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Charge transport near pressure-induced antiferromagnetic quantum critical point in Magnéli-phase vanadium oxides
Solid State Communications 125 (2003) 83–87 www.elsevier.com/locate/ssc
Charge transport near pressure-induced antiferromagnetic quantum critical point in Magne´li-phase vanadium oxides Hiroaki Uedaa,b,*, Koichi Kitazawaa, Takehiko Matsumotoc, Hidenori Takagia,b,d a
Department of Applied Chemistry and Department of Advanced Materials Science, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan b RIKEN (The Institute of Physical and Chemical Research), 2-1, Hirosawa, Wako, Saitama 351-0198, Japan c Materials Engineering Laboratory, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan d Correlated Electron Research Center (CERC), National Institute of Advanced Industrial Science and Technology (AIST), AIST Tsukuba Central 4, Tsukuba, Ibaraki 305-8562, Japan Received 21 July 2002; received in revised form 21 October 2002; accepted 25 October 2002 by G. Luke
Abstract Resistivity (r ) measurements on Magne´li phases V7 O13 and V8 O15 were performed under high pressures up to 3:5GPa: We have achieved a pressure-induced transition from an antiferromagnetic metal to a paramagnetic metal (PM) at critical pressures Pc < 3:4 and 3.3 GPa for V7 O13 and V8 O15 ; respectively. The critical behavior of rðTÞ near Pc turned out to be quite unusual in that no noticeable precursor effect was observed. This strongly contrasts with the canonical quantum critical point behavior observed in chemically modified systems such as NiðS; SeÞ2 and V2 O3 : We propose that the presence of two distinct Fermi surface segments is responsible for the observed unusual behaviors. q 2003 Elsevier Science Ltd. All rights reserved. PACS: 71.10.Hf; 71.27.þa; 71.30.þ h; 72.80.Ga Keywords: A. Magnetically ordered materials; D. Electronic transport; D. Phase transitions; E. Strain, high pressure
One of primary objectives of modern physics is to understand the behavior of complex systems composed of many interacting particles. Of the efforts, the Landau theory has been the most successful in describing the interacting itinerant electron system called Fermi liquid (FL). The characteristic behavior of FL appears particularly in the transport properties, which are governed by low-energy excitations. The resistivity rðTÞ of FL is well described as r ¼ r0 þ AT 2 at low temperatures, where r0 is the residual resistivity. The T 2 term is closely related with the v2 decay of the quasiparticle scattering rate, which is one of the hallmarks of FL. Here, v is the excitation energy of a quasiparticle. Another hallmark of FL is the conservation of * Corresponding author. Address: Magnetic Materials Laboratory, The Institute of Physical and Chemical Research (RIKEN), 2-1, Hirosawa, Wako, Saitama 351-0198, Japan. Tel.: þ 81-484679349; fax: þ 81-484624649. E-mail address: [email protected] (H. Ueda).
the Fermi surface. This manifests itself, for example, in the residual resistivity r0 ; which is essentially scaled only by the inverse of the Fermi surface area, S21 F : Although most metals behave as FL, a growing number of exotic materials have been found to lie outside or on the border of the FL framework [1]. Metals in the vicinity of the magnetic quantum critical point (QCP) are known to fall into such categories and have been attracting considerable interest for the past several decades. At magnetic QCP, lowlying spin fluctuations dominate the physics, and, when the system is a metal, the transport is distinct from that of the conventional FL. Contrary to the T 2 -dependent r of FL, the rðTÞ of many systems at QCP rises with exponents smaller than two. This deviation from FL behavior was found at the QCP of heavy fermion (HF) systems under pressure [2] and chemically modified 3d transition metal (TM) compounds such as NiðS; SeÞ2 and V2 O3 [3]. Many theoretical ideas have been proposed to explore the anomalous metallic state near QCP [4 – 6]. These
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H. Ueda et al. / Solid State Communications 125 (2003) 83–87
theoretical approaches have succeeded in explaining the universally observed unusual behaviors to a certain extent. Among these, the most prevailing and successful theory is the self-consistent renormalization (SCR) theory for spin fluctuations [6]. The SCR theory predicts the non-T 2 behavior of r at QCP, for instance, r / T 3=2 for threedimensional (3D) antiferromagnetic metals (AFM) and r / T for two-dimensional (2D) AFM. These predictions have been successfully applied to the QCP behaviors of many ‘conventional’ HF and chemically modified 3d TM compounds and confirmed on a quantitative level. The exploration of QCP was further accelerated by the discovery of superconductivity (SC) at QCP. In HF systems, such as CePd2 Si2 and CeIn3 ; by controlling the Ne´el temperature by applying pressure, an antiferromagnetic QCP is created, and, surprisingly, SC is found only in the vicinity of the QCP [7]. It is argued that high-temperature superconducting cuprates may fall into the same category as SC at QCP in HF because of the close proximity of the SC phase to the antiferromagnetic phase. Very recently, SC was found even at ferromagnetic QCP in UGe2 [8], UGeRh [9], and ZrZn2 [10]. Through these extensive studies on QCP, it was recently revealed that some systems show distinctly different T dependence of r from the theoretical predictions. CeðCu; AuÞ6 ; a 3D AFM, shows T-linear behavior of r [11] rather than the T 3=2 dependence expected for 3D AFM. The exponent of r for CePd2 Si2 and CeNi2 Ge2 at QCP exhibits a variation in the power law from the expected value of 1.5 to 1, which strongly depends upon the improvement of the sample purity [12]. In addition to this, strong pressure dependence of r0 has been reported in some HF systems [13], though r0 should be constant on the PM phase in a naive FL picture. Even with all of the theoretical discussion and experimentation, the study of the origin of the breakdown of the standard QCP theory is far from complete. To solve this problem, it is essential to explore QCP phenomena with a wide variety of systems. In view of the importance of disorder, it may be informative to employ pressure rather than chemical substitution as a control parameter. Previous studies on pressure-induced QCP had been mainly done on HF systems, with relatively weak magnetic interactions. To establish universal features of QCP phenomena, we believe that 3d TM systems, with a much larger magnetic energy scale than those of HF systems, have particular importance. To pursue this direction experimentally, the choice of material and high pressure are critically important. We have selected the vanadium Magne´li phase as a good candidate for tackling the QCP. Among various TM oxides, vanadium oxides are the ones that are most extensively studied. V2 O3 and VO2 ; which undergo metal-to-insulator transitions (MIT), are well known as prototypical strongly correlated systems. These two compounds can be considered as extremes of Magne´li phases Vn O2n21 ; corresponding to n ¼ 2 and 1, respectively. The vanadium
Magne´li series, bridging V2 O3 and VO2 ; are also of considerable interest because of a systematic change in their physical properties and structures [14]. The crystal structures of vanadium Magne´li phases are related to the rutile structure. VO2 with a rutile structure is composed of infinite chains of edge-sharing VO6 octahedra running along the caxis, which share their corners with each other. In the Vn O2n21 structure, these chains of octahedra are divided into n-VO6 blocks that share their faces. These compounds are mixed-valence compounds, which have ðn 2 2Þ V4þ ions and 2 V3þ ions per unit formula in an ionic picture. They are expected to have a metallic ground state, but, in fact, most of them undergo a transition to an antiferromagnetic insulator (AFI) due to electron correlations with lowering temperature. Among these Magne´li phases, V7 O13 and V8 O15 are the most appropriate compounds for the present study because of the easy access to QCP. V7 O13 is very likely to be located closest to QCP. V7 O13 has a metallic ground state but undergoes a PM– AFM transition at TAF < 43 K: Earlier pressure studies [15,16] showed the suppression of the AFM phase by applying pressure and suggested the presence of QCP around 3 GPa. V8 O15 has the lowest MIT temperature TMI < 69 K among the Magne´li series except for V7 O13 : The AFI phase is suppressed by the application of pressure and gives way to an AFM phase above 0.9 GPa. The transition temperature to the AFM phase of V8 O15 TAF (< 38 K) shows a decrease upon pressure with almost the same rate as that of V7 O13 but does not reach T ¼ 0 K up to 2 GPa. With these features in mind, using V7 O13 and V8 O15 ; we have attempted to create QCP by applying pressure up to 3.5 GPa and examined the possibility of SC. We have achieved QCP but not yet SC. We have examined the transport behaviors in the critical region in detail and have found the absence of the precursor effect to the QCP, which is in marked contrast with those of chemically modified 3d TM systems. We interpret this in terms of the two distinct Fermi surface segments with substantially different coupling to low-lying spin excitations. Single crystals of V7 O13 and V8 O15 were grown by a vapor transport method using TeCl4 as a transport reagent in an evacuated quartz tube. The electrical resistivities under high pressure were measured using a standard four-probe method by a low-frequency resistance bridge. Hydrostatic pressure was generated by a self-clamping type piston cylinder cell with Dapheni oil 73731 as a pressuretransmitting medium. The applied pressure was calibrated by measuring the superconducting transition temperature Tc ðPÞ of indium metal [17], placed right next to the sample. Fig. 1 shows the temperature dependence of resistivity rðTÞ for V7 O13 at various pressures. At ambient pressure, the rðTÞ shows a clear anomaly at a low temperature, below 1
Specially prepared by Idemitsu Co. Ltd, Tokyo, Japan; it is registered as a manufacturing product with the name, Daphne 7373.
H. Ueda et al. / Solid State Communications 125 (2003) 83–87
Fig. 1. Temperature dependence of resistivity under various pressures for V7 O13 single crystals. The pressures measured are ambient pressure, 0.81, 1.66, 3.12, 3.28, and 3.45 GPa. Arrows in this figure indicate TAF defined as a maximal temperature of dr=dT: TAF is rapidly suppressed by applying pressure and disappears at 3.45 GPa. The inset shows the r 2 r0 vs. T 2 plot.
which a broad hump is observed. This resistivity anomaly is known to correspond to an antiferromagnetic ordering [18]. By comparing the susceptibility and the resistivity data, we found that the ordering temperature TAF can be reasonably determined as the temperature of the maximum in the temperature derivative of rðTÞ: As the pressure is increased, the resistive anomaly shifts toward the lower temperature side, indicating that TAF is systematically suppressed upon pressure. Above 3 GPa, the anomaly becomes substantially broad, indicating a rapid decrease of TAF : Eventually, the anomaly disappears at 3.45 GPa. This indicates that a PM– AFM transition takes place at Pc < 3:4 GPa and that an antiferromagnetic QCP is achieved. Fig. 2 shows the rðTÞ of V8 O15 at various pressures. At low pressures, rðTÞ shows a discontinuous jump, indicating the presence of a first order MIT. Above 1.3 GPa, TMI suddenly disappears, and rðTÞ shows a metallic behavior down to the T ¼ 0 limit. This very likely indicates the occurrence of a first order ‘pressure’-induced MIT. An anomaly appears in rðTÞ of the pressure-induced metallic phase, which agrees with a previous report [16]. This very likely represents an antiferromagnetic ordering. We found that, analogous to V7 O13 ; this anomaly gradually shifts to the lower-temperature side with the increase of pressure and completely disappears above Pc < 3:3 GPa: In our measurements on V7 O13 and V8 O15 ; no sign of SC was found down to 1.7 K. It is highly likely that SC at magnetic QCP is anisotropic. Anisotropic SC is known to be extremely sensitive to disorder. Indeed, SC at QCP in an HF system is observed only when very clean samples are measured [7]. From a simple free-electron analysis, the residual resistivity r0 ¼ 50 mV cm in our crystal yields an This appears too short to electron mean free path l0 < 30 A: achieve anisotropic SC. In this sense, we believe, the lack of
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Fig. 2. Temperature dependence of resistivity under various pressures for V8 O15 single crystals. The pressures measured are ambient pressure, 0.89, 1.34, 1.66, 2.42, 2.73, 3.12, and 3.45 GPa. In contrast to V7 O13 ; V8 O15 shows first-order metal–insulator transition at low pressures. The inset shows the expansion of the low-temperature part. It is clearly seen that r0 suddenly drops at 3.45 GPa.
evidence for SC in the present experiment does not necessarily mean the absence of SC at QCP in the Magne´li phase. These results can be summarized as the phase diagrams shown in the upper panels of Figs. 3 and 4. The pressure dependences of TAF are in good agreement with previous studies up to 2 GPa [16].2 Aside from the presence of the PI phase in V8 O15 ; V7 O13 and V8 O15 exhibit quite similar phase diagrams, implying a common physics behind. A rapid decrease of TAF is commonly observed near Pc : The SCR theory predicts that, in the critical region, TAF should be scaled by TAF / ðPc 2 PÞ2=3 in 3D AFM. Fig. 5 demon3=2 strates the TAF vs. P plot for V7 O13 : The linear behavior near QCP is consistent with the prediction of the SCR theory, indicative of the presence of a critical region. Although not as clear as V7 O13 ; we observe a qualitatively similar behavior in V8 O15 : Since the presence of antiferromagnetic QCP has been established, the focus now is on the detailed critical behavior of the transport near QCP. The ðr 2 r0 Þ vs. T 2 plot is shown in the inset of Fig. 1. Below 3.2 GPa, the linear behavior corresponds to the T 2 -dependence of r; indicative of a conventional FL. Only at 3.28 and 3.45 GPa, which are right at QCP, is sublinear behavior observed. The temperature dependence here can be fitted by r ¼ r0 þ A0 T 3=2 at low temperatures, which is consistent with the prediction of SCR theory for 3D AFM. For V8 O15 ; we do not find T 3=2 behavior 2
TMI < 86 K of V8 O15 at ambient pressure is higher than those reported previously. We suspect that this difference of TMI may be due to a small number of defects and believe that this has little effect on the metallic states.
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Fig. 3. Pressure dependence of magnetic and transport parameters for V7 O13 deduced from the rðTÞ data shown in Fig. 1, the antiferromagnetic transition temperature (upper panel), the T 2 coefficient of low-temperature rðTÞ; A (middle panel), and the residual resistivity r0 (lower panel). The line on the upper panel is an eye-guide. TAF reaches 0 K at Pc < 3:4 GPa:
even at Pc : This implies that something unusual is happening at the QCP of the vanadium Magne´li phase. Indeed, contrary to our expectations, no trace of precursor to the QCP could be recognized in the AFM phase below the critical pressures Pc : As shown in the details of the inset in Fig. 1, the variation of rðTÞ is somewhat discontinuous at QCP. This can be visually demonstrated by plotting A as a function of P in the middle panels of Figs. 3 and 4. Below Pc ; A is almost constant and shows a discontinuous drop at Pc : A diverging behavior of A can be seen only for V7 O13 right at QCP, which reflects the T 3=2 dependence of r: In accord with the absence of precursor behavior in A, unusual pressure dependence of r0 was observed, as shown in the lower panels of Figs. 3 and 4. r0 is constant below Pc and suddenly shows a distinct reduction at Pc : Chemically modified 3d TM AFM systems, such as NiðS; SeÞ2 [19], show a noticeable enhancement of A over a certain range of doping near the AFM – PM phase boundary as a precursor to non-T 2 behavior. Accompanied with this enhancement of A, a distinct reduction of r0 with approaching QCP is observed in the AFM phase, and, in contrast, r0 is constant in the PM phase. It is clear that the behaviors observed in the vanadium Magne´li phase contrast those of ‘standard’ QCP behavior in 3d TM AFM. The absence of precursor behavior both in A and r0 of the AFM phase characterizes the QCP of the vanadium Magne´li phase. The constant r0 in the AFM may provide a key to understand the distinct critical behavior. In the FL picture,
Fig. 4. Pressure dependence of magnetic and transport parameters for V8 O15 deduced from the rðTÞ data shown in Fig. 2, the antiferromagnetic transition temperature (upper panel), the T 2 coefficient of low-temperature rðTÞ; A (middle panel), and the residual resistivity r0 (lower panel). The line on the upper panel is an eye-guide. The PI phase disappears above PMI < 1:3 GPa; and the AFM phase disappears above Pc < 3:3 GPa:
r21 0 is scaled only by the area of Fermi surface volume SF and the electron mean free path l0 at T ¼ 0; as r21 0 / SF l0 : l0 can be viewed as a constant under pressure because l0 is determined only by the concentration of impurities. The variation of r0 ; therefore, represents the variation of the Fermi surface volume. For chemically modified 3d TM systems, such as NiðS; SeÞ2 and V2 O3 ; the Fermi surface gradually recovers as the system approaches the PM phase, which manifests itself as a reduction of r0 in the antiferromagnetic phase. The unexpected pressure independence of r0 in the AFM of the vanadium Magne´li phase implies that SF ; which is responsible for transport, is, in fact, constant in the AFM phase and shows a discontinuous jump from AFM to PM. Then, there are two distinct Fermisurface segments; one always lacks a gap, and the other always has a gap in the AFM phase. This contrasts with the conventional wisdom that the gapped region fades out while approaching the QCP. Since A, a measure of the low-lying spin excitations near QCP, is constant in the AFM phase, the gapless Fermi surface, which dominates the transport in the AFM phase, should be almost free from the critical spin scattering. The observed T 3=2 behavior in V7 O13 may represent a negligibly small but finite coupling between the critical spin fluctuation and the gapless Fermi surface. In this two-Fermi-surface-segment picture, we may anticipate a pronounced impurity effect. Since the impurity scattering smears out the distinction between the two Fermisurface segments, the introduction of impurity scattering will result in the recovery of the standard QCP behavior.
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sample preparation. This work was partly supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science, and Technology.
References
Fig. 5. Pressure dependence of the transition temperature TAF for 3=2 3=2 V7 O13 ; plotted as TAF vs. pressure. In the vicinity of Pc ; TAF varies linearly, indicating TAF / ðPc 2 PÞ3=2 :
This may provide a reasonable account for the contrast between the chemically modified 3d TM AFM and the stoichiometric vanadium Magne´li phase. We, further, speculate that the observation of T 3=2 behavior at QCP in V7 O13 originates from a coupling of two Fermi-surface segments through the impurity scattering. In the case of chemically modified systems, the coupling is substantially large due to the averaging effect of doped impurities, and a clear precursor effect in both A and r0 is observed. In summary, we have achieved antiferromagnetic QCP by applying pressures up to 3.5 GPa in the vanadium Magne´li phase. In the vicinity of QCP, no trace of the precursor effect to the QCP was observed. This is shown to be due to the presence of two distinct Fermi-surface segments in which the impurity effect plays an important role. Furthermore, QCP could be considered in HF systems in which the exponent of the temperature-dependent r changes from 2 to 1.5 with an increase in the impurity level. In this context, we suspect that the phenomena we observed are a generic feature of QCP in real material with Fermisurface anisotropy.
Acknowledgements We thank T. Tonogai and Y. Hikita for their help in
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Charge transport near pressure-induced antiferromagnetic quantum critical point in Magne´li-phase vanadium oxides Hiroaki Uedaa,b,*, Koichi Kitazawaa, Takehiko Matsumotoc, Hidenori Takagia,b,d a
Department of Applied Chemistry and Department of Advanced Materials Science, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan b RIKEN (The Institute of Physical and Chemical Research), 2-1, Hirosawa, Wako, Saitama 351-0198, Japan c Materials Engineering Laboratory, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan d Correlated Electron Research Center (CERC), National Institute of Advanced Industrial Science and Technology (AIST), AIST Tsukuba Central 4, Tsukuba, Ibaraki 305-8562, Japan Received 21 July 2002; received in revised form 21 October 2002; accepted 25 October 2002 by G. Luke
Abstract Resistivity (r ) measurements on Magne´li phases V7 O13 and V8 O15 were performed under high pressures up to 3:5GPa: We have achieved a pressure-induced transition from an antiferromagnetic metal to a paramagnetic metal (PM) at critical pressures Pc < 3:4 and 3.3 GPa for V7 O13 and V8 O15 ; respectively. The critical behavior of rðTÞ near Pc turned out to be quite unusual in that no noticeable precursor effect was observed. This strongly contrasts with the canonical quantum critical point behavior observed in chemically modified systems such as NiðS; SeÞ2 and V2 O3 : We propose that the presence of two distinct Fermi surface segments is responsible for the observed unusual behaviors. q 2003 Elsevier Science Ltd. All rights reserved. PACS: 71.10.Hf; 71.27.þa; 71.30.þ h; 72.80.Ga Keywords: A. Magnetically ordered materials; D. Electronic transport; D. Phase transitions; E. Strain, high pressure
One of primary objectives of modern physics is to understand the behavior of complex systems composed of many interacting particles. Of the efforts, the Landau theory has been the most successful in describing the interacting itinerant electron system called Fermi liquid (FL). The characteristic behavior of FL appears particularly in the transport properties, which are governed by low-energy excitations. The resistivity rðTÞ of FL is well described as r ¼ r0 þ AT 2 at low temperatures, where r0 is the residual resistivity. The T 2 term is closely related with the v2 decay of the quasiparticle scattering rate, which is one of the hallmarks of FL. Here, v is the excitation energy of a quasiparticle. Another hallmark of FL is the conservation of * Corresponding author. Address: Magnetic Materials Laboratory, The Institute of Physical and Chemical Research (RIKEN), 2-1, Hirosawa, Wako, Saitama 351-0198, Japan. Tel.: þ 81-484679349; fax: þ 81-484624649. E-mail address: [email protected] (H. Ueda).
the Fermi surface. This manifests itself, for example, in the residual resistivity r0 ; which is essentially scaled only by the inverse of the Fermi surface area, S21 F : Although most metals behave as FL, a growing number of exotic materials have been found to lie outside or on the border of the FL framework [1]. Metals in the vicinity of the magnetic quantum critical point (QCP) are known to fall into such categories and have been attracting considerable interest for the past several decades. At magnetic QCP, lowlying spin fluctuations dominate the physics, and, when the system is a metal, the transport is distinct from that of the conventional FL. Contrary to the T 2 -dependent r of FL, the rðTÞ of many systems at QCP rises with exponents smaller than two. This deviation from FL behavior was found at the QCP of heavy fermion (HF) systems under pressure [2] and chemically modified 3d transition metal (TM) compounds such as NiðS; SeÞ2 and V2 O3 [3]. Many theoretical ideas have been proposed to explore the anomalous metallic state near QCP [4 – 6]. These
0038-1098/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved. PII: S 0 0 3 8 - 1 0 9 8 ( 0 2 ) 0 0 7 1 6 - 0
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H. Ueda et al. / Solid State Communications 125 (2003) 83–87
theoretical approaches have succeeded in explaining the universally observed unusual behaviors to a certain extent. Among these, the most prevailing and successful theory is the self-consistent renormalization (SCR) theory for spin fluctuations [6]. The SCR theory predicts the non-T 2 behavior of r at QCP, for instance, r / T 3=2 for threedimensional (3D) antiferromagnetic metals (AFM) and r / T for two-dimensional (2D) AFM. These predictions have been successfully applied to the QCP behaviors of many ‘conventional’ HF and chemically modified 3d TM compounds and confirmed on a quantitative level. The exploration of QCP was further accelerated by the discovery of superconductivity (SC) at QCP. In HF systems, such as CePd2 Si2 and CeIn3 ; by controlling the Ne´el temperature by applying pressure, an antiferromagnetic QCP is created, and, surprisingly, SC is found only in the vicinity of the QCP [7]. It is argued that high-temperature superconducting cuprates may fall into the same category as SC at QCP in HF because of the close proximity of the SC phase to the antiferromagnetic phase. Very recently, SC was found even at ferromagnetic QCP in UGe2 [8], UGeRh [9], and ZrZn2 [10]. Through these extensive studies on QCP, it was recently revealed that some systems show distinctly different T dependence of r from the theoretical predictions. CeðCu; AuÞ6 ; a 3D AFM, shows T-linear behavior of r [11] rather than the T 3=2 dependence expected for 3D AFM. The exponent of r for CePd2 Si2 and CeNi2 Ge2 at QCP exhibits a variation in the power law from the expected value of 1.5 to 1, which strongly depends upon the improvement of the sample purity [12]. In addition to this, strong pressure dependence of r0 has been reported in some HF systems [13], though r0 should be constant on the PM phase in a naive FL picture. Even with all of the theoretical discussion and experimentation, the study of the origin of the breakdown of the standard QCP theory is far from complete. To solve this problem, it is essential to explore QCP phenomena with a wide variety of systems. In view of the importance of disorder, it may be informative to employ pressure rather than chemical substitution as a control parameter. Previous studies on pressure-induced QCP had been mainly done on HF systems, with relatively weak magnetic interactions. To establish universal features of QCP phenomena, we believe that 3d TM systems, with a much larger magnetic energy scale than those of HF systems, have particular importance. To pursue this direction experimentally, the choice of material and high pressure are critically important. We have selected the vanadium Magne´li phase as a good candidate for tackling the QCP. Among various TM oxides, vanadium oxides are the ones that are most extensively studied. V2 O3 and VO2 ; which undergo metal-to-insulator transitions (MIT), are well known as prototypical strongly correlated systems. These two compounds can be considered as extremes of Magne´li phases Vn O2n21 ; corresponding to n ¼ 2 and 1, respectively. The vanadium
Magne´li series, bridging V2 O3 and VO2 ; are also of considerable interest because of a systematic change in their physical properties and structures [14]. The crystal structures of vanadium Magne´li phases are related to the rutile structure. VO2 with a rutile structure is composed of infinite chains of edge-sharing VO6 octahedra running along the caxis, which share their corners with each other. In the Vn O2n21 structure, these chains of octahedra are divided into n-VO6 blocks that share their faces. These compounds are mixed-valence compounds, which have ðn 2 2Þ V4þ ions and 2 V3þ ions per unit formula in an ionic picture. They are expected to have a metallic ground state, but, in fact, most of them undergo a transition to an antiferromagnetic insulator (AFI) due to electron correlations with lowering temperature. Among these Magne´li phases, V7 O13 and V8 O15 are the most appropriate compounds for the present study because of the easy access to QCP. V7 O13 is very likely to be located closest to QCP. V7 O13 has a metallic ground state but undergoes a PM– AFM transition at TAF < 43 K: Earlier pressure studies [15,16] showed the suppression of the AFM phase by applying pressure and suggested the presence of QCP around 3 GPa. V8 O15 has the lowest MIT temperature TMI < 69 K among the Magne´li series except for V7 O13 : The AFI phase is suppressed by the application of pressure and gives way to an AFM phase above 0.9 GPa. The transition temperature to the AFM phase of V8 O15 TAF (< 38 K) shows a decrease upon pressure with almost the same rate as that of V7 O13 but does not reach T ¼ 0 K up to 2 GPa. With these features in mind, using V7 O13 and V8 O15 ; we have attempted to create QCP by applying pressure up to 3.5 GPa and examined the possibility of SC. We have achieved QCP but not yet SC. We have examined the transport behaviors in the critical region in detail and have found the absence of the precursor effect to the QCP, which is in marked contrast with those of chemically modified 3d TM systems. We interpret this in terms of the two distinct Fermi surface segments with substantially different coupling to low-lying spin excitations. Single crystals of V7 O13 and V8 O15 were grown by a vapor transport method using TeCl4 as a transport reagent in an evacuated quartz tube. The electrical resistivities under high pressure were measured using a standard four-probe method by a low-frequency resistance bridge. Hydrostatic pressure was generated by a self-clamping type piston cylinder cell with Dapheni oil 73731 as a pressuretransmitting medium. The applied pressure was calibrated by measuring the superconducting transition temperature Tc ðPÞ of indium metal [17], placed right next to the sample. Fig. 1 shows the temperature dependence of resistivity rðTÞ for V7 O13 at various pressures. At ambient pressure, the rðTÞ shows a clear anomaly at a low temperature, below 1
Specially prepared by Idemitsu Co. Ltd, Tokyo, Japan; it is registered as a manufacturing product with the name, Daphne 7373.
H. Ueda et al. / Solid State Communications 125 (2003) 83–87
Fig. 1. Temperature dependence of resistivity under various pressures for V7 O13 single crystals. The pressures measured are ambient pressure, 0.81, 1.66, 3.12, 3.28, and 3.45 GPa. Arrows in this figure indicate TAF defined as a maximal temperature of dr=dT: TAF is rapidly suppressed by applying pressure and disappears at 3.45 GPa. The inset shows the r 2 r0 vs. T 2 plot.
which a broad hump is observed. This resistivity anomaly is known to correspond to an antiferromagnetic ordering [18]. By comparing the susceptibility and the resistivity data, we found that the ordering temperature TAF can be reasonably determined as the temperature of the maximum in the temperature derivative of rðTÞ: As the pressure is increased, the resistive anomaly shifts toward the lower temperature side, indicating that TAF is systematically suppressed upon pressure. Above 3 GPa, the anomaly becomes substantially broad, indicating a rapid decrease of TAF : Eventually, the anomaly disappears at 3.45 GPa. This indicates that a PM– AFM transition takes place at Pc < 3:4 GPa and that an antiferromagnetic QCP is achieved. Fig. 2 shows the rðTÞ of V8 O15 at various pressures. At low pressures, rðTÞ shows a discontinuous jump, indicating the presence of a first order MIT. Above 1.3 GPa, TMI suddenly disappears, and rðTÞ shows a metallic behavior down to the T ¼ 0 limit. This very likely indicates the occurrence of a first order ‘pressure’-induced MIT. An anomaly appears in rðTÞ of the pressure-induced metallic phase, which agrees with a previous report [16]. This very likely represents an antiferromagnetic ordering. We found that, analogous to V7 O13 ; this anomaly gradually shifts to the lower-temperature side with the increase of pressure and completely disappears above Pc < 3:3 GPa: In our measurements on V7 O13 and V8 O15 ; no sign of SC was found down to 1.7 K. It is highly likely that SC at magnetic QCP is anisotropic. Anisotropic SC is known to be extremely sensitive to disorder. Indeed, SC at QCP in an HF system is observed only when very clean samples are measured [7]. From a simple free-electron analysis, the residual resistivity r0 ¼ 50 mV cm in our crystal yields an This appears too short to electron mean free path l0 < 30 A: achieve anisotropic SC. In this sense, we believe, the lack of
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Fig. 2. Temperature dependence of resistivity under various pressures for V8 O15 single crystals. The pressures measured are ambient pressure, 0.89, 1.34, 1.66, 2.42, 2.73, 3.12, and 3.45 GPa. In contrast to V7 O13 ; V8 O15 shows first-order metal–insulator transition at low pressures. The inset shows the expansion of the low-temperature part. It is clearly seen that r0 suddenly drops at 3.45 GPa.
evidence for SC in the present experiment does not necessarily mean the absence of SC at QCP in the Magne´li phase. These results can be summarized as the phase diagrams shown in the upper panels of Figs. 3 and 4. The pressure dependences of TAF are in good agreement with previous studies up to 2 GPa [16].2 Aside from the presence of the PI phase in V8 O15 ; V7 O13 and V8 O15 exhibit quite similar phase diagrams, implying a common physics behind. A rapid decrease of TAF is commonly observed near Pc : The SCR theory predicts that, in the critical region, TAF should be scaled by TAF / ðPc 2 PÞ2=3 in 3D AFM. Fig. 5 demon3=2 strates the TAF vs. P plot for V7 O13 : The linear behavior near QCP is consistent with the prediction of the SCR theory, indicative of the presence of a critical region. Although not as clear as V7 O13 ; we observe a qualitatively similar behavior in V8 O15 : Since the presence of antiferromagnetic QCP has been established, the focus now is on the detailed critical behavior of the transport near QCP. The ðr 2 r0 Þ vs. T 2 plot is shown in the inset of Fig. 1. Below 3.2 GPa, the linear behavior corresponds to the T 2 -dependence of r; indicative of a conventional FL. Only at 3.28 and 3.45 GPa, which are right at QCP, is sublinear behavior observed. The temperature dependence here can be fitted by r ¼ r0 þ A0 T 3=2 at low temperatures, which is consistent with the prediction of SCR theory for 3D AFM. For V8 O15 ; we do not find T 3=2 behavior 2
TMI < 86 K of V8 O15 at ambient pressure is higher than those reported previously. We suspect that this difference of TMI may be due to a small number of defects and believe that this has little effect on the metallic states.
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Fig. 3. Pressure dependence of magnetic and transport parameters for V7 O13 deduced from the rðTÞ data shown in Fig. 1, the antiferromagnetic transition temperature (upper panel), the T 2 coefficient of low-temperature rðTÞ; A (middle panel), and the residual resistivity r0 (lower panel). The line on the upper panel is an eye-guide. TAF reaches 0 K at Pc < 3:4 GPa:
even at Pc : This implies that something unusual is happening at the QCP of the vanadium Magne´li phase. Indeed, contrary to our expectations, no trace of precursor to the QCP could be recognized in the AFM phase below the critical pressures Pc : As shown in the details of the inset in Fig. 1, the variation of rðTÞ is somewhat discontinuous at QCP. This can be visually demonstrated by plotting A as a function of P in the middle panels of Figs. 3 and 4. Below Pc ; A is almost constant and shows a discontinuous drop at Pc : A diverging behavior of A can be seen only for V7 O13 right at QCP, which reflects the T 3=2 dependence of r: In accord with the absence of precursor behavior in A, unusual pressure dependence of r0 was observed, as shown in the lower panels of Figs. 3 and 4. r0 is constant below Pc and suddenly shows a distinct reduction at Pc : Chemically modified 3d TM AFM systems, such as NiðS; SeÞ2 [19], show a noticeable enhancement of A over a certain range of doping near the AFM – PM phase boundary as a precursor to non-T 2 behavior. Accompanied with this enhancement of A, a distinct reduction of r0 with approaching QCP is observed in the AFM phase, and, in contrast, r0 is constant in the PM phase. It is clear that the behaviors observed in the vanadium Magne´li phase contrast those of ‘standard’ QCP behavior in 3d TM AFM. The absence of precursor behavior both in A and r0 of the AFM phase characterizes the QCP of the vanadium Magne´li phase. The constant r0 in the AFM may provide a key to understand the distinct critical behavior. In the FL picture,
Fig. 4. Pressure dependence of magnetic and transport parameters for V8 O15 deduced from the rðTÞ data shown in Fig. 2, the antiferromagnetic transition temperature (upper panel), the T 2 coefficient of low-temperature rðTÞ; A (middle panel), and the residual resistivity r0 (lower panel). The line on the upper panel is an eye-guide. The PI phase disappears above PMI < 1:3 GPa; and the AFM phase disappears above Pc < 3:3 GPa:
r21 0 is scaled only by the area of Fermi surface volume SF and the electron mean free path l0 at T ¼ 0; as r21 0 / SF l0 : l0 can be viewed as a constant under pressure because l0 is determined only by the concentration of impurities. The variation of r0 ; therefore, represents the variation of the Fermi surface volume. For chemically modified 3d TM systems, such as NiðS; SeÞ2 and V2 O3 ; the Fermi surface gradually recovers as the system approaches the PM phase, which manifests itself as a reduction of r0 in the antiferromagnetic phase. The unexpected pressure independence of r0 in the AFM of the vanadium Magne´li phase implies that SF ; which is responsible for transport, is, in fact, constant in the AFM phase and shows a discontinuous jump from AFM to PM. Then, there are two distinct Fermisurface segments; one always lacks a gap, and the other always has a gap in the AFM phase. This contrasts with the conventional wisdom that the gapped region fades out while approaching the QCP. Since A, a measure of the low-lying spin excitations near QCP, is constant in the AFM phase, the gapless Fermi surface, which dominates the transport in the AFM phase, should be almost free from the critical spin scattering. The observed T 3=2 behavior in V7 O13 may represent a negligibly small but finite coupling between the critical spin fluctuation and the gapless Fermi surface. In this two-Fermi-surface-segment picture, we may anticipate a pronounced impurity effect. Since the impurity scattering smears out the distinction between the two Fermisurface segments, the introduction of impurity scattering will result in the recovery of the standard QCP behavior.
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sample preparation. This work was partly supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science, and Technology.
References
Fig. 5. Pressure dependence of the transition temperature TAF for 3=2 3=2 V7 O13 ; plotted as TAF vs. pressure. In the vicinity of Pc ; TAF varies linearly, indicating TAF / ðPc 2 PÞ3=2 :
This may provide a reasonable account for the contrast between the chemically modified 3d TM AFM and the stoichiometric vanadium Magne´li phase. We, further, speculate that the observation of T 3=2 behavior at QCP in V7 O13 originates from a coupling of two Fermi-surface segments through the impurity scattering. In the case of chemically modified systems, the coupling is substantially large due to the averaging effect of doped impurities, and a clear precursor effect in both A and r0 is observed. In summary, we have achieved antiferromagnetic QCP by applying pressures up to 3.5 GPa in the vanadium Magne´li phase. In the vicinity of QCP, no trace of the precursor effect to the QCP was observed. This is shown to be due to the presence of two distinct Fermi-surface segments in which the impurity effect plays an important role. Furthermore, QCP could be considered in HF systems in which the exponent of the temperature-dependent r changes from 2 to 1.5 with an increase in the impurity level. In this context, we suspect that the phenomena we observed are a generic feature of QCP in real material with Fermisurface anisotropy.
Acknowledgements We thank T. Tonogai and Y. Hikita for their help in
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