CORRELATED ELECTRON OXIDES AS THE COMPLEX SYSTEM. Yoshinori Tokura

Transcription

1 CORRELATED ELECTRON OXIDES AS THE COMPLEX SYSTEM Yoshinori Tokura When electron-electron Coulomb repulsion interaction is strong in a solid, electrons are almost localized on the respective atomic sites or only barely mobile. An electron in such a solid has three attributes; charge (-e), spin (S=1/2), and orbital. An orbital, which represents the electron s probability-density distribution, may be viewed as the shape of electron cloud in a solid. The charge, spin, orbital degrees of freedom - and their coupled dynamics - can produce complex phases and phenomena such as liquidlike, crystal-like, liquid-crystal-like states of electrons, and electronic phase separation or pattern formation [1,2]. The electronic/magnetic phases of correlated-electron materials can be controlled in unconventional ways and possibly with ultrafast response-time, so that the correlated electron system may provide a seed for novel electronics. The correlation of electrons in a solid typically shows up as the interplay between magnetism and electrical conductance, and this has been a long-standing important problem in the field of condensed matter physics. Since the discovery of hightemperature superconducting (high-t c ) copper oxides in 1986, a more general interest in the Mott transition, i.e. the metal-insulator transition in a correlated electron system, has arousen peripheral fields of science [3]. The high-t c copper oxides are composed of CuO 2 sheets that are separated from each other by atomic barrier units called block layers. The CuO 2 sheet is originally insulating because of the large electron correlation, while possessing one conduction electron (or hole) per Cu site. This is a typical example of the Mott insulator in which all the conduction electrons are tied to the atomic sites and hence immobile. The high-t c superconductivity with unconventional (d-wave) symmetry emerges, when the change in the band filling (number of conduction electrons) is achieved by the change of the block-layer charge to cause the Mott transition. However, the strong antiferromagnetic correlation, originating in the Mott-insulating CuO 2 sheets, subsists in the metallic state and this has been believed to be most relevant to the mechanism of high-t c superconductivity. In the course of the renaissance of the correlated-electron science during this one and half decade, one of the fruits was the rediscovery of the so-called colossal magnetoresistance (CMR) phenomenon [4-6], which is a gigantic decrease of resistance induced by application of a magnetic field and is typically observed for perovskite manganese oxides (manganites). In the following, we will show some examples of

2 dramatic phase changes in CMR manganites which arise from a close interplay among charge, spin, orbital, and lattice degrees of freedom. Spin-Charge-Orbital Coupling Consider a transition-metal ion (M) in a crystal with perovskite sturucture. It is surrounded by six oxygen ions, O 2-, which give rise to the crystal field potential and partly lift the degeneracy of the d electron levels. Wave functions pointing towards O 2- ions (d x2-y2 and d 3z2-r2, called e g orbitals) have higher energy in comparison with those pointing between them (d xy, d yz, and d zx, called t 2g orbitals). In the Mott insulating state, all the d electrons are localized almost on the respective atoms. Thus, the combination of spin and orbital degrees of freedom produces versatile spin-orbital ordering patterns. Prototypical cases are shown in Fig.1 for perovskite type vanadium oxides (t 2g electron systems), (a) LaVO 3 and (b) YVO 3, and for perovskite type manganites (e g electron systems), (c) LaMnO 3 and (d) BiMnO 3. These orbital ordering patterns were determined by tensor components of resonant X-ray scattering and/or inferred by the local MO 6 distortion pattern. In LaVO 3, for example, the antiferromagnetic spin ordering with ferromagnetic chain along the z-direction is known to induce the orbital ordered state with alternate occupancy of d yz and d zx in every x, y, and z direction in addition to the commonly occupied d xy orbital. (In Fig.1(a), the d xy orbital on every V site is omitted for clarity.) Let us call this pattern the C-type spin-ordering and G-type orbital-ordering. In spite of the nearly cubic structure, the electronic structure is highly anisotropic due to the spin/orbital ordering. On the other hand, YVO 3 with a larger lattice distortion from the ideal cubic structure, the staggered spin order (G type) and the d yz or d zx orbital ordered state along the z-axis (C type) emerge simultaneously, as shown in Fig.1(b), as the first-order phase transformation from the high-temperature spin C type and orbital G type order. Thus, the relation between spin and orbital orders is just vise versa between the two compounds[7]. In the perovskite manganites, the orbital degeneracy is easily lifted by the coupling with local deformation of the MnO 6 octahederon (Jahn-Teller effect), such as the elongation and compression of the octahederon along the z-axis favoring the occupation of d 3z 2 -r 2 and d x 2 -y 2 orbital, respectively. Therefore, the orbital ordering coupled with the collective Jahn-Teller distortion emerges at first with decreasing temperature and then regulates the spin ordering pattern at lower temperatures. In LaMnO 3, local linear combination of d 3z 2 -r 2 and d x 2 -y 2 produces the orbital state of d 3x 2 -r 2 and d 3y 2 -r 2 which are alternating on the Mn sites in the ab (xy) plane, as shown in Fig.1(c). In this case, the

3 Jahn-Teller distortion produces the macroscopic lattice strain compressing the z-axis and expanding the xy plane. The spins couple ferromagnetically on the ab plane, while stacking antiferromagnetically along the c-axis, producing the A-type (layered type) antiferromagnetic state. A novel ferromagnet with the orbital ordering is BiMnO 3 (Fig.1(d)). This compound is one of rare examples which show the coexistence of ferroelectricity (or permanent electric polarization) and ferromagnetism. The compound is known to undergo the first-order structural transition from centrosymmetric to noncentrosymmetic around 760K, perhaps concomitantly with the orbital ordering. According to the lattice structure of the polar form[8], it is speculated that the orbitals of y 2 -z 2 and z 2 -x 2 are alternately occupied as shown in Fig.1(d). The presence of Bi lone-pair electrons as well as the orbital-ordering induced Jahn-Teller distortion is likely responsible for the emergence of ferroelectricity for this perovskite with unpaired (magnetically active) d electrons. The ferromagnetic transition occurs around 100K in the firmly orbital-ordered state. Around the Curie temperature, the magnetic field modulation of the dielectric constant is observed, indicative of the coupling between the electric polarization and the magnetization. The ferromagnetic interaction is mediated by superexchange interaction characteristic of an alternately orbital-ordered Mott insulator, like the case of the in-plane ferromagnetic interaction in LaMnO 3. When carriers are doped into Mott insulators, charge degree of freedom may further add the complexity to the electronic phase. In the simplest model, a minimal amount of doping of holes or electrons would be expected to drive the insulator to metal transition. In reality, however, a critical doping level is usually needed to destruct the long-range order in charge, spin, and/or orbital sectors. In some cases that are not rare, the compound remains electrically insulating or marginally metallic over a broad range of band filling, in which a periodic array of doped holes or electrons shows up. The phenomenon is called charge ordering. Figure 2 exemplifies several cases of such charge ordering in some quasi-two-dimensional transition-metal (M) oxides in k 2 NiF 4 - type structure (R,A) 2 MO 4 (R and A being rare-earth and alkaline-earth ions, respectively). In the isolated M-O sheet, the spin, charge, and/or orbital tend to take a form of stripe. In La 2-x Sr x NiO 4 (Fig.2(a)), for example, the hole doping x into the parent Mott insulator La 2 NiO 4 cannot cause the insulator-metal transition until x=0.9 and always result in the formation of the charge (hole) and spin stripe pattern running parallel to the diagonal direction of the NiO 4 squares ( diagonal stripe ), namely along [110] in the tetragonal lattice[8]. At x=1/3, in particular, the charge and orbital stripe state is most stabilized as shown in Fig.2(a).

4 A similar hole stripe is also known to exist in some of high-temperature superconducting copper oxides, as exemplified in Fig.2(b) for the x=1/8 hole-doped La 2 CuO 4 [10]. In this case, the quarter-filled (i.e. 50% hole-doped) stripes are running along the [100] or [010] direction ( vertical stripe ) in the half-filled CuO 2 background. The incommensurate spin order as observed in the underdoped (say, x<0.12) region in La 2 CuO 4 originates from this charge order. Reflecting the quarter-filled nature of the vertical stripe, the electrical conduction along the stripe appears to subsist, which shows up as the one-dimensional charge dynamics and Fermi-surface structure. It is still under controversy whether the metallic stripes are directly relevant to the mechanism of hightemperature superconductivity, yet the electronic object -stripe - exhibiting the liquidcrystalline like characteristics undoubtedly determines some characteristic magnetic and electronic properties in the underdoped region of copper-oxide compounds[1]. Even more complex features show up in the doped manganites as a consequence of close interplay between spin, charge, orbital, and lattice degrees of freedom, as exemplified in Figs.2(c) and 2(d) for the hole-doping levels of x=1/2 [2] and 2/3[11], respectively. In a classical picture, there should half-and-half coexist Mn 4+ (with three t 2g electrons as the local S=3/2 spin) and Mn 3+ (with the S=3/2 local spin plus one e g electron). The charge ordering shows the checker-board pattern, while the orbital on the respective Mn 3+ site shows the larger unit-cell ordering with alternate 3x 2 -r 2 and 3y 2 -r 2 like orbital occupancy. Accordingly, the ferro-orbital diagonal stripe with either 3x 2 -r 2 or 3y 2 -r 2 runs alternately along the diagonal directions. In the case of x=2/3 hole-doping (Fig.2(d)), the diagonal charge-orbital stripe shows the expanded periodicity. In actual materials, such an orbital and charge ordering emerges simultaneously at first accompanying the local Jahn-Teller distortion, and then in lowering temperature the complex antiferromagnetic (so-called CE type) spin ordering takes place as shown in Figs.2(c) and 2(d). The spin ordering pattern as depicted is the compromise of the antiferromagnetic superexchange interaction between the t 2g local spins and the ferromagnetic double-exchange interaction mediated by the e g electron hopping between the Mn 3+ and Mn 4+ sites. The orbital ordering regulates the anisotropic e g electron hopping and hence the Mn 4+ sites adjacent to the lobe of the e g orbital on the nearest Mn 3+ site is linked by the ferromagnetic interaction. As a result, the ferromagnetic zigzag chains show up in the ground state. These kinds of charge-orbital-spin ordering are ubiquitous in the highly-doped, non-metallic manganese oxides with perovskiterelated structure. The metallic counterpart of the doped manganites is the orbital quantum-disordered state with nearly isotropic ferromagnetic double-exchange interaction.

5 Unconventional control of electronic phase The spin-charge-orbital coupling produces complex and intriguing electronic phases. The energy-scale of the dominating interactions in the correlated electron system is of the order of ev, while the competition of the phases (e.g., metallic vs. insulating, or ferromagnetic vs. antiferromagnetic) is usually so subtle as described on a low-energy scale. This means that a minute perturbation as the input can cause a gigantic response accompanying the fast electronic-phase switching as the output. Most dramatic examples are seen in the cases where the two competing electronic phases form the bicritical point. Figure 3(a) shows the case of the perovskite manganite, Pr 0.55 (Ca 1- ysr y ) 0.45 MnO 3 [12], in which the charge-orbital ordered state (as shown in Fig.2(c)) and the ferromagnetic-metallic state compete with each other. Using the Ca/Sr composition as the control parameter, that affects the lattice distortion governing the d-electron hopping interaction [3], the relative stability of the two phases can be critically tuned. This can lead to the formation of the bicritical point at which the critical temperatures of the charge-orbital ordering (T CO ) and the ferromagnetic transition (T C ) coincide wit each other. Near this bicritical point, the temperature-induced phase transition either to the charge-orbital ordered state (CO/OO) or to the ferromagnetic metallic state (FM) has the nature of the first-order transition, and the high-temperature phase above T CO and T C is subject to gigantic phase fluctuation between the competing states. The colossal magnetoresistance (CMR) is also viewed as a hallmark of the bicritical point. The application of external magnetic field causes the transformation from the charge/orbital ordered insulator to the FM state, as depicted in the field dependence of the temperature(t)-dependent resistivity ( ) curves of Fig.3 (b). At low temperatures, in particular, the change of resistivity exceed ten orders of mangnitutes and this also changes the optical reflectivity spectrum of the compound on a fairly large energy scale up to 3eV (magnetochromism effect). At the side showing the FM ground state, the electronic phase immediately above T C is subject to the strong charge-orbital correlations, a sort of fragment of the charge-orbital ordered state as shown in Fig.2(c). The external magnetic field can suppress the critical grow of such a charge-orbital correlation near above T C and urges the first-order phase conversion to the long-range FM state toward higher temperature, as shown in the field-dependent -T curves of Fig.3(c). In such a bicritical region, the presence of the random potential causes dramatic - and sometimes profound- effects on the modification of the electronic phase diagram as

6 well as on the related electronic properties. The random potential in the actual transition-metal (M) oxide systems is produced by quenched disorder such as local lattice distortion and random Coulomb potential due to the solid solution of R 3+ and A 2+, doped impurity atoms on the perovskite M-sites, and the grain boundaries of polycrystalline ceramics specimen. One of the important features induced by quenched disorder is the phase separation on various length-scales ranging from nm to m[6]. In the present bicritical region of the manganite, the phase coexistence of the CO/OO and FM is discerned, for example, in the polycrystalline ceramics and intentionally Cr-doped manganites. The volume fraction ratio can be changed to a large extent with increasing the magnetic field, which causes the percolation type insulator-metal transition. This filed-induced percolation transition in the CO/OO-FM coexisting state is one of the promising scenarios that may explain the CMR phenomena ubiquitously observed in the bicritical region. On the other hand, the random potential sometimes enhances the competition between the two phases and resultantly suppresses the respective long-range order. The moderate randomness arising from the solid solution of the R and A ions with relatively large difference in the ionic radius is that example. In such a compound, the charge-orbital ordering correlation is kept increasing down to T C, as low as 50K, without any trace of its long-range order or phase segregation and then suddenly extinguished to produce the FM state. The external magnetic field is observed to critically suppress the charge-orbital correlation, giving rise to the CMR phenomenon. Thus, the existence of quenched disorder is prerequisite for the emergence of CMR in terms of the magnetic-field tuning of the charge-orbital correlation and/or the CO/OO phase volume. In the CO/OO phase near the bicritical point, the insulator-metal transition can be caused not only by application of external magnetic field but also by other many external stimuli, such as photo-excitation, X-ray irradiation, current injection, electronbeam irradiation, and impurity-atom (e.g. Cr) doping. This may provide a unique opportunity of controlling the electronic phase in an exotic way and on an ultrafast time-scale. Figure 4 exemplifies the transformation from the CO/OO to the FM in Pr 1-x Ca x MnO 3 (x=0.3) by applying (a) magnetic field [5], (b) electric field (current injection)[13], and (c) pulsed light excitation (plus subsequent current injection)[14]. By other stimuli than magnetic field, the induced insulator-metal transition appears to remain local in the whole sample volume, yet the change of resistance (conductance) is huge. This feature is also quite promising for possible application. It has recently been reported that Pr 1-x Ca x MnO 3 (x=0.3) thin film, that shows pulse-voltage driven resistance change, can be used as the basic element for the Resistance Random Access Memory

7 (R-RAM)[15]. The room-temperature operation and the reversibility between the highand low-resistance states are a key for future application to electronic devices. Spintronics and orbitronics Use of both spin and charge degrees of freedom is an essential feature for the emerging spin-electronics or spintronics. Its straightforward application is the control of the electrical current by an external magnetic field. In fact, the invention of the giantmagnetoresistive magnetic mutlilayer (composed of transition metals) was the important fast step to the spintronics and its industrial application. In this context, an important application is the tunneling mangetoresistance (TMR), that is a magnetic field modulation of the tunneling resistance between the two ferromagnetic electrodes intervened by a thin tunneling barrier. The spin polarization of conduction electron should be as large as possible to maximize the TMR magnitude. A half metal, that means the perfect spin-polarization of +100% (or 100%) at the ground state, is therefore of great interest for a general spintronic use. Many of the ferromagnetic metallic transition-metal oxides with strong electron correlation are expected to show such a half-metallic ground state because of potentially strong spin-charge coupling. Hole-doped manganites with perovskite structure, La 1- xsr x MnO 3 (0.2<x<0.5), is a typical example of the half-metal mediated by the strong Hund s-rule coupling between e g electron spin and t 2g local spins. However, TMR characteristics for the junction with use of La 1-x Sr x MnO 3 have been noticed to show unexpected degradation with increasing temperature, say up to 200K, in spite of higher Curie temperature ( K) [5]. It is now speculated that this seemingly rapid fadeout effect of the spin polarization is due to the modification of the interface magnetism of La 1-x Sr x MnO 3 (0.2<x<0.5), facing with the insulating barrier. However, efforts to control the interface electronic states of the correlated-electron perovskites are now being made extensively and in the near future will bring about new progresses in this field of science. More robust and higher-t c half-metals have been sought for in the family of perovskites suitable for the fabrication of the TMR junction device. A fruit of such researches is the finding of ordered double pervskite family with half-metallic characteristics, as represented as Sr 2 B 1 B 2 O 6 (B 1 =Fe or Cr, B 2 =Mo or Re)[16]. In this class of compounds, the perovskite B (transition-metal) sites are alternately occupied by B 1 and B 2 in a rock-salt pattern. The valence of Fe (or Cr) is 3+, corresponding the fully spin-up state of S=5/2 (3/2). The Mo 5+ (4d 2 ) or Re 5+ (5d 2 ) provides the conduction

8 electrons which hybridizes partly with the down-spin state of Fe or Cr and strongly couples antiferromagnetically with the local spins (up-spin states) on Fe or Cr. Thus, the states near the Fermi level are composed of only the down-spin electrons, forming the half-metallic ground state. The advantage of this compound is free from the phase competition, apart from the Mott-insulating ferromagnetic state, and the ferromagnetic transition temperature is very high, say 420K for Sr 2 FeMoO 6 and as high as 615K for Sr 2 CrReO 6. This implies high potential of this class of perovskites as the future spintronic materials. In analogy to the spintronics, we may consider the possibility of controlling electric current in terms of the d-electron orbital state[2]. Here let us call this possible correlated-electron technology orbital-electronics or orbitronics. In a broad context, the CMR phenomenon itself is the field-modification of the orbital correlation and hence may be one such example. As shown in Fig.5(a), in the double-exchange interaction with the strong Hund s-rule coupling, the electron hopping interaction (transfer energy) is determined by the angle of the local spin moments on the adjacent sites. This scheme provides the controllability of the electrical conduction in terms of mangetic field. By analogy, we can utilize the orbital degree of freedom to regulate the electrical conduction, as shown in Fig.5(b). For example, when the orbital ordering composed of x 2 -y 2 orbital is realized in the nearly-cubic perovskite lattice, the charge dynamic is highly anisotropic, namely confined within xy plane and insulating along the z direction, as can be noticed from the transfer energy values listed in Fig.5(b). In reality, such a ferroic orbital ordering is present ubiquitously in overdoped manganites and the highly two-dimensional charge motion is observed in spite of its nearly cubic lattice structure. The key idea of orbitronics is the ultrafast switching of the orbital state and hence of the related spin/charge state in terms of electric field and/or light irradiation. Since the orbital shape, rod or planar, represents the electron s probability-density distribution, the orbital degree of freedom can inherently couple with the electric field. In this context, the orbital manipulation may bear the analogy to the liquid-crystal technology, in which rod- or planar-shaped molecules can respond to the electric field via the anisotropic polarizability. To describe the dynamical response of the orbital to the external field, we need to define the orbital wave or orbiton in the orbital-ordered state (Fig.5(b)). This bears the analogy to the spin wave or magnon in the magnetically ordered state (Fig.5(a)). It has recently been reported [17] that such an orbiton mode (at k=0) is detected for LaMnO 3 (see Fig.1(c)) by Raman spectroscopy. An advantage of use of the orbital degree of freedom in ultrafast control of the electronic and magnetic state is

9 that the orbiton frequency is high enough, perhaps THz, as compared with the typical spin precession frequency (i.e. k=0 magnon energy in a ferromagnet) of GHz. As an example of the photo-modulation of the orbital state, we show in Fig.6 the time-resolved snap-shots for the photo-excited crystal surface of La 0.5 Sr 1.5 MnO 4 [18] which shows the orbital-charge ordered state below T OO =220K. Due to the orbital ordering as shown in Fig.6(a), the originally tetragonal compound shows the optical anisotropy in the ab plane. In the cross-nichol configuration of light polarization we can visualize the orbital-ordered domain. The orbital-disordered state above T OO is optically isotropic in the plane, giving the extinction of cross-polarized reflection lights, while we observe the globally bright image for the orbital ordered state below T OO where the orthorhombic domain and the domain walls (dark stripes) are clearly visible (Fig. 6(a)). (A periodic structure of the domains arises perhaps form the slight residual strain introduced during the crystal growth.) When a pulsed laser light, say 1.5eV with the duration of 100fs, is irradiated on this surface, the optical gap transition locally and then collectively destroys the orbital order within 200fs. The photo-melting of the orbital state is visualized as the darkened region due to the optically-recovered isotropy, as shown in the 100ps image shown in Fig.6(c). The photo-melted orbital state is then stabilized by the subsequent deformation of the lattice, subsists for 10ns, and then disappears via thermal diffusion to recover the fully orbital-ordered state. The correlated-electron science is thus exploiting a broad range of materials and electronic properties in addition to the high-t c and CMR related ones. The recent advance of the epitaxy-growth technologies in the transition-metal oxide this films and superlattices has begun to produce correlated-electron junctions and superlattices with controlled interface electronic-characteristics. The complex correlated-electron phases in such tailor-made correlated-electron materials may provide the most fascinating and challenging arena not only to test many theoretical ideas, but also to seek for the seed of future new electronics. The author would like to thank N. Nagaosa, E. Dagotto, P.B. Littlewood, K. Miyano, T. Kimura, and Y. Okimoto for enlightening discussion and help in preparing the article.

10 References [1] S.A. Kivelson, E. Fradkin, V.J. Emery, Nature, 393, 550 (1998). [2] Y. Tokura and N. Nagaosa, Sicence, 288, 389 (2000). [3]M. Imda, A. Fujimori, and Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998). [4] A.J. Millis, Nature, 392, 147 (1998). [5] Colossal Magnetoresistive Oxides, edited by Y. Tokura (Gordon&Breach Science Publishers, London, 2000) and references therein. [6] E.Dagotto Nanoscale Phase Separation and Colossal Magnetoresistance (Springer-Verlag, Berlin, 2002) ) and references therein. [7] H. Sawad, N. Hamada, K. Terakura K, T. Asada, Phys.Rev. B 53, (1996). [8] T. Atou, H. Chiba, K. Ohoyama, Y. Yamaguchi, and Y. Syono, J.Solid State Chem. 145, 639 (1999). [9] C.H. Chen, S-W. Cheong, A.S. Cooper, Phys. Rev. Lett. 71, 2461 (1993). [10] J.M. Tranquada, B.J. Sternliev, J.D. Axe, Y. Nakamura, and S. Uchida, Nature, 375, 561 (1995). [11].Kimura et al., Phys. Rev. B 65, (2002). [12] Y.Tomioka and Y.Tokura, Phys.Rev.B, 66, (2002) [13] A. Asamitsu, Y. Tomioka, H. Kuwahara, and Y.Tokura, Nature, 388, 50 (1997). [14] K. Miyano K, T. Tanaka, Y. Tomioka, Y. Tokura, Phys. Rev. Lett. 78, 4257 (1997); M.Fiebig, K. Miyano, Y. TOmioka, and Y. Tokura, Sience, 280, 1925 (1998). [15] S.Q. Liu, N.J. Wu, A. Ignatiev, Appl. Phys. Lett. 76, 2749 (2000). [16] K-I.Kobayashi et al., Nature, 395, 677 (1998). [17] E. Saitoh et al., Nature, 410, 180 (2001). [18] T.Ogasawara, T.Kimura,T.Ishikawa, M.Kuwata-Gonokami, and Y.Tokura, Phys.Rev.B, 63, (2001).

11 Figure captions Fig.1: orbital-spin ordering patterns in perovskite-type (a) LaVO 3, (b) YVO 3, (c) LaMnO 3, and (d) BiMnO 3. Fig.2: charge and orbital stripes on the hole-doped two-dimensional metal(m)-oxygen sheets of layered perovskite structure (R,A) 2 MO 4 : (1)La 2-x Sr x NiO 4 (x=1/3), (b) La 2- xba x CuO 4 (x=1/8), (c) La 1-x Sr 1+x MnO 4 (x=1/2), and (d) Nd 1-x Sr 1+x MnO 4 (x=2/3). Fig.3: Phase competition between the charge-orbital ordered insulator (COOI) and the ferromagnetic metal (FM) in Pr 0.55 (Ca 1-y Sr y ) 0.45 MnO 3 with controlled bandwidth (electron transfer energy). (a) The bicritical feature of the competing two phases in the electronic phase diagram as a function of y. The magnetic filed effect on the resistivity is shown for the two compounds, (b) y=0.20 and (c) y=0.25, locating respectively on the both sides of the bicritical point. Fig.4: The insulator-metal phase control in Pr 0.7 Ca 0.3 MnO 3 : (a) resistivity change by application of external magnetic field, (b) resistance change by applying the voltage on the circuit connecting the sample with the electrode distance of 1mm and the load resistance (R L = 1M ) in series, and (c) resistance change upon the 5-ns pulse laser irradiation on the sample with the electrode distance of 0.2mm and the applied voltage of 10V. Inset to (c) shows the region of the current path (a white streak between the gold electrodes with the separation of 0.2mm), reflecting the change of reflectance of the crystal surface due to the local insulator-metal transition. Fig.5: The intersite hopping interaction regulated by (a) the spin configuration in the case of the double-exchange interaction, and (b) the orbital configuration in the case of e g (x 2 -y 2 and 3z 2 -r 2 ) orbital. The left panel shows the schematics for (a) the spin wave or magnon and (b) the orbital wave or orbiton. Fig.6: (a) Charge-orbital ordering pattern on the MnO 2 sheet in La 0.5 Sr 1.5 MnO 4 (x=0.5). (b) Polarization microscope images with cross polarizations parallel to a and b axes for a La 0.5 Sr 1.5 MnO 4 crystal. The left bright image is for the charge/orbital ordered state at 77 K. The orbital disordered state at 298K shows the isotropic optical response and hence merely gives the dark image. (c) Time-resolved microscope pictures after the 100-fs laser pulse excitation with photon energy of 1.5eV. The darkened part indicates

12 the photo-melting of the orbital order.