Giant Anisotropy of Magnetoresistance and "Spin Valve" effect in Antiferromagnetic N d 2−x C e x Cu O 4
T. Wu, C. H. Wang, G. Wu, D. F. Fang, J. L. Luo, G T. Liu, X. H. Chen
aa r X i v : . [ c ond - m a t . s up r- c on ] M a r Giant Anisotropy of Magnetoresistance and ”Spin Valve” effect in Antiferromagnetic
N d − x Ce x CuO T. Wu , C. H. Wang , G. Wu , D. F. Fang , J. L. Luo , G T. Liu and X. H. Chen , ∗
1. Hefei National Laboratory for Physical Science at Microscale and Department of Physics,University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China2. Beijing National Laboratory for Condensed Matter Physics, Institute of Physics,Chinese Academy of Science, Beijing 100080, People’s Republic of China (Dated: November 21, 2018)We have studied anisotropic magnetoresistance (MR) and magnetization with rotating magneticfield (B) within
CuO plane in lightly doped AF Nd − x Ce x CuO . A giant anisotropy in MR isobserved at low temperature below 5 K. The c-axis resistivity can be tuned about one order ofmagnitude just by changing B direction within
CuO plane and a scaling behavior between out-of-plane and in-plane MR is found. A ”Spin valve” effect is proposed to understand the giantanisotropy of out-of-plane MR and the evolution of scaling parameters with the external field. Itis found that the field-induced spin-flop transition of Nd layer under high magnetic field is thekey to understand the giant anisotropy. These results suggest that a novel entanglement betweencharge and spin dominates the underlying physics. PACS numbers: 74.25.Fy; 74.72.Jt
I. INTRODUCTION
It is generally believed that the pairing necessary forhigh- T c superconductivity in cuprates involves the inter-play between doped charges and antiferromagnetic (AF)spin correlation. In this sense, the study of lightly doped,insulating AF state is important to understand the pair-ing mechanism because density of the carriers can besufficiently low so that the interaction between them issmall relative to their interaction with Cu spins. Manyintriguing and anomalous phenomena were observed inlightly doped AF cuprates due to strong coupling be-tween charges and Cu spins. Cu spins orderin an AF collinear structure for the parent compounds ofhole-doped cuprates, while in AF noncollinear struc-ture for that of electron-doped cuprates. All spinspoint either parallel or antiparallel to a single directionin AF collinear structure, while the spins in adjacentlayers are orthogonal in AF noncollinear structure. Atransition from noncollinear to a collinear spin arrange-ment with a spin-flop can be induced by certain magneticfield ( B c ) , which is confirmed in lightly electron-doped P r . − x La . Ce x CuO and N d − x Ce x CuO crystals,and such transition affects significantly both the in-planeand out-of-plane resistivity.In N d CuO , the Cu spins order in three phaseswith two different AF noncollinear spin structures andexperience two reorientation phase transitions .It has been reported by us that MR anisotropy with afourfold symmetry in different AF spin structures uponrotating magnetic field (B) within ab-plane, while witha twofold symmetry at the spin reorientation temper-atures, is observed in lightly doped N d − x Ce x CuO above 10 K. A large anisotropic MR was ob-served in lightly electron-doped
P r . − x La . Ce x CuO and N d − x Ce x CuO . These results indicate strongspin-charge coupling in electron-doped cuprates. In Nd CuO , the magnetic coupling between Nd andCu is very important at low temperature since themagnetic moment of Nd becomes large with decreasingtemperature ( ∼ µ B at 0.4 K). Magnetic structure ofNd is very abundant at low temperature. In thissense, electronic transport at low temperature is expectedto be sensitive for the change of magnetic structure ofNd due to strong spin-charge coupling. It will pro-vide us a chance to understand the spin-charge couplingin electron-doped cuprates. The lightly electron-dopedcuprates are good system to study the coupling betweencharge and Cu spin because: (1) the spin structurecan be tuned by external magnetic field; (2) in con-trast to the buckling of CuO in hole doped cuprates,the CuO plane in electron-doped cuprates is flat, sothat the spin ordering is pure antiferromagnetic withoutferromagnetic component along c-axis occurred in holedoped cuprates, such ferromagnetic component along c-axis makes the study of the coupling between charge and Cu spin complicated. In this work, we study angulardependent magnetoresistance and magnetization below10 K in lightly electron-doped N d − x Ce x CuO . A giantanisotropy in MR is observed, and the c-axis resistiv-ity can be tuned about one order of magnitude just bychanging B direction. Scaling behavior between in-planeand out-of-plane MR is systematically changed with in-creasing magnetic field. The jump in MR with B aroundCu-O-Cu direction coincides with the sudden change inmagnetization at low temperature below 5 K. The un-derlying physics will be discussed below.
II. EXPERIMENT
Growth of single crystals and their resistivity havebeen reported in previous work. Susceptibility and mag-netoresistance were measured with the superconductingquantum interference device (SQUID) with 7 Tesla max-imal magnetic field and quantum design PPMS systemwith 12 Tesla maximal magnetic field, respectively. Inour measurements, the maximal magnetic field is 12 Teslafor MR and 7 Tesla for magnetization. The ρ ab and ρ c stand for in-plane resistivity and out-of-plane resis-tivity, respectively. The magnetoresistance is defined asMR= △ ρ ( B ) ρ (0) = ρ ( B ) − ρ (0) ρ (0) . It should be addressed that allresults discussed as follow are well reproducible. III. RESULT AND DISCUSSION
Fig.1 shows the isothermal out-of-plane MR at 5 Kfor the single crystals with x=0.025 and 0.033 with Balong Cu-Cu and Cu-O-Cu direction, respectively. TheMR behavior is similar to that observed in antiferro-magnetic
P r . − x La . Ce x CuO with x=0.01 crystal. But the magnitude of MR and the MR anisotropy aremuch larger than the case of
P r . − x La . Ce x CuO . Thestep-like increase of MR corresponds to the noncollinear-collinear transition occurring at the critical field B c . Asshown in Fig.1, the critical field B c along Cu-O-Cu di-rection is larger than that along Cu-Cu direction. Above B c , the behavior of MR for B along Cu-Cu direction isquite different from that for B along Cu-O-Cu directionin the collinear structure. The MR with B along Cu-Cu direction slightly changes above B c , while the MRmonotonically increases with increasing B for B alongCu-O-Cu direction. A giant anisotropic MR between Balong Cu-Cu and Cu-O-Cu direction is observed. Forx=0.025 crystal, the MR at 12 T is as high as ∼ ∼
17% withB along Cu-Cu direction.Upon rotating a magnetic field larger than B c withinthe CuO plane, the spins always keep the collinear ar-rangement and the spin structure rotates as a whole, allspins are perpendicular to the magnetic field as shownin Fig.1. In order to study the anomalous and giantanisotropic MR, we carefully investigated the evolutionof in-plane and out-of-plane MR with rotating B within
CuO plane. Fig. 2a and 2b show the evolution of in-plane and out-of-plane MR with the angle between Band Cu-O-Cu ([100]) direction at 5 K for the single crys-tal with x=0.025. Both of in-plane and out-of-plane MRincrease with increasing B, and show a giant anisotropywith fourfold-symmetry, such fourfold symmetry arisesfrom the symmetry of magnetic structure because thereexist two equivalent spin easy axes (Cu-Cu direction) andtwo equivalent spin hard axes (Cu-O-Cu direction) in thecollinear spin structure, which has been confirmed by thedifferent critical fields B c for B along Cu-O-Cu and Cu-Cu directions as shown in Fig.1. A striking feature isobserved that the out-of-plane MR at 12 T sharply in-creases from ∼ ∼ -10 -5 0 5 10 BIICu-CuBIICu-O-Cu B ( x10 Oe) x =0.025 c ( B ) / c ( ) ( % ) x =0.033 BIICu-O-Cu BIICu-CuT=5 K B z=0z=c/2b aCu-O-Cu Cu-Cu B c Bc FIG. 1: Isothermal MR at 5 K with the B along Cu-O-Cuand Cu-Cu direction for the samples Nd − x Ce x CuO withx=0.025 and 0.033, respectively. Zero-field noncollinear spinstructure, only Cu spins are shown; Field-induced transitionfrom noncollinear to collinear spin ordering with B alongCu-O-Cu direction. can be also observed at the angle close to B along Cu-Cu, but the jump is very small compared to the case ofB close to Cu-O-Cu direction.In order to study the effect of temperature on theanisotropy of MR, we systematically investigated the MRbehavior of the x=0.033 crystal because resistivity of thex=0.025 crystal is too large to be measured due to theresistivity divergence at low temperature. Fig.3 showsevolution of the out-of-plane MR upon rotating B within CuO plane at 2, 4 and 5 K under 12 T for the x=0.033crystal. The results are similar to that observed in thecrystal with x=0.025. The MR increases monotonicallyand the anisotropy of MR induced by rotating B withinCu-O plane apparently increases with decreasing temper-ature. The MR under 12 T with B along Cu-Cu directionis about 11.2% at 5 K, 17.1% at 4 K and 27.7% at 2 K;while the MR with B along Cu-O-Cu direction is about133% at 5 K, 203% at 4 K and 656% at 2 K, respec-tively. It indicates that a giant anisotropy of resistivityis induced by magnetic field with B along Cu-O-Cu andCu-Cu at low temperature. At 2 K, the resistivity under12 T with B along Cu-O-Cu direction is about one orderof magnitude larger than that with B along Cu-Cu di-rection. Such giant anisotropy in resistivity induced justby changing B direction within CuO plane should berelated to the magnetic structure and magnetic momentinduced by B because the magnetic field along Cu-O-Cuor Cu-Cu just changes the spin structure and inducesthe different magnitude of the magnetic moment. To un-derstand the jump in MR with B close to the Cu-O-Cudirection, the MR at 5 K is measured with rotating Bin clockwise direction and in anti-clockwise direction, re-spectively. It is found that the MR jumps observed withrotating B in clockwise direction and in anti-clockwise
80 90 1001820 c ( B ) / c ( ) ( % ) Angle (deg.)
B=12 T 10 T 8 T 6 T (b) a b ( B ) / a b ( ) ( % ) B =
12 T 10 T 8 T 6 T (a) a b ( B ) / a b ( ) ( % ) Angle (deg.)
FIG. 2: (a): Isothermal in-plane and (b): Out-of-plane MRat 5 K under different B as a function of angle between B andCu-O-Cu direction upon rotating B within
CuO plane forthe single crystal with x=0.025. The inset in (a): magnifiedin-plane MR with B = 12 T.
80 100100110120130140 c ( T ) / c ( ) ( % ) Angle (deg.) c ( T ) / c ( ) ( % ) Angle (deg.)
T=2 K 4 K 5 K
FIG. 3: Out-of-plane MR as a function of angle between Band Cu-O-Cu direction upon rotating B within
CuO planeat 2K, 4K and 5 K, respectively, for the single crystal withx=0.033 (B=12 T). direction are symmetric relative to the B along Cu-O-Cudirection as shown in the inset of Fig.3. It indicates thatthe spin does not prefer to the Cu-O-Cu direction, andthe spin jump always occurs around Cu-O-Cu directionwhen B is rotated within CuO plane. Therefore, thejump arises from the spin-flop induced by B.As shown in Fig.4, the same data of in-plane andout-of-plane MR shown in Fig.2a and 2b are plotted in∆ ρ c ( B ) /ρ c (0) as a function of ∆ ρ ab ( B ) /ρ ab (0). Only the l og ( M R c ) ( % ) log(MR ab ) (%) l og ( M R c ) ( % ) log(MR ab ) (%) log(MR ab ) (%) l og ( M R c ) ( % )
10 T(c) log(MR ab ) (%) l og ( M R c ) ( % )
12 T(d)
FIG. 4: The same data shown in Fig.2 are plotted in∆ ρ c ( B ) / ( ρ c (0)) as a function of ∆ ρ ab ( B ) / ( ρ ab (0)). Theline is the fitting results with the formula ∆ ρ c ( B ) /ρ c (0)= β + α (∆ ρ ab ( B ) /ρ ab (0)) υ . At 6 T and 8 T, the parameter β = 0.TABLE I: Fitting parameters α , β and υ with the formula∆ ρ c ( B ) /ρ c (0)= β + α (∆ ρ ab ( B ) /ρ ab (0)) υ under different field.Field β α υ data of in-plane and out-of-plane MR between 45 and 90degree is plotted in Fig.4 because in-plane and out-of-plane MR exhibit the exactly same oscillation. All dataabove can be fitted by MR c = β + α · MR υab very well. Thefitting parameters are list in Table I. It is found that thefitting parameter β is zero below 10 T. The fitting param-eter υ increases from ∼ ∼ CuO plane for the AF N d − x Ce x CuO with x=0, 0.025, 0.06 and 0.13. It isfound that magnetization shows the same fourfold sym-metry with rotating B within CuO plane as that ob-served in MR shown in Fig.2. The amplitude of the os-cillation and the magnetization decrease with increasingx. A striking feature is observed that the magnetizationshows a jump with B around Cu-O-Cu direction at whicha corresponding jump is observed in MR as shown in theinset of Fig.5. However, this fourfold symmetry grad-ually disappears with increasing temperature as shownin Fig.6. As we know, the magnetic moment of Nd increases prominently at low temperature, and the mag-netization is very sensitive to magnetic moment of Nd below 5 K . Therefore, the fourfold symmetry in mag-netization and the jump in magnetization are related tothe magnetic structure of Nd . In the other hand, thefourfold symmetry shown in Fig.5 indicates a magneticordering of Nd . The spontaneous ordering of the Nd subsystem at low temperature due to Nd -Nd inter-action remains controversial. X-ray magnetic scatteringdata indicate that Nd ions are polarized at 37 K . Theremoval of the Kramers doublet degeneracies observedby crystal field infrared transmission indicates that theseions are already polarized by the Cu subsystem at atemperature as high as 140 K . An enhancement ofneutron scattering magnetic peak intensities around 3K has been interpreted as Nd ordering due to Nd -Nd interaction , while Lynn et al. have estimated theNd ordering temperature around 1.5 K . Recently, anabnormal peak around 5 K observed in ultrasonic mea-surement is explained to be somehow related to localmagnetic domains . Since the Nd -Cu and Nd -Nd interactions are opposite, the former is dominatedabove 5 K and makes Nd parallel to Cu as shownin Fig.8(a), while the later is dominated below 5 K andmakes Nd prefer to be perpendicular to Cu as shownin Fig.8(b). Due to the frustration of the Nd mag-netic subsystem arising from the competition betweenNd -Cu and Nd -Nd interaction, the local mag-netic domain is formed with Nd not parallel to Cu
170 180 19031.932.032.132.2 M a gn e t i z a t i on ( e m u / g ) Angle (deg.) x=0.0x=0.13x=0.06 M a gn e t i z a t i on ( e m u / g ) x=0.025 Angle (deg.)
FIG. 5: The magnetization measured under magnetic fieldof 7 Tesla at 2 K as a function of angle between B andCu-O-Cu direction upon rotating B within
CuO plane forthe samples with x=0, 0.025, 0.06, 0.13. Inset shows a jumpin magnetization at certain angle corresponding to the jumpobserved in MR. M agne t i z a t i on ( e m u / g ) (a) (b) Angle ( ) (c) FIG. 6: The increment of magnetization measured undermagnetic field of 6.5 Tesla at (a): 2 K, (b): 3.5 K and (c):5 K relative to the magnetization at 7.5 K as a function ofangle between B and Cu-O-Cu direction upon rotating Bwithin
CuO plane for the samples with x= 0.025. magnetic moment below 5 K. The magnetic structure ofNd subsystem with magnetic moment of Nd perpen-dicular to Cu can be stabilized by the external field.The observed fourfold symmetry below 5K in magneti-zation could arise from the reorientation of Nd spin.Richard et al. have given evidence that the magneticstructure below 5 K has anisotropic field-dependence .As shown in Fig.7, the field dependent magnetization ofx=0.025 sample at 2 K shows an anomaly at 0.6 T and3.6 T for both Cu-Cu and Cu-O-Cu directions, respec-tively. However, no such anisotropy is observed above 5K. To make the anisotropy clear, the magnetization at 2K subtracted the 5 K magnetization is shown in Fig.7(b).Such anomaly has been attributed to spin-reorientationof Nd in Nd CuO . The spin reorientation of Nd occurs due to a transition from the magnetic structureshown in Fig.8(a) to that shown in Fig.8(b). It is sur-prising that the magnetization for two directions has across around 6 T and the magnetization shows somehowsaturation as shown in Fig. 7. It is suggested that the (a) (b) M agne t i z a t i on ( e m u / g ) B (Tesla)
Cu-Cu
Cu-O-Cu B c2 B c1 M agne t i z a t i on ( e m u / g ) B (Tesla)
Cu-Cu 2 K
Cu-O-Cu 2 K
Cu-Cu 5 K
Cu-O-Cu 5 K
FIG. 7: (Color online) (a): Magnetization as a function ofmagnetic field along Cu-Cu and Cu-O-Cu direction at 2 Kand 5 K; (b): M(2K)-M(5K). magnetic structure under high magnetic field is differ-ent from that under low magnetic field. Similar resulthas been reported in Nd CuO . Recently, a crossoverfrom antiferromagnetic to paramagnetic configuration in-duced by high magnetic field is proposed by Richard etal. . The corresponding magnetic structures given byRichard et al. are shown in Fig.8(c)-(f). When in-planemagnetic field B < -Nd interaction is larger than Nd -Nd inter-action. When in-plane magnetic field B > -Nd inter-action is dominated and the magnetic structure changesfrom antiferromagntic to paramagnetic configuration asshown in Fig.8 (d) and (f), in which the Nd spinsare aligned in applied magnetic field and thus behave asferromagnetic-like. The cross at about 6 T in magnetiza-tion could be related to the change of magnetic structureshown in Fig.8.The fourfold symmetry in magnetoresistance has beenobserved above 5 K in the same sample in previousresult , while similar symmetry in magnetization arosefrom Nd spin is observed only below 5 K. There-fore, the fourfold symmetry in MR should arise fromanisotropic magnetic structure of Cu as discussed inour previous work . As shown in Fig.2 and Fig.6, thegiant anisotropy in MR below 5 K coincides with themagnetic ordering of Nd with the same fourfold sym-metry. These results indicate that the fourfold symmetryof MR results from spin ordering of Cu , and the spinordering of Nd enhances the fourfold symmetry in MRbelow 5 K and leads to a giant anisotropy in MR. It isevident that the jump of out-of-plane MR with B alongCu-O-Cu direction shown in Fig.2 is related to the sud-den change in magnetization shown in the inset of Fig.5.Therefore, the change of MR below 5 K relative to hightemperature MR can be mainly ascribed to the orderingof Nd spin. As shown in Fig.4, there exists a scal-ing behavior between the out-of-plane MR and in-planeMR with MR c = β + α · MR υab . But the fitting parameters FIG. 8: (Color online) Magnetic configuration of Nd CuO in the noncollinear antiferromagnetic phase (a): above 5 K;(b): below 5 K; Magnetic configuration of Nd CuO in thecollinear phase assuming an antiferromagnetic alignment ofNd spins (c): B k [100]; (e): B k [110]], and a ferromagnetic-like alignment of the Nd spins (d): B k [100]; (f): B k [110]. β , α and υ show a systematic change with increasingexternal field as listed in Table 1. Change of the scal-ing behavior is closely related to the change of magneticstructure of Nd induced by external field since the in-crease of external field from 6 T to 12 T cannot lead tochange of magnetic structure of Cu subsystem. It issupported by the fact that the change of in-plane MRwith increasing magnetic field is much smaller than thatof out-of-plane MR, and the anisotropy of out-of-planeMR is much larger than that of in-plane MR as shownin Fig.2. Richard et al., pointed out that the mag-netic structure of Nd subsystem can change from an-tiferromagnetic to paramagnetic configuration at certaincritical magnetic field. It is possible that the evolutionof scaling parameters listed in Table 1 is related to thechange of magnetic structure of Nd . It is well knownthat the neighboring CuO plane with antiferromagneticconfiguration is separated by Nd-O layer. As discussedabove, the magnetic structure of Nd subsystem canbe turned by external field. Therefore, the out-of-planetransport can be switched by magnetic field assuming theNd-O layer as a barrier. In this sense, this phenomenoncan be well understood with ”Spin Valve” effect. Themagnetic excitations are different with B along Cu-Cuand Cu-O-Cu directions because the magnetic structureis more frustrated around Cu-O-Cu . In ”Spin Valve”picture, the different magnetic excitations in Nd layerlead to different transport along c-axis. Therefore, thespin-flop transition is the key to understand the giantanisotropy of out-of-plane MR. Thermal conductivity re-sults indicate that in-plane magnetic field can result in aclose of anisotropic gap ( ∼ . The critical magnetic field isabout 4.5 T and 2.5 T in Cu-O-Cu and Cu-Cu direction,respectively. The closure of anisotropic gap correspondsto spin-flop transition for Cu spin. This result indi-cates that the spin-flop transition can lead to a closure ofanisotropic gap. At low temperature below 5 K, anothergap related to spin-flop transition of Nd is closed un-der high magnetic field and this gap is anisotropic. Thegap can be estimated with B=∆/g µ B ( B ∼ T ), the gapis about 0.5 meV with magnetic field along Cu-O-Cu di-rection. This spin-flop should originate from Nd sub-system because magnons from Cu have energy above5 meV , and four optical Nd magnon branches liein the range 0.2 to 0.8 meV . The study on magneticstructure under high magnetic field at low temperatureis lacking. This picture needs further experimental inves-tigation to confirm. These results give a strong evidencethat a nontrivial correlation between charge and AF or-dering background exists, the charge transport can beaffected not only by Cu spins but also Nd spins,especially below 5 K.The huge changes in resistivities as induced by the in-plane magnetic field seem to be a highly nontrivial phe-nomenon. Note that the applied in-plane magnetic fieldshould only affect the spins of the system via the Zee-man effect without directly influencing the orbital mo-tion of charge carriers in the in-plane case, and presum-ably with only a weak orbital effect for the out-of-planecase as the resistivity itself is divergent at low tempera-ture. It thus implies the existence of some kind of strong“entanglement” between the spin and charge degrees offreedom such that by tuning the magnetic ordering withan in-plane magnetic field can result in a big enhance-ment of resistivities seen in the measurements. Further-more, the large MR behavior in this insulating regimealso strongly suggests that the divergence of resistivitiesat low-temperature may not be simply a conventional lo-calization effect due to disorders since spin structures canaffect resisitivities so much. Although the microscopicmechanism remains unclear, the novel spin-charge entan-glement does exist in strongly correlated models. For ex-ample, in the t-J model, a so-called phase string effect has been shown to be present as a non-local mutual frus-tration between the charge and spin degrees of freedominduced by doped charge carriers moving in an antiferro-manget. In fact, the localization of the charge carriers inthe magnetic ordered phase has been interpreted basedon such a phase string effect and it is thus conceivablethat the change of the spin structure may strongly affectthe resistivities via the phase string effect. The scalingbetween in-plane and out-of-plane MR is strongly depen-dent on spin structure of Nd which emerges at low tem-perature since strong Cu -Nd interaction and can beeasily tuned by external magnetic field. It provides agood chance to show a evidence for the spin-charge en-tanglement. IV. CONCLUSION
In this paper, we study anisotropic magnetoresistance(MR) and magnetization with rotating magnetic field (B)within
CuO plane in lightly doped AF N d − x Ce x CuO . A giant anisotropy in MR is observed, and the c-axis re-sistivity can be tuned by about one order of magnitudejust with changing B direction. These results provide ev-idence to support the spin-flop transition of Nd ionsinduced by high magnetic field. The change of magneticstructure induced by different external field leads to asystematic evolution of the scaling behavior between in-plane and out-of-plane MR. ”Spin Valve” effect is usedto well understand the out-of-plane MR behavior. Suchnovel entanglement of charge and spin dominates the un-derlying physics. Acknowledgment:
The authors would like to thankZ. Y. Weng for stimulating discussions and constructiveopinion. We acknowledge T. Xiang and Q. H. Wang forhelpful discussions. This work is supported by the Na-ture Science Foundation of China and by the Ministryof Science and Technology of China (973 project No:2006CB601001) and by National Basic Research Programof China (2006CB922005). ∗ Corresponding author,
Electronic address: [email protected] Tineke Thio, T. R. Thurston, N. W. Preyer, P. J. Picone,M. A. Kastner, H. P. Jenssen, D. R. Gabbe, C. Y. Chen,R. J. Birgeneau and Amnon Aharony,
Phys. Rev. B ,905-908 (1988); Tineke Thio, C. Y. Chen, B. S. Freer, D.R. Gabbe, H. P. Jenssen, M. A. Kastner, P. J. Picone, N.W. Preyer and R. J. Birgeneau, Phys. Rev. B , 231-239(1990). Yoichi Ando, A. N. Lavrov, and Kouji Segawa,
Phys. Rev.Lett. , 2813-2816 (1999). Yoichi Ando, A. N. Lavrov, and Seiki Komiya,
Phys. Rev.Lett. , 247003 (2003). A. N. Lavrov, H. J. Kang, Y. Kurita, T. Suzuki, SeikiKomiya, J. W. Lynn, S.-H. Lee, Pengcheng Dai, and YoichiAndo,
Phys. Rev. Lett. , 227003 (2004). X. H. Chen, C. H. Wang, G. Y. Wang, X. G. Luo, J. L. Luo, G. T. Liu, and N. L. Wang,
Phys. Rev. B , 064517(2005). D. Vaknin, S. K. Sinha, D. E. Moncton, D. C. Johnston,J. M. Newsam, C. R. Safinya, and H. E. King, Jr.,
Phys.Rev. Lett. , 2802-2805 (1987). J. M. Tranquada, D. E. Cox, W. Kunnmann, H. Moud-den, G. Shirane, M. Suenaga, P. Zolliker, D. Vaknin, S. K.Sinha, M. S. Alvarez, A. J. Jacobson, and D. C. Johnston,
Phys. Rev. Lett. , 156-159 (1988). S. Skanthakumar, J. W. Lynn, J. L. Peng and Z. Y. Li,
Phys. Rev. B , 6173-6176 (1993). I. W. Sumarlin, J. W. Lynn, T. Chattopadhyay, S. N. Bar-ilo, D. I. Zhigunov and J. L. Peng,
Phys. Rev. B , 5824-5839 (1995). V. P. Plakhty, S. V. Maleyev, S. V. Gavrilov, F. Bourdarot,S. Pouget and S. N. Barilo,
Europhys. Lett. , 534-540(2003). S. Skanthakumar, H. Zhang, T. W. Clinton, W-H. Li, J.W. Lynn, Z. Fisk and S. -W. Cheong,
Physica C ,124-128 (1989) M. Matsuda, K. Yamada, K. Kakurai, H. Kadowaki, T. R.Thurston, Y. Endoh, Y. Hidaka, R. J. Birgeneau, M. A.Kastner, P. M. Gehring, A. H. Moudden, and G. Shirane,
Phys. Rev. B , 10098-10107 (1990). S. Skanthakumar, J. W. Lynn, J. L. Peng and Z. Y. Li,
J.Appl. Phys. , 6326-6328 (1993). A. S. Cherny, E. N. Khats’ko, G. Chouteau, J. M. Louis,A. A. Stepanov, P. Wyder, S. N. Barilo and D. I. Zhigunov,
Phys. Rev. B , 12600-12603 (1992). P. Richard, M. Poirier and S. Jandl,
Phys. Rev. B ,144425 (2005). P. Richard, S. Jandl, M. Poirier, P. Fournier, V. Nekvasil,M. L. Sadowski,
Phys. Rev. B , 014506 (2005). J. W. Lynn, I. W. Sumarlin, S. Skanthakumar, W-H. Li,R. N. Shelton, J. L. Peng, Z. Fisk and S-W. Cheong,
Phys.Rev. B J. P. Hill, A. Vigliante, D. Gibbs, J. L. Peng, and R. L.Greene,
Phys. Rev. B , 6575 (1995). S. Jandl, P. Richard, V. Nekvasil, D. I. Zhigunov, S. N.Barilo, and S. V. Shiryaev,
Physica C , 189 (1999). R. Jin, Y. Onose, Y. Tokura, D. Mandrus, P. Dai, and B.C. Sales,
Phys. Rev. Lett. , 146601 (2003). P. Bourges, A. S. Ivanov, D. Petitgrand, J. Rossat-Mignod,and L. Boudarene,
Physica B , 925 (1993). D. Petitgrand, S. V. Maleyev, Ph. Bourges, A. S. Ivanov,
Phys. Rev. B , 1079 (1999). A. S. Ivanov, P. Bourges, D.Petitgrand, J. Rossatmignod,
Physica B , 60-62 (1995). W. Henggeler, T. Chattopadhyay, P. Thalmeier, P. Vorder-wisch, A. Furrer,
Europhys. Lett. , 537-542 (1996). H. Casalta, P. Bourges, D. Petitgrand, A. Ivanov,
SolidState Commun. , 683-686 (1996). Z. Y. Weng, D. N. Sheng, Y.-C. Chen, and C. S. Ting,
Phys. Rev. B , 3894-3906 (1997). S. P. Kou and Z. Y. Weng
Eur. Phys. J. B47