efros and B. I. Shklovskii, J. Phys. C 8, L49 共1975兲. 14 B. I. Shklovskii and A. L. Efros, Electronic Properties of Doped Semiconductors 共Springer, Berlin, 1984兲. 15 S. Nakatsuji, V. Dobrosavljevic, D. Tanaskovic, M. Minakata, H. Fukazawa, and Y. Maeno, Phys. Rev. Lett. 93, 146401 共2004兲. 16 Y. Meir, Phys. Rev. Lett. 77, 5265 共1996兲. 17 E. N. Economou and M. H. Cohen, Phys. Rev. Lett. 25, 1445 共1970兲. 18 J. M. D. Coey, M. Viret, and L. Ranno, Phys. Rev. Lett. 75, 3910 共1995兲. 19 M. Viret, L. Ranno, and J. M. D. Coey, Phys. Rev. B 55, 8067 共1997兲. 20 C. Kittel, Introduction to Solid State Physics, 2nd ed. 共Wiley, New York, 1956兲. 1
2
where ␦0 is the width of Gaussian distribution at M = 0, M is the magnetization, M S is the saturation magnetization. Figure 4共a兲 shows the shape of the LDOS at M = 0 and M = 0.5 M S respectively. According to the mean field theory of ferromagnetism, the temperature dependent M near Tc 共Fig. 3 inset兲 is well described by the following:20 M⬀T 1−T TC TC
This work was supported by NNSF 共Grant 60707022 and 60527005兲, NGF Project 共Grant 2007CB924901兲, Shanghai Project 共Grant 10XD1404800兲, and CAS 共Grant Nos. YZ200835 C2-39兲.
3
