Avoided ferromagnetic quantum critical point: Antiferromagnetic ground state in substituted CeFePO
Anton Jesche, Tanita Balle, Kristin Kliemt, Christoph Geibel, Manuel Brando, Cornelius Krellner
pphysica status solidi
Avoided ferromagnetic quantumcritical point: Antiferromagneticground state in substituted CeFePO
A. Jesche , T. Ball ´e , K. Kliemt , C. Geibel , M. Brando , C. Krellner Max-Planck-Institute for Chemical Physics of Solids, D-01187 Dresden, Germany Center for Electronic Correlations and Magnetism, Augsburg University, D-86159 Augsburg, Germany Institute of Physics, Goethe University Frankfurt, D-60438 Frankfurt am Main, GermanyReceived XXXX, revised XXXX, accepted XXXXPublished online XXXX
Key words:
CeRuPO, CeFeAsO, ferromagnetic Kondo lattice, ZrCuSiAs structure-type, crystal growth ∗ Corresponding author: e-mail [email protected]
We have investigated single crystals of two substitu-tion series Ce(Ru − x Fe x )PO and CeFe(As − y P y )O inthe vicinity to the quantum critical material CeFePOby means of magnetic-susceptibility and specific-heatmeasurements. We observe an antiferromagnetic groundstate in the vicinity of the quantum critical point, withpronounced metamagnetic transitions for H (cid:107) c , whichis the magnetically hard direction. Our results verify thata ferromagnetic quantum critical point is avoided in sub-stituted CeFePO, because we clearly demonstrate thatthe ferromagnetic ground state changes into an antifer-romagnetic one, when approaching the quantum criticalpoint. AFMFM T g CeFe(As P )O
Ce(Ru Fe )PO / T e m pe r a t u r e ( K ) x y Temperature-substitution phase diagram of the seriesCe(Ru − x Fe x )PO and CeFe(As − y P y )O. Copyright line will be provided by the publisher
In recent years, ferromagnetic (FM)heavy-fermion metals were intensively investigated andthe main question is whether a FM quantum critical point(QCP) generally exists and, if not, which are the possibleground states of matter that replace it. Substantial experi-mental and theoretical efforts were made to investigate thisproblem, revealing a wide range of possibilities [1,2,3]. Ontheoretical grounds, it was shown that in 2D and 3D thequantum phase transition from a metallic paramagnet toan itinerant ferromagnet in the absence of quenched disor-der is inherently unstable, either towards a first order phasetransition or towards an inhomogeneous magnetic phase(modulated or textured structures) [4,5,6]. The mechanism behind this phenomenon is analogous to what is known asa fluctuation-induced first-order transition in superconduc-tors and liquid crystals [3].In f systems, the theoretical description of the inter-play of ferromagnetism and the local Kondo-interaction ismuch less explored and different scenarios are proposed [7,8]. From the experimental point of view, three main scenar-ios have been observed in the vicinity of a FM instability.In the first case, like in CeRu Ge [9], the FM transitionchanges into antiferromagnetic (AFM) order, when the or-dering temperature is suppressed to T → by e.g., hydro-static pressure. Similar behavior was observed in CeAgSb where a crossover to AFM order was observed at 3.5 GPa Copyright line will be provided by the publisher a r X i v : . [ c ond - m a t . s t r- e l ] M a y A. Jesche et al.: Avoided FM QCP in substituted CeFePO [10]. In the second case, like in the alloy CePd − x Rh x [11], it seems that local disorder-driven mechanisms suchas Kondo disorder or the quantum Griffiths phase scenarioare responsible for the non-Fermi liquid (NFL) propertiesaround the QCP, but not the quantum critical fluctuations.Characteristic of this scenario are phase diagrams, wherethe FM transition temperature, T C , smears out as func-tion of the control parameter. A third case was recentlyreported, namely the clear evidence of a FM QCP in aheavy-fermion metal in arsenic-doped YbNi P , which isa quasi-1D system [12], [13]. The existence of a FM QCPwas also suggested in recent studies by Kitagawa et al. [14,15] in the compound Ce(Ru − x Fe x )PO with x = 0 . , de-termined by NMR measurements on polycrystalline sam-ples in finite magnetic field.In this article, we will present magnetization andspecific-heat data measured on single crystals of this alloyseries which clearly reveal that a transition to an AFMground state is observed before the QCP is reached. The heavy fermion (HF) metalCeFePO has been intensively investigated due to its prox-imity to a magnetic quantum critical point (QCP). Char-acteristic of this material are strong ferromagnetic (FM)fluctuations together with a pronounced two-dimensionalanisotropy of the crystal structure. CeFePO is isoelectronicto the parent compound of iron-pnictide superconductors,CeFeAsO, and to the FM Kondo lattice CeRuPO. Zimmer et al. synthesized polycrystalline samples of CeFePO al-ready in 1995 [16], however, no physical properties werereported at that time. From the volume plot of the lan-thanide series a mixed or intermediate valence state wasproposed.Initial physical measurements on polycrystalline sam-ples reveal a Ce state and a paramagnetic heavy-fermionground state with a large Sommerfeld coefficient of γ =0 . Jmol − K − [17]. Already at that time the vicinity toa FM QCP was proposed for CeFePO, concluded from astrongly field dependent and enhanced magnetic suscep-tibility at low temperatures. Shortly after, the occurrenceof magnetic Ce was confirmed by Kamihara et al. [18]which propose that superconductivity is absent in CeFePOin contrast to the isoelectronic LaFePO, because of themagnetic Ce-moments. Subsequently, the band-structureof CeFePO and the role of the d - f hybridization wastheoretically determined using the local density approxi-mation combined with dynamical mean-field theory [19].First single crystals were grown using a high-temper-ature Sn-flux technique [20], similar to what was used forthe crystal growth of CeRuPO [21]. These single crys-tals were investigated with angle-resolved photoemissionspectroscopy, which corroborate the sizable d - f hy-bridization in CeFePO. Polycrystalline samples of theCeFe(As − y P y )O substitution series were synthesized byLuo et al. [22], which reveal a complex magnetic phase di-agram. At the As-rich side the phase diagram is dominated by the intricate interplay between d and f moments,which leads to a variety of new phenomena for y = 0 . [23]. At the P-rich side, the d -magnetism is vanished andthe ground state is dominated by the interaction of the4 f -moments. There, a FM ground state of the f -electronswas proposed for . ≤ y ≤ . , although no remanentmagnetization could be resolved for the y = 0 . sample[22]. The same group also reported a study of the sameseries containing 5% fluorine substituted on the oxygensite [24]. For CeFePO this F-doping leads to a stabilizationof the magnetic phase, although the nature of the groundstate could not be definitively determined, because onlymeasurements on polycrystals down to 2 K were reported.The magnetic nature of Fe in CeFePO was probed by FeM¨ossbauer spectroscopy down to 10 K. No magnetic split-ting was observed indicating a paramagnetic phase of theFe sublattice [25].Resistivity measurements under pressure on CeFePOsingle crystals were conducted by Zocco et al. [26]. Theyobserved a stabilization of the Kondo screening with pres-sure, which is reflected in an increase of the coherence tem-perature. This result is in agreement with the general be-havior of Ce-based Kondo-lattice systems under pressure[1]. A thorough P-NMR study on oriented powder re-vealed a metamagnetic transition at 4 T, when the field wasapplied in the basal plane of aligned powder [27]. Further-more, Kitagawa et al. show that around the metamagnetictransition the nuclear spin-lattice relaxation rate, /T T ,increases with decreasing temperature down to 100 mK,a hallmark of non-Fermi liquid behavior. They propose aKondo-breakdown scenario at this metamagnetic transitionaccompanied with a drastic change of the Fermi surface.Later on, a comprehensive study of the ac susceptibility,specific-heat and µ SR measurements on CeFePO singlecrystals reveal, in contrast to the results on polycrystals,a strongly correlated short range ordered state below thefreezing temperature T g = 0 . K [28]. This unusual short-range ordered state was ascribed to the avoidance of a FMQCP in this system. However, the strong sample depen-dency, the paramagnetic Fermi-liquid ground state for thepolycrystals and the short range strongly correlated statefor the single crystals, is reminiscent to what was observedfor the prototypical CeCu Si [29] and proves the impor-tance of quantum fluctuations for the ground state of thissystem. The recent statement of the existence of a FM QCPin the series Ce(Ru − x Fe x )PO for x = 0 . [14,15] fur-ther stimulated the interest in this layered compound andwe address this issue by investigating single crystals grownin Sn-flux.The single crystal growth of 1111-type iron pnictidecompounds is a real challenge. After the discovery of high-temperature superconductivity in F-substituted LaFeAsOin 2008 [30] the initial flurry of activities mainly were per-formed on the LnFePnO (Ln = rare earth, Pn = P, As) sys-tems (1111), however, shortly after the focus has rapidlybeen shifted towards the AFe As (A = Ba, Sr, Ca) abbre- Copyright line will be provided by the publisher ss header will be provided by the publisher 3 viated as 122 and FeSe/Te superconductors (11 materials),even though the latter two classes of materials have lower T c [31]. Meanwhile, the 122 and 11 compounds are themodel systems among iron-pnictide superconductors, be-cause large and homogeneously doped single crystals caneasily be achieved. However, the magnetic and electronicanisotropies are much weaker, and T c is lower in the 122compared to the 1111 systems. In contrast, the growth ofsizable high-quality single crystals of the 1111 compoundsis extremely challenging, despite extensive worldwide ef-forts, slowing down the scientific progress in this type ofcompounds. Conventional solid-state reactions have beenpredominantly used to synthesize polycrystalline dopedand undoped LnFeAsO. The main problems with the singlecrystal growth of the 1111 system are the following [32]:(i) The multicomponent phase diagrams are unknown. (ii)The compounds form strongly peritecticly. (iii) The pres-ence of stable secondary phases (e.g. stable rare-earth ox-ides). (iv) The low solubility of oxygen in metallic and saltfluxes. In the literature, mainly the flux method was re-ported for the successful crystal growth of the 1111-typeof materials, using NaCl/KCl, NaI, NaAs as the flux [33,34,35]. Here, we employed thehigh-temperature Sn-flux method, which was foundto be a suitable flux for CeRuPO [21] and the seriesCeFe(As − y P y )O [20]. In a first step, Pn and Sn wereheated up to 600 ◦ C for 5 h in an alumina crucible whichwas sealed inside an evacuated silica ampoule. In a secondstep, Ce, Fe, RuO , SnO , and Sn were added and the alu-mina crucible was sealed inside a Ta container under argonatmosphere. The mixture was then heated up to 1500 ◦ C,slowly cooled down to 900 ◦ C within one week followedby fast cooling down to room temperature. To remove theexcess Sn, the samples were centrifugated at 500 ◦ C andthen put into diluted hydrochloric acid for 10 min. Thisresulted in platelike single crystals with a side length oftypical 0.5 mm but in some cases going up to more thanone millimeter. We have grown several substitution levelsof the two series Ce(Ru − x Fe x )PO and CeFe(As − y P y )O .The iron, x , and phosphorous, y , concentrations are givenin nominal values. Energy dispersive X-ray analysis andX-ray powder diffraction set an upper limit for the rela-tive error of the actual content ∆xx ∼ . . X-ray powderdiffraction patterns of ground single crystals were recordedon a Stoe diffractometer in transmission mode or a BrukerD8 diffractometer using Cu K α -radiation. The refined lat-tice parameters were found to be in good agreement withthe values reported in Ref. [14] for Ce(Ru − x Fe x )PO andin Ref. [22] for CeFe(As − y P y )O . Magnetic measure-ments were performed in a commercial SQUID VSM andthe VSM option of the PPMS. Specific heat was measuredwith the He3-option of the PPMS. M / H (10-6 m3/mol) M / H (10-6 m3/mol) C e
R u
F e
P O H || c H ^ c (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) H ( T ) 0 . 1 1 . 0 7 . 0 M / H (10-6 m3/mol) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) H ( T ) 0 . 1 1 . 0 1 . 2 7 . 0 H ^ cH || c C e F e
A s P OC e
R u
F e
P O (cid:1) (cid:1) (cid:1) (cid:1) (cid:2) H ( T ) 0 . 1 1 . 0 5 . 0 H ^ cH || c T ( K ) Figure 1 (Color online) Temperature dependence of themagnetization divided by magnetic field (dc-susceptibility)for single crystals with x = 0 . , x = 0 . , and y = 0 . .Closed (open) symbols present data measured with themagnetic field perpendicular (parallel) to the crystallo-graphic c -axis. Copyright line will be provided by the publisher
A. Jesche et al.: Avoided FM QCP in substituted CeFePO ( c ) C e F e
A s P O( b ) C e
R u
F e
P O H || cH ^ c M ( m B/Ce) H || cH ^ c M ( m B/Ce) ( a ) C e
R u
F e
P O H ^ c M ( m B/Ce) (cid:1) H ( T ) H || c H || c H || c Figure 2 (Color online) Magnetic-field dependence of themagnetization at T = 2 K for single crystals with x = 0 . , x = 0 . , and y = 0 . . Black (red) points present datameasured with the magnetic field perpendicular (parallel)to the crystallographic c -axis. In the insets for x = 0 . and y = 0 . , metamagnetic behavior is visible for H (cid:107) c . In Fig. 1, we present the tem-perature dependence of the magnetization divided by mag-netic field,
M/H ( T ) , for three different single crystals.For x = 0 . , no magnetic phase transition was observeddown to 1.8 K. The magnetic anisotropy caused by thecrystalline-electric field (CEF) is similar to what was ob-served in CeRuPO and CeFePO, i.e., the susceptibility islarger for magnetic field perpendicular to the c -direction C e F e
A s P O C e
R u
F e
P OC e
R u
F e
P O T ( K ) C T (J mol-1K-2) Figure 3 (Color online) f -contribution to the specificheat as function of temperature at zero magnetic field forsamples with x = 0 . (squares), x = 0 . (up-pointingtriangle), and y = 0 . (down-pointing triangle).(easy-plane system). For x = 0 . and y = 0 . the dc-susceptibility curves for H ⊥ c are strongly comparable toeach other. A magnetic phase transition is apparent above2 K, with distinct maxima at small fields. Below 10 K apronounced magnetic-field dependence of the M/H ( T ) curves is observed for both field directions, with decreasingabsolute values for increasing magnetic field. This showsthat FM interactions are still present in this systems, how-ever, the overall behavior of the M/H ( T ) is not that of asimple ferromagnet.This scenario becomes more evident from the magne-tization curves, M ( H ) , at 2 K for both field directions,which are shown in Fig. 2 for the same three crystals asin Fig. 1. For all three concentrations, x = 0 . , x = 0 . ,and y = 0 . , the magnetization is larger for H ⊥ c (blackcurves) compared to H (cid:107) c (red curves) with a tendencytowards saturation at high fields. For the magnetically or-dered systems, x = 0 . and y = 0 . , no remanent magneti-zation at zero field is observed in the magnetically orderedphase, neither for H ⊥ c , nor for H (cid:107) c . This excludes aFM ground state in these materials. Comparing these datato the established ferromagnetic materials at x = 0 (Fig. 4in Ref. [21]) and y = 0 . (Fig. 2b in Ref. [23]), one wouldhave expected a finite remanent magnetization for H (cid:107) c .Instead, a linear M ( H ) is observed for ≤ µ H ≤ . Tfor x = 0 . and ≤ µ H ≤ . T for y = 0 . . In additionat higher magnetic fields a metamagnetic increase of themagnetization is found, which is enlarged in the insets ofFig. 2b,c. Remarkably, these metamagnetic transition lookvery similar for the two different substitutions, with a smallhysteresis loop, indicating a first-order type transition be-low 1 T. In contrast to recent NMR studies [27], we do notfind metamagnetic behavior up to µ H = 7 T within themagnetically easy plane ( H ⊥ c ). Copyright line will be provided by the publisher ss header will be provided by the publisher 5
The temperature dependence of the specific heat, C f /T ( T ) , for the three substitution levels is presentedin Fig. 3. For x = 0 . , no phase transition is observeddown to 0.4 K, instead, C f /T strongly increases withdecreasing temperature, typical for a heavy-fermion sys-tem in the vicinity of a quantum-critical point. However,there is not a unique temperature dependence over morethan a decade in temperature and it seems that the di-vergence gets weaker below 1 K. Presently, we cannotexclude that the weakening of the divergence is due toshort-range magnetic order at lower temperatures, whichin case of single-crystalline CeFePO has lead to a broadhump, centered around T g ∼ . K [28]. The applica-tion of a magnetic field leads to a saturation of C f /T at low T . For µ H = 5 T a constant Sommerfeld co-efficient, C f T /T = 0 . Jmol − K − , is observed be-low 1 K, which decreases further with increasing fieldto C f T /T = 0 . Jmol − K − for µ H = 9 T.For x = 0 . and y = 0 . , the specific-heat data inzero magnetic field present a large anomaly at the magneticphase transition. For y = 0 . the transition takes placeat a slightly higher temperature compared to the x = 0 . sample in agreement with the susceptibility data. The largeanomaly proves that the magnetic phase transition is dueto long-range magnetic order. This is further corroboratedby an analysis of the magnetic entropy, obtained by inte-grating C f /T over temperature. The increase in entropyfrom T = 0 . K to K amounts to . R ln 2 for x = 0 . ,and . R ln 2 for y = 0 . , respectively. These values arewell above the observed entropy gain for the short-rangeordered state in CeFePO, which was only . R ln 2 , butstill below the expected R ln 2 due to a pronounced Kondoscreening.The obtained results are summarized in a temperature-concentration phase diagram presented in Fig. 4, whichis markedly different to the reported phase diagram inRef. [14] because we have found clear evidence that theferromagnetic transition changes into an antiferromag-netic one, when approaching the quantum critical point.Presently, we cannot put an exact boundary of the FM toAFM transition, therefore a shaded color code with an in-dicative line was used to show, that at some concentrationthis transition takes place. A similar change from ferro-magnetism to antiferromagnetism was also observed insingle crystalline CeRuPO samples under pressure. There,the transition occurs at p ∗ ∼ . GPa [36]. This pressurecorresponds to a relative volume change of 0.83% usingthe experimental bulk modulus of K = 105(1) GPa,determined by X-ray diffraction under pressure [37]. As-suming Vegard’s law for the lattice volume of the se-ries Ce(Ru − x Fe x )PO , such a volume change would beachieved already for x = 0 . , but experimentally we stillobserve the ferromagnetic ground state for x = 0 . .However, the lattice parameters a and c in the seriesCe(Ru − x Fe x )PO do not evolve equally, a decreases withincreasing x , whereas c increases with x [14]. Therefore, AFMFM T g CeFe(As P )O
Ce(Ru Fe )PO / T e m pe r a t u r e ( K ) x y Figure 4 (Color online) Temperature-substitution phasediagram of the series Ce(Ru − x Fe x )PO (circles, lower ab-scissa) and CeFe(As − y P y )O (diamonds, upper abscissa)obtained from magnetic measurements. The small graypoint at x = 0 . was taken from Ref. [14]. A transitionfrom ferromagnetism to antiferromagnetism indicated bythe shaded bar occurs before reaching the quantum criticalpoint at x = 0 . .chemically induced pressure is expected to be differentcompared to hydrostatic pressure, as the c/a ratio devel-ops differently. This might be also the reason why in thepressurized CeRuPO no QCP could be reached, which isclearly the case for Ce(Ru − x Fe x )PO . We have succeeded in growing singlecrystals of the two substitution series Ce(Ru − x Fe x )POand CeFe(As − y P y )O , which are large enough to deter-mine the magnetic ground state by means of magnetic-susceptibility and specific-heat measurements. We clearlydemonstrate that the ferromagnetic ground state at x =0 . and y = 0 . changes into an antiferromagnetic one,when approaching the quantum critical point. This is man-ifested by the absence of a remanent magnetization at zerofield in the magnetically ordered state. However, ferro-magnetic interactions are still present in these materials,reflected by pronounced metamagnetic transitions below1 T for H (cid:107) c , which is the magnetically hard direction.Our results verify that a ferromagnetic quantum criticalpoint is avoided in substituted CeFePO, similar to whatwas observed in other two-dimensional heavy-fermion fer-romagnets, when T C was tuned towards zero [3]. Theseresults further corroborate that the key towards ferromag-netic quantum criticality, which was observed in YbNi P ,might be the quasi-one-dimensional crystal and electronicstructure present in that system. Acknowledgements
The authors thank U. Burkhardt andP. Scheppan for energy dispersive X-ray analysis of the samples
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A. Jesche et al.: Avoided FM QCP in substituted CeFePO as well as R. Weise and K.-D. Luther for technical assistance.This work was supported by the DFG priority program SPP 1458.
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