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non - superconducting prba@xmath0cu@xmath1o@xmath2 compound attracted considerable attention in the last two decades because of its intriguing magnetic and electronic properties within the reba@xmath6cu@xmath7o@xmath2 family of compounds ( re = rare earth atom).@xcite in spite of the great efforts from both experimental and theoretical sides , numerous problems remain unresolved such as the suppression of superconductivity and the nature of the long - range ordered state of pr sublattice with a unique , about an order of magnitude larger than for other rare earth atoms , ordering temperature . although , there exists a discussion whether the ground state of prba@xmath0cu@xmath1o@xmath2 is really a non - superconducting , insulating material with a magnetically ordered cu and pr sublattices , herein we consider this modification of prba@xmath0cu@xmath1o@xmath2 as `` canonical '' and treat it solely herein . we note that superconductivity in prba@xmath0cu@xmath1o@xmath2 was reported@xcite and a non - magnetic pr ground state was found by @xmath8pr nmr.@xcite it was suggested that these observations may result from a non - stoichiometric compound , i.e. when pr occupies only about a half of the rare - earth sites , and the other half is occupied by the non - magnetic ba.@xcite    the theoretical model of fehrenbacher and rice , i.e. the hybridization of pr @xmath9 and the nearest neighbor o @xmath10 orbitals is the most accepted model to account for the absence of superconductivity in prba@xmath0cu@xmath1o@xmath2 . it is suggested that the localization of holes in the hybridized @xmath9-@xmath10 orbitals renders the material non - superconducting.@xcite although the non - superconducting nature of prba@xmath0cu@xmath1o@xmath11 compound is a challenging and interesting problem , we concentrate herein exclusively on the low - temperature pr ordering . prba@xmath0cu@xmath1o@xmath2 is an insulator for every @xmath12 and the cu spins in the cuo@xmath0 planes order antiferromagnetically at temperatures of @xmath13k and @xmath14k for @xmath15 and @xmath16 , respectively.@xcite as the temperature is further decreased , the pr sublattice also undergoes a phase transition@xcite in the temperature range @xmath17k depending on @xmath12 , which appears as an anomaly in the temperature dependence of thermodynamic quantities.@xcite mssbauer spectroscopy,@xcite neutron diffraction,@xcite and nmr@xcite showed that the pr magnetic moments order antiferromagnetically below @xmath18 . however , there is no consensus among these experiments with respect to the magnitude of the ordered pr moment , its direction , and the nature of this transition . neutron diffraction studies found @xmath19 ( @xmath20 ) and @xmath21 ( @xmath22 ) ordered moment with direction tilted out from the @xmath4-plane.@xcite the rotation of cu moments within the cuo@xmath0 plane was found to accompany the pr ordering,@xcite which was suggested to result from the strong coupling between the pr and cu subsystems . however , the magnitude of the coupling , its character , and its influence on the magnitude of the ordered pr magnetic moment , and for the ordering temperature is yet unexplained . we give herein a comprehensive description of the pr ordering in prba@xmath0cu@xmath1o@xmath23 on the basis of a model of localized @xmath24 electrons of the pr ion . we construct the general form of the cu - pr interaction allowed by the symmetry and identify the pr order parameter from the rotation of cu spins below @xmath5 observed by neutron diffraction.@xcite although pseudo - dipole cu - pr interaction has been already proposed,@xcite we derive the cu - pr interaction in general including all pr multipole moments and arbitrary wave vectors . we describe a crystalline electric field ( cef ) model which takes a ground state quasi - triplet composed by a doublet and a singlet states and also includes coupling between the pr and cu subsystems . this low - energy scheme is consistent with the neutron diffraction results@xcite and also with the high - temperature susceptibility data.@xcite we also discuss the enhancement of the pr ordering temperature due to the cu - pr coupling and the magnitude of pr magnetic moment in the ordered state . in prba@xmath0cu@xmath1o@xmath23 , the cu spins are antiferromagnetically ordered along the @xmath25 $ ] direction in the cuo@xmath0 planes with the ordering vector @xmath26 $ ] below the temperature @xmath27k ( phase afi).@xcite as the temperature is further decreased , the pr sublattice also undergoes an ordering at temperature @xmath28k . this ordering is accompanied by the rotation of cu spins within the cuo@xmath0 planes in such a way that the new spin structure is non - collinear along the @xmath29-direction ( phase afiii).@xcite the cu spin rotation is characterized by the ordering vector @xmath30 $ ] . the cu spin structure in the cuo@xmath0 planes is shown in fig . [ cu - pr - fig ] in the temperature range @xmath31 . planes and pr dipole moments in the @xmath4-plane in the temperature range @xmath32 . the central pr ion in the @xmath4-plane is located at position @xmath33 , and the numbers label the cu sites , i.e. cu[1 - 8 ] used in the text . ] first , we construct the invariant form of the interaction between the multipole moments of a pr ion at position @xmath33 and the surrounding eight cu spins , cu[1 - 8 ] , shown in fig . [ cu - pr - fig ] . although the local symmetry at pr site is tetragonal , a cu - pr pair has lower symmetry . for example , the cu[1]-pr pair has reflection symmetry with respect to the @xmath34 $ ] mirror plane . the transformation of total angular momentum @xmath35 of pr ion under this operation is : @xmath36 , @xmath37 , and @xmath38 . the same transformation is applied for the cu spin @xmath39 . thus , spin operators @xmath40 ( @xmath41 ) and @xmath42 ( @xmath43 ) are odd , while @xmath44 ( @xmath45 ) is even under this reflection . not only the bilinear products of the pr dipole moments and cu spins appear in the interaction but also the bilinear products of rank-3 octupole and rank-5 triakontadipole@xcite operators of pr ion and cu spins since they are allowed by the time - reversal symmetry . the octupole operators @xmath46 and @xmath47 are even , while @xmath48 and @xmath49 are odd operators under the present transformation . in the case of tetragonal symmetry , there is one more independent magnetic operator , namely the rank-5 triakontadipole operator @xmath50 which is even under the present reflexion . thus , the invariant form of the interaction for the cu[1]-pr pair is constructed as @xmath51 & = & ( s_{x}+s_{y})\left [ c_{11}(j_{x}+j_{y } ) + c_{12 } t^{\beta}_{z } + c_{13}a_{1u }     \right ] \nonumber\\ & + &    ( s_{x}-s_{y})\left [ c_{21}(j_{x}-j_{y } ) + c_{22 } j_{z } + c_{23 } t_{xyz }      \right ] \nonumber\\ & + & s_{z}\left [ c_{31}(j_{x}-j_{y } ) + c_{32 } j_{z } + c_{33 } t_{xyz }      \right ] ,   \label{int1}\end{aligned}\ ] ] where @xmath52 are constants which are not determined by the symmetry itself . the pair cu[2]-pr is connected to the pair cu[1]-pr by a @xmath53 rotation around the @xmath29-axis . under this operation the transformation of the angular momentum components is given by @xmath54 , @xmath37 , and @xmath55 . the same transformation holds also for the cu spin components . thus , the form of the interaction for the cu[2]-pr pair can be obtained from eq . ( [ int1 ] ) by applying the @xmath53 rotation . repeating further the appropriate rotations and reflections , the interaction can be obtained for all the eight cu - pr pairs . the cu spin at position @xmath56 is expressed by fourier transformation as @xmath57 . using this expression , we obtain the total interaction as    @xmath58 =   8\sum_{\bf q } \left\ { ( c_{11 } + c_{21})(s_{x}^{\bf q}j_{x}+s_{y}^{\bf q}j_{y})c_{x}c_{y}c_{z }   +   ( c_{11 } - c_{21})(s_{x}^{\bf q}j_{y}+s_{y}^{\bf q}j_{x})s_{x}s_{y}c_{z } \right . \nonumber\\ & + & \left . c_{22}j_{z } \left [ s_{x}^{\bf q } s_{x } c_{y } s_{z } - s_{y}^{\bf q } c_{x } s_{y } s_{z }   \right ]   +   c_{31 } \left [ j_{x } s_{z}^{\bf q } s_{x } s_{y } c_{z } - j_{y } s_{z}^{\bf q } c_{x } s_{y } s_{z } \right ]    + c_{32 } j_{z } s_{z}^{\bf q } c_{x } c_{y } c_{z } \right . \nonumber\\ & + & \left .   c_{12 } t^{\beta}_{z } \left [ s_{x}^{\bf q } s_{x } c_{y } s_{z } + s_{y}^{\bf q } c_{x } s_{y } s_{z }   \right ]   +   c_{13 } a_{1u } \left [ s_{x}^{\bf q } c_{x } s_{y } s_{z } + s_{y}^{\bf q } s_{x } c_{y } s_{z }   \right ] +   c_{23 } t_{xyz }   \left [ s_{x}^{\bf q } c_{x } s_{y } s_{z } - s_{y}^{\bf q } s_{x } c_{y } s_{z }   \right ] \right . \nonumber\\ & + & \left . c_{33 } t_{xyz } s_{z}^{\bf q } s_{x } s_{y } c_{z }     \right\ } , \label{int}\end{aligned}\ ] ]    where @xmath59 denotes @xmath60 for @xmath61=@xmath12 , @xmath62 , and @xmath63 for @xmath61=@xmath64 . now we discuss the multipole order of pr sublattice based on expression ( [ int ] ) . in phase afi , the cu spin component @xmath65 with @xmath66 is non - zero . in this phase there is no coupling between the cu spins and pr magnetic moments because the wave vector @xmath67 leads to @xmath68 and @xmath69 , which gives that none of the terms survives in expression ( [ int ] ) . on the other hand , a coupling of cu spins and pr moments is present in phase afiii . the non - collinear cu spin structure in phase afiii can be described by the appearance of the extra spin component @xmath70 in addition to the component @xmath71 . the wave vector @xmath72 gives @xmath73 , @xmath74=1 , and @xmath75 , @xmath76 in expression ( [ int ] ) . together with the condition @xmath77 , we find that the only surviving term in the form of cu - pr interaction is the coupling @xmath78 . we note that the coupling @xmath79 is also allowed by symmetry since the @xmath25 $ ] and @xmath80 $ ] domains in phase afi are equivalent , which gives that the domains @xmath81 and @xmath82 are also equivalent . thus , we conclude that the neutron diffraction result for the cu spin rotation below @xmath5 is compatible with pr dipole moments lying along the crystalline @xmath25 $ ] or @xmath80 $ ] direction , and no deviation from this direction is allowed by symmetry in contrast to the structure proposed in ref .  . since the @xmath83 cu spin components alternate along the @xmath84 and @xmath85 directions , the pr dipole moments also form an afm structure in the @xmath4-planes with the ordering vector @xmath72 . the magnetic structure for the cu spins and pr dipole moments below @xmath5 has the structure shown in fig .  [ cu - pr - fig ] . we now turn to discuss a cef model of the pr ion @xmath9 electrons to describe the pr ordering in prba@xmath0cu@xmath1o@xmath23 . the model consists of the coupled pr and cu subsystems and allows to calculate experimentally relevant quantities . the pr ion has 4@xmath86 electronic configuration in prba@xmath0cu@xmath1o@xmath23 , which gives @xmath87 as the total angular momentum based on the hund s rule for the ground state . in the pr subsystem , we consider afm interaction between the in - plane @xmath88 and @xmath89 dipole moments described by the hamiltonian @xmath90 , \label{ham - pr}\end{aligned}\ ] ] where @xmath91 is the number of nearest - neighbor pr ions and @xmath92 is the coupling constant . the hamiltonian ( [ ham - pr ] ) is taken in a quasi - triplet subspace , where the ground state is the doublet latexmath:[\ ] ] which ratio can be checked in the nmr or esr experiments . acting on the local magnetic probe by changing the direction of the external magnetic field in the @xmath164 $ ] ( _ top _ ) and @xmath165 $ ] ( _ bottom _ ) planes with @xmath167 and @xmath168 , respectively . in the plot we take the exemplifying values @xmath169 and @xmath170 . the field angles are defined in the text . , title="fig : " ] +   acting on the local magnetic probe by changing the direction of the external magnetic field in the @xmath164 $ ] ( _ top _ ) and @xmath165 $ ] ( _ bottom _ ) planes with @xmath167 and @xmath168 , respectively . in the plot we take the exemplifying values @xmath169 and @xmath170 . the field angles are defined in the text . , title="fig : " ] we studied the nature of the pr ordered phase in prba@xmath0cu@xmath1o@xmath23 in a quasi - triplet cef model of 4@xmath86 electrons , where we also included the symmetry allowed coupling between the pr and cu ions . the reason to include cu - pr coupling is the cu spin rotation observed at the pr ordering temperature in neutron diffraction,@xcite which has not been observed for other rare earth reba@xmath0cu@xmath1o@xmath23 compounds . in the 4@xmath171 rare - earth series , the localized electrons of pr ion tend to hybridize rather strongly with conduction electrons as in e.g. prfe@xmath172p@xmath173 . this can be the reason why the cu - re coupling is much stronger in reba@xmath0cu@xmath1o@xmath23 for re = pr compared to the other rare - earth ions , re . we showed by a general symmetry analysis that there is no coupling between the cu and pr subsystems in phase afi , but a coupling emerges in phase afiii . we prove that only the afm ordering of @xmath174 dipole moments of pr ions is consistent with the cu spin rotation observed at @xmath100 by neutron diffraction.@xcite the interpretation of the neutron diffraction data in ref . includes a tilting of the ordered pr magnetic moments out of the @xmath4-plane . however , the presence of non - zero @xmath42 dipole component does not follow from the general symmetry analysis as it was shown in section  [ cu - pr - interaction ] .    upon identifying of the pr order parameter , we studied the pr ordering temperature in the cu - pr coupled quasi - triplet cef model by changing the interaction and cef parameters . we found that the cu - pr coupling enhances the pr ordering temperature , @xmath5 , compared to the uncoupled ordering temperature , @xmath124 .    by fixing the pr - pr and pr - cu interaction parameters to the values obtained by neutron diffraction,@xcite and the cef parameter to that obtained by high - temperature susceptibility measurements,@xcite we found that the pr ordering temperature is considerably enhanced due to the cu - pr coupling in the parameter range @xmath175k . namely , the enhancement of the ordering temperature is as large as @xmath176 in this interval . this observation explains the uniquely large ordering temperature for re = pr in the series reba@xmath0cu@xmath1o@xmath2 . in addition , we predicted the magnetic field angle dependence of the local magnetic field acting at a pr site in the afm ordered phase of the pr ions . this can be directly compared to measured nmr or esr spectra which detect the local magnetic field by a local magnetic probe . our model contains the minimal number of parameters which is required to account quantitatively for the experimental data . given that the parameter values are assumed from independent measurements and no fit is performed , the agreement is reasonable . first , the realistic estimate @xmath175k gives a @xmath5 of @xmath177k which is to be compared to the experimental @xmath5 of @xmath178k . we note that this estimated range gives the pr transition temperature @xmath124 for the uncoupled system as @xmath179k , which is close to the typical values of the ordering temperatures for other rare - earth ions such as yb ( @xmath180k ) , nd ( @xmath181k ) or dy ( @xmath182k ) . this fact may also indicate that the uniquely large ordering temperature for pr arises from the cu - pr coupling . second , the interval @xmath175k is not very far from the estimate @xmath183k based on the analysis of the high - temperature susceptibility data.@xcite furthermore , the estimated interval for @xmath94 and also the splitting pattern of the quasi - triplet subspace is consistent with the results of neutron scattering,@xcite which found that the splitting of the ground state quasi - triplet does not exceed @xmath184mev above @xmath5 , and two inelastic lines are observed at energies @xmath185mev and @xmath186mev at @xmath187k in the ordered phase . finally , for the interval @xmath175k our cef model gives the ordered pr magnetic moment at low temperatures as @xmath188 , which is to be compared to the observed value @xmath189.@xcite the quantitative discrepancies between the results of our model and the experimental data arise because of the simplicity of our model and minimal number of parameters .    in summary , the model we propose herein describes the main features of prba@xmath0cu@xmath1o@xmath23 system , and demonstrates the importance of the cu - pr coupling which may be the key point to understand the anomalous behavior of this compound such as the enhancement of the pr ordering temperature . further studies which include also the itinerant character of @xmath24 electrons are necessary to give an extensive description of this rather complicated system . this work was supported by the hungarian state otka grant k73455 and by the european research council grant nr . ak acknowledges the postdoctoral programme of the magyary foundation and egt norway grants .
theoretical model is presented to describe the anomalous ordered phase of pr ions in prba@xmath0cu@xmath1o@xmath2 below @xmath3k . 
 the model considers the pr multipole degrees of freedom and coupling between the cu and pr subsystems . 
 we identify the symmetry allowed coupling of cu and pr ions and conclude that only an @xmath4-plane pr dipole ordering can explain the cu spin rotation observed at @xmath5 by neutron diffraction by boothroyd _ 
 et al . _ 
 [ a. t. boothroyd _ 
 et al . _ , 
 phys . 
 rev . 
 lett . * 78 * , 130 ( 1997 ) ] . a substantial enhancement of the pr ordering temperature is shown to arise from the cu - pr coupling which is the key for the anomalous magnetic behavior in prba@xmath0cu@xmath1o@xmath2 .