⇦Chinese Physics Letters, 2017, Vol. 34, No. 8, Article code 087201Express Letter⇨ Pressure-Induced Charge-Order Melting and Reentrant Charge Carrier Localization in the Mixed-Valent Pb$_{3}$Rh$_{7}$O$_{15}$ * Yan Li(李妍)1, Zhao Sun(孙朝)1, Jia-Wei Cai(蔡嘉伟)1, Jian-Ping Sun(孙建平)2,6, Bo-Sen Wang(王铂森)2,6, Zhi-Ying Zhao(赵志颖)3,4, Y. Uwatoko5, Jia-Qiang Yan(闫加强)3, Jin-Guang Cheng(程金光)2,6** Affiliations 1College of Materials Science and Engineering, Beijing Institute of Petrochemical Technology, Beijing 102617 2Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190 3Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA 4Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA 5The Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan 6University of Chinese Academy of Sciences, Beijing 100049 Received 9 July 2017 ^*Supported by the "Shi-Pei Ji Hua", the National Science Foundation of China under Grant Nos 51402019 and 11574377, the Beijing Natural Science Foundation under Grant No 2152011, the National Basic Research Program of China under Grants No 2014CB921500, the Strategic Priority Research Program and Key Research Program of Frontier Sciences of the Chinese Academy of Sciences under Grant Nos XDB07020100 and QYZDB-SSW-SLH013, the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, and the CEM, and NSF MRSEC under Grant No DMR-1420451.
^**Corresponding author. Email: jgcheng@iphy.ac.cn Citation Text: Li Y, Sun Z, Cai J W, Sun J P and Wang B S et al 2017 Chin. Phys. Lett. 34 087201 Abstract The mixed-valent Pb$_{3}$Rh$_{7}$O$_{15}$ undergoes a Verwey-type transition at $T_{\rm v} \approx 180$ K, below which the development of Rh$^{3+}$/Rh$^{4+}$ charge order induces an abrupt conductor-to-insulator transition in resistivity. Here we investigate the effect of pressure on the Verwey-type transition of Pb$_{3}$Rh$_{7}$O$_{15}$ by measuring its electrical resistivity under hydrostatic pressures up to 8 GPa with a cubic anvil cell apparatus. We find that the application of high pressure can suppress the Verwey-type transition around 3 GPa, above which a metallic state is realized at temperatures below $\sim $70 K, suggesting the melting of charge order by pressure. Interestingly, the low-temperature metallic region shrinks gradually upon further increasing pressure and disappears completely at $P >7$ GPa, which indicates that the charge carriers in Pb$_{3}$Rh$_{7}$O$_{15}$ undergo a reentrant localization under higher pressures. We have constructed a temperature-pressure phase diagram for Pb$_{3}$Rh$_{7}$O$_{15}$ and compared to that of Fe$_{3}$O$_{4}$, showing an archetype Verwey transition. DOI:10.1088/0256-307X/34/8/087201 PACS:72.80.Ga, 71.30.+h, 74.62.Fj © 2017 Chinese Physics Society Article Text As one of the most dramatic manifestations of electron correlation, the metal-insulator transition (MIT) has attracted enduring interest in the contemporary condensed matter physics.[1,2] The charge order involving the spatial ordering of different valence states in materials is one of the most important mechanisms for MITs. In particular, the intimated interplay of charge, spin, orbital and lattice degrees of freedom in the transition metal oxides can result in complex and competing ordered ground states, which are usually fragile and thus prone to dramatic changes under some external stimuli.[2] For example, magnetic-field induced melting of the charge-ordered antiferromagnetic insulating state in the half-doped manganite perovskites can result in the colossal magnetoresistance,[3] while a carrier doping-induced dynamic fluctuations of charge-ordered stripes in cuprates has been considered as an important ingredient for realizing the high-temperature superconductivity.[4] Therefore, manipulation of the charge-order-induced MIT is interesting from the viewpoints of both fundamental research and practical applications. In this Letter, we focus on an interesting $4d$-transition-metal oxide, Pb$_{3}$Rh$_{7}$O$_{15}$, which was recently reported to undergo a charge-order-induced MIT at $T_{\rm v}\approx 180$ K.[5] It crystallizes in the hexagonal space group $P6_{3}/mcm$ with lattice parameters $a = 10.3537$ Å and $c = 13.2837$ Å at room temperature. The crystal structure shown in Fig. 1(a) illustrates the arrangement of the RhO$_{6/2}$ octahedra located at four different crystallographic sites (labelled as Rh1 to Rh4). As can be seen, the Rh2, Rh3, and Rh4 octahedra share edges to form a two-dimensional (2D) sheets with periodic octahedral voids; these 2D octahedral sheets are interconnected along the $c$ axis by the face-shared Rh1 octahedral dimers via sharing common oxygens at the void positions. According to the calculations of bond valence sums above $T_{\rm v}$, Rh1 and Rh3 are close to 3+, and Rh4 is close to 4+, whereas Rh2 is mixed-valent 3.5+. Figure 1(b) depicts the charge distribution within the 2D octahedral sheet above $T_{\rm v}$, leading to an approximated formula of Pb$_{6}$Rh$_{5}^{3+}$Rh$_{6}^{3.5+}$Rh$_{3}^{4+}$O$_{30}$. The presence of mixed-valent Rh2 hexagonal rings renders a conducting state above $T_{\rm v}$, featured by a weak temperature dependence of resistivity.[5] Although it has not been decisively determined, it was proposed that the Rh$^{3.5+}$ cations would separate into Rh$^{3+}$ and Rh$^{4+}$ in an ordered fashion below $T_{\rm v}$, giving rise to a charge-ordered state as illustrated in Fig. 1(c), which can be described as Pb$_{3}$Rh$_{4}^{3+}$ Rh$_{3}^{4+}$O$_{15}$. Such a charge ordering process in Pb$_{3}$Rh$_{7}$O$_{15}$ resembles the famous Verwey transition of magnetite (Fe$_{3}$O$_{4}$) at $T_{\rm v} \approx 120$ K, i.e. from [Fe$^{3+}$][Fe$^{2.5+}$]$_{2}$O$_{4}$ above $T_{\rm v}$ to [Fe$^{3+}$][Fe$^{2+}$Fe$^{3+}$]O$_{4}$ below $T_{\rm v}$.[6,7]

Fig. 1. (a) A schematic drawing of the crystal structure for Pb$_{3}$Rh$_{7}$O$_{15}$ having four kinds of RhO$_{6}$ octahedra displayed in different colors. The charge distributions of RhO$_{6}$ octahedra for (b) $T > T_{\rm v}$ and (c) $T < T_{\rm v}$.

It has been reported that the Verwey transition of Fe$_{3}$O$_{4}$ can be suppressed gradually by the application of hydrostatic pressure, leading to a metallic ground state at $P_{c} \sim 6$-8 GPa.[8] It is thus interesting to explore whether the charge-ordered insulating state in Pb$_{3}$Rh$_{7}$O$_{15}$ can be melted by high pressure as found in Fe$_{3}$O$_{4}$. To address this question, we undertook a high-pressure study on the Pb$_{3}$Rh$_{7}$O$_{15}$ single crystal by measuring its resistivity $\rho (T)$ under various hydrostatic pressures up to 8 GPa. It is found that the application of high pressure can indeed suppress the Verwey-type transition around 3 GPa, signaling the melting of charge ordered state under pressure. However, unlike Fe$_{3}$O$_{4}$, the metallic region above 3 GPa appears only in a limited temperature range below $\sim$ 70 K, shrinks gradually upon further increasing pressure and disappears completely at $P$ $\sim$ 7 GPa. This result indicates that the charge carriers in Pb$_{3}$Rh$_{7}$O$_{15}$ undergo a reentrant localization under higher pressures. We have compared these results with the pressure effects on Fe$_{3}$O$_{4}$ showing the archetype Verwey transition. Single crystals of Pb$_{3}$Rh$_{7}$O$_{15}$ used in the present study were grown out of the PbO flux according to the procedure described by Mizoguchi et al.[5] Phase purity of the obtained crystals was confirmed by the powder x-ray diffraction at room temperature. Measurements of physical properties including the resistivity, magnetic susceptibility, specific heat, and Hall coefficient at ambient pressure were performed with a physical property measurement system (PPMS) and a magnetic property measurement system (MPMS-III) from Quantum Design. The high-pressure resistivity measurements up to 8 GPa were carried out with the standard four-probe method using the Palm cubic anvil cell apparatus.[9,10] Glycerol was employed as the pressure-transmitting medium. The pressure was calibrated at room temperature by monitoring the characteristic resistance changes of Bismuth at 2.55 and 7.7 GPa.

Fig. 2. Physical properties of Pb$_{3}$Rh$_{7}$O$_{15}$ single crystals: (a) in-plane resistivity $\rho (T)$ and its derivative $d\ln \rho /dT$, (b) in-plane magnetic susceptibility $\chi (T)$, (c) specific heat divided by temperature $C/T$, and (d) carrier density $n$ and mobility $\mu$ derived from the Hall resistivity. The vertical dotted line indicates the transition at $T_{\rm v} = 180$ K.

Figure 2 summarizes the physical properties of Pb$_{3}$Rh$_{7}$O$_{15}$ single crystal at ambient pressure. All these properties show distinct anomalies near the Verwey-type transition at $T_{\rm v} \approx 180$ K, in excellent agreement with the results reported by Mizoguchi et al.[5] As shown in Fig. 2(a), the resistivity $\rho (T)$ exhibits a very weak temperature dependence at $T > T_{\rm v}$, and undergoes a quick increase below $T_{\rm v}$, which can be defined clearly from the sharp peak of $d\ln \rho /dT$. The increase of $\rho (T)$ at $T_{\rm v}$ signals the opening of band gap associated with the development of charge order. However, it should be noted that the charge-ordered state of Pb$_{3}$Rh$_{7}$O$_{15}$ below $T_{\rm v} $ is not very insulating, featured by a total two-order-of magnitude increase and a relatively small $\rho (2\,{\rm K}) \sim 0.4$ $\Omega$$\cdot$cm. In comparison, the $\rho (T)$ of Fe$_{3}$O$_{4}$ exhibits an abrupt jump by two orders of magnitude at $T_{\rm v}$, followed by increase of more than four orders upon further decreasing temperatures, reaching over 10$^{6}$ $\Omega$$\cdot$cm at low temperatures.[6,8] This comparison indicates that the charge degree of freedom is not completely frozen in Pb$_{3}$Rh$_{7}$O$_{15}$, presumably due to the spatially more extend $4d$ orbitals and thus reduced columbic repulsion. Figure 2(b) shows the temperature dependence of magnetic susceptibility $\chi (T)$ measured under zero-field cooling (ZFC) and field-cooling (FC) modes. As can be seen, the ZFC/FC-$\chi (T)$ curves overlap with each other in the whole temperature range and experience a clear drop at $T_{\rm v}$, which should be ascribed to the reduction of density of states due to the development of charge order. The specific heat $C(T)$ in Fig. 2(c) measured on a single-crystal sample displays a clear $\lambda $-shaped anomaly at $T_{\rm v}$, and the absence of divergent behavior is consistent with the second-order phase transition without discernable structural changes at $T_{\rm v}$.[5] In comparison, the Verwey transition of Fe$_{3}$O$_{4}$ is strongly first order with a discontinues change of $C(T)$ and a symmetry lowering structural transition at $T_{\rm v}$.[11] The charge localization at $T_{\rm v}$ is further supported by our measurements of Hal effect, which was not reported in the previous study.[5] The Hall resistivity $\rho _{xy}(H)$ curves all are linear in field with a positive slope, signaling a dominant hole carrier in the whole temperature range. Figure 2(d) shows the extracted carrier density $n = 1/R_{H}$ and mobility $\mu = R_{H}/\rho e$, where $R_{H} \equiv d \rho _{xy}/dH$ is the Hall coefficient. As shown in Fig. 2(d), the carrier density $n$ exhibits a quick reduction at $T_{\rm v}$, while the mobility $\mu$ increases monotonically from room temperature down to $\sim$70 K with only a minor anomaly at $T_{\rm v}$. Below $\sim$70 K, $n$ changes slightly while $\mu$ exhibits a quick reduction before leveling off. These results provide us new microscopy information for understanding the electronic transport properties of Pb$_{3}$Rh$_{7}$O$_{15}$; i.e. the sudden increase of $\rho (T)$ at $T_{\rm v}$ is mainly attributed to the reduction of charge carrier due to the formation of Rh$^{3+}$/Rh$^{4+}$ charge order, while the further increase of $\rho (T)$ below $\sim$70 K after the resistivity plateau should be ascribed to the reduced mobility. These ambient-pressure characterizations confirm that Pb$_{3}$Rh$_{7}$O$_{15}$ undergoes a conductor-to-insulator transition at $T_{\rm v} \approx 180$ K, which is attributed to the development of Rh$^{3+}$/Rh$^{4+}$ charge order according to the previous study.[5] In order to check if the charge order can be melted by high pressure as observed in Fe$_{3}$O$_{4}$, we measured the temperature dependence of resistivity $\rho (T)$ of Pb$_{3}$Rh$_{7}$O$_{15}$ single crystal under various hydrostatic pressures up to 8 GPa. Figure 3(a) shows the $\rho (T)$ curves upon warming up in the pressure range 0–3.5 GPa. As can be seen, the transition temperature $T_{\rm v}$ defined from the peak position of $d\ln \rho /dT$ moves to lower temperatures gradually with increasing pressure, reaching $\sim$88 K at 3 GPa. Accompanying the decrease of $T_{\rm v}$ for $P \le 3$ GPa, the magnitude of $\rho (T)$ below $T_{\rm v}$ decreases monotonically, while $\rho (T)$ above $T_{\rm v}$ increases slightly and keeps a semiconducting-like temperature dependence, i.e. $d \rho /dT < 0$. When increasing pressure to 3.5 GPa, a metallic state with $d \rho /dT > 0$ is realized for $T < T_{\max} \approx 70$ K, signaling the breakdown of the charge-ordered state in Pb$_{3}$Rh$_{7}$O$_{15}$. However, the metallic phase is not achieved in the whole temperature range, in contrast with the situation seen in Fe$_{3}$O$_{4}$.[8]

Fig. 3. High-pressure resistivity $\rho (T)$ of Pb$_{3}$Rh$_{7}$O$_{15}$ single crystal under various hydrostatic pressures: (a) 0–3.5 GPa, (b) 3.5–8 GPa. The transition temperatures at $T_{\rm v}$ below 3.5 GPa are determined from the peak of $d\ln \rho/dT$ as shown in the top panel of (a). An enlarged view in (c) marks the evolution of the resistivity maximum $T_{\max}$ (up-pointing arrows) and minimum $T_{\min}$ (down-pointing arrows) as a function of pressure.

Upon further increasing pressure to above 3.5 GPa, the resistivity peak position at $T_{\max}$ shifts gradually to lower temperatures as shown by the up-pointing arrows in Fig. 3(c). Interestingly, the magnitude of $\rho (T)$ for $T$ $ < T_{\max}$ increases again with pressure, and an upturn develops below a $T_{\min}$, which moves up with pressure for $P > 4$ GPa and results in a gradual shrink of the metallic phase between $T_{\max}$ and $T_{\min}$. Eventually, the metallic region disappears completely at 8 GPa. Meanwhile, a clear reduction of $\rho (T)$ at $T > T_{\max}$ is also evidenced in Fig. 3(b), leading to a slope change of $\rho (T)$ at $T_{0} \sim 80$–90 K as indicated by the arrow. These results imply that the charge carriers in Pb$_{3}$Rh$_{7}$O$_{15}$ undergo a reentrant localization under higher pressures. The characteristic temperatures $T_{\rm v}$, $T_{\max}$, $T_{\min}$ and $T_{0}$ determined from the above $\rho (T)$ data are plotted in Fig. 4 as a function of pressure. A contour plot of all the $\rho (T)$ data is also superimposed in Fig. 4 to illustrate the characteristic changes of resistivity in different pressure ranges. As can be seen, the Verwey-type transition at $T_{\rm v}$ is suppressed gradually by pressure and disappears around 3 GPa, above which a metallic region ($d \rho /dT > 0$) emerges in a limited temperature range. The confined metallic phase between $T_{\max}$ and $T_{\min}$ shrinks with pressure and vanishes completely at $\sim$7 GPa. The $\rho (T)$ curves at 7–8 GPa exhibit an enhancement below $T_{0}$. Thus, the temperature-pressure phase diagram of Pb$_{3}$Rh$_{7}$O$_{15}$ is featured by a melting of charge-ordered insulating state around 3 GPa and a reentrant charge localization above 7 GPa with a confined metallic phase between them.

Fig. 4. Temperature-pressure phase diagram of Pb$_{3}$Rh$_{7}$O$_{15}$ based on the high-pressure resistivity measurements.

This present work is the first study attempting to clarify the hydrostatic pressure effects on the Pb$_{3}$Rh$_{7}$O$_{15}$ with a Verwey-type transition as Fe$_{3}$O$_{4}$. Thus, it is instructive to compare the effects of pressure on Pb$_{3}$Rh$_{7}$O$_{15}$ with that of Fe$_{3}$O$_{4}$. (i) $T _{\rm v}$ versus $P$: Although the former has a higher $T_{\rm v}$ than the latter, the charge-ordered state below $T_{\rm v}$ in Pb$_{3}$Rh$_{7}$O$_{15}$ is not as insulating as that of Fe$_{3}$O$_{4}$ as mentioned above. The critical pressure $P_{c} \approx 3$ GPa for melting the charge-ordered insulating phase in Pb$_{3}$Rh$_{7}$O$_{15}$ is about half of the $P_{c} \approx 6$-8 GPa for Fe$_{3}$O$_{4}$. These differences may originate from the distinct orbital characters, i.e. $4d$ versus $3d$; the larger spatial extension of the $4d$ orbitals makes it relatively easier to destabilize the charge ordered state in Pb$_{3}$Rh$_{7}$O$_{15}$. (ii) The pressure-induced metallic state: After the melting of the charge-ordered state above $P_{c}$, the metallic state in Pb$_{3}$Rh$_{7}$O$_{15}$ appears only in a confined temperature and pressure range, and is destabilized under higher pressures. In contrast, the metallic ground state is realized above $P_{c}$ in the whole temperature range for Fe$_{3}$O$_{4}$. Such a difference arises from the opposite response to pressure of the semiconducting state above $T_{\rm v}$. (iii) The semiconducting state above $T _{\rm v}$: Despite of a less insulating state below $T_{\rm v}$, the semiconducting states above $T_{\rm v}$ in Pb$_{3}$Rh$_{7}$O$_{15}$ is very robust against pressure. As illustrated in Fig. 3(a), the $\rho (T)$ of Pb$_{3}$Rh$_{7}$O$_{15}$ at $T > T_{\rm v}$ actually increases with pressure and the semiconducting-like behavior persists in the whole investigated pressure range. In sharp contrast, the $\rho (T)$ of Fe$_{3}$O$_{4}$ at $T > T_{\rm v}$ decreases monotonically with pressure, and changes from semiconducting-like to metallic at lower pressures than $P_{c}$. (iv) The reentrant charge carrier localization under higher pressure: The robustness of the semiconducting state in Pb$_{3}$Rh$_{7}$O$_{15}$ should connect with the diminishing of the metallic phase and the reentrant charge localization under higher pressures. In a recent high-pressure study on Fe$_{3}$O$_{4}$, a reentrant insulating behavior is observed at $P > 23$ GPa, which has been attributed to the pressure-induced structural transition from the cubic to an orthorhombic phase.[12] Whether there exists a pressure-induced structural transition in Pb$_{3}$Rh$_{7}$O$_{15}$ deserves further studies. In summary, we have grown the Pb$_{3}$Rh$_{7}$O$_{15}$ single crystal with the flux method and characterized its physical properties at ambient pressure. Our new Hall data provide microscopic evidences for the reduction of charge carrier at $T_{\rm v} \approx 180$ K due to the development of the Verwey-type Rh$^{3+}$/Rh$^{4+}$ charge ordering. We further investigate the effect of pressure on the Verwey-type transition of Pb$_{3}$Rh$_{7}$O$_{15}$ by measuring its resistivity under hydrostatic pressures up to 8 GPa. We find that the Verwey transition can be suppressed around 3 GPa, above which the charge-ordered insulating state is melted to a metallic state below $\sim$70 K. However, the low-temperature metallic region shrinks gradually upon further increasing pressure and disappears completely at $P > 7$ GPa, which indicate that the charge carriers in Pb$_{3}$Rh$_{7}$O$_{15}$ undergo a reentrant localization under higher pressures. A side-by-side comparison between Pb$_{3}$Rh$_{7}$O$_{15}$ and Fe$_{3}$O$_{4}$ highlights that the different $4d$ versus $3d$ orbital characters may be responsible for the distinct responses to external pressure in these two compounds. A high-pressure structural study on Pb$_{3}$Rh$_{7}$O$_{15}$ is needed to further understand the reentrant charge carrier localization under higher pressures. References Metals, nonmetals and metal-nonmetal transitions: some recollectionsMetal-insulator transitionsColossal magnetoresistant materials: the key role of phase separationImplications of Charge Ordering for Single-Particle Properties of High-

T_{c}

SuperconductorsPossible Verwey-Type Transition in Pb ₃ Rh ₇ O ₁₅Electronic Conduction of Magnetite (Fe3O4) and its Transition Point at Low TemperaturesLong Range Charge Ordering in Magnetite Below the Verwey TransitionMetallization of magnetite at high pressuresDevelopment of Palm Cubic Anvil Apparatus for Low Temperature PhysicsIntegrated-fin gasket for palm cubic-anvil high pressure apparatusThe Verwey transition - a topical reviewElectrical resistance of single-crystal magnetite (Fe ₃ O ₄ ) under quasi-hydrostatic pressures up to 100âGPa

[1]	Mott N 1984 Rep. Prog Phys. 47 909
[2]	Imada M, Fujimori A and Tokura Y 1998 Rev. Mod. Phys. 70 1039
[3]	Dagotto E, Hotta T and Moreo A 2001 Phys. Rep. 344 1
[4]	Salkola M I, Emery V J and Kivelson S A 1996 Phys. Rev. Lett. 77 155
[5]	Mizoguchi H, Ramirez A P, Siegrist T, Zakharov L N, Sleight A W and Subramanian M A 2009 Chem. Mater. 21 2300
[6]	Verwey E J W 1939 Nature 144 327
[7]	Wright J P, Attfield J P and Radaelli P G 2001 Phys. Rev. Lett. 87 266401
[8]	Mori N, Todo S, Takeshita N, Mori T and Akishige Y 2002 Physica B 312-313 686
[9]	Uwatoko Y, Matsubayashi K, Matsumoto T, Aso N, Nishi M, Fujiwara T, Hedo M, Tabata S, Takagi K, Tado M and Kagi H 2008 Rev. High Press. Sci. Technol. 18 230
[10]	Cheng J G, Matsubayashi K, Nagasaki S, Hisada A, Hirayama T, Hedo M, Kagi H and Uwatoko Y 2014 Rev. Sci. Instrum. 85 093907
[11]	Walz F 2002 J. Phys.: Condens. Matter 14 R285
[12]	Muramatsu T, Gasparov L V, Berger H, Hemley R J and Struzhkin V V 2016 J. Appl. Phys. 119 135903