Magnetic state in URu Si , UPd Al and 2 2 2 3 UNi Al probed by point contacts 1 2 3 0 0 2 Yu. G. Naidyuka,b, O. E. Kvitnitskayaa,b, A. G. M. Jansena, C. n a Geibelc, A. A. Menovskyd, P. Wydera J 5 ] el aGrenobleHighMagneticFieldLaboratory, Max-Planck-Institutfu¨rFestko¨r- - perforschung and Centre National de la Recherche Scientifique, Grenoble Cedex r t 9, F-38042, France s . t a bB. Verkin Institute for Low Temperature Physics and Engineering, NAS of m Ukraine, 61164 Kharkiv, Ukraine - d cMax-Planck Institut fu¨r chemische Physik fester Stoffe, Dresden, D-01187, n Germany o c [ d Van der Waals-Zeeman Laboratory, University of Amsterdam 1018 XE, The Netherlands 1 v 2 6 0 Abstract 1 0 Theantiferromagnetic(AFM)statehasbeeninvestigatedinthethree 1 heavy-fermioncompoundsURu2Si2,UPd2Al3,andUNi2Al3bymeasuring 0 dV/dI(V) curves of point contacts at different temperatures (1.5-20K) / t and magnetic fields (0-28T). The zero-bias maximum in dV/dI(V) for a m URu2Si2pointstoapartiallygappedFermi-surfacerelatedtotheitinerant nature of the AFM state contrary to UPd2Al3 where analogous features - d have not been found. The AFM state in UNi2Al3 has more similarities n with URu2Si2. For URu2Si2, the same critical field of about 40 T along o the easy c axis is found for all features in dV/dI(V) corresponding to c the N´eel temperature, the gap in the electronic density of states, and : presumably theordered moments. v i X PACS numbers: 71.28.+d, 73.40.Jn,75.30.Mb r a 1 The U-basedheavy-fermion(HF) systems URu2Si2, UPd2Al3, and UNi2Al3 exhibitingantiferromagnetic(AFM)orderfollowedbyasuperconductingtransi- tionatlowertemperaturesattractmuchinterestinviewofthepossiblecoupling between superconducting and magnetic order. The on the first sight similar AFM ground state in the mentioned HF compounds reveals essential differ- ences. While neutron-scattering experiments resolved an AFM ordered struc- ture in URu2Si2 with a tiny ordered moment 0.03±0.01µB/U-atom below the N´eeltemperature TN=17.5K along the c-axis [1], UPd2Al3 has below TN=14K in the basal plane aligned U-moments equal to 0.85±0.03µB [2]. Although the lattercompoundhasthelargestmomentamongtheHFsuperconductors,ithas the largest superconducting critical temperature Tc of about 2K compared to typically 1.4K in URu2Si2. UNi2Al3 has been investigated much less than the other two compounds probably due to specific difficulties in the preparation of good samples. This compound is isostructural and isoelectronic to UPd2Al3, but hasa few times smallermagnetic momentofabout0.24±0.10µB [3] aswell as lower critical (∼1K) and N´eel (∼5K) temperatures. Pronounced anomalies in specific heat, magnetic susceptibility, resistivity etc. for all three compounds indicate the phase transition into an AFM state. The specific resistivity in URu2Si2 has a well defined N-like structure at TN which looks like a kink for UPd2Al3 andis even more shallowfor UNi2Al3. For the interpretation of the mentioned anomalies a transition into a spin-density wave (SDW) state has been considered [4] with a partial opening of a gap at the Fermi surface [4, 5, 6] of about 10 mV. Tunneling experiments which can determine the gap in the electronic DOS and its anisotropy yield for all three compounds a gap in the range 10 to 20 mV in the basal plane [7, 8]. However, far infrared absorption [9] did not resolve any gap-like features for UPd2Al3 unlike in URu2Si2. For URu2Si2, the most investigated compound among this class of HF systems, it is still under discussion how the large anomalies in the transportand thermodynamic properties at TN can be reconciled with the tiny ordered moments. Therefore, the understanding of the nature of the magnetic order parameter in the AFM state of URu2Si2 remains a challenge. Recent transportandneutronscatteringmeasurementsinahighmagneticfieldrevealed different transition fields for the AFM order or TN (∼ 40 T, [10]) and for the tiny staggered magnetic moments (∼14 T, [11]). This has led to a speculation about some additional ’hidden’ magnetic order parameter in URu2Si2. To clarify some aspects of the mentioned magnetic ordered state, we have performeda comparativepoint-contact study on these U-based HF compounds in strong magnetic fields. Of the three compounds the normal state proper- tieshavebeeninvestigatedpreviouslyusingpoint-contactspectroscopyonlyfor URu2Si2 [12,13,14,15],howevernotinappliedmagneticfields. ThedV/dI(V) characteristics of point contacts with URu2Si2 show an N-type feature related to local contact heating above the N´eel temperature [15] and a zero-bias maxi- mumwhichhasbeenanalyzedintermsofapartialsuppressionofthedensityof states relatedto anitinerantAFM groundstate [12, 14,15]. The presentstudy allows to follow these characteristics of the AFM ground state in a magnetic field with a complete temperature dependent study of the phenomena. 2 We have investigated both homocontacts between the same HF compounds and heterocontacts between a HF compound and normalmetals like Cu or Ag. The main difference was only in the degree of asymmetry of the dV/dI(V) curves with respect to bias-voltage polarity, which is more pronounced for het- erocontacts. The originofthe asymmetryis stillunderdiscussion[15]. Because this effect has no influence on the main conclusions of the present investiga- tions, we will put no more attention to it. In the case of the URu2Si2 single crystal,theheterocontactswereestablishedinsuchawaythatbothcontactaxis and magnetic field were parallel to the c-axis or perpendicular to it. For the UPd2Al3 single crystal the contact axis and magnetic field were aligned along the easy basal plane direction whereas we used UNi2Al3 samples of unknown orientation. The measurements were carried in magnetic fields up to 28 T at 4.2K, but for UNi2Al3 down to about 2K and up to 10T. The measured dV/dI(V) curves of URu2Si2 contacts can be separated into three groups. In the first group the dV/dI(V) curves mimic the behaviour of bulk ρ(T). The differential resistance increases with voltage and exhibits a N- typefeatureatabout20mV(Fig.1a)similartoρ(T)atTN [6]. Thesecondtype of dV/dI(V) revealsa pronouncedasymmetric zero-biasmaximum(ZBM) ofa width of about 10 mV in dV/dI(V) (Fig.1b) followed by gradually increasing signal at higher voltages. The third one contains simultaneously both kinds of structures in dV/dI(V). We note that the temperature dependence of the contact resistance (Fig.1, insets) corresponds in all cases to ρ(T) independent of the type of dV/dI(V) behaviour. This indicates that the material in the constriction reflects the bulk properties. The mentioned features, namely N- type kink and ZBM, vanish at the N´eel temperature (Fig.1) and are therefore connected with the magnetic state. The voltage position of the N-kink (marked by Vk in Fig.1a) is determined by TN and corresponds to the transition of the contact region from the AFM to the paramagnetic state most likely due to bias-voltage heating in the con- striction. The temperature dependence p1−(T/TN)2 ofVk showninFig.2ais expected for such a local contact heating [15]. The ZBM is more pronounced for curves with shallow or not resolved kink peculiarities. Moreover, the ZBM cannotbe described in the thermalmodel whatcan be directlyseen upon com- paring dV/dI(V > 0) with dV/dI(V = 0,T) = R(V = 0,T) (see Fig.1b). These observations point to the spectral nature of ZBM. The latter has been related(see e. g. [15]) with the existence ofa gapin the excitationspectrum of the electrons due to the formation of a SDW below TN. The ZBM has a width whichiscomparablewiththegapvalueestimatedin[4,5,6,8]. Theintensityof the ZBM gradually decreases with increasing temperature [12, 15] analogously to the intensity of AFM Bragg peaks describing the behaviour of the staggered magnetic moments or the order parameter [16]. Therefore, it is tempting to connect the ZBM also with the magnetic order parameter, although the micro- scopic nature of the tiny staggered magnetic moments in URu2Si2 as well as its influence on the measured dV/dI are still unknown. Because the intensity of ZBM depends on the chosen criterion for the subtraction of the increased with a voltage background, we suggest to take voltage position of the minima 3 3.5 8 3 (a) 5 (b) T) T) 0, 0, R ( R ( 2 3.2 0 10 20 0 10 20 6 T (K) T (K) Ω) dI ( 4 V / d T(K) 4 17.5 T(K) 16.5 18 15.5 17 14 16 12 15 8.5 13 R = 2 Ω 4.3 R =3.2Ω 10 2 0 Vk 3 0 Vm 4.7 -40 -20 0 20 40 -20 0 20 V (mV) Figure 1: Two types of behaviour, (a) and (b), in the dV/dI(V) curves for singlecrystalURu2Si2 homocontactsestablishedinthebasalplaneatincreasing temperature up to TN. The curves are offset vertically for clarity. The insets showthetemperaturedependenceofthezerobiasresistance,whichmimicsρ(T) for bulk samples. 1 1 BCS ) 0) 0 ( V(k (1 - (T/TN)2)1/2 V m / k / m V V (a) (b) 0 0 0 0.5 1 0 0.5 1 T / T N Figure 2: Temperature dependence of the reduced voltage positions Vk (a) and Vm (b) (see for definition Fig.1) for a few URu2Si2 homocontacts established in the basal plane. The solid circles for both figures correspond to the same homocontact. The solid line in both figures is the mean-field BCS dependence while the dashed curve describes the thermal regime behaviour [15]. 4 3.0 B=28T B//c a) b) 26 15 k 24 V 22 2.5 20 Ω) 10 M 1 ( 18 I dI 15 V/ 2.0 10 d V m 0 k 5 V 1-(B/B )2 c 1.5 V (1-(B/B )3/2)1/2 m 0 c 0 -30 -20 -10 0 10 20 30 0 20 40 V (mV) B (T) Figure 3: (a) dV/dI(V) curves for a URu2Si2-Cu heterocontact in magnetic fields along the easyc axis atT=4.2K.The solidcurvescorrespondto the field sweep up, while the dashed one to the field sweep down. The arrows show definition of the kink Vk and minimum Vm positions. The curves are offset verticallyforclarity. (b) Dependence ofVk,Vm (left scale)andZBMintegrated intensity IM (right scale) versus magnetic field. Note, position of Vk, Vm and ZBM intensity was taken after symmetrizing of dV/dI(V) curves. The solid lines represent dependence (1 −(B/Bc)2) characteristic for TN(B) and spin- wave gap ∆(B) [10] while dashed line p1−(B/Bc)3/2 is taken from [11] for staggeredmagnetic moments. Vm (see Fig.1b) as an additional measure for the magnetic order parameter as supported by the mean-field (BCS-like) Vm(T) dependence from Fig.2b as also found in [13, 14]. Thepoint-contactdatapresentedinFig.3aformagneticfieldsparalleltothe easyc-axisexhibitbothtypesoffeaturesdiscussedabove,i. e. ZBMandN-kink. The integrated intensity of the ZBM (after subtracting a polynomal voltage- dependent background) is close to the p1−(B/Bc)3/2 behaviour like that for magnetic moments [11]. As shown in Fig.3b, the same dependence is found for Vm as well. On the other hand, Vk follows the magnetic field dependence (1 − (B/Bc)2) like for TN [10](shown in Fig.3b). The latter dependence is found also for the width of ZBM (not shown), which is related to the SDW gap. Thus, the mentioned features in dV/dI(V) - Vk, ZBM width and ZBM intensity or Vm measured on the same contact - are described by the magnetic 5 field dependencies characteristic for the behaviour of transition temperature TN, magnetic gap width [10] and magnetic order parameter [11], respectively. Moreover, as can be seen in Fig.3b, independent of the type of behaviour in all cases the critical field is estimated to be about 40 T what coincides with Bc values measured by magnetoresistance [17]. Therefore, unlike in [10, 11] where for the ordered magnetic moments the critical field is estimated to be about 14T our data show the presence of one order parameter, which vanishes at TN=17.5 K and Bc ≃40 T. This is in line with the recent observation of van Dijk et al. [16] that the ordered moments remain coupled to the energy gap in the magnetic excitation spectrum in fields at least up to 12 T. We should emphasize that by measuring URu2Si2 contacts in a field perpendicular to the easy c-axis direction we did not found any remarkable influence of a magnetic field on dV/dI(V) testifying that the point contact data really reflect the bulk properties. Let us turn to the other compounds. The dV/dI(V) curve of UPd2Al3 contacts (see Fig.4) show a minimum at V=0 with edge maxima or shoulders which are connected with the AFM transition due to the heating effect [18], analogouslytotheN-typefeatureinthecaseofURu2Si2. However,forUPd2Al3 contacts we have never seen even a shallow ZBM neither for homo- nor for heterocontacts after the study of more than 20 contacts both below and above the N´eel temperature. Therefore no evidence of the partially gapping of the FermisurfaceisobservedforUPd2Al3 unlikeinURu2Si2 whatpointstoaquite different magnetic groundstate as well as to the different nature of the ordered moments for both compounds. A magnetic field along the easy basal plane modifies the dV/dI(V) curves of UPd2Al3 as can be seen from Fig.4a. The maxima slightly shift (≈ 15 %) to lower energies and broaden with increasing magnetic field up to 18T, and than vanishin higher fields. The width of the dV/dI(V) minimum at V=0 has a minimum at 18T, while the contact resistance has a kink at this field both at zero bias and finite bias voltage (see Fig.4b,c). Hence the metamagnetic transition at 18T [19] is clearly resolved in point contact measurements, while no other phase boundary was observed both at lower and higher fields up to 28T. From measurements of the dc susceptibility, dc magnetization, transverse magnetoresistivity, and magnetostriction, Grauel et al. [20] have also found a phaseboundaryinUPd2Al3 atacriticalfieldofabout4Talongthebaseplane. However, the influence of this low-field transition on the resistivity is at least one order of magnitude smaller compared to the transition at 18 T. Moreover, de Visser et al. [19] did not found a 4-T transition in their magnetoresistance data indicating that a re-orientation of the AFM domains could play a role in this phenomenon. The dV/dI(V) curves of UNi2Al3 represent usually a smooth broad almost symmetric minimum around zero-bias. However often a shallow ZBM can be observedaroundV=0 (Fig.5). The distance between the minima in dV/dI(V) withZBMisaboutafewmV(oftenupto10mV)andZBMdisappearsatabout 5K (between 10-15K for wider maxima). For ZBM with critical temperature of about 5K critical field was about 10T. From this point of view UNi2Al3 6 2 B=0 T B // ab 10 16 18 20 W 24 dI 28 V/1.5 d 1 1.1 15 -R0 V=10 mV R=0.09Ω 0 V) m V=0 W ( 0.8 B (T) 5 B (T) 1 0 10 20 0 10 20 30 -20 -10 0 10 20 V (mV) Figure4: dV/dI(V)curvesforaUPd2Al3-CuheterocontactwithR0=4.3Ωat differentmagneticfieldsalongthebasalplaneandT=4.2K.Horizontallinewith arrowsshowsdeterminationofthewidthoftheminimum. Thecurvesareoffset vertically for clarity. Right inset: width of the minimum versus magnetic filed for the previous contact and for another contact with R0=0.09 Ω. Left inset: magnetoresistance of the contact with R0=4.3 Ω at zero bias and at 10mV. 7 UPd Al 2 3 1.4 4 I UNi Al d 2 3 / V 1.2 d 2 1 - 0 R 1 0 0.8 URu Si 2 2 -40 -20 0 20 40 V (mV) Figure5: ComparisonofdV/dI(V)curvesforhomocontactswiththree studied HF compounds: UPd2Al3 (R0=0.61 Ω, T=4.2K), UNi2Al3 (R0=1.5 Ω, T= 2.3K)and URu2Si2 (R0 =3.2Ω, T=4.2K). A ZBMis only resolvedfor the two latter compounds. The curve for URu2Si2 is shifted down by 0.15. behavessimilartoURu2Si2whathintstothedevelopingofamagneticstatewith partiallygappingoftheFermisurfaceinthiscompoundtoo. Itshouldbenoted that we didn’t resolve any feature in dV/dI(V) for UNi2Al3 (Fig.5) connected withTN like thatinURu2Si2 (Fig.1a)andUPd2Al3 (Fig.5). Thistransitionat TN is also very shallow in the ρ(T) dependence of UNi2Al3. Probably, a better quality of the UNi2Al3 samples is required to register the AFM transition and to study the temperature behaviour of ZBM in dV/dI(V). Summarizing, the point-contact measurements for the investigated U-based heavy fermion compounds yield information on the differences in the AFM groundstateofthesesystems. TheZBM-structureindV/dI(V)fortheURu2Si2 contacts points to a partially gapped Fermisurface in the magneticallyordered state, but no evidence of an analogous structure has been found in the case of UPd2Al3 unlike for UNi2Al3 whereit is possible to resolvea shallowZBM.The results for URu2Si2 in the H −V,T diagram yield only one critical N´eel tem- peratureof17K andone criticalfield ofabout40T alongthe easyc-axisforall featuresindV/dI(V)testifyingthattheyresultfromthesameorderparameter in the magnetic state. 8 References [1] Brocholm C., Kjems J. K., Buyers W. J. L., Matthews P., Palstra T. T. M., Menovsky A. A. and Mydosh J. A., Phys. Rev. Lett. 58 (1987) 1467. [2] Krimmel A., Fischer P., Roessli B., Maletta H., Geibel C., Schank C., Grauel A., Loidl A. and Steglich F. Z. Phys. B 86 (1992) 161. [3] Schr¨oder A., Lussier J. G., Gaulin B. D., Garrett J. D., Buyers W. J. L., Rebelsky L., and Shapiro S. M. Phys. Rev. Lett. 72 (1994) 136. [4] Maple M. B., Chen J. W., Dalichaouch Y., Kohara T., Rossel C., TorikachviliM. S., McElfrechM. W. andThompsonJ.D. Phys. Rev. Lett. 56 (1986) 185. [5] PalstraT.T.M.,MenovskyA.A.,vanderBergJ.,DirkmaatA.J.,KesP. H., Nieuwenhuys G. J. and Mydosh J. A. Phys. Rev. Lett. 55 (1985)2727. [6] Mydosh J. A. Physica Scripta T19 (1987) 260. [7] Aliev F.G.,KovachikV.,MoshchalkovV.V., PryadunV.V., Alekseevskii N. E.,Mitin A. V., AgraitN., VieraS., Villar R.J. of Low Temp. Phys 85 (1991) 359. [8] Aarts J., Volodin A. P., Menovsky A. A., Nieuwenhuys G. J. and Mydosh J. A. Europhys. Lett., 26 (1994) 203. [9] Degiorgi L., Thieme S., Ott H. R., Dreessel M., Gru¨ner G., Dalichaouch Y.,MapleM.B.,FiskZ.,GeibelC.andSteglichF.Z. Phys. B.102(1997) 367. [10] Mentink S. A. M., Mason T. E., Su¨llow S., Nieuwenhuys G. J., Menovsky A. A., Mydosh J. A. and Perenboom J. A. A. J. Phys. Rev. B 53 (1996) 6014. [11] Mason T. E., Buyers W. J. L., Petersen T., Menovsky A. A. and Garrett J. D. J. Phys.:Condens. Matter 7 (1995) 5089. [12] Hasselbach K., Kirtley J. R. and Lejay P. Phys. Rev. B. 46 (1992) 5826. [13] Escudero R., Morales F. and Lejay P. Phys. Rev. B. 49 (1994) 15271. [14] ThiemeSt.,SteinerP.,DegiorgiL.,WachterP.,DalichaouchY.,andMaple M. B. Europhys. Lett. 32 (1995) 367. [15] NaidyukYu.G.andYansonI.K.J.Phys.:Condens. Matter10(1998)8905. [16] van Dijk N. H., Bourdarot F., F˚ak B., Lapierre F., Regnault L. P., Burlet P., BossyJ., Pyka N. andMenovsky A.A. Physica B 234-236(1997)693. [17] SugiyamaK.,Fuke H., Kindo K.,Shimohata K.,MenovskyA. A., Mydosh J. A. and Date M. J. Phys. Soc. Jpn. 59 (1990) 3331. 9 [18] Kvitnitskaya O. E., Naidyuk Yu. G., Nowack A., Gloos K., Geibel C., Jansen A. G. M. and Wyder P. Physica B 259-261 (1999) 638. [19] de Visser A., Bakker K., Tai L.T., Menovsky A.A., Mentink S. A. M., Nieuwenhuys G. J. and Mydosh J. A. Physica B 186-188 (1993) 291. [20] GrauelA., B¨ohmA., Fischer H., Geibel C., K¨ohlerR., Modler R., Schamk C., Steglich F., Weber G., Komatsubara T. and Sato N. Phys. Rev. B 46 (1992) 5818. 10