The magnetic excitations in Ca1.8Sr0.2RuO4 were studied across the
metamagnetic transition and as a function of temperature using inelastic
neutron scattering. At low temperature and low magnetic field the magnetic
response is dominated by a complex superposition of incommensurate
antiferromagnetic fluctuations. Upon increasing the magnetic field across the
metamagnetic ransition, paramagnon and finally well-defined magnon scattering
is induced, partially suppressing the incommensurate signals. The high-field
phase in Ca1.8Sr0.2RuO4 has, therefore, to be considered as an intrinsically
ferromagnetic state stabilized by the magnetic field

K. Schmalzl

M. Braden

P. Link

P. Steffens

S. Nakatsuji

S. W. Lovesey

T. Moriya

Y. Maeno

Y. Sidis

English

arXiv

The magnetic excitations in Ca1.8Sr0.2RuO4 were studied across the metamagnetic transition and as a function of temperature using inelastic neutron scattering. At low temperature and low magnetic field the magnetic response is dominated by a complex superposition of incommensurate antiferromagnetic fluctuations. Upon increasing the magnetic field across the metamagnetic transition, paramagnon and finally well-defined magnon scattering is induced, partially suppressing the incommensurate signals. The high-field phase in Ca1.8Sr0.2RuO4, therefore, has to be considered as an intrinsically ferromagnetic state stabilized by the magnetic field

Steffens, P.

Sidis, Y.

Link, P.

Schmalzl, K.

Nakatsuji, S.

Maeno, Y.

Braden, M.

Juelich Shared Electronic Resources

Field-Induced Paramagnons at the Metamagnetic Transition of Ca1:8Sr0:2RuO4P. Steffens,1 Y. Sidis,2 P. Link,3,* K. Schmalzl,4 S. Nakatsuji,5 Y. Maeno,6 and M. Braden11II. Physikalisches Institut, Universita¨t zu Ko¨ln, Zu¨lpicher Strasse 77, D-50937 Ko¨ln, Germany2Laboratoire Le´on Brillouin, C.E.A./C.N.R.S., F-91191 Gif-sur-Yvette CEDEX, France3Forschungsneutronenquelle Heinz Maier-Leibnitz (FRM-II), TU Mu¨nchen, Lichtenbergstrasse 1, 85747 Garching, Germany4Juelich Centre for Neutron Science, Forschungszentrum Juelich, Outstation ILL, 38042 Grenoble, France5Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan6Department of Physics, Kyoto University, Kyoto 606-8502, Japan(Received 30 March 2007; published 19 November 2007; corrected 21 November 2007)The magnetic excitations in Ca1:8Sr0:2RuO4 were studied across the metamagnetic transition and as afunction of temperature using inelastic neutron scattering. At low temperature and low magnetic field themagnetic response is dominated by a complex superposition of incommensurate antiferromagneticfluctuations. Upon increasing the magnetic field across the metamagnetic transition, paramagnon andfinally well-defined magnon scattering is induced, partially suppressing the incommensurate signals. Thehigh-field phase in Ca1:8Sr0:2RuO4, therefore, has to be considered as an intrinsically ferromagnetic statestabilized by the magnetic field.DOI: 10.1103/PhysRevLett.99.217402 PACS numbers: 78.70.Nx, 74.70.Pq, 75.40.GbMetamagnetic (MM) transitions have recently attractedconsiderable interest as, despite their typically first ordercharacter, a quantum phase transition can be realized whenthe critical end point is driven to zero temperature. Byvarying the direction of the applied field, this suppressionof the critical end point can be achieved in the double-layerruthenate Sr3Ru2O7 inducing fascinating quantum-criticalphenomena [1].Ca1:8Sr0:2RuO4 belongs to the single-layered ruthenatesbut exhibits a MM transition very similar to that inSr3Ru2O7. Ca1:8Sr0:2RuO4 is a metal on the border of thetransition into the Mott-insulating state [2]. The very highelectronic specific-heat coefficient in the range of values intypical heavy-fermion compounds indicates strong mag-netic fluctuations [3]. At magnetic fields of 2–8 T (depend-ing on the field orientation) Ca1:8Sr0:2RuO4 undergoes theMM transition into a state with high magnetic polarizationof about 0:7B per Ru [3] accompanied by a shift in theoccupation of the Ru 4d t2g states [4,5]. However, it is stillan open issue whether the high-field phase is intrinsicallyferromagnetic (FM) or just polarized, in Ca1:8Sr0:2RuO4 aswell as in Sr3Ru2O7. The MM transition in Ca1:8Sr0:2RuO4is smeared out due to the intrinsic disorder caused by thechemical doping. As a consequence, any quantum-criticalscaling might be strongly modified [6]. However, the sim-pler crystal structure with only one RuO2 layer and theresulting simpler (essentially two-dimensional) electronicband structure render Ca1:8Sr0:2RuO4 more favorable foran analysis of the underlying mechanism. Previous studieson related ruthenates, Ca2xSrxRuO4 with x  0:62 [7]and Sr3Ru2O7 [8,9], have revealed the complexity of themagnetic response at zero field but did not address the MMtransition.The cross section for magnetic inelastic neutron scatter-ing is given by the imaginary part of the susceptibility00Q; ! [10]: d2dd!/ F2Q1 exp @!kBT00Q; !:FQ is the magnetic form factor. We used two coalignedsingle crystals of Ca1:8Sr0:2RuO4 of about 3 mm diameterand 15 mm length each, grown at Kyoto University. Themeasurements were performed on different neutron triple-axis spectrometers: 2 T and 4 F at the LLB, Saclay, IN22 atthe ILL, Grenoble, and PANDA at FRM-II, Garching. Onthe latter two we applied magnetic fields up to 10 T usingvertical cryomagnets, i.e., perpendicular to the scatteringplane. Two different sample orientations were used: onewith the a and the b axis, and one with the a and the c axisin the scattering plane. Throughout this Letter, we use thepseudotetragonal notation a  b  3:76 A and c 12:55 A in accordance with the majority of the literature,neglecting the structural distortions [11]. The sample wastwinned, with approximately equal amounts of both ortho-rhombic twins.Let us first consider the spin dynamics in Ca1:8Sr0:2RuO4at zero magnetic field and low temperature, T  2 K.Figure 1 shows the neutron intensity at constant energytransfer of @!  2:5 meV mapped out in reciprocal spacearound Q  1; 0; 0. For the description of the magnetismwe restrict ourselves on the two dimensions formed by theRuO2 plane (ab plane), because the correlation of adjacentplanes, i.e., along the c axis, is negligible [7,12]. Therefore,Q  1; 0; 0 can be regarded as a FM zone center, andthe area shown in Fig. 1 covers already a full Brillouinzone. The magnetic scattering is broadly distributedaround the FM zone center resembling that observed inCa1:38Sr0:62RuO4 [7], where the MM transition is stronglysuppressed. At the temperature of 2 K in Ca1:8Sr0:2RuO4,PRL 99, 217402 (2007) P H Y S I C A L R E V I E W L E T T E R S week ending23 NOVEMBER 20070031-9007=07=99(21)=217402(4) 217402-1 © 2007 The American Physical Societywe always find a minimum at the FM center 1; 0; 0 in cutsalong the [100] or [110] directions [Figs. 1, 2(a), and 2(b)].Furthermore, the data cannot be described by a singlecontribution centered on the a or b axes; the scans along[010] show steep edges at Q  1;0:35; 0 and a rela-tively broad and flat plateau between 1;0:1; 0 and1;0:3; 0. For a phenomenological description, we fitthe magnetic scattering by two Gaussian contributions oneach side of 1; 0; 0 with approximately equal intensityand width. These contributions are centered at q1 1; 0:12 0:01; 0 and q2  1; 0:27 0:01; 0 and theequivalent positions in pseudotetragonal symmetry. Wemay exclude that the inner signal stems from an isotropicparamagnon signal, as there is no evidence for a ring ofscattering in Fig. 1 and as the intensity does not show theexpected increase [10] when approaching 1; 0; 0 and lowenergies. There is no visible shift of the q1, q2 signals as afunction of energy, but rather a broadening that finallysuppresses the minimum at the center. In agreement withthe study on Ca1:38Sr0:62RuO4 [7], the q1, q2 fluctuationsexhibit a characteristic energy of 2:7 0:2 meV. From theanalysis of the geometrical factor at different equivalent Qpoints, we deduce that for these fluctuations 00c is signifi-cantly smaller than 00ab, which is opposite to the finding inSr2RuO4 [13].In the layered ruthenates, the Fermi surface consists ofseveral sheets related with the three t2g states of the Ru 4dshell [14]: two sheets arise from nearly one-dimensionalbands of dxz=yz character, named  and , and the  sheetoriginates from the two-dimensional 4dxy band. We as-sume that the q1, q2 signals arise from the  band, sincethis band has been shown to carry the magnetization inCa1:5Sr0:5RuO4 [15], although its topology (electronlike orholelike [16]) in the structurally distorted compound is notfully established yet.The magnetic excitations described above strongly re-semble those observed in Sr3Ru2O7 with two incommen-surate contributions on the a or b axes at almost the samepositions (x  0:09 and 0.25) [8]. This remarkable agree-ment suggests that magnetic properties and, in particular,the MM mechanism should be very similar in theseruthenates.The diagonal scans in Fig. 2(b) show a weaker signal atQ  0:7;0:3; 0, at the position where the dominantmagnetic fluctuations occur in Sr3RuO4 due to nesting inthe  and  Fermi-surface sheets [12,14]. The structuraldistortions in Ca1:8Sr0:2RuO4 cause a folding of the elec-tronic bands with respect to 0:5; 0:5; 0 implying a com-plex Fermi surface as well as a complex Lindhard function.However, the strong nesting tendency observed in Sr2RuO4should be rather robust and can be taken as a roughestimate of the band filling. In Ca1:8Sr0:2RuO4 the fillingof the ,  bands seems thus to be similar to that inSr2RuO4, clearly contradicting the proposal of an orbital-selective Mott transition [17] requiring a significant redis-tribution of orbital occupation.Upon heating to intermediate temperatures of the orderof 10 K, the magnetic response changes significantly,developing strong paramagnon scattering of truly FMcharacter on top of the already complex low-temperatureantiferromagnetic (AFM) response described above. Uponcooling, the paramagnon contribution appears below50 K, passes a maximum, and becomes suppressed atthe lowest temperatures; see Fig. 3. The paramagnon scat-tering exhibits a significantly smaller characteristic energyof the order of 0.2–0.6 meV, which strongly depends ontemperature. Via calibration by an acoustic phonon, weFIG. 2. Constant energy scans: (a) along b, (b) along thediagonal of the Brillouin zone. The sketch on top illustratesthe positions of the incommensurate magnetic signals as de-scribed in the text, and the bold arrows are the trajectories of thescans in reciprocal space. The crosses are the weaker =nesting signal at 1; 0; 0 	 0:3;0:3; 0. The lines are fitswith Gaussians centered at the positions shown in the sketch.FIG. 1 (color online). Mapping of the magnetic intensity in thea=b plane of reciprocal space around Q  1; 0; 0. Data aretaken at T  2 K and at an energy transfer of 2.5 meV. A smoothbackground is subtracted. The inset shows the same data, butfully symmetrized and corrected for the magnetic form factorFQ.PRL 99, 217402 (2007) P H Y S I C A L R E V I E W L E T T E R S week ending23 NOVEMBER 2007217402-2may determine 00Q;! in absolute units, as shown inFig. 3, which then allows us to calculate 0Q; 0 byKramers-Kronig analysis. For a single relaxor 00Q;! 0Q;0!2	!2 , 0Q; 0 amounts to twice the maximum of theimaginary part (at !  ). 00QFM; ! consists of twocontributions due to the strong in-plane anisotropy, andthe average 00QFM; 0:4 meV 	 00QFM; 1 meV is areasonable estimate for 0QFM; 0. Figure 3(c) comparesthis estimate with the susceptibility measured by a macro-scopic method yielding good agreement. The incipient FMinstability in Ca1:8Sr0:2RuO4, which due to the orbitalrearrangement [4–6] is suppressed at low temperature, isthus carried by the paramagnon fluctuations.Let us now focus on the effect of a magnetic field. TheMM transition in Ca1:8Sr0:2RuO4 occurs approximately at6 T for a magnetic field along the c direction and at 3 T forB k a; b [3,5]. The even stronger in-plane anisotropy be-tween the two orthorhombic axes (diagonals in our nota-tion) is not relevant in our experimental geometry with Bparallel to [010]; see Fig. 4. There is a drastic change at theMM transition field (BMM  3 T), which corresponds to anonly low-energy scale gBB  0:17 meV: below the tran-sition, we observe the incommensurate AFM fluctuations.Above, the response is dominated by a broad paramagnonsignal around the 2D FM zone center 0; 0; 1:6. The datacan be described in a very simple model of two contribu-tions: an AFM one (taken to have always the same shape asat B  0) and a FM one. It is clearly seen that the funda-mental change takes place between 2 and 4 T, i.e., at theMM transition. A small AFM contribution persists tohigher fields getting fully suppressed only far above thetransition. The energy scans at the FM zone center,Fig. 4(c), confirm that upon applying a magnetic field theFM response is enhanced and that its spectral weight shiftsto higher energies at fields above the transition. The tran-sition is further seen in the field dependence of the intensityat fixed energy [Fig. 4(d) and 4(e)]. Low-energy paramag-non fluctuations seem to govern the thermodynamics of theMM transition. Their enhancement at the critical fieldshown in Fig. 4(e) may explain the observation that theelectronic specific heat passes a maximum at the transition[18], because the low-energy magnetic fluctuations give alarge contribution to the electronic specific heat; see alsoRef. [7].The quantitative analysis of the paramagnon signal inthe B k 010 configuration is difficult. Because of the lowvertical resolution of the focusing spectrometer, the dis-persion along b is averaged. Furthermore, the measuredsusceptibility consists of a superposition of several com-ponents. At Q  0; 0; L we measure the sum of the in-plane components 00ab. Because the field is along b, 00absplits into two components, k and ?, parallel and trans-verse to the applied field. The transverse susceptibility isassociated with electronic spin-flip processes. Therefore, aFIG. 3 (color online). Temperature dependence of the para-magnon scattering. (a) Constant energy scans at three differenttemperatures. In (b) we plot the intensity of the (2D) zone centerQFM  0; 0; 1:6 as a function of temperature for 0.4 and 1 meVenergy transfer (lines are guides to the eye, 0.4 meV data shiftedby 400 2BeV ). From the smoothed curves in (b) we estimate the realpart of the susceptibility at !  0 (see text), which is plotted in(c) together with the macroscopic susceptibility (in-plane aver-age) from Ref. [2].FIG. 4 (color online). Magnetic scattering for magnetic fieldsapplied along the b axis: (a) Constant energy scans along [100].Lines assume a superposition of an AFM and a FM contribution[the latter centered at QFM  0; 0; 1:6], a sketch of thesecontributions is drawn in (b). (c) Energy scans at the FM positionQFM. The intensities of the FM and AFM contributions fitted tothe scans in (a) relative to their values at 0 and 8 T, respectively,are shown in (d) as a function of the field. (e) The fielddependence of the low-energy part at QFM. [Lines in (c) and(e) are guides to the eye.]PRL 99, 217402 (2007) P H Y S I C A L R E V I E W L E T T E R S week ending23 NOVEMBER 2007217402-3Zeeman-type energy gap, gBB  1 meV for a field of10 T, superposes the spin-orbit coupling induced anisot-ropy gap for the transverse channel ?, whereas k ex-hibits only an anisotropy gap.The quantitative analysis is simpler when the field isapplied along the c axis; see Fig. 5. The low verticalresolution then averages along c, where the magneticdispersion is negligible. Again there is a drastic changeat the MM transition (BMM  6 T); see Figs. 5(a) and 5(b)and the zero field data taken under the same conditions inFig. 2. At 10 T, there is clear evidence for a well-definedmagnon mode. This mode disperses outwards from1; 0; 0, rapidly broadens, and dies away with increasingfrequency. It can be described by a quadratic dispersion[Fig. 5(c)] similar to a conventional ferromagnet: @! gBBeff 	Dq2 with a stiffness constant of 60 meV A2.Since the external field superposes the anisotropy terms, aneffective field enters the dispersion relation. Assuming thatthe single-ion anisotropies nearly average out in this ge-ometry, we set Beff  Bexternal. The dispersion of the mag-non unambiguously proves that the high-magnetizationphase does not only arise from the magnetic polarizationof the spins, but has to be considered as a true FM statewith an intrinsic FM interaction stabilized by the magneticfield. In contrast, the FM correlation seems to be sup-pressed in the low-temperature low-field phase due to theorbital effects [4,5].We mention that an enhancement of magnetic scatteringnear FM q vectors has also been observed in the MMtransition in the heavy-fermion compound CeRu2Si2[19], but a well-defined magnon mode has not been estab-lished in any MM transition so far.In conclusion, our results indicate that a magnetic fieldcorresponding to low electronic energy scales causes afundamental change of the magnetic correlations inCa1:8Sr0:2RuO4. Below the MM transition, the interactionsare AFM with several incommensurate scattering con-tributions. In particular, there is a weak signal near0:3; 0:3; qL, i.e., very close to the position of the domi-nant nesting signal in Sr2RuO4. Magnetic correlations inCa1:8Sr0:2RuO4 fundamentally change upon an increase ofeither temperature or magnetic field. In both cases we findstrong paramagnon scattering. In the high-magnetizationphase we even find a well-defined magnon mode corrobo-rating the dominance of the FM interaction and the intrin-sic FM character of the high-field state.The paramagnon fluctuations should govern the thermo-dynamics in Ca1:8Sr0:2RuO4 close to its MM quantum-critical point and further document that layered ruthenatesin general may exhibit an intrinsic FM instability—possi-bly an important ingredient to understand superconductiv-ity in Sr2RuO4.The work at Universita¨t zu Ko¨ln was supported by theDeutsche Forschungsgemeinschaft through the Sonder-forschungsbereich No. 608.*Also at Spektrometer PANDA, Institut fu¨rFestko¨rperphysik, TU Dresden, Dresden, Germany.[1] S. A. Grigera et al., Science 294, 329 (2001); R. S. Perryet al., Phys. Rev. Lett. 86, 2661 (2001); S. A. Grigeraet al., Science 306, 1154 (2004).[2] S. Nakatsuji and Y. Maeno, Phys. Rev. Lett. 84, 2666(2000); Phys. Rev. B 62, 6458 (2000).[3] S. Nakatsuji et al., Phys. Rev. Lett. 90, 137202 (2003).[4] M. Kriener et al., Phys. Rev. Lett. 95, 267403 (2005).[5] L. Balicas et al., Phys. Rev. Lett. 95, 196407 (2005).[6] J. Baier et al., J. Low Temp. Phys. 147, 405 (2007).[7] O. Friedt et al., Phys. Rev. Lett. 93, 147404 (2004).[8] L. Capogna et al., Phys. Rev. B 67, 012504 (2003).[9] M. B. Stone et al., Phys. Rev. B 73, 174426 (2006).[10] See, for instance, S. W. Lovesey, Theory of NeutronScattering from Condensed Matter (Clarendon, Oxford,1984), Vol. 2; T. Moriya, Spin Fluctuations in ItinerantElectron Magnetism (Springer, New York, 1985).[11] O. Friedt et al., Phys. Rev. B 63, 174432 (2001).[12] Y. Sidis et al., Phys. Rev. Lett. 83, 3320 (1999); M. Bradenet al., Phys. Rev. B 66, 064522 (2002).[13] M. Braden et al., Phys. Rev. Lett. 92, 097402 (2004).[14] C. Bergemann et al., Adv. Phys. 52, 639 (2003); I. Mazinand D. Singh, Phys. Rev. Lett. 79, 733 (1997).[15] A. Gukasov et al., Phys. Rev. Lett. 89, 087202 (2002).[16] S. C. Wang et al., Phys. Rev. Lett. 93, 177007 (2004).[17] V. I. Anisimov et al., Eur. Phys. J. B 25, 191 (2002).[18] J. Baier et al., Physica (Amsterdam) 378B, 497 (2006).[19] M. Sato et al., J. Phys. Soc. Jpn. 73, 3418 (2004).FIG. 5. (a) Constant energy scans above the MM transition(B  10 T, B k c) in the same configuration as the scans inFig. 2. The lines are fits consisting of two contributions: the AFMone was taken to be the same as in Fig. 2(a) times a variable scalefactor  1; the magnon was added as two Gaussians at sym-metric positions, but variable width to account for focusingeffects of the spectrometer. In (b) the 2 meV scans at 0 and6 T are compared. In (c), the fitted peak positions are plottedtogether with a parabolic dispersion.PRL 99, 217402 (2007) P H Y S I C A L R E V I E W L E T T E R S week ending23 NOVEMBER 2007217402-4

Field-Induced Paramagnons at the Metamagnetic Transition of Ca1.8Sr0.2RuO4

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Field-Induced Paramagnons at the Metamagnetic Transition of
                    
                      
                        Ca

Field-induced paramagnons at the metamagnetic transition in
  Ca1.8Sr0.2RuO4

Field-induced paramagnons at the metamagnetic transition in Ca1.8Sr0.2RuO4

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