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ESR study of the orbitally induced Peierls phase transition in polycrystalline CuIr2S4
Physica B 411 (2013) 136–139
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ESR study of the orbitally induced Peierls phase transition in polycrystalline CuIr2 S4 Lei Zhang a,n, Wei Tong a, Jiyu Fan b, Changjin Zhang a, Li Pi a,c, Shun Tan c, Yuheng Zhang a,c a
High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031, People’s Republic of China Department of Applied Physics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People’s Republic of China c High Magnetic Field Laboratory, University of Science and Technology of China, Hefei 230026, People’s Republic of China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 2 November 2012 Received in revised form 3 December 2012 Accepted 3 December 2012 Available online 10 December 2012
In this work, we investigate the polycrystalline CuIr2 S4 , which exhibits an orbitally induced Peierls phase transition at T MI 230 K, by the electron spin resonance (ESR) spectroscopy. A corresponding change occurs to the ESR spectra, as well as in the obtained ESR parameters such as resonance field Hr and g-factor ðg eff Þ. It is suggested that the ESR signals originate from the paramagnetic moments caused by lattice defects, which are affected by the spin-dimerization transition. However, ESR signals from a few non-dimerized Ir4 þ maybe also exist. In addition, an anomalous change below 50 K is detected by the ESR parameters. A possible explanation was proposed to interpret the experimental results. & 2012 Elsevier B.V. All rights reserved.
Keywords: ESR spectrum Orbitally induced Peierls phase transition
1. Introduction The spinel sulphide CuIr2 S4 has drawn much attention due to the extraordinary metal-insulator transition at the transition temperature T MI 230 K [1–4]. The phase transition was confirmed to be of first-order accompanied by a structure transformation from cubic (space group Fd3m) to triclinic ðP1Þ with a cell volume shrinkage of 0.7% [5,6]. Simultaneously, the magnetization changes from Pauli paramagnetism in the metallic state to diamagnetism in the insulating phase due to the spindimerization [6]. An insulating energy gap of 0:15 eV below TMI was observed by both optics and photoemission experiments [7–9]. The copper in CuIr2 S4 was verified to be monovalent [9–11]. The iridium presents a mixed-valence of þ3.5 in the metallic state, which is localized equally as Ir3 þ (S ¼ 0Þ and Ir4 þ ðS ¼ 1=2Þ in the insulating state, where spin- and latticedimerization occur to Ir4 þ ions forming spin singlets [12]. The structure in the insulating phase has been clarified by the high resolution neutron diffraction, where an intriguing octamer model of charge ordering was proposed [12]. Consequently, the unusual charge ordering was explained as an orbitally driven Peierls transition caused by orbits of Ir 5d electrons [13,14]. It is suggested that dxy orbits of Ir4 þ render the quasi-onedimensional Peierls instability along the /110S, so-called orbitally induced Peierls phase transition [14,15].
n
Corresponding author. Tel.: þ86 551 65595141; fax: þ 86 551 65591149. E-mail address: zhanglei@hmfl.ac.cn (L. Zhang).
0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2012.12.004
Recently, a structural transition from triclinic to tetragonal induced by the light illumination was found below 50 K, which triggers a renewed interest on CuIr2 S4 [7,16–18]. Furthermore, an in-gap state with band-gap opening of 0:09 eV was determined at low temperatures [19]. These results imply a new state below 50 K. In this work, we investigate the polycrystalline CuIr2 S4 by the electron spin resonance (ESR) spectroscopy, where the ESR parameters are obtained. The resonance field (Hr) and g-factor (geff) exhibit a corresponding change at TMI. In addition, an anomalous changes below 50 K are observed on the ESR parameters.
2. Experiment Polycrystalline CuIr2 S4 was prepared by the solid-reaction method described elsewhere [20]. The structure and phase purity were checked by the X-ray diffraction (XRD). The sample for the ESR measurement was ground to powder. The ESR measurement was carried out at selected temperatures using a Bruker EMX-plus model spectrometer operating at X-band frequencies ðn 9:4 GHzÞ, and microwave power of 1 mW was used. 3. Results and discussion Fig. 1(a) presents the integral ESR spectra ðPÞ for polycrystalline CuIr2 S4 from 2 kOe to 4 kOe at selected temperatures from 2 K to 300 K. An absorption peak appears for each spectrum at 3100 Oe. In addition a weak peak slightly above 3100 Oe was
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Fig. 1. (a) The integral ESR intensity ðPÞ from 2 kOe to 4 kOe at selected temperatures from 2 K to 300 K (the back ground color shows the intensity of the spectrum: red color corresponds to higher intensity while blue to lower intensity; the ESR spectra are fitted by Lorentz curves, where only fitting results of 300 K, 30 K and 2 K are shown) and (b) the derivative ESR spectra (dP/dH). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
observed on the spectrum below 30 K. The weak peaks below 30 K are clearly seen on the derivative curve of absorption spectra (dP/dH), as shown in Fig. 1(b). No singular behavior was observed in H o 2 kOe and H 4 4 kOe. The absorption intensity increases with the decrease of temperature. In fact, in a polycrystalline CuIr2 S4 , it has been suggested that the ESR signals are produced by moments captured by lattice defects rather than CuIr2 S4 itself [21]. As we know, the copper and sulphur elements exist in Cu þ and S2 states with full outer-shell electrons, both of which will not produce an ESR signal. In addition, the ESR lines in polycrystal are very different to that of Ir ions dissolved in single crystal MgO or CaO, where the hyperfine splitting of spectra was found due to the nuclear moments [22,23]. Therefore, the ESR spectra produced by Ir can be ruled out. On the other hand, the magnetic moments captured by lattice defects can produce strong ESR signals owing to the breaking of the covalent bonds [21]. Thus, Kang et al. suggested that the ESR signals in polycrystalline CuIr2 S4 originate from structural defects related to the breaking of the covalent bonds [21]. Nevertheless, the ESR spectra produced by lattice defects can be used as a device to investigate the phase transition. The substructure of the spectra below 30 K may be caused by a few non-dimerized Ir4 þ . In order to have a deep analysis, the ESR spectra were fitted by the Lorentz function to yield the parameters, as shown in Fig. 1(a). As you can see, the spectra below 30 K are fitted by two Lorentz functions. Fig. 2(a) shows temperature dependence of resonance field Hr1 and Hr2 (the solid curve is guided on eye), and the inset gives temperature dependence of magnetization [M(T)] for comparison. As you can see, Hr1 (defined as the peak of ESR spectrum) exhibits a drop at TMI, the behavior of which is similar to that of the M(T) curve. Likewise, Hr1 also present a rise below 50 K similar to the M(T) curve. These results indicate that there is intimate relation between the ESR spectra and the magnetization. Fig. 2(b) presents the g-factor (geff) as a function of temperature, which is defined as geff ¼hn=mB Hr (h is the Plank’s constant; n 9:4 GHz is the
Fig. 2. (a) The resonance field Hr vs T with the curve guided on eye (the inset shows temperature dependence of magnetization) and (b) g-factor as a function of T with the curve guided on eye (the inset depicts the derivative g1 vs T).
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microwave frequency; mB is the Bohr magneton). For an independent spin (IS), there is geff ¼2, which in turn yields HIS r 3300 Oe. The g1 above TMI approaches 2, indicating a paramagnetic state. However, all g1 below TMI are larger than 2, which indicates a change between the resonance spins and the environment. The inset of Fig. 2(b) gives the derivative g1 as a function of temperature. It can be seen that a nadir appears at 225 K, which corresponds to TMI. Besides, a upwarp of the curve happens below 50 K. The ESR lineshapes and the constant line intensity at the metal–insulator transition indicate that skin effect does not play any role in the metallic phase, which confirms that the ESR signals originate from lattice defects. As for g2, it may be produced by a few non-dimerized Ir4 þ ions. In fact, two g-factors were also found by Kang et al., where it was suggested to be related to iridium [21]. As is well known, the peak-to-peak linewidth DHpp , which is an effective parameter in ESR spectrum, usually implies the level of the coupling of spins with the environment. The DHpp is usually obtained as distance between the peak and trough on the differential spectrum, as illustrated in Fig. 1(b). Fig. 3(a) plots DHpp as a function of temperature (the solid curve is guided on eye). It is noted that DH1pp increases slightly with decreasing temperature without obvious change at TMI. However, it decreases drastically below 50 K, which corresponds to the rise below 50 K on the M(T) and Hr1 curves. The steep decrease indicates that the coupling of resonances spins with the environment become weaker below 50 K. Due to the weaker correlation of the resonance with the environment, the resonance electron tends to free electron. Consequently, Hr1 increases towards 3300 Oe. Correspondingly, g1 has the tendency to 2 below 50 K. Fig. 3(b) presents
Fig. 3. Temperature dependence of (a) peak-to-peak width DHpp and (b) ESR intensity IESR (the curves are guided on eye).
the ESR intensity IESR, which is obtained as Z H P dH IESR ¼
ð1Þ
0
As can be seen, IESR increases monotonously with temperature decreasing. At low temperature below 50 K, IESR increases sharply with decreasing temperature. Therefore, the rise of the magnetization below 50 K cannot be easily attributed to the Curie paramagnetism. In fact, an anomalous state below 50 K also be certified by other studies, such as investigations of photoluminescence, resistivity and so on. Recently, a radiation-induced structural phase transition from triclinic to tetragonal was found below 50 K [7,16–18]. Besides, it is found that the resistivity r below 50 K can be fitted well by the variable range hopping (VRH) model. However, rðTÞ from 50 K to TMI cannot be fitted by the VRH model. On the other hand, it is noted that the ln rðTÞ increases almost linearly with temperature decreasing as a relation of ln r ¼ ABT in the temperature range of 50 K to TMI as shown in Fig. 4, i.e. r expðBTÞ (A and B are constant). Based on the experimental results, an explanation is proposed. As we know, a chemical dimerization takes place on the lattice due to the orbitally induced Peierls transition, where the Ir4 þ ions are dimerized as robust Ir4 þ 2Ir4 þ dimers [12]. Above TMI, the transport behavior is in metallic state where the carriers are free to move, as shown in Fig. 5(a). Therefore, the microwave is shielded in a metal, leading to the weak intensity of the ESR spectrum. Below TMI, the carriers are localized into the Ir4 þ 2Ir4 þ dimers, as illustrated in Fig. 5(b). Namely, the carriers are sunk into the independent potential wells in pairs. However, these carriers have probability to hop out of the potential wells (decoupling), which produces carriers in the insulating state. This type of variation has been analyzed by Tredgold et al. in theory, who treated the problem of electron tunneling between nearest neighbors through potential barriers that vary randomly with time [24]. Supposing that the number of de-coupling carriers follows the exponent relation n ¼n0 expðBTÞ, the electronic conductivity s ¼ nem ¼ n0 em expðBTÞ. Consequently, the resistivity is obtained as r ¼ 1=s ¼ r0 expðBTÞ, where r0 ¼ ðn0 emÞ1 . This relation of resistivity is consistent very well with the experimental rðTÞ from 50 K to TMI. In addition, the linear increase of DH1pp with temperature decreasing from TMI to 50 K also confirms this proposal. However, below 50 K, the mechanism changes. When temperature decreasing below 50 K, the dimerized electrons do not have enough energy to hop out of the potential wells. On the
Fig. 4. Temperature dependence of resistivity (solid curve below 50 K is fitted by VRH model, and curve between 50 K to TMI is fitted according to r ¼ r0 eBT ).
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Acknowledgments This work was supported by the National Natural Science Foundation of China through Grant nos. 11004196 and 11004194, the Knowledge Innovation Program of the Chinese Academy of Sciences through Grant no. 106CS31121 (Hefei institutes of Physical Science, CAS), and the State Key Project of Fundamental Research of China through Grant no. 2010CB923403.
References
Fig. 5. (a) and (b) Schematic graph for the dimerization transition (the circles represent carriers) and (c) the VRH mechanism.
other hand, in the Mott charge-ordered insulators, the introduced disorders often induce electronic states observed within the band gaps, which are responsible for the hopping transport in the insulating phase [25,26]. This may explain the resistivity at low temperatures below 50 K. As shown in Fig. 5(c), the electrons have probability to hop from the valence band (EV) to conduction band (EC) due to energy levels caused by the impurities, the grain boundaries and interfaces. However, there is a controversy about the dimension of the VRH. Cao et al. [27,28]; Kang et al. [29] and Andreev et al. [30] suggested a three-dimensional VRH ½r expðT 0 =TÞ1=4 . On the other hand, Yagasaki et al. have interpreted that result as one-dimensional VRH or an Efros–Shklovski mechanism [31,32]. In fact, it is demonstrated that the oxygen impurities can affect the resistivity behavior [31]. Nevertheless, the resistivity behavior below TMI still cannot be described by a single mechanism even in the system without oxygen impurities. Our previous study shows that three-dimensional VRH is better to fit the resistivity, especially in Al-ion-doped CuIr2x Alx S4 system [33]. Thus, we choose three-dimensional VRH here as the fitting model. As shown in Fig. 4, the resistivity below TMI can be well fitted. The VRH electrons below 50 K can produce paramagnetic ESR signals, which rise the g1 and decrease the DH1pp below 50 K. On the other hand, an in-gap state has been observed by the ultraviolet photoemission spectroscopy (UPS), which corresponds to the VRH transport observed in resistivity [19]. The UPS investigation demonstrated that the Ir4 þ 2Ir4 þ bipolaronic hopping and disorder effects are responsible for the conductivity of CuIr2 S4 [19]. Thus, some disorders in the charge-ordered state is the origin of the in-gap spectral feature and the VRH transport. The explanation here is in agreement with the UPS results.
4. Conclusion In summary, the polycrystalline CuIr2 S4 is investigated by the ESR spectroscopy. A corresponding change at around TMI is manifested on the ESR spectra, as well as the obtained ESR parameters. It is suggested that the ESR signals in the polycrystalline sample are mainly produced by lattice defects, which can be used as an effective device to detect the phase transition. In addition, an anomalous change below 50 K is observed on the ESR parameters. A possible explanation was proposed to the experimental results.
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Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
ESR study of the orbitally induced Peierls phase transition in polycrystalline CuIr2 S4 Lei Zhang a,n, Wei Tong a, Jiyu Fan b, Changjin Zhang a, Li Pi a,c, Shun Tan c, Yuheng Zhang a,c a
High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031, People’s Republic of China Department of Applied Physics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People’s Republic of China c High Magnetic Field Laboratory, University of Science and Technology of China, Hefei 230026, People’s Republic of China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 2 November 2012 Received in revised form 3 December 2012 Accepted 3 December 2012 Available online 10 December 2012
In this work, we investigate the polycrystalline CuIr2 S4 , which exhibits an orbitally induced Peierls phase transition at T MI 230 K, by the electron spin resonance (ESR) spectroscopy. A corresponding change occurs to the ESR spectra, as well as in the obtained ESR parameters such as resonance field Hr and g-factor ðg eff Þ. It is suggested that the ESR signals originate from the paramagnetic moments caused by lattice defects, which are affected by the spin-dimerization transition. However, ESR signals from a few non-dimerized Ir4 þ maybe also exist. In addition, an anomalous change below 50 K is detected by the ESR parameters. A possible explanation was proposed to interpret the experimental results. & 2012 Elsevier B.V. All rights reserved.
Keywords: ESR spectrum Orbitally induced Peierls phase transition
1. Introduction The spinel sulphide CuIr2 S4 has drawn much attention due to the extraordinary metal-insulator transition at the transition temperature T MI 230 K [1–4]. The phase transition was confirmed to be of first-order accompanied by a structure transformation from cubic (space group Fd3m) to triclinic ðP1Þ with a cell volume shrinkage of 0.7% [5,6]. Simultaneously, the magnetization changes from Pauli paramagnetism in the metallic state to diamagnetism in the insulating phase due to the spindimerization [6]. An insulating energy gap of 0:15 eV below TMI was observed by both optics and photoemission experiments [7–9]. The copper in CuIr2 S4 was verified to be monovalent [9–11]. The iridium presents a mixed-valence of þ3.5 in the metallic state, which is localized equally as Ir3 þ (S ¼ 0Þ and Ir4 þ ðS ¼ 1=2Þ in the insulating state, where spin- and latticedimerization occur to Ir4 þ ions forming spin singlets [12]. The structure in the insulating phase has been clarified by the high resolution neutron diffraction, where an intriguing octamer model of charge ordering was proposed [12]. Consequently, the unusual charge ordering was explained as an orbitally driven Peierls transition caused by orbits of Ir 5d electrons [13,14]. It is suggested that dxy orbits of Ir4 þ render the quasi-onedimensional Peierls instability along the /110S, so-called orbitally induced Peierls phase transition [14,15].
n
Corresponding author. Tel.: þ86 551 65595141; fax: þ 86 551 65591149. E-mail address: zhanglei@hmfl.ac.cn (L. Zhang).
0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2012.12.004
Recently, a structural transition from triclinic to tetragonal induced by the light illumination was found below 50 K, which triggers a renewed interest on CuIr2 S4 [7,16–18]. Furthermore, an in-gap state with band-gap opening of 0:09 eV was determined at low temperatures [19]. These results imply a new state below 50 K. In this work, we investigate the polycrystalline CuIr2 S4 by the electron spin resonance (ESR) spectroscopy, where the ESR parameters are obtained. The resonance field (Hr) and g-factor (geff) exhibit a corresponding change at TMI. In addition, an anomalous changes below 50 K are observed on the ESR parameters.
2. Experiment Polycrystalline CuIr2 S4 was prepared by the solid-reaction method described elsewhere [20]. The structure and phase purity were checked by the X-ray diffraction (XRD). The sample for the ESR measurement was ground to powder. The ESR measurement was carried out at selected temperatures using a Bruker EMX-plus model spectrometer operating at X-band frequencies ðn 9:4 GHzÞ, and microwave power of 1 mW was used. 3. Results and discussion Fig. 1(a) presents the integral ESR spectra ðPÞ for polycrystalline CuIr2 S4 from 2 kOe to 4 kOe at selected temperatures from 2 K to 300 K. An absorption peak appears for each spectrum at 3100 Oe. In addition a weak peak slightly above 3100 Oe was
L. Zhang et al. / Physica B 411 (2013) 136–139
137
Fig. 1. (a) The integral ESR intensity ðPÞ from 2 kOe to 4 kOe at selected temperatures from 2 K to 300 K (the back ground color shows the intensity of the spectrum: red color corresponds to higher intensity while blue to lower intensity; the ESR spectra are fitted by Lorentz curves, where only fitting results of 300 K, 30 K and 2 K are shown) and (b) the derivative ESR spectra (dP/dH). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
observed on the spectrum below 30 K. The weak peaks below 30 K are clearly seen on the derivative curve of absorption spectra (dP/dH), as shown in Fig. 1(b). No singular behavior was observed in H o 2 kOe and H 4 4 kOe. The absorption intensity increases with the decrease of temperature. In fact, in a polycrystalline CuIr2 S4 , it has been suggested that the ESR signals are produced by moments captured by lattice defects rather than CuIr2 S4 itself [21]. As we know, the copper and sulphur elements exist in Cu þ and S2 states with full outer-shell electrons, both of which will not produce an ESR signal. In addition, the ESR lines in polycrystal are very different to that of Ir ions dissolved in single crystal MgO or CaO, where the hyperfine splitting of spectra was found due to the nuclear moments [22,23]. Therefore, the ESR spectra produced by Ir can be ruled out. On the other hand, the magnetic moments captured by lattice defects can produce strong ESR signals owing to the breaking of the covalent bonds [21]. Thus, Kang et al. suggested that the ESR signals in polycrystalline CuIr2 S4 originate from structural defects related to the breaking of the covalent bonds [21]. Nevertheless, the ESR spectra produced by lattice defects can be used as a device to investigate the phase transition. The substructure of the spectra below 30 K may be caused by a few non-dimerized Ir4 þ . In order to have a deep analysis, the ESR spectra were fitted by the Lorentz function to yield the parameters, as shown in Fig. 1(a). As you can see, the spectra below 30 K are fitted by two Lorentz functions. Fig. 2(a) shows temperature dependence of resonance field Hr1 and Hr2 (the solid curve is guided on eye), and the inset gives temperature dependence of magnetization [M(T)] for comparison. As you can see, Hr1 (defined as the peak of ESR spectrum) exhibits a drop at TMI, the behavior of which is similar to that of the M(T) curve. Likewise, Hr1 also present a rise below 50 K similar to the M(T) curve. These results indicate that there is intimate relation between the ESR spectra and the magnetization. Fig. 2(b) presents the g-factor (geff) as a function of temperature, which is defined as geff ¼hn=mB Hr (h is the Plank’s constant; n 9:4 GHz is the
Fig. 2. (a) The resonance field Hr vs T with the curve guided on eye (the inset shows temperature dependence of magnetization) and (b) g-factor as a function of T with the curve guided on eye (the inset depicts the derivative g1 vs T).
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microwave frequency; mB is the Bohr magneton). For an independent spin (IS), there is geff ¼2, which in turn yields HIS r 3300 Oe. The g1 above TMI approaches 2, indicating a paramagnetic state. However, all g1 below TMI are larger than 2, which indicates a change between the resonance spins and the environment. The inset of Fig. 2(b) gives the derivative g1 as a function of temperature. It can be seen that a nadir appears at 225 K, which corresponds to TMI. Besides, a upwarp of the curve happens below 50 K. The ESR lineshapes and the constant line intensity at the metal–insulator transition indicate that skin effect does not play any role in the metallic phase, which confirms that the ESR signals originate from lattice defects. As for g2, it may be produced by a few non-dimerized Ir4 þ ions. In fact, two g-factors were also found by Kang et al., where it was suggested to be related to iridium [21]. As is well known, the peak-to-peak linewidth DHpp , which is an effective parameter in ESR spectrum, usually implies the level of the coupling of spins with the environment. The DHpp is usually obtained as distance between the peak and trough on the differential spectrum, as illustrated in Fig. 1(b). Fig. 3(a) plots DHpp as a function of temperature (the solid curve is guided on eye). It is noted that DH1pp increases slightly with decreasing temperature without obvious change at TMI. However, it decreases drastically below 50 K, which corresponds to the rise below 50 K on the M(T) and Hr1 curves. The steep decrease indicates that the coupling of resonances spins with the environment become weaker below 50 K. Due to the weaker correlation of the resonance with the environment, the resonance electron tends to free electron. Consequently, Hr1 increases towards 3300 Oe. Correspondingly, g1 has the tendency to 2 below 50 K. Fig. 3(b) presents
Fig. 3. Temperature dependence of (a) peak-to-peak width DHpp and (b) ESR intensity IESR (the curves are guided on eye).
the ESR intensity IESR, which is obtained as Z H P dH IESR ¼
ð1Þ
0
As can be seen, IESR increases monotonously with temperature decreasing. At low temperature below 50 K, IESR increases sharply with decreasing temperature. Therefore, the rise of the magnetization below 50 K cannot be easily attributed to the Curie paramagnetism. In fact, an anomalous state below 50 K also be certified by other studies, such as investigations of photoluminescence, resistivity and so on. Recently, a radiation-induced structural phase transition from triclinic to tetragonal was found below 50 K [7,16–18]. Besides, it is found that the resistivity r below 50 K can be fitted well by the variable range hopping (VRH) model. However, rðTÞ from 50 K to TMI cannot be fitted by the VRH model. On the other hand, it is noted that the ln rðTÞ increases almost linearly with temperature decreasing as a relation of ln r ¼ ABT in the temperature range of 50 K to TMI as shown in Fig. 4, i.e. r expðBTÞ (A and B are constant). Based on the experimental results, an explanation is proposed. As we know, a chemical dimerization takes place on the lattice due to the orbitally induced Peierls transition, where the Ir4 þ ions are dimerized as robust Ir4 þ 2Ir4 þ dimers [12]. Above TMI, the transport behavior is in metallic state where the carriers are free to move, as shown in Fig. 5(a). Therefore, the microwave is shielded in a metal, leading to the weak intensity of the ESR spectrum. Below TMI, the carriers are localized into the Ir4 þ 2Ir4 þ dimers, as illustrated in Fig. 5(b). Namely, the carriers are sunk into the independent potential wells in pairs. However, these carriers have probability to hop out of the potential wells (decoupling), which produces carriers in the insulating state. This type of variation has been analyzed by Tredgold et al. in theory, who treated the problem of electron tunneling between nearest neighbors through potential barriers that vary randomly with time [24]. Supposing that the number of de-coupling carriers follows the exponent relation n ¼n0 expðBTÞ, the electronic conductivity s ¼ nem ¼ n0 em expðBTÞ. Consequently, the resistivity is obtained as r ¼ 1=s ¼ r0 expðBTÞ, where r0 ¼ ðn0 emÞ1 . This relation of resistivity is consistent very well with the experimental rðTÞ from 50 K to TMI. In addition, the linear increase of DH1pp with temperature decreasing from TMI to 50 K also confirms this proposal. However, below 50 K, the mechanism changes. When temperature decreasing below 50 K, the dimerized electrons do not have enough energy to hop out of the potential wells. On the
Fig. 4. Temperature dependence of resistivity (solid curve below 50 K is fitted by VRH model, and curve between 50 K to TMI is fitted according to r ¼ r0 eBT ).
L. Zhang et al. / Physica B 411 (2013) 136–139
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Acknowledgments This work was supported by the National Natural Science Foundation of China through Grant nos. 11004196 and 11004194, the Knowledge Innovation Program of the Chinese Academy of Sciences through Grant no. 106CS31121 (Hefei institutes of Physical Science, CAS), and the State Key Project of Fundamental Research of China through Grant no. 2010CB923403.
References
Fig. 5. (a) and (b) Schematic graph for the dimerization transition (the circles represent carriers) and (c) the VRH mechanism.
other hand, in the Mott charge-ordered insulators, the introduced disorders often induce electronic states observed within the band gaps, which are responsible for the hopping transport in the insulating phase [25,26]. This may explain the resistivity at low temperatures below 50 K. As shown in Fig. 5(c), the electrons have probability to hop from the valence band (EV) to conduction band (EC) due to energy levels caused by the impurities, the grain boundaries and interfaces. However, there is a controversy about the dimension of the VRH. Cao et al. [27,28]; Kang et al. [29] and Andreev et al. [30] suggested a three-dimensional VRH ½r expðT 0 =TÞ1=4 . On the other hand, Yagasaki et al. have interpreted that result as one-dimensional VRH or an Efros–Shklovski mechanism [31,32]. In fact, it is demonstrated that the oxygen impurities can affect the resistivity behavior [31]. Nevertheless, the resistivity behavior below TMI still cannot be described by a single mechanism even in the system without oxygen impurities. Our previous study shows that three-dimensional VRH is better to fit the resistivity, especially in Al-ion-doped CuIr2x Alx S4 system [33]. Thus, we choose three-dimensional VRH here as the fitting model. As shown in Fig. 4, the resistivity below TMI can be well fitted. The VRH electrons below 50 K can produce paramagnetic ESR signals, which rise the g1 and decrease the DH1pp below 50 K. On the other hand, an in-gap state has been observed by the ultraviolet photoemission spectroscopy (UPS), which corresponds to the VRH transport observed in resistivity [19]. The UPS investigation demonstrated that the Ir4 þ 2Ir4 þ bipolaronic hopping and disorder effects are responsible for the conductivity of CuIr2 S4 [19]. Thus, some disorders in the charge-ordered state is the origin of the in-gap spectral feature and the VRH transport. The explanation here is in agreement with the UPS results.
4. Conclusion In summary, the polycrystalline CuIr2 S4 is investigated by the ESR spectroscopy. A corresponding change at around TMI is manifested on the ESR spectra, as well as the obtained ESR parameters. It is suggested that the ESR signals in the polycrystalline sample are mainly produced by lattice defects, which can be used as an effective device to detect the phase transition. In addition, an anomalous change below 50 K is observed on the ESR parameters. A possible explanation was proposed to the experimental results.
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