Electronic nature of the lock-in magnetic transition in CeXAl4Si2
J. Gunasekera, L. Harriger, A. Dahal, A. Maurya, T. Heitmann, S. Disseler, A. Thamizhavel, S. Dhar, D. K. Singh
EElectronic nature of the lock-in magnetic transition in Ce X Al Si J. Gunasekera , L. Harriger , A. Dahal , A. Maurya , T. Heitmann ,S. Disseler , A. Thamizhavel , S. Dhar , and D. K. Singh , ∗ Department of Physics and Astronomy, University of Missouri, Columbia, MO 65211 NIST Center for Neutron Research, Gaithersburg, MD, 20899 Tata Institute of Fundamental Research, Mumbia, India University of Missouri Research Reactor, University of Missouri, Columbia, MO 65211 and ∗ email: [email protected] We have investigated the underlying magnetism in newly discovered single crystal Kondo latticesCe X Al Si , where X = Rh, Ir. We show that the compound undergoes an incommensurate-to-commensurate magnetic transition at T c = 9.19 K (10.75 K in Ir). The spin correlation in theincommensurate phase is described by a spin density wave configuration of Ce-ions, which locks-into the long-range antiferromagnetic order at T = T c . The qualitative analysis of the experimentaldata suggests the role of the Fermi surface nesting, instead of the lattice distortion causing theUmklapp correction or the soliton propagation, as the primary mechanism behind this phenomenon. PACS numbers: 75.25.-j, 75.30.Fv, 71.27.+a
Strongly correlated electrons systems provide a fer-tile research avenue that encompasses a host of elec-tronic phenomena, such as quantum critical behavior, un-conventional superconductivity, multiferroic and unusualelectronic properties associated with the reconstructionof the Fermi surface.[1–7] Among the strongly correlatedelectrons family, heavy electron compounds are of specialinterests.[8–10] Many of these materials exhibit an inter-play between magnetism and unconventional supercon-ductivity where novel magnetic quantum critical effect isfound to play the key role.[11, 12] The heuristic quantumcritical phenomenon is often accompanied by a changein the Fermi surface properties.[9, 13] Another unusualmagnetic phenomenon, which may be arising due to thechange in the electronic properties in a magnetic mate-rial, is associated to magnetic phase transition betweencommensurate and incommensurate order as a functionof temperature; often referred to as the lock-in magnetictransition.[14] Although it is argued that the instabilityin the Fermi surface, causing the separation of hole andelectron pockets (the nesting of Fermi surfaces), is thepredominant mechanism, the underlying physics behindthis phenomenon is a subject of debate. Similar behavioris also ascribed due to at least two other effects: (a) thedistortion in the crystal structure leading to the Umklappcorrection to the Landau free energy expression (for ex-ample, in CaFe As ), and (b) step-like incommensuratepeaks impersonating domain walls propagation of softsolitons that merge to the commensurate wave-vector viathe first order phase transition (for instance, the lock-intransition in TaS ).[15, 16]We have performed detailed neutron scattering mea-surements on high quality single crystals of newly dis-coverd Kondo lattices Ce X Al Si , X = Rh, Ir, to inves-tigate the underlying magnetism as functions of temper-ature and magnetic field. We have found that both com-pounds undergo incommensurate-to-commensurate mag- netic transition at T c (cid:39) X = Rhand Ir, respectively. The incommensurate magnetic or-der, which is field-independent and develops below T IC (cid:39)
14 K in CeRhAl Si (16 K in X = Ir), is given bythe temperature-dependent propagation wave-vector k =(0.016,0.016,0.5) at T = 10 K. The magnetic configura-tion in the incommensurate phase is best described by aspin density wave correlation of Ce-spins for 9 K ≤ T ≤
14K (10.7 K ≤ T ≤ X = Ir), with Ce moments spa-tially fluctuating along the z - axis. As the temperatureis decreased below T (cid:39) ≤
10 K in X = Ir), theincommensurate (IC) peaks lock-in to the long-range an-tiferromagnetic order via the first order magnetic transi-tion. The qualitative analysis of neutron data, combinedwith previous magnetic, electrical and heat capacity mea-surements on single crystal sample,[17] suggest that thelock-in magnetic transition arises due to the changes inthe electronic properties of the system. The incommen-surate magnetic structure at intermediate temperaturesis related to the separation of electron and hole pockets inCe X Al Si , as opposed to the lattice distortion causingthe Umklapp correction to the free energy or the solitonpropagation of domain walls.Ce X Al Si , a dense Kondo lattice, crystallizes in theEuIrAl Si -type tetragonal lattice structure (space groupP4/mmm) with lattice parameters of a = b = 4.216 ˚ A (4.221 ˚ A ) and c = 7.979 ˚ A (7.949 ˚ A ) in X = Rh (Ir),as shown in the inset of Fig. 1a. Previous magnetic andheat capacity measurements on powder and single crystalspecimens suggest strong anisotropic nature of magneticsusceptibilities, with large discrepancies in Curie-Weisstemperature, Θ CW , for field applications along differentcrystallographic directions and full ordered moment val-ues in CeRhAl Si and CeIrAl Si .[17–19] In particular,for field application along [100] direction, Θ CW and fullmoment values are found to be -155 K (-140 K) and 2.65 µ B (2.62 µ B ) in CeRhAl Si ( X = Ir), respectively.[17] a r X i v : . [ c ond - m a t . s t r- e l ] S e p (a) [H,H,0.5] (r.l.u) I n t en s i t y ( a . u . ) (b) T ( K ) [H,H,0.5] (r.l.u) FIG. 1: (color online) Representative scans exhibitingcommensurate and incommensurate magnetic reflections inCe X Al Si . (a) Elastic scan along [HH0.5] reciprocal direc-tion, depicting commensurate magnetic reflection, at T = 5 Kand at different field values in CeRhAl Si . The elastic dataremains unaffected to magnetic field application up to H =10 T. Similar behavior is observed in X = Ir. Inset shows thecrystal structure. (b) Elastic scans along [HH0.5] direction,depicting incommensurate magnetic reflections, at T = 11 Kin CeIrAl4Si2. Similar behavior is observed in X=Rh. In-set shows the color map of incommensurate to commensuratetransition as a function of temperature. Magnetic and electrical measurements in applied field onsingle crystal CeRhAl Si ( X = Ir) further reveal theonset of a spin-flop transition around H (cid:39) ≥
10 K.[17]Detailed neutron scattering measurements were per-formed on high quality single crystal samples ofCeRhAl Si and CeIrAl Si , with respective masses of0.63 g and 0.17 g, on cold triple axis spectrometer SPINSat the NIST Center for Neutron Research and on ther-mal triple axis spectrometer TRIAX at the Missouri Uni-versity Research Reactor. Single crystal samples weresynthesized using the flux growth method and the highquality of the samples were verified using X-ray diffrac-tion measurements.[17] Small samples with flat geometryreduces neutron absorption cross-section, thus help us inthe quantitative analysis of the neutron data. For SPINSmeasurements, the single crystal sample was mounted atthe end of a 1 K stick and cooled in He environmentin a 10 T magnet. For elastic measurements, the colli-mator settings were M-80 (cid:48) -Be filter-Sample-Be filter-80 (cid:48) -5 blades flat analyzer-detector. The measurements on I n t en s i t y S ( a . u . ) CeRhAl Si [H,H,0.5]S(r.l.u) CeIrAl Si [H,H,0.5]S(r.l.u) FIG. 2: (color online) Incommensurate to commensurate lock-in magnetic transition. (a) Elastic scans along [HH0.5] direc-tion at different temperatures, exhibiting incommensurate tocommensurate magnetic transition (T c (cid:39) Si . Experimental data arewell described by a Gaussian lineshape. (b) Similar behav-ior is observed in X = Ir, albeit the transition happens at aslightly higher temperature (T c (cid:39) TRIAX were performed using a closed cycle refrigeratorwith the base temperature of (cid:39) (cid:48) -Sample-PG filter-60 (cid:48) -flat analyzer-detector. Sin-gle crystal samples were aligned in [HHL] plane of thereciprocal space, such that the applied field direction wasalong (-110).Previous neutron scattering measurements on powderCe X Al Si , X = Rh, Ir, were not conclusive enoughto identify the magnetic correlation at intermediatetemperature,[18] as inferred from the susceptibility andheat capacity measurements.[17] Unlike the powder sam-ple, single crystal specimen allows for a much more de-tailed investigation of structural and magnetic proper-ties. As shown in representative Fig. 1b, the incommen-surate magnetic pattern, indicating a different magneticstructure than the collinear antiferromagnetic configura-tion at low temperature, develops at intermediate tem-perature. Since both materials crystallize in the sametetragonal structure with same ligands coordination, theobservation of incommensurate magnetic pattern in bothsystems, albeit with different onset temperatures (as dis-cussed below), is not a surprise.Next, we have performed measurements to study theevolution of spin correlation as a function of tempera-ture. Representative scans along the reciprocal direction[HH0.5] at different temperatures in both compounds areplotted in Fig. 2a and 2b. As the measurement temper-ature is reduced below 14 K (16 K in X = Ir), a pair oftemperature-dependent incommensurate (IC) magneticpeaks develop with the propagation wave vector of k IC = (0.016,0.016,0.5) at T (cid:39)
10 K. The position of IC peak,with respect to the nearest nuclear peak, is described bythe wave vector: q = Q ± k , where Q represents thenuclear peak position. As the temperature is further re-duced, the incommensurate peaks first get stronger be-fore gradually diminishing to the background level at T (cid:39) X = Ir). Around the same tempera-ture, new magnetic peaks with the commensurate propa-gation vector k C = (0,0,0.5) develop in both compounds.The commensurate magnetic peaks become stronger astemperature is reduced to T → (cid:39)
10 K (11 K in X = Ir) occurs in temperature, the sharp temperature-dependence of the order parameter in the commensuratephase (especially in X = Ir compound) suggests a firstorder magnetic transition. However, elastic neutron datadid not exhibit any magnetic field dependence, as shownin Fig. 1b.Magnetic peaks in Ce X Al Si , Fig. 2, are best de-scribed by a Gaussian lineshape of width limited by theinstrument resolution. It indicates the presence of long-range magnetic order in the system. More quantitativeinformation is derived from the elastic neutron data thathelp us further understand the underlying magnetism inCe X Al Si . In Fig. 3c and 3d, we have plotted the tem-perature dependence of the incommensurate peak, nomi-nally at q IC = (0.98,0.98,0.5). As the measurement tem-perature is reduced, IC peak gradually moves towards thecommensurate wave-vector. The spectral weight shiftsfrom IC peak to the commensurate peak in a very nar-row temperature range around T (cid:39) (cid:39) X = Ir), suggesting the lock-in magnetic transition in thesystem (see the inset of Fig. 1b and Fig. 2). In principle,this behavior can arise due to any of the three reasons:lattice distortion, soft soliton creation or the changes inthe electronic properties due to the Fermi surface recon-struction. According to the Landau-Lifshitz expressionfor the free energy, the magnetic order parameter η cantransform from an incommensurate to a commensuratephase due to the Umklapp correction to the total energy,given by:[15, 20] G = G + 12 a ( T − T c ) η + uη + V η p cospϕ (1), where G is the free energy, T c is the transition tempera- Rah I n t en s i t y l R a . u h T c =l9.198lK 5 10 150100200300 T c =10.755lKR1,1,0.5h Rbh
TlRKh H l Rr . l . u h Rch
TlRKh
Rdh − [H,H,1]lRr.l.uh I n t en s i t y l R a . u h TlRKh a = b l R A h [0,0,L]lRr.l.uh TlRKh c l R A h RfhReh
CeRhAl Si CeIrAl Si FIG. 3: (color online) Commensurate and incommensuratemagnetic order parameter and movement of IC peaks. (a)and (b) Magnetic order parameters in both commensurateand incommensurate (IC) phases as a function of tempera-ture in CeRhAl Si (Fig. a) and CeIrAl Si (Fig. b). Whilethe IC peaks form a dome-type structure in temperature, thetransition to the commensurate phase is mostly first order innature. (c) and (d) Center of IC peak as a function of tem-perature, nominally at q IC = (0.98,0.98,0.5). The IC peakmoves towards the commensurate wave-vector as the mea-surement temperature is reduced. (e) and (f) Representativescans across structural peaks as a function of temperature inCeRhAl Si (Fig. e) and CeIrAl Si (Fig. f). Clearly, nochange in the position or the peak intensity of nuclear peaksare observed as the temperature is reduced through the lock-inmagnetic transition, ruling out the effect of crystal distortionin the occurrence of the lock-in magnetic transition. ture and ϕ is the phase of the distorted wave, which cantake any of the p -values. Minimization of the above ex-pression for η yields three values of ϕ , corresponding tothree different lattice structures associated to the first or-der transition to the commnesurate magnetic phase.[20]The Umklapp correction is more prominent in the caseof significant lattice distortion in the system, primarilycausing the crystal symmetry group transformation atlow temperature. Measurements were performed to de-termine the applicability of this possibility. Representa-tive scans across structural peaks and the lattice param-eters in Ce X Al Si are plotted in Fig. 3e and 3f. Clearly, [H,H] (r.l.u) L (r . l . u ) FIG. 4: (color online) Top left panel manifests the simulatedmagnetic pattern in the incommensurate phase, which is con-sistent with the experimental data. Top right inset shows thespin correlation of Ce-ions in the commensurate phase. Whilethe commensurate phase is described by the antiferromagneticcorrelation of Ce-ions along the z -axis, the incommensuratestructure (as shown in lower panel) is best described by aspin density wave with Ce-spins spatially fluctuating alongthe z -axis. the tetragonal lattice structure remains intact through-out the measurement; hence, rules out the possibility ofthe Umklapp correction causing an incommensurate-to-commensurate magnetic phase transition in Ce X Al Si .Second possibility involves the creation of soft solitonsat higher temperature that merge to the commensuratewave-vector via the first order transition as the mea-surement temperature is reduced.[16, 20] Soft solitonsare accompanied by a step-like function of incommen-surate (IC) reflections of higher harmonics. Also, the ICpeaks get closer to each other as temperature is reduced.Ce X Al Si exhibits at least two characteristics of soli-tons: a first order-type magnetic transition to the com-mensurate phase (more prominently in X = Ir) and thetemperature-dependent movement of IC peaks towardsthe commensurate wave-vector. However, no evidence ofthe step-like function of higher harmonic IC peaks wereobserved in neutron scattering measurements. More re-search is needed to further verify or, completely rule outthe possibility of soliton propagation in this dense Kondolattice system. Under present circumstances, it is im-perative to consider that the changes in the electronicproperties, involving the separation of electron and holepockets at intermediate temperatures, causes the lock-inmagnetic transition in Ce X Al Si . In a more recent re-port, it was shown that the compound RM Al Si , where R = La, Ce and M = Rh, Ir, Pt, have quasi-2D electronicstructure with electron and hole pockets separated by asimilar wave-vector.[19] This is in agreement with ourqualitative analysis.Finally, we discuss the nature of long range magneticcorrelation in Ce X Al Si . The incommensurate mag-netic reflections are usually associated to the long-rangemagnetic order of a density wave or the square wave pat-tern. Measurements were performed to higher order Bril- louin zones (BZ) at two temperatures, T = 5 K and 10K, to understand the nature of magnetic correlations. Atlow temperature, magnetic peak intensities across the ex-tended BZ is best described by an antiferromagnetic spincorrelation with Ce-spins pointing along the z -axis, seethe inset of Fig. 4. The ordered moment of correlatedCe-ions is found to be 1.12(0.17) µ B and 0.89(0.16) µ B in X = Rh and Ir, respectively. This is also consistentwith a previous report of neutron scattering measure-ments on powder Ce X Al Si .[18] In order to determinethe spin correlation associated to IC peaks at relativelyhigher temperature ( T (cid:39)
10 K), numerical modeling of theexperimental data was performed using the following ex-pression for the ordered moment S ij :[21, 22] Sij = A i cos ( k.rj + ψ j ) + B i sin ( k.rj + ψ j ) (2), where S ij is the moment of the i th ion in the j th unitcell and k is the propagation wave vector of the spindensity wave.[22] The numerical modeling also involvedaveraging the magnetic structure factor over four equallypopulated domains. Magnetic structure in the IC phaseis best described by a spin density wave (SDW) con-figuration of propagation vector k = (0.016,0.016,0.5).The spin correlation of Ce spins, spatially fluctuat-ing along the z -axis, is shown in Fig. 4. The or-dered moment associated to the SDW configuration isfound to be 0.65(0.2) µ B and 0.45(0.16) µ B in X =Rh and Ir, respectively. The ordered moment values,in both the commensurate and incommensurate phases,are much smaller than full moment values in respectivecompounds. Since Ce X Al Si is a dense Kondo latticematerial, the smaller value of ordered moment possiblyillustrates strong Kondo screening of the localized mo-ment by surrounding conduction electrons.In summary, we have performed detailed experimentalinvestigation of the underlying magnetism and associatedlock-in magnetic transition in single crystals Ce X Al Si .Both compounds exhibit sharp magnetic transition froman incommensurate phase, at intermediate temperatures,to the commensurate phase at low temperatures. Thespin structures in commensurate and incommensuratephases are manifested by long range antiferromagneticand spin density wave configurations of correlated Ce-ions, respectively. The qualitative analysis of the ex-perimental data, in conjuction with a recently publishedreport,[19] suggests that the incommensurate phase canbe arising due to the Fermi surfaces nesting, which causesthe separation of electron and hole pockets at interme-diate temperatures. Further theoretical works involv-ing the calculation of the propagation wave vector in anested Fermi surface, using Linear Muffin Tin Orbital(LMTO) method or other analytical techniques, are verydesirable. Previously, similar theoretical methods wereemployed to establish the correlation between the Fermisurfaces nesting and the incommensurate magnetic struc-ture in heavy fermion compounds, such as CeCu Si andCeCu Ge .[23, 24] Also, detailed inelastic neutron scat-tering measurements on bigger samples will be helpful infurther understanding the role of possible soliton propa-gation in these newly discovered Kondo lattices.[20]Authors acknowledge the support provided by the De-partment of Commerce facility NIST Center for NeutronResearch. Authors are thankful to J. Leo and A. Ye forhelp with the neutron scattering experiments. [1] C. M. Varma, Rev. Mod. Phys. , 219-238 (1976).[2] S. Sachdev, Quantum phase transitions. (CambridgeUniv. Press, New York, 1999).[3] Z. Fisk et al. , Science , 33 (1988)[4] S. Saxena et al. , Nature , 587 (2000).[5] W. Eerenstein, N. D. Mathur and J. F. Scott,
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