You are an expert at summarizing long articles. Proceed to summarize the following text: 
the doped rare earth manganites @xmath4mno@xmath2 ( @xmath5 is a rare earth such as la and @xmath6 is a divalent element such as sr or ca ) due to their peculiar correlation between magnetism and conductivity have been extensively studied during 1950s and 60s @xcite . the most throughly investigated was the la@xmath0sr@xmath1mno@xmath2 system . undoped ( @xmath7=0 ) , lamno@xmath2 is an antiferromagnetic insulator . upon doping with sr , this perovskite oxide becomes a ferromagnetic metal ; the connection between metallicity and ferromagnetism was well explained by the double exchange hopping mechanism @xcite . the discovery of colossal magnetoresistance phenomena in samples with sr dopant densities in the 0.2@xmath80.4 regime @xcite brought a revival of the interest to these sytems . the mn@xmath9 ion in the hole - undoped compound lamno@xmath2 has the high - spin @xmath10 electron configuration @xmath11 . the @xmath12 orbitals hybridize with o2p orbitals much more weakly than the @xmath13 orbitals and can be regarded as forming the localized spin ( @xmath14=3/2 ) . in contrast to that , @xmath13 orbitals , which have lobes directed to the neighboring oxygen atoms , hybridize strongly with o2p producing in the result rather broad bands . the strong exchange interaction with @xmath15 subshell leads to the splitting of the @xmath13 band into unoccupied @xmath16 and half - occupied @xmath17 subbands . the half filled @xmath17 subband is a typical example of the jahn - teller system , and , indeed , lamno@xmath2 has an orthorombic crystal structure @xcite with distorted ( elongated ) mno@xmath18 octahedra . this cooperative jahn - teller effect is usually considered responsible for the opening of the gap in the half - filled @xmath17 band and an insulator ground state of lamno@xmath2 . the orthorombic crystal structure of lamno@xmath2 ( @xmath19 space group ) can be described as a perovskite with two types of distortion from a cubic structure : 1)tilting ( rotation ) of the mno@xmath18 octahedra , so that mn - o - mn angles become less than 180@xmath20 , and 2)jahn - teller distortion of the octahedra , with one long mn - o bond and two short bonds . with doping by sr the orhtorombicity ( the deviation of the values of the lattice parameters @xmath21 and @xmath22 from @xmath23 ) becomes smaller and for @xmath24 the stable crystal structure at room temperature becomes rombohedral , where only tilting of oxygen octahedra is present but all three mn - o bonds are equal . around the same value of the doping @xmath7 , la@xmath0sr@xmath1mno@xmath2 becomes metallic .    for sr doping with 0.2@xmath80.4 , la@xmath0sr@xmath1mno@xmath2 is a ferromagnetic metal at low temperatures . however , as the temperature increases and approaches the curie temperature @xmath25 a sudden increase of the resistivity is observed @xcite . as the temperature dependence of the resistivity @xmath26 has typically semiconducting behavior ( @xmath27 ) above t@xmath28 , this increase in resistivity at around @xmath25 is usually desribed as a metal - insulator transition . the colossal magnetoresistance effect happens when the temperature is close to @xmath25 : the external magnetic field leads to suppression of the resistivity increase or to shifting the metal - insulator transition to higher temperatures resulting in a very large negative value of @xmath29/\rho(0)$ ] . the crucial point in the understanding of the effect of the colossal magnetoresistance is the nature of the metal - insulator transition with the temperature variation across @xmath25 . it was shown @xcite that the double exchange mechanism alone is not enough to explain such transition . _ @xcite suggested local jahn - teller distortions ( jahn - teller polarons ) as a main mechanism causing localization . their idea is that a @xmath30 ratio ( @xmath31 is self - trapping jahn - teller polaron energy and @xmath32 is effective band width ) is close to the critical value in la@xmath0sr@xmath1mno@xmath2 and as @xmath32 decreases with destroying the ferromagnetic order above @xmath25 ( the effective hopping takes the maximum value for a parallel spin alignment ) , this ratio becomes larger than the critical value to result in polaron localization . varma @xcite argues that lamno@xmath2 is not an insulator due to the jahn - teller distortion but is a mott insulator and the jahn - teller distortion occurs parasitically . he explains localisation of the holes in the paramagnetic phase by spin polaron mechanism .    by replacing la with other trivalent ions with smaller ionic radius , the mn - o - mn bond angle becomes smaller and the @xmath13 band width @xmath32 is reduced to enhance the tendency to the carrier localization and lattice distortion . variety of dramatic phenomena have been observed in ( pr , nd , sm)(sr , ca)mno@xmath2 systems . as one of such examples , we study pr@xmath3ca@xmath3mno@xmath2 in the present paper . this system has a very peculiar phase diagram @xcite . at low temperature , it is an antiferromagenetic insulator with a charge ordering of mn@xmath33 and mn@xmath34 accompanied by an orbital ordering : the orbital ordering and spin ordering is of ce - type . between @xmath35 ( @xmath36 k ) and @xmath37 ( @xmath38 k ) , there is no long - range magnetic ordering but the system remains to be insulating because of the persisitence of the charge ordering . above @xmath39 , it is a paramagnetic insulator .    the local spin density approximation ( lsda)@xcite was used by several groups for theoretical investigation of the electronic structure of la@xmath0sr@xmath1mno@xmath2 @xcite . those calculations have confirmed the importance of the jahn - teller distortion for correct description by the lsda of the insulating antiferromagnetic ground state of the undoped lamno@xmath2 , because the calculations with an undistorted cubic perovskite crystal structure produce a half - filled metallic @xmath17 band . however in order to address the charge and orbital order observed in doped manganites it is necessary to go beyond lsda by including the intra d - shell coulomb interaction ( lsda+u method @xcite ) . recently such an approach was used for treating the charge ordering in magnetite fe@xmath2o@xmath40 , where lsda gives a metallic uniform solution . the lsda+u calculation gave a charge ordered insulator as the ground state of this compound @xcite . in this paper we describe the results of the electronic structure calculation for pr@xmath0ca@xmath1mno@xmath2 for @xmath41 and 0.5 in the lsda+u approximation . the problem of the charge ordering can not be treated properly by the standard lsda because of the non - vanishing self - interaction . in contrast to the hartree - fock approximation , where the self - interaction is explicitly excluded for every orbital , in the lsda it is canceled to a good approximation in the total energy , but rather poorly in the local one - electron potentials , which are orbital - independent . the spurious self - interaction present in the lsda leads to an increase in the coulomb interaction when the distribution of the electron charge deviates from the uniform one . this effect can be illustrated in the following way . if we consider the system having less than one electron per site in the partially filled electronic subshell ( for example @xmath13-electrons in la@xmath0sr@xmath1mno@xmath2 ) then the potential which this electron feels at some site must not depend on the orbital occupancy of this particular site , as the electron does not interact with itself . however , as the lsda potential is a functional of the electron density only , increasing the electron density at one site and decreasing it at another one , with a formation of the charge ordering , will lead to an increase of the potential at the first site and a decrease at the second one . as a result , in the self - consistency loops , the charge distribution will return to the uniform density . in order to cure this deficiency , it is necessary to remove the self - interaction . the lsda+u method @xcite is one of the practical methods to solve the self - interaction problem . let us introduce the d - orbitals occupation matrix defined by :    @xmath42    where @xmath43 are the elements of the green function matrix ( @xmath44 : index of atom site , @xmath45 : main and orbital quantum numbers ( for example 3@xmath46 ) , @xmath47 : index of a particular @xmath46-orbital and @xmath48 : spin projection index ) . in terms of the elements of this occupation matrix @xmath49 , the lsda+u functional @xcite is defined as follows :    @xmath50=e^{lsda}[\rho ^\sigma ( { \bf r)}]+e^u[\{n^\sigma \}]-e_{dc}[\{n^\sigma \}]\ ] ]    where @xmath51 is the charge density for spin-@xmath52 electrons and @xmath53 $ ] is the standard lsda ( local spin - density approximation ) functional . @xmath54 $ ] is the hartree - fock type electron - electron interaction energy given by @xmath55=\frac 12\sum_{\{m\},\sigma } \{\langle m , m^{\prime \prime } \mid v_{ee}\mid m^{\prime } , m^{\prime \prime \prime } \rangle n_{mm^{\prime } } ^\sigma n_{m^{\prime \prime } m^{\prime \prime \prime } } ^{-\sigma } \\ \\ -(\langle m , m^{\prime \prime } \mid v_{ee}\mid m^{\prime } , m^{\prime \prime \prime } \rangle -\langle m , m^{\prime \prime } \mid v_{ee}\mid m^{\prime \prime \prime } , m^{\prime } \rangle ) n_{mm^{\prime } } ^\sigma n_{m^{\prime \prime } m^{\prime \prime \prime } } ^\sigma \ } , \end{array}\ ] ] where @xmath56 is the screened coulomb interaction among the @xmath45 electrons . finally , the last term in eq.([u1 ] ) corrects for double counting and is given by    @xmath57=\frac 12un(n-1)-\frac 12j[n^{\uparrow } ( n^{\uparrow } -1)+n^{\downarrow } ( n^{\downarrow } -1)],\ ] ]    were @xmath58 and @xmath59 @xmath60 and @xmath61 are screened coulomb and exchange parameters @xcite . in addition to the usual lsda potential , the variation of the functional ( [ u1 ] ) gives an effective single - particle potential to be used in the single - particle hamiltonian :    @xmath62    @xmath63    the matrix elements of the screened coulomb interaction @xmath56 can be expressed in terms of complex spherical harmonics and effective slater integrals @xmath64@xcite as @xmath65 where @xmath66 and    @xmath67    for d - electrons one needs @xmath68 and @xmath69 and these can be linked to the coulomb- and stoner parameters @xmath60 and @xmath61 obtained by the lsda - supercell procedures @xcite via @xmath70 and @xmath71 with the ratio @xmath72 being to a good accuracy a constant @xmath73 for the 3d elements @xcite . the lsda+u approximation was realized in the framework of the linear muffin - tin orbital method in the atomic sphere approximation ( lmto - asa)@xcite . the values of @xmath60=7.9 ev and @xmath61=0.9 ev were used as obtained from the constrained lsda supercell calculations . as a first step the electronic structure of the undoped prmno@xmath2 was calculated . this compound has practically the same properties as lamno@xmath2 . the only difference is that due to the smaller ionic radius of pr ion compared with that of la ion , the tilting of the oxygen octahedra in orthorombic @xmath19 crystal structure is stronger , resulting in smaller effective @xmath74 hopping between mn atoms and narrower band width .    the crystal structure of the doped pr@xmath0ca@xmath1mno@xmath2 does not show transition to the rombohedral symmetry , as it is the case for la@xmath0sr@xmath1mno@xmath2 , preserving the orthorombic @xmath19 space group@xcite . however the values of the lattice parameters @xmath23,@xmath21 and @xmath22 for @xmath7=0.5 are so close that it can be called a pseudocubic structure . in this structure only the tilting of the oxygen octahedra is present , but octahedra themselves are not jahn - teller distorted as in the undoped crystal structure . in order to study effects of the orbital polarization purely due to the intrashell d - d coulomb interaction without any influence of the jahn - teller lattice distortion the calculation for the undoped prmno@xmath2 was performed with the crystal structure parameters corresponding to pr@xmath3ca@xmath3mno@xmath2 . kugel and khomskii @xcite demonstrated for a wide range of jahn - teller magnetic compounds that the exchange mechanism ( caused by an interplay between on - site coulomb interaction @xmath60 and intersite hopping @xmath75 ) by itself , without taking janh - teller distortions into consideration , is able to give a correct picture of the spin and orbital ordering . in this case the change in the lattice structure ( the structural transition ) is a secondary effect . one may say that the system shows the `` jahn - teller ordering '' without the `` jahn - teller interaction '' . actually an exchange mechanism acts jointly with the jahn - teller and the quadrupole mechanisms . it is quite difficult to determine just which mechanism will be predominant in each specific case due to complexity of the real compound . one of the possible ways to answer this question in the frame of _ ab - initio _ band structure calculations is to use a crystal structure excluding distortions caused by the jahn - teller interaction . such kind of approach was used for the cooperative jahn - teller system kcuf@xmath2 @xcite . it also has the perovskite crystal structure , but there is no tilting of the cuf@xmath18 octahedra and all cu - f - cu angles are equal to 180@xmath20 . divalent copper ion in this compound has a @xmath76 configuration ( @xmath77 ) known to be a jahn - teller ion , and , indeed , the jahn - teller distortion is observed in the form of the elongated cuf@xmath18 octahedra with long axes alternatively along @xmath23 and @xmath21 axes in the @xmath78-plane . kugel and khomskii @xcite showed that a simple hubbard model type calculation in a mean - field approximation without taking into account the electron - phonon interaction could predict the orbital ordering ( alternating @xmath79 and @xmath80 cu3d - orbitals for electrons or @xmath81 and @xmath82 orbitals for holes ) corresponding to the symmetry of the experimentally observed lattice distortions . the lsda+u functional ( eq.[u1 ] ) has a definite important improvement upon the lsda : explicit cancellation of the self - interaction and the proper description of the lowering of coulomb interaction energy with development of the orbital polarization . the functional ( eq.[u1 ] ) is also rotationally invariant ( the total energy does not change with the unitary transformation of the d - orbital basis set @xmath83 ) , meaning that if the local coordinate system ( and , correspodingly d - orbital basis set @xmath83 ) was chosen inappropriately for describing the resulting orbital polarisation , the unitary transformation which diagonalizes the non - diagonal occupation matrix @xmath84 ( eq.[occ ] ) will give a proper orbital basis set .    the lsda+u calculation for kcuf@xmath2 @xcite in _ cubic _ perovskite crystal structure gave results fully confirming kugel - khomskii s prediction - alternating @xmath79 and @xmath80 orbital order . moreover , it was not just the lowest total energy configuration among many possible stationary configurations as in the model calculation @xcite , but the _ only one stable solution_. the lattice relaxation to minimize the total energy is in good agreement with experimental data . note that the standard lsda did not show the lattice instability with respect to the jahn - teller distortion in kcuf@xmath2 . we would like to emphasize that the orbital polarization caused by the d - d coulomb interactions practically did not change with the lattice distortion @xcite . the use of the crystal structure parameters corresponding to pr@xmath3ca@xmath3mno@xmath2 ( with undistorted oxygen octahedra ) for prmno@xmath2 may correspond to the use of the cubic perovskite crystal structure for kcuf@xmath2 . however , for prmno@xmath2 , we have to take into account the tilting of mno@xmath18 octahedra ( present in pr@xmath3ca@xmath3mno@xmath2 structure ) , which is essential for the proper description of the reduction in the effective @xmath74 hopping due to the bending of the mn - o - mn bond . the lsda+u calculation with the experimental a - type antiferromagnetic spin alignment resulted in a non - diagonal occupation matrix for spin density ( for the @xmath85 subspace ( @xmath86 and @xmath87 orbitals ) of one particular mn atom ) : @xmath88 the diagonalization of this matrix gives two new @xmath17 orbitals : @xmath89 with occupancy 0.71 and @xmath90 with occupancy 0.18 . for the second type of mn atom @xmath91 and @xmath92 orbitals can be obtained by transposition of @xmath7 and @xmath93 . the resulting orbital order can be presented graphically by plotting the angle distribution of the @xmath13-electron spin density : @xmath94 as a mn@xmath9 ion has formally only one electron in partially filled @xmath17 subshell , the @xmath13-spin density must correspond to the density of this electron ( fig.1 ) . the plot of fig.1 and the form of the @xmath91 and @xmath92 orbitals diagonalizing the spin density occupation matrix show that the orbital order obtained in our lsda+u calculations for prmno@xmath2 is of the same symmetry as the one in kcuf@xmath2 . the `` parasitical '' lattice distortion , which one could expect from such orbital ordering : elongation of mno@xmath18 octahedra in the direction of the lobes of @xmath91 orbitals , will reproduce the experimentally observed jahn - teller lattice distortion . the orbital polarization is far from being 100% , the difference in the occupancy of @xmath91 and @xmath92 orbitals is only 0.53 . the reason for this is the strong hybridization of @xmath17-orbitals with oxygen 2p - orbitals . in fig.2 , the total and partial densities of states ( dos ) for prmno@xmath2 are shown ( for @xmath13-electrons dos projected on @xmath91 and @xmath92 orbitals are also presented ) . the electronic structure obtained in our lsda+u calculation is semiconducting with a band gap of 0.5 ev . note that the standard lsda needs the jahn - teller distorted crystal structure to reproduce the non - metallic ground state . the @xmath17-band is split by this gap into two subbands : the occupied one with the predominantly @xmath91 character , and the empty one with the @xmath92 character . however there is significant admixture of @xmath92 in the occupied subband and @xmath91 in the empty one .    after checking that our calculation scheme gives a proper orbital order in the undoped prmno@xmath2 , we applyed it to pr@xmath3ca@xmath3mno@xmath2 . in order to treat the experimentally observed ce - type of antiferromagnetism it was necessary to quadruple the @xmath19-type unit cell and the supercell had 16 formula units . the distribution of the pr and ca atoms in the lattice was chosen according to a model where all pr ions have only ca as their nearst neighbores in the lanthanide sublattice . we did not impose any symmetry restrictions in our calculation , the integration in the reciprocal space being performed for the whole brillouin zone , and the self - consistency iteration was started from a uniform distribution of @xmath13-electrons over both @xmath13-orbitals of all mn atoms . the result of the self - consistent calculation was a charge and orbital ordered insulator . the @xmath13-electron spin - density - plot calculated by eq.[f1 ] is presented in fig.3 . this is in a striking agreement with the orbital order derived in @xcite from the neutron diffraction mesuarements ( fig.4 ) . the unexpected result is that the total number of d - electrons at all types of mn sites are nearly equal ( 4.99 and 5.01 ) , so that formally mn@xmath34 ions ( in the fig.3 the ones with symmetric in - plane density distribution ) and mn@xmath33 ions ( the ones with the density strongly anisotropic ) have nearly the same number of 3d - electrons . however the difference in the magnetic moment values is more pronounced : 3.34@xmath95 for mn@xmath34 and 3.44 @xmath95 for mn@xmath33 . the results of our lsda+u calculations for pr@xmath0ca@xmath1mno@xmath2 demonstrate that taking into account the coulomb interaction inside the d - shell of mn together with the intersite hopping is enough to reproduce not only the orbital order present in the undoped manganites , but also the localization and ordering of the holes in the doped materials . naturally the lattice relaxation ( jahn - teller and polaron lattice distortions ) will significantly renormalize the total energies , gap values , charge disproportion and magnetic moments . however it seems that the symmetry of the ordered state can be obtained without explicitly including the electron - lattice interactions . this is in clear contrast to the standard lsda where energy band splitting and orbital polarization appear only as results of the jahn - teller crystal structure distortion . v.i.a . and m.a.k . acknowledge the nair guest research program . the present work is supported partly by russian foundation for basic research ( rfbr grant 96 - 02 - 16167 ) , new energy and industrial development organization in japan and also by a grant - in - aid for scientific research in the priority area `` anomalous metallic states near the mott transition '' from the ministry of education , science and culture of japan . 99 g. h. jonker and j. h. van santen , physica ( amsterdam ) * 16 * , 337 ( 1950 ) ; j. h. van santen and g. h. jonker , physica ( amsterdam ) * 16 * , 599 ( 1950 ) . c. zener , phys . rev . * 82*,403 ( 1951 ) ; p. w. anderson and h. hasegava , phys . rev . * 100 * , 675 ( 1955 ) ; p. g. de gennes , phys . rev . * 118 * , 141 ( 1960 ) . r. m. kusters , j. singleton , d. a. keen , r. mcgreevy and w. hayes , physica ( amsterdam ) * 155b * , 362 ( 1989 ) ; a. urushibara , y. moritomo , t. arima , a. asamitsu , g. kido and y. tokura , phys . rev.b * 51*,14103 ( 1995 ) . j. b. a. a. elemans , b. van laar , k .r . van der veen and b. o. loopstra , j. solid state chem . * 3 * , 238 ( 1971 ) . a. j. millis , p. b. littlewood and b. shraiman , phys . . lett . * 74 * , 5144 ( 1995 ) . a. j. millis , b. shraiman and r. mueller , phys . lett . * 77 * , 175 ( 1996 ) . c. m. varma , preprint . z. jirak , s. krupicka , v. nekvasil , e. pollert , g. villeneuve and f. zounova , j. magn . magn . mater . * 15 - 18 * , 519 ( 1980 ) ; z. jirak , s. krupicka , z. simsa , m. dlouha and z. vratislav , @xmath96 * 53 * , 153 ( 1985 ) . y. tomioka , a. asamitsu , h. kuwahara , y. moritomo and y. tokura , phys . rev . b*53 * , r1689 ( 1996 ) . p. hohenberg and w. kohn , phys . rev . * 136 * , b864 ( 1964 ) ; w. kohn and l. j. sham , _ ibid . _ * 140 * , a1133 ( 1965 ) . n. hamada , h. sawada and k. terakura , in _ spectroscopy of mott insulators and correlated metals _ , edited by a. fujimori and y. tokura ( springer - verlag , berlin , 1995 ) , pp.95 - 105 . w. pickett and d. singh , phys . rev.b * 53 * , 1146 ( 1996 ) . s. satpathy , z. popovic and ph . vukajlovic , phys . 76 * , 960 ( 1996 ) . v. i. anisimov , j. zaanen and o. k. andersen , phys . b * 44 * , 943 ( 1991 ) . v. i. anisimov , i. v. solovyev , m. a. korotin , m. t. czyzyk and g. a. sawatzky , phys.rev . b * 48 * , 16929 ( 1993 ) . a. i. lichtenstein , j. zaanen and v. i. anisimov , phys . rev.b*52 * , r5467 , ( 1995 ) . v. i. anisimov , i. s. elfimov , n. hamada and k. terakura , phys.rev.b * 54 * , 3847 ( 1996 ) o. gunnarsson , o. k. andersen , o. jepsen and j.zaanen , phys . rev . b*39 * , 1708 ( 1989 ) . v. i. anisimov and o. gunnarson , phys . b * 43 * , 7570 ( 1991 ) . b. r. judd , operator techniques in atomic spectroscopy , mcgrow - hill , new york,1963 . f. m. f. de groot , j. c. fuggle , b. t. thole and g. a. sawatzky , phys . b * 42 * , 5459 ( 1990 ) . o. k. andersen , phys . b * 12 * , 3060 ( 1975 ) . k. i. kugel and d. i. khomskii , usp . fiz . nauk . * 136 * , 621(1982 ) [ sov . phys . -usp . * 25 * , 231(1982 ) ] . the lsda works much better in lamno@xmath2 and perhaps also in prmno@xmath2 than in kcuf@xmath2 . in the latter case , the lsda does not give even a stable antiferromagnetic state . however , in lamno@xmath2 and prmno@xmath2 , the antiferromagnetic state can be obtained by lsda . our recent calculation ( h. sawada , et al . ) for lamno@xmath2 reproduces about 50% of the experimental jahn - teller distortion by the theoretical structural optimization for experimental lattice parameters . 2 . the total and partial densities of states ( dos ) from the result of lsda+u calculation of prmno@xmath2 . a)total dos per unit cell ( 4 formula units ) ; b)partial @xmath13 dos of mn . solid lines are for the @xmath91-projected dos , and dashed lines for the @xmath92-projected dos with @xmath91 and @xmath92 -orbitals diagonalizing the occupation matrix . ; c ) and d ) partial dos for two types of oxygen orbitals .      fig . the scheme of the spin , charge and orbital order in pr@xmath3ca@xmath3mno@xmath2 deduced from the neutron difraction data @xcite . the open circles with the lobe of the @xmath13 electron density distribution denote mn@xmath33 and the filled circles mn@xmath34 . the arrows denote the magnetic moments .
the electronic structure of the doped manganites pr@xmath0ca@xmath1mno@xmath2 was calculated by the lsda+u method which takes into account the local coulomb interaction between d - electrons of transition metal ions . 
 in contrast to the standard local spin density approximation ( lsda ) no jahn - teller lattice distortions are needed to reproduce the experimentally observed orbital ordering in the undoped prmno@xmath2 . 
 the correct ground state : a charge and orbital ordered antiferromagnetic insulator , was obtained for pr@xmath3ca@xmath3mno@xmath2 . 
 the results are in good agreement with the neutron diffraction data .