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rare earth titanates ( r@xmath0ti@xmath0o@xmath1 ) are an interesting family of materials showing rich ferroelectric @xcite and magnetic properties @xcite . the common crystal structures @xcite for these materials are cubic pyrochlore for small rare earth ions ( sm@xmath3  lu@xmath3 ) and monoclinic for large rare earth ions ( la@xmath3  nd@xmath3 ) . the magnetic properties of the former have been explored extensively during the recent years @xcite . the subtle interplay among the various interactions including crystal field , exchange and dipole - dipole , coupled with geometrical frustration specific to the pyrochlore lattice @xcite , has led to exotic magnetic phases such as spin ice @xcite and spin liquid @xcite . these phases are extremely sensitive to doping and external stimuli such as pressure @xcite and magnetic fields @xcite . interesting dynamic processes have also been identified @xcite . on the other hand , the rare earth titanates with a monoclinic structure have received much less attention . due to the removal of geometric frustration , these materials are believed to possess magnetically ordered phases at low temperatures . however , the competition between the crystal field and exchange interactions ( plus dipole - dipole ) with close energy scales may lead to interesting and unusual dynamic freezing processes towards the ordered states . in this regard , it is essential to retrieve the magnitude of the crystal field , exchange and the dipole - dipole interactions , in order to study the magnetic freezing processes . here we focus on the monoclinic nd@xmath0ti@xmath0o@xmath1  ( nto ) . some features of nto , such as the ferroelectricity @xcite , the optical magnetoelectric effect @xcite and the photo - catalysis effect @xcite , receive current interests in these materials . in this work , we study the dc susceptibility and specific heat of nto single crystals . the anisotropic paramagnetism is investigated in detail . we found that crystal field interactions dominate the anisotropy , and exchange interactions @xmath4 are estimated by combining the results of the diluted samples . the ground state of nd@xmath3 spins splits into five kramers doublets in the crystal field associated with the @xmath5 site in @xmath6 space group . the magnetic field splits the ground state doublet into two singlets , as is evidenced by the specific heat at different fields , showing a two - level schottky scheme with the energy gap proportional to the field . these studies lay solid ground for further investigation of this system under doping and external perturbations . single crystals of nd@xmath0ti@xmath0o@xmath1  and nd@xmath7la@xmath8ti@xmath0o@xmath1  were grown by the floating zone method in flowing oxygen . seed rods for the single crystal growth were polycrystalline nd@xmath0ti@xmath0o@xmath1  and nd@xmath7la@xmath8ti@xmath0o@xmath1  sintered by the standard solid state reaction in oxygen atmosphere , with starting materials of stoichiometric mixture of nd@xmath0o@xmath9 , la@xmath0o@xmath9 and tio@xmath0 powder ( alfa aesar ) . oxygen atmosphere was used to avoid oxygen deficiency . the lattice constants were obtained by fitting the peak positions of the x - ray diffraction pattern on polycrystals obtained by crushing nd@xmath0ti@xmath0o@xmath1  single crystals . the single crystals were cleaved along @xmath10 direction , and the in - plane @xmath11 and @xmath12 directions were determined by the laue diffraction . dc susceptibility were measured with a quantum design superconducting interference device magnetometer ( squid mpms-5 ) with fields of up to 5 t. dc susceptibility at higher fields were measured by the vibrating sample magnetometer option in a quantum design physical property measurement system ( ppms ) . the in - plane angular dependence of the magnetization were measured using a commercial sample rotator in mpms , the diamagnetic background of the sample holder was carefully subtracted . for the susceptibility measurement along different crystalline directions , the alignment of the crystal along the direction of the magnetic field was maintained within the error of @xmath13 . specific heat was measured in a ppms using the thermal relaxation technique . the as - grown nto single crystals are of high quality and large size benefiting from the floating zone method . the samples are monoclinic in space group @xmath6 , the diffraction peaks of the polycrystals obtained by crushing nto single crystals are well indexed as shown in fig . [ xrd](a ) , and resultant lattice parameters are @xmath14  , @xmath15  , @xmath16  , and @xmath17 , @xmath18 . due to the layered structure , the crystal cleaves naturally along the ( 100 ) direction , as is shown in the xrd pattern in fig . [ xrd ] ( b ) . in fig . [ xrd ] ( c ) , the full width at half maximum ( fwhm ) of 0.09@xmath19 of the rocking curve further indicates good crystallinity of the sample . the single crystals were cleaved and shaped into disks with typical dimensions of diameter @xmath20 1.5 mm and thickness @xmath20 0.2 mm . the disk shape mitigated the effect of demagnetization factor in the in - plane anisotropy of magnetization . however , we still corrected the demagnetization using the calculated value @xcite @xmath21 for @xmath22 and 0.12 for @xmath23 respectively . in fig . [ pm ] ( a1)(c1 ) , we show @xmath24 at 1000 oe with @xmath25 and @xmath22 for a single crystal and a polycrystal sample , respectively . the zero - field - cooled and field - cooled @xmath24 overlap in the entire temperature range in study ( 2  300 k ) , showing typical paramagnetic behavior . however , @xmath24 is clearly anisotropic when comparing the behavior of the single crystal with @xmath25 and @xmath22 , as well as that of a polycrystal . above 150 k , the system follows the curie - weiss law with the effective moment of 3.44  3.49 @xmath26 , close to the theoretical value of 3.62 @xmath26 ( an experimental value @xcite is 3.5 @xmath26 ) . the resultant weiss temperature @xmath27 varies from 10.4 k for @xmath25 to @xmath28 k for @xmath22 . @xmath27 for the polycrystal , which can be taken as the average effect from all the crystalline directions , is @xmath29 k. the negative weiss temperature of the polycrystal indicates an effective antiferromagnetic correlation between nd@xmath3 spins . by comparing fig . [ pm ] ( a1 ) with ( b1 ) , we see that the in - plane magnetization is more than three times larger than the @xmath22 case , this suggests that the nd@xmath3 spins prefer to align in the @xmath30 plane . [ pm ] ( a2)(c2 ) show the isothermal magnetization curves for @xmath31 along different crystalline directions . as is expected for a paramagnetic system , @xmath32 shows no hysteresis , is linear at high temperatures , and shows convex curvatures at low temperatures due to the spin polarization process . the @xmath32 curves measured with the field applied along different directions again show strong anisotropy . moreover , the in - plane @xmath32 curves themselves show anisotropy . [ m - theta ] ( a)(d ) show the angular dependence of the in - plane magnetization . a two - fold symmetry is found at all fields and temperatures . the normalized in - plane anisotropy @xmath33 , where @xmath34 is the mean value of @xmath35 , i.e. , @xmath36 , is shown in fig . [ m - theta ] ( e ) . the magnetization along the @xmath12 axis is roughly two times larger than that along the @xmath11 axis . as we already noted that the nd@xmath3 spins prefer to align in the @xmath30 plane , the @xmath12 axis is thus determined to be the easy axis of nd@xmath3 spins .    we also show @xmath37 with fields along different in - plane directions in fig . [ m - theta ] ( f ) . @xmath37 at different in - plane angles are parallel to each other at @xmath38 k , as expected for paramagnetism with the same effective moments but different weiss temperatures . the angular dependence of weiss temperatures @xmath27 is shown in fig . [ m - theta ] ( g ) . magnetic anisotropy , in particular magnetization anisotropy in paramagnets were previously reported in rare earth compounds @xcite . the primary origin of this anisotropy is the crystal electric field . when an ion is placed within a crystal lattice , the degeneracy of the hund s rule ground state multiplet can be lifted by the electric field from the surrounding atoms . in a rare earth compound such as nto , the cystal field can overcome the external field and pull the total moment resulting from the spin - orbit coupling into a certain direction . the anisotropic exchange coupling also contributes to the magnetic anisotropy . to separate the contribution of crystal field from exchange to the magnetic anisotropy , a series of diluted samples nd@xmath7la@xmath8ti@xmath0o@xmath1 were studied . nonmagnetic la@xmath3 has very close ionic radius to that of nd@xmath3 , it dilutes the nd@xmath3 spins and keeps the lattice almost unchanged . thus , in a good approximation , the crystal field does not change with dilution while the exchange interaction decreases systematically with increasing la@xmath3 content . because the weiss temperature of the system reaches as low as @xmath39 k for nd@xmath40la@xmath41ti@xmath0o@xmath1 , and even lower for samples with lower nd@xmath3 content , which makes it difficult to realize a reliable fitting using the curie - weiss law with the @xmath42 data in the temperature range of 2  300 k , only the data of nd@xmath40la@xmath41ti@xmath0o@xmath1 is presented here . the nd@xmath3 content is determined indirectly by calculating the effective moment of the powder sample . by writing down the magnetic hamiltonian , it is possible to extract both exchange and crystal field contributions to the angular dependent magnetization by assuming a constant crystal field contribution for the la@xmath3 diluted sample . following the approach in ref . @xcite , the magnetic hamiltonian consists of two parts , the exchange energy @xmath43 and the crystal field energy @xmath44 ( the dipolar interaction can be assimilated in the exchange energy @xcite ) . the exchange interaction is anisotropic and can be expressed as    @xmath45    where @xmath46 denote the three crystalline directions , and @xmath47 , @xmath48 and @xmath49 are the exchange constants for nd@xmath3 spins along @xmath50 and @xmath12 directions , respectively . the crystal field part , for the low - symmetry @xmath5 site of the nd@xmath3 , is known to be @xmath51 where @xmath52 are crystal field parameters , and @xmath53 are stevens equivalent operators . it is known that the high temperature susceptibility of a system with only one spin species can be expressed as @xcite    @xmath54    where @xmath55 is the curie constant , @xmath12 is the percentage of the magnetic ions on the spin lattice , in nd@xmath7la@xmath8ti@xmath0o@xmath1 case , @xmath56 . @xmath57 and @xmath58 are the exchange tensor and the crystal field tensor , and can be expressed by the parameters in eq . [ eq - exchange ] and eq . [ eq - cf ] respectively . when the three axes of the crystal are of at least second - order symmetry ( symmetry no lower than @xmath59 ) , eq . [ eq - ki-1 ] can be expressed with the parameters in eq . [ eq - exchange ] and [ eq - cf ] along each crystalline direction as    @xmath60    here , @xmath61 denotes the crystalline direction @xmath10 , @xmath11 or @xmath12 , @xmath62 are the exchange constants as already appeared in eq . [ eq - exchange ] , and @xmath63 is the @xmath61 direction component of tensor @xmath58 . in specific symmetries , @xmath63 can be expressed explicitly with the crystal field parameters @xmath52 . the weiss temperature is then    @xmath64    however , in the nto case , the symmetry of nd@xmath3 site is barely @xmath5 , an explicit expansion of @xmath58 is thus difficult . therefore only the exchange parameter @xmath4 is extracted and the second term in eq . [ eq - theta ] is left as a single parameter @xmath65 to be determined . the results of the curie - weiss fitting for diluted samples suggest that the contributions to the weiss temperature from the exchange interactions @xmath66 and crystal field interactions @xmath67 are of opposite signs . the fitted weiss temperature @xmath27 , and the contributions from exchange interaction and crystal field @xmath68 and @xmath65 in all three crystallographic orientations for nto and nd@xmath40la@xmath41ti@xmath0o@xmath1 are listed in table i. with these weiss temperatures , the exchange constants are determined to be @xmath69 k , @xmath70 k and @xmath71 k. it can be seen that the exchange constants are positive in all crystallographic orientations . this illustrates the dominant role of the crystal field contribution to the magnetic anisotropy . while the exchange interactions are always ferromagnetic , the apparent exchange deduced from the weiss temperature in different directions can be either positive or negative . this is because the crystal field contributes a large negative part to the weiss temperature . as seen from table i , @xmath65 is a couple of times larger in magnitude than @xmath68 along @xmath10 and @xmath11 axes and comparable in magnitude along the @xmath12 axis , making the weiss temperature large and negative along @xmath10 , @xmath11 directions and small but positive along the @xmath12 direction . it is also worth to note that eq . [ eq - ki ] is independent of the magnetic field . indeed , we see that in fig . [ m - theta ] ( e ) , the normalized in - plane anisotropy @xmath33 is nearly constant for different fields at the same temperature . only when spins are polarized significantly by the field , i. e. , m(h ) curve is not linear anymore , @xmath33 at different fields bifurcate , as is the case at 2 k.    as we have discussed , the monoclinic nto does not accommodate geometrical frustration . however , with the absence of a magnetic transition down to at least 2 k , and the average weiss temperature @xmath72 k , the frustration index as defined by @xmath73 ( ref . @xcite ) of this system reaches about 21 , and is even higher along @xmath10 and @xmath11 directions . the large frustration index may indicate an unusual ground state and interesting spin freezing processes . these investigations are currently under way . the magnetic ground state of @xmath74 nd@xmath3 on the @xmath5 site in the @xmath6 space group should split into five kramers doublets due to the crystal field . calculations on the nd@xmath3 in the same symmetry in other compounds indeed revealed the five doublets scheme @xcite , while a detailed calculation on nto is still lacking . the specific heat measurement provides more information on the magnetic ground state . [ specific - heat ] ( a)(c ) show the magnetic specific heat of nto for h @xmath75 a , h @xmath75 bc and that of nd@xmath40la@xmath41ti@xmath0o@xmath1 for h @xmath75 a at different fields . the magnetic specific heat is obtained by subtracting the lattice contribution using the specific heat data of a nonmagnetic la@xmath0ti@xmath0o@xmath1 single crystal . the zero - field specific heat in principle detects any magnetic phase transitions , and the magnetic entropy associates directly with the ground state degeneracy . in fig . [ specific - heat ] ( a ) , the zero - field magnetic specific heat shows no anomaly for a magnetic transition , which is consistent with the paramagnetic behavior above 2 k. there is a progressive upturn as @xmath76 decreases , which signals the presence of a large portion of the magnetic entropy below 2 k. the magnetic entropy is therefore difficult to integrate due to the limited temperature range . however , this problem is bypassed by using the specific heat in a magnetic field . as shown in fig . [ specific - heat ] ( a ) , @xmath77 in a field shows a broad peak with the magnitude of around 3.6 j / mol@xmath78 k at low temperatures , and the maximum moves to higher temperatures with its magnitude almost unchanged as the field increases . these indicate that the peaks are schottky anomalies associated with the ground state doublet splitting in the presence of a magnetic field . the two - level schottky specific heat is , @xmath79 where @xmath80 is the gas constant , and @xmath81 is the energy gap between the two levels . [ eq3 ] describes the data nicely as shown by the solid lines in fig . [ specific - heat ] ( a ) . it can be seen in fig . [ specific - heat ] ( d ) that the fitting parameter @xmath81 scales linearly with magnetic field . this further proves that the gap between the two schottky levels are caused by the zeeman splitting of the ground state doublet . using @xmath82 , the @xmath2 factor for nto with @xmath31 along @xmath10 is found to be 1.99 . the magnetic specific heat is also studied in nd@xmath0ti@xmath0o@xmath1  with @xmath23 and in nd@xmath40la@xmath41ti@xmath0o@xmath1 with @xmath22 . for nto with @xmath23 , the @xmath2 factor is 3.10 . the anisotropy in @xmath2 factor again points to the presence of strong crystal field , and these @xmath2 values should be corroborated with future crystal field calculations . in conclusion , we have studied both single- and poly - crystalline nd@xmath0ti@xmath0o@xmath1  with angle - dependent dc susceptibility and specific heat . the anisotropic paramagnetism is observed and is mainly attributed to the crystal field effect . the easy axis is determined to be the @xmath12-axis in the @xmath30 plane . the contributions to weiss temperature from exchange interactions and crystal field interactions are separated . the exchange interactions are ferromagnetic , while the crystal field contributes a large negative part to the weiss temperature , along all three crystallographic directions . this leads to large negative @xmath27 values along @xmath10 and @xmath11 axes and small positive @xmath27 along the @xmath12 axis . the @xmath74 ground state multiplet of nd@xmath3 splits into five kramers doublets . the ground state doublet further splits into two singlets in a magnetic field , and this two - level ground state scheme is revealed by the magnetic specific heat . @xmath2 factors show anisotropy too , again due to the crystal field . these studies provide solid foundations for further investigations of this system , including the magnetic ground state and the spin freezing processes . this work is supported by the nsfc ( grant no . 10634030 ) , us nsf dmr-0547036 , the fundamental research funds for the central universities of china ( grant no . 2010qna3026 ) , and national basic research program of china ( grant no . 2007cb925001 ) .      shcherbakova l g , mamsurova l g , and sukhanova g e , _ russ . rev . _ * 48 * , 228 ( 1979 ) . winfield g , azough f , and freer r , _ ferroelectrics _ * 133 * , 181 ( 1992 ) . gardner j s , gingras m j p , and greedan j e , _ rev . * 82 * , 53 ( 2010 ) . bramwell s t , giblin s r , calder s , aldus r , prabhakaran d , and fennell t , _ nature _ * 461 * , 956 ( 2009 ) . moessner r and ramirez a r , _ physics today _ * 59 * , 24 ( 2006 ) . harris m j , bramwell s t , mcmorrow d f , zeiske t , and godfrey k w , _ _ * 79 * , 2554 ( 1997 ) . ramirez a p , hayashi a , cava r j , siddharthan r , and shastry b s , _ nature _ * 399 * , 333 ( 1999 ) . bramwell s t and gingras m j p , _ science _ * 294 * , 1495 ( 2001 ) . gardner j s , gaulin b d , berlinsky a j , waldron p , dunsiger s r , raju n p , and greedan j e , _ _ * 64 * , 224416 ( 2001 ) . mirebeau i , goncharenko i n , cadavez - peres p , bramwell s t , gingras m j p , and gardner j s , _ nature _ * 420 * , 54 ( 2002 ) . cao h , gukasov a , mirebeau i , bonville p , and dhalenne g , _ _ * 101 * , 196402 ( 2008 ) snyder j , ueland b g , slusky j s , karunadasa h , cava r j , mizel a , and schiffer p , _ _ * 91 * , 107201 ( 2003 ) xing h , he m , feng c , guo h , zeng h , and xu z a , _ _ * 81 * , 134426 ( 2010 ) . cho b k , harmon b n , johnston d c , and canfield p c , _ _ * 53 * , 2217 ( 1996 ) . skumryev v , kuzmin m d , gospodinov m , and fontcuberta j , _ _ * 79 * , 212414 ( 2009 ) . boutron p , _ _ * 7 * , 3226 ( 1973 ) . ramirez a p , _ annual review of materials science _ * 24 * , 453 ( 1994 ) . agnieszka m , gajek z , karbowiak m and rudowicz c , _ j. phys . : condens matter _ * 20 * , 385205 ( 2008 ) . .the weiss temperatures @xmath27 for nd@xmath0ti@xmath0o@xmath1 and nd@xmath40la@xmath41ti@xmath0o@xmath1 along @xmath10 , @xmath11 and @xmath12 directions . the fitting errors are estimated to be within 3 k. the contributions from the exchange interactions and crystal field interactions are isolated as @xmath68 and @xmath65 using eq . [ eq - theta ] . [ cols="^,^,^,^,^,^,^,^,^,^",options="header " , ]     ( color online ) ( a ) the x - ray diffraction pattern of the polycrystals obtained by crushing nd@xmath0ti@xmath0o@xmath1  single crystals . most peaks are indexed in the monoclinic structure in the space group @xmath6 , the index of some small peaks are not marked explicitly . ( b ) the x - ray diffraction pattern of a nd@xmath0ti@xmath0o@xmath1  single crystal . crystals cleave naturally along the ( 100 ) direction . ( c ) the rocking curve of the ( 400 ) peak with fwhm = 0.09@xmath19 indicates good crystallinity . ] ( color online ) ( a1)-(c1 ) : zero - field - cooled and field - cooled susceptibility vs temperature at 1000 oe for @xmath25 , @xmath22 of a nd@xmath0ti@xmath0o@xmath1  single crystal and a polycrystal sample , respectively . insets are fittings by the the curie - weiss law . ( a2)-(c2 ) : isothermal magnetization curves at 2 , 10 , 150 k for @xmath25 , @xmath22 and polycrystal respectively . ]    ( color online ) ( a)-(d ) : the angular - dependent in - plane magnetization @xmath35 of nd@xmath0ti@xmath0o@xmath1  at 2 , 10 , 100 , 300k in the field of 0.5 , 2 , 5 t. ( e ) : the angular dependence of the normalized magnetization @xmath83 , where @xmath34 is the mean value of @xmath35 . ( f ) the temperature dependence of the inverse susceptibility of a nd@xmath0ti@xmath0o@xmath1  single crystal with the in - plane field along @xmath84 @xmath85 , @xmath86 , @xmath87 , @xmath88 , @xmath89 , @xmath90 , @xmath91 , @xmath92 and @xmath93 . ( g ) : the in - plane angular dependence of the weiss temperature by fitting @xmath37 above 200 k in ( f ) . dashed lines labeled with @xmath11 and @xmath12 denote the in - plane crystalline @xmath11 and @xmath12 directions as determined by the laue diffraction . ] ( color online ) magnetic specific heat of ( a ) a nd@xmath0ti@xmath0o@xmath1  single crystal with @xmath22 ; ( b ) a nd@xmath0ti@xmath0o@xmath1  single crystal with @xmath23 ( the field is not applied intentionally along a specific in - plane direction ) ; ( c ) nd@xmath40la@xmath41ti@xmath0o@xmath1 with @xmath22 . solid lines in ( a)-(c ) are two - level schottky fittings ; ( d ) the energy gap @xmath81 obtained by the two - level schottky fittings . ]
the anisotropic paramagnetism and specific heat in nd@xmath0ti@xmath0o@xmath1  single crystals are investigated . 
 angular dependence of the magnetization and weiss temperatures show the dominant role of the crystal field effect in the magnetization . by incorporating the results from the diluted samples , contributions to weiss temperature from exchange interactions and crystal field interactions 
 are isolated . 
 the exchange interactions are found to be ferromagnetic , while the crystal field contributes a large negative part to the weiss temperature , along all three crystallographic directions . 
 the specific heat under magnetic field reveals a two - level schottky ground state scheme , due to the zeeman splitting of the ground state doublet , and the @xmath2-factors are thus determined . 
 these observations provide solid foundations for further investigations of nd@xmath0ti@xmath0o@xmath1 .