The magnetic field dependence of the magnetisation ($M$) and the temperature
dependence of the ac susceptibility ($\chi' = dM/dH$) of CePd(1-x)Rh(x) single
crystals with $0.80 \leq x \leq 0.86$ are analysed within the frame of the
quantum Griffiths phase scenario, which predicts $M \propto H^{\lambda}$ and
$\chi' \propto T^{\lambda-1}$ with $0 \leq \lambda \leq 1$. All $M$ vs $H$ and
$\chi'$ vs $T$ data follow the predicted power-law behaviour. The parameter
$\lambda$, extracted from $\chi'(T)$, is very sensitive to the Rh content $x$
and varies systematically with $x$ from -0.1 to 0.4. The value of $\lambda$,
derived from $M(H)$ measurements on a \cpr single crystal, seems to be rather
constant, $\lambda \approx 0.2$, in a broad range of temperatures between 0.05
and 2 K and fields up to about 10 T. All observed signatures and the $\lambda$
values are thus compatible with the quantum Griffiths scenario.Comment: 4 pages, 3 figure

C Geibel

F Steglich

M Brando

M Deppe

P Gegenwart

Pikul A P

T Westerkamp

Vojta T

Journal of Physics : Conference Series

English

arXiv

Brando, M.

Westerkamp, T.

Deppe, M.

Gegenwart, Philipp

Geibel, C.

Steglich, F.

OPUS Augsburg

Journal of Physics: Conference SeriesOPEN ACCESSQuantum Griffiths phase in CePd1−xRhx with x ≈0.8To cite this article: M Brando et al 2010 J. Phys.: Conf. Ser. 200 012016 View the article online for updates and enhancements.Related contentMagnetic scaling of non-Fermi-liquidUCu5-xPdx (x = 0.8, 0.9, 1, 1.2)André M Strydom, Paul de V du Plessisand Robert Troc-Disorder-driven non-Fermi liquid behaviourof correlated electronsE Miranda and V Dobrosavljevi-H – T phase diagram of YbCo2Si2 with H //[100]L Pedrero, M Brando, C Klingner et al.-Recent citationsComprehensive studies of thetransformation between antiferromagneticCeCoGe3 and heavy fermion CeFeGe3compoundsP. Skokowski et al-Suppression of long-range ferromagneticorder in the CexLa1xTiGe3 systemJeonghun Lee et al-Site dependence of the Kondo scale inCePd1xRhx due to Pd-Rh disorderU. Stockert et al-This content was downloaded from IP address 137.250.102.74 on 17/05/2021 at 12:09Quantum Griffiths phase in CePd1−xRhx with x ≈ 0.8M Brando1, T Westerkamp1, M Deppe1, P Gegenwart2, C Geibel1and F Steglich11 Max Planck Institute for Chemical Physics of Solids, Dresden 01178, Germany2 I. Physikalisches Institut, Georg-August-Universität, Göttingen 37077, GermanyE-mail: manuel.brando@cpfs.mpg.deAbstract. The magnetic field dependence of the magnetisation (M) and the temperaturedependence of the ac susceptibility (χ′ = dM/dH) of CePd1−xRhx single crystals with0.80 ≤ x ≤ 0.86 are analysed within the frame of the quantum Griffiths phase scenario, whichpredicts M ∝ Hλ and χ′ ∝ T λ−1 with 0 ≤ λ ≤ 1. All M vs H and χ′ vs T data follow thepredicted power-law behaviour. The parameter λ, extracted from χ′(T ), is very sensitive to theRh content x and varies systematically with x from -0.1 to 0.4. The value of λ, derived fromM(H) measurements on a CePd0.2Rh0.8 single crystal, seems to be rather constant, λ ≈ 0.2, ina broad range of temperatures between 0.05 and 2 K and fields up to about 10 T. All observedsignatures and the λ values are thus compatible with the quantum Griffiths scenario.1. IntroductionCe- and Yb-based f -electron Kondo-lattice (KL) systems have shown the most drastic formsof non-Fermi-liquid (NFL) behaviour [1]. In these heavy-fermion (HF) materials, the groundstate sensitively depends on the balance between two competing interactions, which are bothdetermined by the strength of the 4f -conduction electron hybridisation J : Whereas the Kondointeraction leads to a screening of the local moments below a Kondo temperature TK , resultingin a paramagnetic (PM) ground state with itinerant 4f -electrons, the indirect exchange coupling(RKKY interaction) can mediate long-range magnetic ordering [2].One of the explanations for such NFL phenomena is the presence of a quantum critical point(QCP) at a particular Jc: If the transition temperature TM of the long-range magnetic orderis continuously shifted to zero by an external parameter x(J), e.g. pressure, magnetic field orchemical substitution, a 2nd order quantum phase transition (QPT) takes place at xc(Jc) andT = 0, to which a QCP is associated. Here, the typical length and time scales of order parameterfluctuations diverge when approaching the transition point. These fluctuations are believed tobe responsible for the observed NFL corrections to the FL prediction for the heat capacityC/T (T ) = const., magnetic susceptibility χ(T ) = const., electrical resistivity ρ(T ) ∝ T 2 etc.QCPs are not the only mechanism to provide NFL behaviour. If the magnetic order changesfrom long-range to short-range and disorder comes into play, spatial regions (also called “rareregions”) can show local magnetic order, although the bulk system is in a PM state [3]. The orderparameter fluctuations of these regions can become strong enough to destroy the QPT and cangive rise to NFL effects [4, 5, 6]. Here, the length scale of order parameter fluctuations becomesfinite, while the time scale still diverges. As a consequence in, e.g., the quantum Griffiths phase(QGP) scenario, power-law corrections, C/T ∝ χ′ ∝ T λ−1 and M ∝ Hλ with 0 ≤ λ ≤ 1, areInternational Conference on Magnetism (ICM 2009) IOP PublishingJournal of Physics: Conference Series 200 (2010) 012016 doi:10.1088/1742-6596/200/1/012016c© 2010 IOP Publishing Ltd 1expected in a broad region across the QCP and not only at the QCP itself [7]. The globalphase transition is then smeared [8], as observed in doped ferromagnetic (FM) materials, as ,e.g., the itinerant Zr1−xNbxZn2 [9], the 5f -based HF system URh1−xRuxGe [10] and the Ce-based CePd1−xRhx [11]. The ground state of such systems depends on several factors and canbe very exotic, as in CeNi1−xCux, where a percolative cluster scenario has been proposed [12].Recently, we reported on the formation of a “Kondo-cluster-glass” state in CePd1−xRhx for0.7 ≤ x ≤ 0.9, caused by the freezing of clusters with predominantly FM coupling: theyform below a temperature Tcl and freeze at a lower temperature T ∗c [13]. In CePd1−xRhx, thechemical substitution of the Ce-ligand Pd by Rh induces not just a negative volume effect, but,more importantly, it locally increases the hybridisation strength J of the cerium 4f electrons,leading to a strong enhancement of the local TK . Simultaneously, disorder is introduced tothe system, which induces a statistical distribution of TK . Both effects create regions where fmoments are still unscreened and can form FM clusters because of the RKKY interaction [14].In the temperature region T ∗c < T < Tcl we have observed power-law behaviour of severalthermodynamic quantities, i.e. C/T (T ), χ′(T ), M(H) [13, 15], and we concluded that thequantum Griffiths phase scenario might be realised in CePd1−xRhx for Rh content 0.8 ≤ x ≤ 0.9.For x < 0.8 the system is too close to the FM long-range order to be considered in the QGP.In this article we take a closer look at the magnetic susceptibility χ′ and magnetisation M insingle crystals with Rh content xc ≈ 0.8 within the frame of the QGP scenario.Before starting with the analysis of the results, we have to consider that the QGP is restrictedto a small region of the temperature - magnetic field (T − H) phase diagram. This region islimited to the ranges T ∗c < T < Tcl and H(T ∗c ) < H < H(Tcl), where H(T ∗c ) and H(Tcl) are,respectively, the magnetic fields necessary to destroy the glass state and to remove the effectof the cluster formation (cf. inset of Fig. 1 (b)). Both T ∗c and H(T ∗c ) have very low values ofthe order of mK and mT. To study the dynamic processes in the region close to x = 0.8, χ′was measured down to 0.02 K (Fig. 1), at a frequency of 113 Hz, with a modulation field of 0.1 1 10 0.01  0.1  1χ ′ (10-6 m3/mol)T (K)CePd1-xRhx(a)x = 0.80, λ = -0.12x = 0.82, λ = +0.1x = 0.85, λ = +0.4x = 0.86, λ = +0.45 11χ ′ (10-6 m3/mol)T (K)CePd0.2Rh0.80 mT10 mT(b) 15432M (10-3µ B/Ce)5 mT10 mTFigure 1. Frame (a): Ac susceptibility χ′ of four single crystals plotted as a function of thetemperature on a double-logarithmic scale. The lines indicate fits with χ′ ∝ T λ−1 above T ∗c .The curves present a hump at about 3 K, which is possibly due to impurity phases. Frame(b): χ′ vs T of CePd0.2Rh0.8 at different magnetic fields: 0, 5 and 10 mT. The line represents alinear fit performed between 3.5 K and 1.5 K. Inset of frame (b): FC and ZFC measurements ofthe magnetisation at constant fields of 5 and 10mT down to 2 K. The FC and ZFC data splitsslightly below Tcl in 5 mT, where clusters form; a field of 10 mT is enough to remove this effect.International Conference on Magnetism (ICM 2009) IOP PublishingJournal of Physics: Conference Series 200 (2010) 012016 doi:10.1088/1742-6596/200/1/0120162µ0hac = 11 µT. The dc magnetisation M was measured with a SQUID (Quantum Design) athigh temperatures and with a high-resolution Faraday magnetometer, in magnetic fields as highas 11 T and at temperatures down to 0.05 K (Fig. 2 and 3)[16]. The magnetic field has beenapplied along the c axis in all the measurements presented here. It is worth mentioning that themagnetic anisotropy of the system is low for x > 0.7 [17] and poly- and single crystals exhibitsimilar behaviour [13].In frame (a) of Fig. 1, the real part of the ac susceptibility is plotted as a function of T ina double-logarithmic scale for four crystals of CePd1−xRhx with 0.8 ≤ x ≤ 0.86. The peaktemperature is T ∗c . In frame (b), χ′ is shown only for the crystal with x = 0.8 at differentfields. Tcl ≈ 5 K has been determined as the temperature where the field-cooled (FC) andzero-field-cooled (ZFC) measurements of M split, as illustrated in the inset of the same frame.As in polycrystals, χ′ follows a T λ−1 power-law function above T ∗c where the exponent λ variessystematically with x between -0.12 and 0.45 [13], as expected in the QGP scenario. The value ofthe exponents seems to be independent of the impurity phases observed at about 3 K (see curvefor x = 0.82). The negative λ value for the sample with x = 0.8, different from the one measuredin a polycrystal with the same x (λ = 0.13), suggests that this sample is still too close to theFM instability. Moreover, the error in estimating the composition by energy dispersive X-rayspectrometry amounts to 1 at. % Rh. Taking into account that the sample with slightly higherRh content x = 0.82 shows λ = 0.1, it is not possible from this measurement to discern whetherthe sample with x = 0.8 can be considered in the QGP or not. Furthermore, the exponent isaffected by the freezing which already takes place at T ∗c ≈ 0.4 K. Focussing on the temperaturerange between T ∗c and Tcl, the χ′ vs T plot changes slope slightly at about 3.5 K, and again atabout 1.5 K (indicated by arrows). We have fitted this range to extract λ, considering that inthe 10 mT curve the fit range can be expanded to even lower temperatures.To verify the presence of a QGP in this sample, we have measured M vs H at differenttemperatures. In Fig. 2 the isotherms are shown: In frame (a), the curve at 2 K is plottedtogether with those for two FM concentrations, x = 0.4 and 0.6, to emphasise the strongdecreasing of the magnetic moment with x; in frame (b), the isotherms at 0.05 K and 2 K are 0 0.5 1 1.5 2 0  2  4  6  8M (µ B/Ce)µ0H (T)CePd1-xRhxx = 0.4x = 0.6x = 0.8(a)T = 2 K 0  2  4  6  8  10  12 0 0.1 0.2 0.3 0.4M (µ B/Ce)µ0H (T)CePd0.2Rh0.80.05 K2 K(b)-0.05 0 0.05-0.1  0  0.10.05 KFigure 2. Frame (a): M vs H for three selected single crystals of CePd1−xRhx with x = 0.4,0.6 and 0.8 at 2 K. Dotted lines are guide to the eye. Frame (b): M vs H of CePd0.2Rh0.8 at0.05 and 2 K. Inset of frame (b): By zooming into the field range −0.1 ≤ µ0H ≤ 0.1 T at 0.05 K,a very small FM hysteresis can be observed. The magnetic field was applied along the c axis.International Conference on Magnetism (ICM 2009) IOP PublishingJournal of Physics: Conference Series 200 (2010) 012016 doi:10.1088/1742-6596/200/1/0120163 0 0.1 0.2 0.3 0.4 0.5 0.6  0.8  1  1.2  1.4  1.6  1.8M (µ B/Ce)µ0Hλ (T)CePd0.2Rh0.8T = 0.05 K, λ = 0.21T = 0.5 K, λ = 0.22T = 2 K, λ = 0.25Figure 3. Magnetisation ofCePd0.2Rh0.8 plotted as a function ofHλ at three different temperatures: 0.05, 0.5and 2 K. The linear behaviour of the threecurves for fields 0.4 . µ0H . 10 T indicatethat the power-law M ∼ Hλ holds with analmost constant λ in this entire field range.Linear dotted lines are just guide to the eye.compared. The magnetisation at 0.05 K shows a very small hysteresis (inset of Fig. 2), due tofreezing at T ∗c ≈ 0.4 K, and it is far from reaching saturation at 10 T. We consider the valueof the coercive field to be H(T ∗c ) ≈ 0.1 T. Since Tcl ≈ 5 K ≈ µ · H, we can assume H(Tcl) tobe close to 12 T, as the magnetic moment µ at 12 T is only 0.4 µB. It is thus plausible to lookfor QGP in M vs H for fields between 0.1 and 12 T. M vs Hλ is plotted in Fig. 3 at threetemperatures; below T ∗c (0.05 K), just above it (0.5 K) and close to Tcl (2 K). The curves followa power-law behaviour, with an almost constant value of λ ≈ 0.2, close to those observed inχ′(T ) for the other crystals, as expected in the QGP. Since M vs H plots are less sensitive toparamagnetic impurities, and for H > H(T ∗c ) the freezing does not affect the power law, theseplots can be considered as signatures of a QGP in CePd0.2Rh0.8.As discussed in the introduction, there is a fundamental difference between the NFL behaviourgiven by long-range and short-range order fluctuations. The presence of clusters and the power-law corrections to susceptibility and magnetisation in CePd1−xRhx indicate that the expectedQPT at xc ≈ 0.8 is replaced by disordered phases, possibly like the Griffiths one.We wish to thank T. Vojta for helpful discussions. Supported by the DFG Research Unit 960”Quantum phase transition”.References[1] von Löhneysen H, Rosch A, Vojta M and Wölfle P 2007 Rev. Mod. Phys. 79 1015 and references therein[2] Doniach S 1977 Physica B 91 231[3] Vojta T 2006 J. Phys. A: Math. Gen. 39 R143-R205[4] Miranda E, Dobrosavljević V and Kotliar G 1997 Phys. Rev. Lett. 78 290[5] Castro Neto A H, Castilla G and Jones B A 1998 Phys. Rev. Lett. 81 3531[6] Castro Neto A H and Jones B A 2000 Phys. Rev. B 62 14975[7] Vojta T and Schmalian J 2005 Phys. Rev. B 72 045438[8] Hoyos J A and Vojta T 2008 Phys. Rev. Lett. 100 240601; Hoyos J. A. , Kotabage C. and Vojta T 2007 Phys.Rev. Lett. 99 230601[9] Sokolov D A, Aronson M C, Gannon W and Fisk Z 2006 Phys. Rev. Lett. 96 116404[10] Huy N T, Gasparini A, Klaasse J C P, de Visser A, Sakarya S and van Dijk N H 2007Phys. Rev. B 75 212405[11] Sereni J G, Westerkamp T, Küchler R, Caroca-Canales N, Gegenwart P and Geibel C 2007 Phys. Rev. B 75024432[12] Marcano N, Gómez Sal J C, Espeso J I, De Teresa J M, Algarabel P A, Paulsen C and Iglesias J R 2007Phys. Rev. Lett. 98 166406[13] Westerkamp T, Deppe M, Küchler R, Brando M, Geibel C, Gegenwart P, Pikul A P and Steglich F 2009Phys. Rev. Lett. 102 206404[14] Dobrosavljević V and Miranda E 2005 Phys. Rev. Lett. 94 187203[15] Pikul A P, Caroca-Canales N, Deppe M, Gegenwart P, Sereni J G, Geibel C and Steglich F J. Phys. Condens.Matter 18 L535[16] Sakakibara H, Mitamura H, Tayama T and Amitsuka H 1994 Jpn. J. Appl. Phys. 33 5067[17] Deppe M, Pedrazzini P, Caroca-Canales N, Geibel C and Sereni J G 2006 Physica B 378-380 96International Conference on Magnetism (ICM 2009) IOP PublishingJournal of Physics: Conference Series 200 (2010) 012016 doi:10.1088/1742-6596/200/1/0120164

Quantum Griffiths phase in CePd1−x Rh x with x ≈ 0.8

Gegenwart, P.

MPG.PuRe

Quantum Griffiths phase in CePd<sub>1-x</sub>Rh<sub>x</sub> with x ≈ 0.8

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Quantum Griffiths phase in CePd1-xRhx with x ≈ 0.8

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Quantum Griffiths phase in CePd
                    
                      1−
                      x

https://opus.bibliothek.uni-augsburg.de/opus4/files/86530/M_Brando_2010_J._Phys.__Conf._Ser._200_012016.pdf

Quantum Griffiths phase in CePd(1-x)Rh(x) with x ~ 0.8

Quantum Griffiths phase in CePd(1-x)Rh(x) with x ~ 0.8

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