We report ^59Co-NMR measurements in UCoAl where a metamagnetism occurs due to
enhancement of ferromagnetism by magnetic field. The metamagnetic transition
from a paramagnetic (PM) state to a ferromagnetic state is a first order
transition at low temperatures, but it changes to a crossover at high
temperatures on crossing the critical end pint (CEP) at T_CEP ~ 12 K. The
contrasting behavior between the relaxation rates 1/T_1 and 1/T_2 suggests that
the longitudinal magnetic fluctuation of U moment is strongly enhanced
especially near the CEP. A wide diffusion of the fluctuation from the CEP can
be confirmed even in the PM state where the magnetic transition does not occur.Comment: 5pages, 6 figures, to be published in J. Phys. Soc. Jp

Andreev A. V.

Aoki D.

Belitz D.

Binz B.

Harada A.

Holmes A. T.

Imada M.

Ishii Y.

Iwamoto Y.

Javorský P.

King E.

Kotegawa H.

Matsuda T. D.

Millis A. J.

Miyake K.

Murani A. P.

Mushnikov N. V.

Pfleiderer C.

Taufour V.

Uhlarz M.

Wu W.

Yamada H.

Yamaji Y.

English

arXiv

Hiroki Nohara

Hisashi Kotegawa

Hideki Tou

Tatsuma D. Matsuda

Etsuji Yamamoto

Yoshinori Haga

Zachary Fisk

Yoshichika Ōnuki

Dai Aoki

Jacques Flouquet

Crossref

Journal of the Physical Society of Japan

Strong Longitudinal Magnetic Fluctuations Near Critical End Point in UCoAl: A <sup>59</sup>Co-NMR Study

We report 59Co-NMR measurements in UCoAl where metamagnetism occurs owing to the enhancement of ferromagnetism by a magnetic field. The metamagnetic transition from a paramagnetic (PM) state to a ferromagnetic state is a first-order transition at low temperatures, but it changes to a crossover at high temperatures on crossing the critical end point (CEP) at Tcep ∼ 12 K. The contrasting behavior between the relaxation rates 1/T 1 and 1/T2 suggests that the longitudinal magnetic fluctuation of the U moments is strongly enhanced, especially near the CEP. A wide diffusion of the fluctuation from the CEP can be confirmed even in the PM state where the magnetic transition does not occur. © 2011 The Physical Society of Japan

Nohara, Hiroki

Kotegawa, Hisashi

Tou, Hideki

Matsuda, Tatsuma D

Yamamoto, Etsuji

Haga, Yoshinori

Fisk, Zachary

Ōnuki, Yoshichika

Aoki, Dai

Flouquet, Jacques

eScholarship - University of California

UC IrvineUC Irvine Previously Published WorksTitleStrong Longitudinal Magnetic Fluctuations Near Critical End Point in UCoAl: A 59Co-NMR StudyPermalinkhttps://escholarship.org/uc/item/6mf4k0mvJournalJournal of the Physical Society of Japan, 80(9)ISSN0031-9015AuthorsNohara, HirokiKotegawa, HisashiTou, Hidekiet al.Publication Date2011-09-15DOI10.1143/jpsj.80.093707Copyright InformationThis work is made available under the terms of a Creative Commons Attribution License, availalbe at https://creativecommons.org/licenses/by/4.0/ Peer reviewedeScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaarXiv:1107.5224v1  [cond-mat.str-el]  26 Jul 2011Journal of the Physical Society of Japan LETTERSStrong Longitudinal Magnetic Fluctuationsnear Critical End Point in UCoAl: A 59Co-NMR StudyHiroki Nohara1, Hisashi Kotegawa1 ∗, Hideki Tou1, Tatsuma D. Matsuda2,Etsuji Yamamoto2, Yoshinori Haga2, Zachary Fisk2,3, Yoshichika Ōnuki2,4,Dai Aoki5, Jacques Flouquet51Department of Physics, Kobe University, Kobe 657-8501, Japan2ASRC, JAEA, Tokai, Ibaraki 319-1195, Japan3University of California, Irvine, Calfornia 92697, U.S.A.4Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan5INAC/SPSMS, CEA-Grenoble, 17 rue des Martyrs, 38054 Grenoble, FranceWe report 59Co-NMR measurements in UCoAl where a metamagnetism occurs due to enhancement offerromagnetism by magnetic field. The metamagnetic transition from a paramagnetic (PM) state to aferromagnetic state is a first order transition at low temperatures, but it changes to a crossover at hightemperatures on crossing the critical end pint (CEP) at TCEP ∼ 12 K. The contrasting behavior between therelaxation rates 1/T1 and 1/T2 suggests that the longitudinal magnetic fluctuation of U moment is stronglyenhanced especially near the CEP. A wide diffusion of the fluctuation from the CEP can be confirmed evenin the PM state where the magnetic transition does not occur.KEYWORDS: critical end point, UCoAl, metamagnetism, NMRA terminal point of a first order phase transition iscalled a critical end point (CEP), beyond which the tran-sition changes to a crossover. Generally a strong first or-der transition does not provide fluctuations between twophases, but they are expected at the CEP. The CEPcan be seen in various phase diagrams. One of familiarexamples is a liquid-gas transition of water. The firstorder phase transition of water encounters the CEP ata high pressure and a high temperature, above whicha new exotic state with fluctuations called supercriticalwater appears. Another example is a valence transition.Cerium element shows a first order transition betweenγ phase and α phase under pressure accompanied bya change in the valence.1, 2) The first order line of thisγ − α transition similarly terminates at a high pressureand a high temperature. It has been pointed out that asimilar valence CEP with the valence fluctuations givesa driving force for exotic superconductivity under pres-sure in CeCu2Si2.3, 4) On the other hand, a metamag-netic transition between a paramagnetic (PM) phase anda ferromagnetic (FM) phase occurs when the system islocated at the PM side in the vicinity of a first orderFM critical point at zero field.5, 6) The first order meta-magnetic transition at low temperatures changes to thecrossover at high temperatures on crossing the CEP atTCEP. Interestingly this TCEP decreases under pressureand the FM CEP reaches zero temperature at a highpressure and a high magnetic field, which is generallycalled quantum critical end point (QCEP). Such QCEPhas been extensively studied theoretically,5–10) but ex-perimentally the first order plane connecting the CEPat a finite temperature and the QCEP has been drawnschematically because of lack of the systems with largeplane.11, 12) Recently, sufficiently large first order planes∗E-mail address: kotegawa@crystal.kobe-u.ac.jphave been experimentally determined in UGe2, UCoAl,and Sr3Ru2O7 (H ‖ ab).13–15) Because of the benefit ofthe large plane, we can separate the QCEP from theFM critical point at zero field and address the evolutionin the physical quantities over wide pressure and fieldranges. In this letter, before addressing the QCEP, wefocus on investigating the magnetic fluctuations near theCEP at the finite temperature and ambient pressure inUCoAl by means of nuclear magnetic resonance (NMR)measurements.UCoAl crystallizes in the ZrNiAl-type hexagonal struc-ture stacked by U-Co(1) layer and Co(2)-Al layer (seeFig. 2). UCoAl is a paramagnet but uniaxial pressureeffect and chemical substitution have revealed that it islocated in the vicinity of a FM critical point.16–18) Itis considered that the FM state at zero field is alreadysuppressed at the negative pressure of ∼ −0.2 GPa.18)First order metamagnetic transition to the FM statewith ∼ 0.3 µB/U occurs at Hm ∼ 0.7 T for H ‖ c axisat low temperatures.19) The FM moment mainly origi-nates in U-5f electrons.20) The transition changes to thecrossover above TCEP ∼ 11− 13 K, where the transitionoccurs at ∼ 1 T.14, 18) Thus UCoAl possesses the CEP atTCEP ∼ 11− 13 K and HCEP ∼ 1 T, where the magneticfluctuations are expected. NMR measurement has beenperformed previously to investigate the magnetic fluctu-ation in UCoAl,21) but measurements near the CEP wasnot performed sufficiently. In this letter, we investigatedin detail where the fluctuation is strong in the field -temperature phase diagram. Our NMR results show thatthe longitudinal magnetic fluctuations strongly developsnear the CEP and they widely diffuse even to the PMphase.We used powdered single crystals with orienting alongH ‖ c for NMR measurements. The single crystalwas grown using Czochralski method in a tetra-arc1J. Phys. Soc. Jpn. LETTERSfurnace.22) Magnetization (M) measurements was per-formed using a MPMS (Quantum Design). NMR wasperformed using a standard spin-echo method. The spin-spin relaxation time T2 was determined by fitting the spinecho decay to a single exponential function, although thedeviation from the single component in the volume of∼ 10% was observed near the CEP.0 10 20 30 40 500.00.10.20.30.40.5  M (B/U)T (K)UCoAlH // c5.0 T4.03.02.01.61.41.21.00.90.750.650.40.2(a)0 1 2 3 4 5010203040CEPFM  T (K)H (T)PM(b)UCoAlH // c1st orderFig. 1. (color online) (a) Temperature dependence of magneti-zation at several magnetic fields. (b) Magnetic field - temperaturephase diagram for UCoAl. The first order phase transition changesto the crossover at the CEP (TCEP ∼ 12 K and HCEP ∼ 1.0 T).Figure 1(a) shows temperature dependence of M forH ‖ c. Details of magnetization data will be publishedelsewhere.22) Below 0.65 T, M shows a broad peakaround 20 K and the system is in the PM state down tolow temperatures. A discrete increase in M can be seenbetween 0.75 and 0.9 T due to the first order transition.The hysteresis in M(T ) is observed at these fields and itdisappears above 1.0 T.22) The temperature variation ofM shows an obvious broadening above 1.0 T changing tothe crossover. We determined a magnetic field - temper-ature phase diagram for UCoAl as shown in Fig. 1(b).Both closed and open squares indicate temperature ofthe peaks in dM/dT , where the first order transitions(closed squares) are distinguished by the existence of thehysteresis. This phase diagram shows that the CEP islocated at TCEP ∼ 12 K and HCEP ∼ 1.0 T for UCoAlat ambient pressure.Figures 2(a-c) show the field-sweep NMR spectra mea-sured at different temperatures and resonance frequen-cies. UCoAl consists of an U site, two Co sites and anAl site as shown in the right panel of Fig. 2. At 60 Kin the PM state (Fig. 2(a)), the spectrum consists of19 lines arising from Co(1) and Co(2) sites (I = 7/2)and Al site (I = 5/2) as reported previously.21) Eachgyromagnetic ratio γN is 10.03 MHz/T for59Co nucleiand 11.094 MHz/T for 27Al nuclei. The sharp peaks en-AlCo(1)Co(2)UccFig. 2. (color online) (a-c) NMR spectra for UCoAl measured at60 K and 4.2 K. The spectrum is discontinuous on crossing Hm.The NMR lines of Co(1) site, Al site, and 2 lines of Co(2) site areoverlapped at low temperature. (right panel) The crystal structureof UCoAl.sure the high orientation of the powdered sample alongH ‖ c. The satellite lines for Co(2) site are widely sepa-rated due to the large quadrupole frequency νQ of about4.3 MHz compared with other sites. At low temperature(Fig. 2(b)), we observe two kinds of spectra for the PMstate and the FM state because of the discrete enhance-ment of M by the metamagnetic transition at Hm ∼ 0.7T. When the resonance frequency is increased (Fig. 2(c)),all the lines enter in the FM state, but the lines of Co(1)site, Al site, and 2 lines of Co(2) site are overlapped.Thus, to avoid the overlap of data, we measured the nu-clear spin-lattice relaxation ratio (1/T1) and the nuclearspin-spin relaxation ratio (1/T2) at the satellite line of−5/2 ↔ −3/2 transition of Co(2) site.Figure 3 shows temperature dependence of the NMRshift (∆H/H0) measured at fixed magnetic fields, where∆H is an internal field at Co(2) site and H0 is an ap-plied field. At 0.5 T, ∆H/H0 has a broad maximum at0 20 40 60 80 1000204060801001200.0 0.1 0.2 0.3 0.4020406080100120  H / H0 (%)T (K) 1 T 0.5 TFM  H / H0 (%)M/H0 (B/T) 1 T 0.5 TPMFig. 3. (color online) Temperature dependence of the NMR shift∆H/H0 at H0 = 0.5 T and 1 T. The inset shows the relationshipbetween the shift and M/H0. The linear relationship gives Acspin =2.58 (T/µB).2J. Phys. Soc. Jpn. LETTERSaround 20 K as well as temperature dependence of M .The ∆H/H0 at 1 T shows a drastic increase between15 K and 5 K due to the FM transition. As mentionedlater, the small signal by short T2 obstructs to measurethe convincing data in this temperature range at 1 T.The inset shows ∆H/H0 vs. M/H0. In general the shiftconsists of temperature-dependent spin part, which isproportional to the spin susceptibility, and temperature-independent orbital part. The linear fitting in the PMrange suggests that the orbital part is negligibly smallcompared with the spin part, giving a hyperfine couplingconstant Acspin = 2.58 (T/µB). The data at the FM statealso satisfy the linear relationship, indicating the changein the hyperfine coupling constant is small within the ex-perimental precision between the PM state and the FMstate, even though the change in the band structure isexpected between two phases.012341 10 100110100(a)  1/T 1T (sec-1K-1 ) 5 T 2  1 0.5(b)T (K)  1/T 2 (msec-1 ) 5 T 2  1.6 1 0.5 0.2Fig. 4. (color online) Temperature dependence of (a) 1/T1T and(b) 1/T2 at several fixed fields. 1/T2 has a strong enhancementnear the CEP, while 1/T1T does not, suggesting that the observedfluctuations are longitudinal mode of U moments.Figure 4 shows temperature dependence of (a) 1/T1T ,and (b) 1/T2 at several fixed fields. First we should stressthat 1/T2 shows a strong enhancement in the temper-ature range of 7 − 15 K at H = HCEP(= 1 T). Wecould not measure the relaxation times near 10 K ow-ing to the small signal by short T2 and the broadeningof spectrum. This strong enhancement of 1/T2 is dras-tically suppressed on leaving away from 1 T. At lowerfields (0.2 T and 0.5 T), the peaks in 1/T2 are weaken,but still remain at around 10 K even though the magnetictransition does not occur. The enhancement of 1/T2 alsosurvives at higher field side (1.6 T, 2 T and 5 T) and theyare almost field independent above 2 T. In the previousmeasurement,21) similar anomaly in 1/T2 was observedat 4.5 T and no anomaly was seen at around 10 K at0 T. On the other hand the 1/T1T gradually increaseswith decreasing temperature and shows a constant be-havior below 20 K at 0.5 T where susceptibility exhibitsthe maximum. 1/T1T is independent of field at high tem-peratures, but it decreases gradually below ∼ 20 K at 2T (∼ 30 K at 5 T), respectively. The peaks are observedin the wide field range in 1/T2, whereas 1/T1T does notshow such peaks. 1/T1 and 1/T2 are expressed generallyas follows.1T1=γ2N2∫∞−∞〈δH−(t)δH+(0)〉 exp(−iωN t)dt, (1)1T2=12T1+γ2N2limω→0∫∞−∞〈δHz(t)δHz(0)〉 exp(−iωt)dt. (2)Here 〈δH−(t)δH+(0)〉 [〈δHz(t)δHz(0)〉] are time cor-relation functions for magnetic fluctuations perpendic-ular [parallel] to the quantum axis of nuclear spin, re-spectively, and ωN is the resonance frequency. 1/T1 cor-responds to the magnetic fluctuations perpendicular tothe magnetic field, that is, the fluctuations perpendicularto the c axis. 1/T2 indicates the fluctuations along themagnetic field, that is, the fluctuations along the c axis.Here, as shown in Fig. 2, the position of the Co(2) siteis just above the center of triangle formed by three Uatoms. The components along the c-axis of U momentsinduce the internal field only along the c axis at Co(2)site because of the cancelation of the dipole fields. Thus1/T1 at Co(2) site detects the transverse fluctuation ofU moment, while 1/T2 at Co(2) site detects the longitu-dinal fluctuation of U moment. In the strict sense 1/T2includes the fluctuation of electric field gradient, sinceit corresponds to the fluctuation of the resonance fre-quency. The magnetostriction between the PM phase andthe FM phase has been reported.14) However, the changein νQ between two phases was less than 0.02 MHz. Thisis quite smaller than the change of ∼ 6 MHz in the res-onance frequency by the internal field, indicating thatthe contribution of electron field gradient in T2 is small.The absence of anomalies in 1/T1T indicates that theobserved magnetic fluctuation is the longitudinal fluctu-ation of U moment along the c axis and the transversefluctuation of U moment is weak. This supports thatmagnetic character near the CEP is a strong Ising-type.Figure 5 shows the field dependence of 1/T1T and 1/T2at 1.6 K and 12 K(∼ TCEP). At 1.6 K both 1/T1T and1/T2 exhibit step-like anomalies at Hm without the en-hancement of fluctuations. The relationship that 1/T1Tis proportional to the square of the density of state atFermi level N(EF ) gives the reduction of 16% in N(EF ),which is almost consistent with the specific heat mea-surements,14, 23) as confirmed similarly in the previousstudy.21) The 1/T2 also shows the drop at Hm. Thischange might be affected by both the change in the mag-nitude of fluctuation and the change in the nuclear-dipoleinteractions because the spectrum in the FM state isbroaden. At 12 K, 1/T2 shows the enhancement towardthe CEP at 1 T, while it is independent of field above 2T. We could not measure T1 in the range of 0.5 − 2 T,but the absence of anomaly in 1/T1T as shown in Fig. 4implies that 1/T1T has no strong enhancement towardthe CEP.3J. Phys. Soc. Jpn. LETTERS01234560 1 2 3 4 50.1110100HCEP  1/T 1T (sec-1K-1)Hm12 K1.6 K  1/T 2 (msec-1 )H (T)1.6 K12 KFig. 5. (color online) Magnetic field dependence of 1/T1T and1/T2. At 12 K 1/T2 increases on approaching the CEP. Both 1/T1Tand 1/T2 show the step-like anomalies at Hm at low temperature.0 1 2 3 4 50510152025303540FMPM  T (K)H (T)0.30001.00010.00CEPshort T2long T2Fig. 6. (color online) The profile of 1/T2 in UCoAl. The strongenhancement of 1/T2 is observed near the CEP. This longitudinalfluctuation survives in the wide field range. The solid and dottedlines are determined by the peak of dM/dT as shown in Fig. 1(b).Figure 6 shows the profile of 1/T2 in the field - tem-perature phase diagram for UCoAl. It is obvious thatstrong fluctuation is induced near the CEP. It is sup-pressed in the first order transition region at low tem-peratures and the crossover region at high temperaturesand high fields. On the other hand, the fluctuation of theCEP is diffused even to the PM state where M(T ) and∆H/H0 have no anomaly. It is an unexpected behaviorthat field-insensitive fluctuations survive near 10 K up tohigh magnetic field. The absence of anomaly in 1/T1T in-dicates these fluctuations are also the longitudinal mode.It is worthy to note that M(T,H) has no strong variationin this field and temperature range as shown in Fig. 1(a).We cannot conclude the origin of these fluctuations, butmeasurements under pressure will help us to understandthe origin. When looking back on NQR study (H = 0)under pressure in a similar metamagnetic system UGe2,unknown peak in 1/T1T has been observed in the PMstate at 25 K and 1.5 GPa.24) This is conjectured to bethe similar diffused fluctuations from the CEP, since theCEP at 1.5 GPa in UGe2 is located at ∼ 20 K and ∼ 0.7T.25)In summary, we performed 59Co-NMR measurementsin UCoAl with FM CEP at (HCEP ∼ 1 T, TCEP ∼ 12 K).The strong enhancement of 1/T2 was observed near theCEP. 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Strong Longitudinal Magnetic Fluctuations Near Critical End Point in UCoAl: A 59Co-NMR Study

Strong Longitudinal Magnetic Fluctuations near Critical End Point in
  UCoAl: A ^59Co-NMR Study

Strong Longitudinal Magnetic Fluctuations near Critical End Point in UCoAl: A ^59Co-NMR Study

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