Nonlinear magnetic response in ruthenocuprates
aa r X i v : . [ c ond - m a t . s t r- e l ] A p r Nonlinear magnetic response in ruthenocuprates
I.ˇZivkovi´c, V.P.S. Awana, and H. Berger Institute of Physics, P.O.B.304, HR-10 000, Zagreb, Croatia National Physical Laboratory, Dr. K.S. Krishnan Marg, New Delhi-110012, India Institut de Physique de la Mati`ere Complexe, EPFL, CH-1015 Lausanne, Switzerland (Dated: October 29, 2018)We have performed an investigation of the nonlinear magnetic response in ruthenocuprates. Anegative, diverging-like peak at the main magnetic transition T N in RuSr RE Cu O ( RE = Gd, Y)indicates a possible canted antiferromagnetic order. Another well defined feature above T N pointsto a blocking of superparamagnetic particles through the T − dependence of the third harmonicat higher temperatures. Below T N a nondiverging peak appears, which is strongly affected by theaddition of 10% of Cu ions in the RuO planes. In RuSr RE − x Ce x Cu O the main magnetictransition T M is accompanied by two characteristic temperatures in the third harmonic of the acsusceptibility, in agreement with recent studies from µ SR and M¨ossbauer spectroscopy. We findthat the spin-spin correlation temperature is the same in both families of ruthenocuprates.
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INTRODUCTION
A possibility of coexistence of superconducting andferromagnetic order on the microscopic scale has at-tracted a lot of attention to ruthenocuprates. Al-though a respectable amount of experimental work hasbeen published so far, a complete and detailed descrip-tion of the magnetic properties of the ruthenocupratesis still lacking. The ruthenocuprate family ofmaterials consists of two well investigated phases,RuSr RE Cu O (Ru1212) and RuSr RE − x Ce x Cu O (Ru1222) and RuSr RECe Cu O (Ru1232) (RE =rare-earth) recently synthesized through a high-pressure-high-temperature (HPHT) procedure [1] with a compo-sition RuSr RECe Cu O (Ru1232) (RE = rare-earth).All ruthenocuprates have similar planar structure withRuO planes responsible for the magnetic ordering andCuO planes for the superconductivity. Between the twoCuO planes there is a RE layer (as in YBa Cu O ,where RuO planes are replaced with CuO chains), a RE − x Ce x O block or a RE Ce O block for Ru1212,Ru1222 and Ru1232, respectively. Due to the presence ofthe RE − x Ce x O block, the Ru1222 system has adjacentRu ions shifted along the c -axis by ( a + b ) / T N = 130 K while theRu1222 system is characterized by two: one around T FM = 180 K and the second one around T M = 100 K (de-pends slightly on the RE /Ce ratio). Although early re-ports have suggested a ferromagnetic order in Ru1212 [2]and Ru1222 [3], neutron scattering results have indicatedthe presence of antiferromagnetism [4, 5, 6] with an upperlimit of 0 . µ B for a ferromagnetic component. Moreover,the direction of the magnetic moment has been deter-mined to be along the c -axis, contradicting the µ SR [2],EPR [7] and NMR [8] measurements where it was con- cluded that the moments lie in the ab -plane.To reconcile the proposed hypotheses, a weak ferro-magnetism [5, 9], a phase separation [10], a combinationof two [11] and a spin-glass scenario [12] have been sug-gested. Recently, a µ SR study [13] on the Ru1222 systemhas shown that at T FM only 15% of the material gets or-dered. This finding has been confirmed in a M¨ossbauerstudy [11]. The rest of the sample orders at T M . As forthe Ru1212 system, Xue and coworkers [10] have showedthat substituting the Ru ions with the Cu ions leads toa separation of the ferromagnetic and the antiferromag-netic ordering temperatures. Moreover, a recent investi-gation of the nonlinear dynamics and the magnetizationdecay on the Ru1212 ( RE = Gd) composition [14] hasrevealed an existence of ferromagnetic clusters with anordering temperature only few Kelvins above the T N ,the antiferromagnetic ordering temperature. A similarobservation has been found on the Ru1212Y composi-tion [15], although with a different sign of the third har-monic around T N , which will be discussed later.In this paper we extend our investigation of the nonlin-ear magnetic behavior in ruthenocuprates. We confirmour previous claim that the Ru1212 system, for RE =Gd, Y, shows a negative third harmonic in the ac sus-ceptibility which is not compatible with a simple AFMordering of Ru ions. Through a detailed study of theac field dependence of the ac susceptibility we show thatat the main magnetic transition T N the third harmonicshows diverging-like behavior, where in simple AFM sys-tem, no divergence is observed both above and below T N . Additional features are visible in both pure anddoped Ru1212 systems which can be ascribed to a super-paramagnetic behavior. The third harmonic for different RE /Ce ratios in the Ru1222 system is qualitatively thesame. Two characteristic temperatures around T M arefound which indicates that a long-range ordering sets inat T M . EXPERIMENTAL DETAILS
We have performed the measurements onthe following compositions: RuSr GdCu O (Ru1212Gd), Ru . Sr YCu . O . (Ru1212Y) andRuSr RE − x Ce x Cu O (Ru1222Eu) with x rangingfrom 0.6 to 1.0. The polycrystalline samples usedin this study have been measured previously, seeRefs. [3, 16, 17]. Ac susceptibility measurements wereperformed using the commercial CryoBIND system withthe frequency of the driving field equal to 990 Hz.Nonlinear susceptibilities can be defined through theexpansion of the magnetization M in the power series ofthe magnetic field HM = M + χ H + χ H + χ H + ..., (1)where χ is the linear (or a first order) susceptibility and χ and χ are the second and the third order suscep-tibilities, respectively. Although usually much smallerthen the linear component, χ and χ often provide ad-ditional information about the investigated system. Ithas been shown that the divergence of χ characterizesthe spin-glass transition [18]. It has been used to dis-tinguish spin-glasses from superparamagnets [19, 20, 21],both showing similar behavior in the linear component χ . For long-range-ordered systems χ shows divergenceon both sides of T C in ferromagnets [18, 22, 23, 24], whilefor antiferromagnets χ has a nondiverging, asymmetricshape at the transition with a positive sign of χ below T N [18, 25, 26, 27].Even order susceptibilities vanish when the magnetiza-tion has inversion symmetry with respect to the magneticfield applied. χ has been used to provide the evidence ofthe coexistence of the ferromagnetic and glassy behaviorin reentrant spin-glass systems [28] and doped cobalt-based perovskites [29].When an ac field H = H cos ωt with a frequency ω isapplied, an induced voltage in the coils detected with alock-in amplifier involves higher harmonic terms in addi-tion to the first harmonic:∆ V ∝ − dMdt ∝ ωH [ χ exp sin ωt ++ χ exp H sin 2 ωt + 34 χ exp H sin 3 ωt + · · · ] (2)The harmonics are related to the higher-order suscepti-bilities through the following relations: χ exp = χ + 34 χ H + 58 χ H + . . . ,χ exp H = χ H + χ H + 1516 χ H + . . . , χ exp H = 34 χ H + 1516 χ H + 6364 χ H + . . . (3)For small amplitudes H we can put χ = χ exp , χ = χ exp and χ = χ exp . There are no general rules as how large H is allowed to be before higher order terms shouldbe taken into account. The best option is to use as small H as possible.As explained above, the sign of the third harmonic isoften more important in determining the qualitative as-pects of the material under investigation then the abso-lute magnitude of the signal. Therefore, we have checkedthe sign of χ by measuring the triangular wave as aninput signal for the lock-in amplifier [22]. In addition tothat, the sign is also verified by observing the responsefrom the superparamagnetic particles which should al-ways be negative (see the following section).Measurements for the ac field dependence of the thirdharmonic (Fig. 3) have been performed by measuring thesignal in a temperature window around the peak since themaximum shift as the ac field is increased. RESULTS AND DISCUSSIONRu1212
We have investigated the Ru1212 system containingtwo rare-earth elements, Gd and Y. The real part of theac susceptibility for the two systems is shown in Fig. 1a.Ru1212Gd shows a somewhat larger susceptibility thanRu1212Y with a peak positioned at T N = 135 K. ForRu1212Y the peak is more rounded with a maximumvalue around 140 K. The imaginary part of the ac suscep-tibility is displayed in the inset of Fig. 1a. A sharp peakis seen for Ru1212Gd system, while for Ru1212Y thereare two broad maximums located around 110 K and 180K, with a kink at 140 K where χ ′ has a maximum.Figure 1b shows the nonlinear susceptibility forRu1212Gd measured in various ac fields. Three distinctfeatures can be noticed, which occur at T = 152 K, T = 137 K and T = 131 K. In the inset of Fig. 1b thepeak at T is shown enlarged. For small fields T is barelyvisible and for larger fields it gets smeared out due to thegrowth of the peaks at T and T . The peak at T isvery sharp for all the fields applied but it overlaps withthe feature at T as the field increases. T peak showsa rapid growth as the field is increases, with a long tailbelow the temperature where the minimum occurs.In Fig. 1c the third harmonic for the Ru1212Y sys-tem is presented. A broad maximum around 180 K hasbeen attributed to the formation of the superparamag-netic particles [15]. This feature leaves a visible imprintin the first harmonic as well (Fig. 1a). On the other hand,in Ru1212Gd neither χ ′ nor χ ′′ show visible deviation at T . Below 150 K χ ′ starts to grow (in negative values)with a kink at 140 K (where a maximum in χ ′ is located)for small fields. As the field is increased, a peak devel-ops at a temperature slightly above 140 K with a tailfor lower T. No T peak is observed in the Ru1212Y sys-tem. Taking into account that the RuO planes in the FIG. 1: (Color online) (a) Temperature dependence of the realpart of the ac susceptibility for Ru1212Gd and Ru1212Y sys-tems measured with H AC = 1 Oe. The inset shows the imagi-nary part. (b) Temperature dependence of the third harmonicof the ac susceptibility for the Ru1212Gd system. From topto bottom H AC = 3 , ,
20 Oe. Inset: enlarged view around T . (c) Temperature dependence of the third harmonic forthe Ru1212Y system. From top to bottom H AC = 5 , , Ru1212Y system investigated in this paper are slightlydisordered due to the doping with extra Cu ions, it isnaturally to conclude that the features observed at T and T are intrinsic to Ru1212 ruthenocuprate (as seenfor the Ru1212Gd composition).It has been shown [20] that the existence of the super-paramagnetic particles can be verified through the T − FIG. 2: (Color online) T − dependence of χ ′ for Ru1212Yand Ru1212Gd measured in 10 Oe and 20 Oe, respectively.Solid lines represent the best fit to Wohlfarth’s model (seetext). dependence of χ ′ . According to the Wohlfarth’s super-paramagnetic blocking model [30], χ ′ of the assembly ofsuperparamagnetic particles follows a Curie law abovethe blocking temperature T B while χ ′ shows negative T − dependence, χ ′ = n h µ i h µ i k B T (4) χ ′ = − n h µ i (cid:18) h µ i k B T (cid:19) , (5)where n is the number of particles per unit volume, h µ i isthe average magnetic moment of the single particle and k B is the Boltzmann constant. In Fig. 2 we show ap-propriate plots for Ru1212Gd and Ru1212Y. The lineardependence of χ ′ on T − is found only in a small temper-ature interval: between 188 K and 203 K for Ru1212Yand between 156 K and 161 K for Ru1212Gd. Althoughin conventional superparamagnetic systems the particle’sinternal spin-spin correlation temperature is much higherthan the blocking temperature T B [19, 31], it has beenshown recently [32] that for Li . Ni . O a similar behav-ior occurs with a 10 K wide temperature interval wherethe third harmonic is linear in T − . We are aware that a5 K interval observed in the Ru1212 system is probablytoo small and it can serve only as an indication. What isimportant is that a doped system Ru1212Y shows quali-tatively the same behavior as a pure system ( RE = Gd)corroborating the hypothesis that these features are in-trinsic to material and that they are not the consequenceof the existence of impurities.From equations (4) and (5) one can extract the averagemagnetic moment of the superparamagnetic particle [19].However, due to the presence of the ordering at T N andthe paramagnetic contribution from the Gd ions (in theRu1212Gd system), it was in this case not possible toextract the magnetic moment.It is indicative that for the Ru1212Y composition, forwhich 10% of Ru ions have been replaced by Cu ions, T peak is larger then in the stoichiometric Ru1212Gd com-position and has shifted to higher temperatures. Thesame happens for the first harmonic of Ru1212Y (seeFig. 1). This suggests that the incorporation of Cu ionsin the RuO plane enhances the formation of superpara-magnetic particles. It doesn’t affect the main transitionsince T shows the same behavior for both compositions. χ ′ gradually vanishes at higher temperatures ( ≈ −
280 K). This applies for both investigated Ru1212 sys-tems, indicating a common mechanism behind the build-up of correlations.In both Ru1212 RE systems ( RE = Gd, Y) investigatedhere, the third harmonic remains negative, contrary tothe report of Cimberle and coworkers [14]. In Ref. [14]two positive peaks have been observed with the interpre-tation that there are one positive and one negative peak,the negative one hollowing the positive peak. The posi-tive peak has been ascribed to an AFM order while thenegative peak has been attributed to the blocking of thesuperparamagnetic particles [14]. The close inspectionreveals that the only difference between Ref. [14] and ourresults lies in the sign of the third harmonic, since thetwo peaks from Ref. [14] are the T and T peaks fromFig. 1b.The detailed ac field dependence (Fig. 3a, 3b) showsthat the T and T peaks have substantially differentbehavior in the small field regime, which has not beenprobed in Ref. [14]. T shows a divergent-like behavior,while T starts to decrease below ≈ T in the Ru1212 system with a T − de-pendence indicates an occurrence of superparamagneticparticles. There is no doubt that this results in a neg-ative χ (eq. (5)), as reproduced in our measurements. T is a natural explanation for the occurrence of blockedsuperparamagnetic particles which gives rise to time re-laxations of magnetization [14]. We may assume thatthe phase of the third harmonic in Ref. [14] was simplychanged by 180 degrees, either before the measurementor during the data analysis.The main magnetic transition in the Ru1212 system ischaracterized by a negative, diverging peak at T for bothcompositions investigate. Due to the presence of the ad-jacent peaks and relatively small signal, we were unableto perform the critical analysis which would allow us to FIG. 3: (Color online) ac field dependence of the amplitudeof the peaks in χ for various ruthenocuprates. The peaksshift in temperature as the ac field is increased and the labelscorrespond to the low-field value. Dotted lines are guides forthe eye. determine to which class this transition belongs. Diver-gence in the limit of H AC → H AC → T C . The negative character of T peak is in disagreement with the proposed C-type AFMsystem [4] for which it is expected to show a positive,nondiverging third harmonic for T < T N and vanishinglysmall signal for T > T N [18, 27]. On the other hand, ithas been shown [27] that canted AFM systems divergenegatively on both sides of the transition. In addition,another well defined peak has been observed in [27] belowthe transition, which has been ascribed to an interactionof domain walls with an external field. We also see theappearance of a peak at T for larger fields. Based onthis experimental evidence, we suggest a canted AFMordering to occur in the Ru1212 system.Canted AFM structure has been previously proposedfor the Ru1212 system [5]. Calculations of the local spin-density approximation of Nakamura and Freeman [34]showed that canted AFM has a slightly lower energy thenc-type ordering seen in the neutron scattering. Investi-gation of ac susceptibility in dc-bias field [35] revealed ametamagnetic transition which was suggested to be be-tween the canted AFM state for fields below the criticalfield and FM state above.Since an upper limit for a ferromagnetic component at0.1 µ B has been obtained [4], it was hard to accommo-date large canting angles to explain three times largermagnetic moment revealed from the magnetization mea-surements [36]. Xue and coworkers [10] suggested a phaseseparation into an AFM matrix and FM particles whicheliminates the need for a large canting angles of the AFMmatrix. This scenario is also supported by our measure-ments.The largest difference between the two Ru1212 com-positions investigated in this work is revealed below themain transition. In the Gd-based compound there isanother well-defined peak T with a strong ac field de-pendence while the Y-based compound shows only abroad feature with a modest field dependence. T peakshows nondiverging behavior while the broad feature inRu1212Y is visible even for smallest measuring fields.Very similar observation has been reported in the caseof a canted AFM system [27]. The appearance of a peakbelow the main transition has been attributed to the ef-fect of the external field on magnetic domains formed byweak ferromagnetic moments. Taking into account thefact that the T peak is missing in Ru1212Y where Cuions to some extent alter the genuine magnetic order inRuO planes, we conclude that it is intrinsic to the mag-netic order in Ru1212. Ru1222
The first harmonic in the Ru1222Eu system for theconcentrations ranging from x = 1 . x = 0 .
6, alongwith Ru1212Gd data, is presented in Fig. 4. In general,susceptibility of the Ru1222 system is approximately anorder of magnitude larger than for the Ru1212 system.As x decreases both the temperature T M and the size ofthe peak decrease, from 121 K for x = 1 . x = 0 .
6. For concentrations with x ≤ . < T ANOM <
140 K,shown in the inset of Fig. 4. No correlation has beenobserved between either the size of the anomaly or thetemperature at which anomaly occurs with respect to thenominal Eu/Ce ratio, in agreement with [38]. In µ SRstudy [13], conducted on the x = 0 . x = 0 . x = 1 . T M .The third harmonic for the RuSr Eu . Ce . Cu O ( x = 0 .
7) composition measured in 1 and 10 Oe is shownin Fig. 5. Three distinct magnetic features can be dis-cerned in larger fields: a small negative peak around thetemperature where the anomaly in χ has been observed( T ANOM ), a negative peak above T M and a positive peakbelow T M . On lowering the temperature the signal be-comes smaller, until the superconducting order sets inbelow 30 K. The third harmonic measurements have beenrecently used to prove the coexistence of ferromagneticand superconducting order parameters [39]. For otherconcentrations the results are very similar, with T P OS and T NEG shifting in temperature according to the shiftin T M . In the inset there is an enlarged view of the hightemperature part for H AC = 10 Oe where we show thedissapearence of the third harmonic in the same temper-ature range as for the Ru1212 system (Fig. 2).As we have mentioned in the introduction, it is veryimportant to measure the higher order harmonics in assmall a field as possible, to be able to use the approx-imation χ = χ exp (see eq. (3)). In Fig. 6 we show allthe investigated concentrations of the Ru1222Eu systemmeasured in 1 Oe. All the curves show a similar pattern:a positive peak below T M (vertical dashed lines) and asmall negative dip above T M . This is a strong indicationthat T P OS and T NEG are related to the main magnetictransition T M . For x = 0 . x = 1 . T ANOM is al-ready observed for H AC = 1 Oe.The occurrence of two characteristic temperaturesaround the main magnetic transition in the Ru1222system has been reported in recent investigations by µ SR [13] and M¨ossbauer spectroscopy [11]. These re-ports showed the existence of two internal magnetic fieldsappearing around the main magnetic transition T M . Inaddition, the existence of the ordering just above T M FIG. 4: (Color online) The first harmonic for Ru1222Eu and Ru1212Gd compositions. Inset: enlarged temperature windowwhere the anomaly for the Ru1222 system occurs. No systematic behavior has been observed, either in the temperature or inthe size of the anomaly.FIG. 5: (Color online) The third harmonic for the Ru1222Eusystem with x = 0 . has been indicated in our previous reports [40, 41]. Atemperature dependence of the time relaxations of theac susceptibility [40] and the peculiar inverted hystere-sis [41] has shown that these phenomena originate at aslightly higher temperature than T M and fully developbelow T M .With respect to the occurrence of the anomaly, all com-positions show the same behavior, even the parent com-pound ( x = 1 . x = 1 . T M for x = 1 .
0. It has been suggested that for x < . ions surrounded by oxygen holes reduce to Ru ,which has been assumed to be related to the occurrenceof the anomaly. Our measurements show that if the clus-tering of Ru ions is related to this feature, it is not theCe content that drives the reduction from Ru to Ru ions, since the RuSr EuCeCu O ( x = 1 .
0) compound isstoichiometric. NMR experiments on Ru1212 [8], whichis also stoichiometric, indicated the coexistence of Ru and Ru ions which has been associated with the trans-fer of electrons from CuO to RuO planes and the oc-currence of superconductivity in this compound. We pro-pose that a similar mechanism might also be present inthe Ru1222 system. The transfer of electrons must beweaker than in the Ru1212 system, since x = 1 . x = 0 . for Ce ions additional holes are intro-duced to CuO planes which induces superconductivityfor x ≤ . T P OS , T NEG and T ANOM . We have only shown the results forthe Ru1222Eu x = 0 . x = 1 .
0, reveal qualitatively similarresults. Fig. 3c shows that T P OS has a diverging charac-ter, while T NEG and T ANOM are nondiverging, althoughthis is only evident in fields smaller then 2 Oe, which in-dicates the importance of the small-field measurements.A very similar observation in an amorphous ferromag-net, Fe Co Ni − x Cr x B Si with x = 5 [24], has beenexplained invoking a clusterization above the main tran-sition, before the full FM order sets in. This resulted ina negative, nondiverging third harmonic above T C anda positive, diverging harmonic below T C . We proposethat a similar situation occurs in the Ru1222 system. Asshown by µ SR study [13], just above T M a majority ofthe volume orders and from our results it seems clear thatthere is no long-range order. Eventually at T M , where therest of the sample gets ordered [13], χ diverges indicat-ing a long-range order. This is to be contrasted with re-cent neutron scattering results on Ru1222, x = 0 . T M is actually related to the impurity phaseof unknown origin and that Ru ions incorporated in theRu1222 phase do not contribute significantly to the ob-served magnetic behavior in the Ru1222 system. Thesystematic change of characteristic temperatures with x in linear and nonlinear magnetic dynamics presented inthis report and in previous investigations, with variousdopants for Ru ions [38] suggest an intrinsic scenario be-hind the magnetism in the Ru1222 system. More exper-iments are needed in order to elucidate the microscopicnature of magnetic ordering in this material.Some features are not visible in small fields ( ∼ H AC = 10 Oe. The anomaly is now clearly visible forall the concentrations, with the x = 0 . x = 1 . T ANOM is overlaps with a large, negative peak at T NEG . Above T ANOM there is another deviation, 170 K < T ∗ <
180 K, which for some concentrations developsinto a peak and for others creates only a barely visible
FIG. 6: (Color online) The third harmonic for the Ru1222Eusystem measured with 1 Oe. The curves have been verticallydisplaced for clarity. The vertical dashed lines mark T M , themaximum in χ . shoulder. The most pronounced peak is again seen forthe x = 0 . µ SR [13] showed the existence of magnetic order in15% of the sample below T ∗ . The weak, negative sign ofthe third harmonic supports the hypothesis of a minorvolume fraction ordering locally and giving rise to mag-netism above the main magnetic transition T M . Due tothe small signal and large background from other peaks,we were unable to find an appropriate temperature in-terval with a T − dependence, as we have shown for theRu1212 system (see Fig. 2). The Wohlfarth’s model,which predicts a T − dependence, assumes a constantaverage moment of the particle (see eqs. (4) and (5)). Assuggested in Ref. [43], due to the different temperaturedependence of the FM and AFM interactions inside theclusters, the average magnetic moment is temperaturedependent. This implies a nondiverging third harmonicwith a temperature dependent slope in the χ versus T − plot, as in our case.The origin of the high-temperature ordering continuesto be a subject of debate. Except for the obvious intrin-sic scenario, an impurity-based explanation has been pro-posed [38] with Sr-Ru-Cu-O phase showing similar tem-perature dependence of the coercive field as the Ru1222system. Cu ions are thought to be inhomogeneouslydistributed in both Ru and Sr sites which causes Sr-Ru-Cu-O phase to act as an independent particle inside theRu matrix. This study has been conducted on a systemwith a long-range ferromagnetic order where magnetic FIG. 7: (Color online) Measurement of the third harmonicwith H AC = 10 Oe for all the investigated concentrationsof the Ru1222Eu system. T ANOM is developed for all theconcentrations. x = 1 . T ANOM and T NEG overlapped. domains and domain walls play a dominant role in themechanism behind the coercivity. On the other hand,nanosized particles incorporated in the Ru1222 matrixcan be considered as monodomain structures, with a su-perparamagnetic blocking as the main mechanism gener-ating the coercive field. Although an anisotropy ( K ) isinvolved in both processes, a temperature dependence ofthe coercive field in a bulk system should not be takenas an indicator for nanosized particles. This leaves theintrinsic scenario as a probable mechanism, but we arestill missing the microscopic explanation of it.Other features observed in this report are also unlikelyto be related to the presence of impurities. The Ru1212system has been investigated before [14] and, apart fromthe sign of the third harmonic, the same features havebeen observed. Furthermore, through the investigationof Ru . Sr YCu . O . (Ru1212Y) we have shown thatupon introduction of a structural disorder due to the in-corporation of Cu ions into the RuO planes, the Ru1212system’s predominant ordering at T does not change.On the other hand, the peak at T , which presumably re-flects the interaction of domain walls in the canted AFMstate with the external field, is strongly influenced withthe imposed disorder, indicating that the magnetic re-sponse from the Ru1212Gd compound is intrinsic to theRu1212 system.In the Ru1222 system all the different RE /Ce ratiosshow consistent behavior between the first and the thirdharmonic. T P OS and T NEG change in accordance withthe change in T M and in the µ SR experiment [13] it hasbeen shown that this involves more than 90% of the sam-ple’s volume. The detection limit of x-ray diffractionmeasurements for our samples indicates <
3% of impu- rities [3, 16, 17], confirming that T P OS and T NEG areintrinsic to the Ru1222 system. The anomaly around120 K has been observed in all previously investigatedRu1222 samples and has been linked to the high temper-ature transition around 180 K [38, 43]. Substitution ofRu ions with Mo ions [38] showed that while the mainmagnetic transition is shifted, the anomaly remains un-changed. If the anomaly is related to some sort of im-purities in the Ru1222 system, one would expect drasticchanges in position and intensity, which has not been ob-served. In addition, the higher harmonics are orders ofmagnitude weaker than the first harmonic and we haveshown that the anomaly appears even for the smallestfields used. This strongly implies that the anomaly isintrinsic to the Ru1222 system.
CONCLUSION
Several novel features have been observed in our studyof the nonlinear susceptibility of ruthenocuprates. InRu1212 we have found a negative third harmonic of theac susceptibility, with a clear separation between themain magnetic transition and the formation of super-paramagnetic particles. The divergent-like behavior ofthe third harmonic at the main magnetic transition in-dicates a long-range ordered state. Previous reports fa-vored a canonical AFM state with magnetic momentspointing along the c-axis. Our results contradict this hy-pothesis since canonical AFM systems are expected toshow a nondiverging positive third harmonic. We pro-pose that the majority of magnetic moments order ina canted AFM state, in accordance with the neutrondiffraction results. The dominant ferromagnetic responsecomes from the separated, short-range ordered particleswhich are blocked below a temperature slightly higherthan the temperature of the main magnetic transition.The peak appearing below T N for larger magnetic fieldshas been ascribed to an interaction between domains ofweak ferromagnetic moments and the applied field.Nonlinear response in the Ru1222 system revealed twocharacteristic temperatures around T M , in line with µ SRand M¨ossbauer results. The charateristic lower temper-ature T P OS coincides with the main magnetic transition T M seen in the linear response. The divergence of thethird harmonic at T P OS is an indication of the onset ofa long-range order. We have observed a small negativefeature in χ around 180 K for all compositions. Thisis a possible signature of a minority phase ordering intosupeparamagnetic particles.In both ruthenocuprate systems the third harmonicstarts to show in the temperature range ≈ − [1] V.P.S. Awana H. Kishan, T. 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