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DOI: 10.1063/1.5004547
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DIRETORIA DE TRATAMENTO DA INFORMAÇÃO Cidade Universitária Zeferino Vaz Barão Geraldo
CEP 13083-970 – Campinas SP Fone: (19) 3521-6493 http://www.repositorio.unicamp.br
Electron spin resonance of Gd
31in the intermetallic Gd
1–xY
xNi
3Ga
9(0 £ x £ 0.90) compounds
E. C.Mendonc¸a,1L. S.Silva,1S. G.Mercena,1C. T.Meneses,1C. B. R.Jesus,1,2
J. G. S.Duque,1,2J. C.Souza,2P. G.Pagliuso,2R.Lora-Serrano,3and A. A.Teixeira-Neto4
1
Programa de Pos-Graduac¸~ao em Fısica, Campus Prof. Jose Aluısio de Campos, UFS, 49100-000 S~ao Cristov~ao, SE, Brazil
2
Instituto de Fısica “Gleb Wataghin”, UNICAMP, 13083-970 Campinas-S~ao Paulo, Brazil
3
Instituto de Fısica, Universidade Federal de Uberl^andia, 38408-100 Uberl^andia, MG, Brazil
4
Brazilian Nanotechnology National Laboratory (LNNano), Brazilian Center for Research in Energy and Materials (CNPEM), 13083-970 Campinas-S~ao Paulo, Brazil
(Received 13 September 2017; accepted 14 October 2017; published online 30 October 2017) In this work, experiments of X-ray diffraction, magnetic susceptibility, heat capacitance, and Electron Spin Resonance (ESR) carried out in the Gd1–xYxNi3Ga9(0 x 0.90) compounds grown through a Ga self flux method are reported. The X-ray diffraction data indicate that these com-pounds crystallize in a trigonal crystal structure with a space groupR32. This crystal structure is unaffected by Y-substitution, which produces a monotonic decrease of the lattice parameters. For the x¼ 0 compound, an antiferromagnetic phase transition is observed at TN¼ 19.2 K, which is continuously suppressed as a function of the Y-doping and extrapolates to zero atx 0.85. The ESR data, taken in the temperature range 15 T 300 K, show a single Dysonian Gd3þline with nearly temperature independentg-values. The linewidth follows a Korringa-like behavior as a func-tion of temperature for all samples. The Korringa rates (b¼ DH=DT) are Y-concentration-depen-dent indicating a “bottleneck” regime. For the most diluted sample (x¼ 0.90), when it is believed that the “bottleneck” effect is minimized, we have calculated the q-dependent effective exchange interactions between Gd3þ local moments and the c-e of hJ2
fceðqÞi 1=2
¼ 18(2) meV and Jfceðq ¼ 0Þ ¼ 90(10) meV. Published by AIP Publishing.https://doi.org/10.1063/1.5004547
I. INTRODUCTION
The study of dilution effects on magnetically ordered sys-tems has been an important tool to investigate chemical and physical phenomena such as the percolation of magnetic cor-relations and magnetically ordered phases.1–3For instance, it can help to understand the nature of long and short range mag-netic interactions in ferro and/or antiferromagmag-netic materials. In most of the cases, dilution suppresses the ordering state allowing the observation of important features near the ferro and/or antiferromagnetic transitions as they are reduced towards zero with a complete suppression of the magnetically ordered state. In this sense, in the last years, many studies in literature have reported on dilution studies in complex materi-als, for instance, in the family of heavy-fermion superconduc-tors CeMIn5 (M¼ Rh; Co; Ir).
4–7
There, the insertion of non-magnetic ions has proved to be a valuable tool as a tuning parameter in the interplay between the Kondo effect and the long range Ruderman–Kittel–Kasuya–Yoshida (RKKY) mag-netic interaction and crystal field (CF) effects. It is important to say, that the competition between these effects as a function of doping may tune the ground state of a system driving it from a heavy-fermion paramagnetic metal or an unconven-tional superconductor to an ordered AFM state.4,8–16 In this scenario, the use of microscopic techniques, such as electron spin resonance (ESR), has been largely employed in order to identify which microscopic tuning parameter is mainly affected by dilution. ESR is a sensitive and powerful
microscopic tool to provide information about CF effects, site symmetries, valency of paramagnetic ions, g-values, and fine and hyperfine parameters.17In the Gd-compounds, the Gd3þ ions are excellent ESR probes to reveal details about the microscopic interaction between the Gd3þ4f electrons and the conduction electrons c-e. Furthermore, for insulator samples with a very small level of Gd3þ(a few ppm), although the CF effects are a second order effect for the Gd3þions, the evolu-tion of the CF may be inferred from ESR studies.18
Recently, the RNi3Ga9(R¼ Tb, Dy, Ho, and Er) series of intermetallic compounds have been shown to present a very interesting competition between anisotropic RKKY interactions and the CF effect strongly affected by the c/a ratio of the lattice parameters on their crystal structures.19
In this work, we have synthesized Gd1xYxNi3Ga9 (0 x 0.90) intermetallic compounds using a Ga self flux method. The X-ray diffraction data shows diffraction pat-terns, consistent with a single phase of a trigonal crystal structure (space groupR32). These compounds were charac-terized via measurements of magnetic susceptibility, heat capacitance, and ESR. A continuous decreasing in the order temperature as a function of the doping was observed in both magnetic susceptibility and heat capacitance measurements. The ESR data taken in the temperature range 15 T 300 K for all samples, revealed a single line that can be fitted to a single Dysonian resonance which is consistent with Gd3þin a metallic host. The analysis of the Gd3þESR temperature dependent data for the Gd1–xYxNi3Ga9compounds allows us
to conclude that our samples are in a “bottleneck” regime and for the most diluted samples (x¼ 0.90), we have esti-mated q-dependent effective exchange interactions between Gd3þlocal moments and thec-e,hJ2
fceðqÞi 1=2
¼ 18(2) meV andJfceðq ¼ 0Þ ¼ 90(10) meV.
II. EXPERIMENT
Single crystals of Gd1–xYxNi3Ga9 (0 x 1.0) were grown from a Ga self flux method. The starting elements with purities of 99.9% in a molar ratio of 1(Gd):3(Ni):30(Ga) were placed into an alumina crucible and sealed under vacuum in a quartz tube. The ampoules were then heated from room tem-perature to 1050C, kept at this temperature for 5 h, and slowly cooled down at 5C/h until 650C, where the excess of Ga flux was decanted off from the platelet-like crystals by centrifugation. The crystalline structures (ErNi3Al9-like) were checked by X-ray powder diffraction. Susceptibility measure-ments were made in a commercial dc superconducting quan-tum interference device (SQUID) magnetometer. Specific heat measurements were performed in a commercial small-mass calorimeter system that employs a quasiadiabatic ther-mal relaxation technique for samples ranging from 5 to 30 mg. The ESR experiments were carried out in a commercial X-band spectrometer, using a helium gas flux4–300 K adapted to a room-temperature TE102cavity. In order to increase the ESR signal to noise ratio, powdered crystals were used in the ESR measurements.
III. EXPERIMENTAL RESULTS AND DISCUSSION
Figure 1 shows (a) the lattice parameters (extracted from Rietveld refinement) (䊊) a and (ⵧ) c as a function of Y-concentration and (b) the X-ray powder diffraction pat-terns for the Gd1–xYxNi3Ga9(0 x 0.90) samples taken at room temperature. The solid curves represent the calculated pattern from the model structure used in the Rietveld refine-ment to fit the experirefine-mental data. The solid line in the bottom of each measurement means the difference between the experimental and calculated data. The vertical bars represent the Bragg peak positions according to the model ErNi3Al9 -type structure [Crystallographic Open Database (COD: 96-210-0947)]. From these results, the trigonal ErNi3Al9-type structure, space groupR32, can be confirmed for all the stud-ied samples. The goodness-of-fit parameters, v2, lattice parameters (a and c), and the volume for each refinement can be found in TableI. As we show in the upper panel of Fig. 1(a), a slight and monotonic change in both lattice parameters,a and c, gives rise to a small contraction of the unit cell volume as a function of Y-doping.
Figure 2 presents the v(T) measured at H¼ 1 kOe for Gd1xYxNi3Ga9(0 x 0.90). From the fits, we have extracted the effective momentp¼ 8.4(3) lBfor Gd3þin the studied com-pounds, which is in agreement with the expected theoretical value. In the inset, we present the temperature of the maximum susceptibility and HCWas a function of the Y-doping. A linear extrapolation using the initialdTN/dx slopes yields a critical con-centrationxc 0.80, which is consistent with the percolation
threshold of a three dimensional Heisenberg magnetic lattice which is near 15% dilution of the magnetic sites.4,20–23For the
x¼ 0 compound, the v(T) data show a maximum around T¼ 19.2 K which we will show is consistent with the tempera-ture at which the anomaly in the specific heat data takes place (see below). It is well-known that this maximum usually occurs at the vicinity of the onset of the long range AFM order. It can be noticed in Fig.2that a further increase in the Y-doping pro-duces a shift of the maximum to the low temperature region. For x 0.70, no clear anomaly associated with the magnetic
FIG. 1. (a) Lattice parameters, (䊊) a and (ⵧ) c, as a function of x and (b) X-ray powder diffraction data (open symbols) for Gd1xYxNi3Ga9
(0 x 0.90) at room temperature. The solid lines are the patterns calcu-latedvia Rietveld refinement and the difference between experimental data and calculated patterns. The bars in the bottom panels represent the Bragg indexation according to the structural model - taken from the COD code: 96-210-0947.
TABLE I. Experimental parameters extracted from Rietveld refinement (Rp,
Rwp, v2,a, c, and V). x Rpð%Þ Rwpð%Þ v2ð%Þ a (A˚ ) c (A˚ ) V (A˚3) 0.00 3.26 3.95 2.09 7.266(1) 27.501(5) 1257.39(7) 0.15 3.32 4.20 2.20 7.263(1) 27.490(5) 1255.26(7) 0.30 3.15 3.85 2.08 7.261(1) 27.487(4) 1255.52(6) 0.50 3.31 4.01 2.17 7.258(1) 27.477(4) 1252.08(6) 0.70 3.68 4.55 2.39 7.255(1) 27.468(4) 1251.46(6) 0.80 3.33 4.04 2.21 7.254(1) 27.462(4) 1251.49(6) 0.90 3.87 4.89 2.63 7.255(1) 27.455(4) 1250.83(6)
transition is observed (see the inset), and the susceptibility fol-lows a Curie–Weiss law for all temperature ranges. Moreover, it is interesting to notice that HCWis only slightly larger thanTN indicating that frustration effects are negligible. It is also important to state that the nominal concentrations have been checked for using wavelength dispersive spectroscopy (WDS), X-ray photoelectron spectroscopy (XPS), and magnetization measurements.
Figure 3displays the magnetic contribution to the spe-cific heat (Cmag) in the temperature range 2 T 50 K for Gd1xYxNi3Ga9(0 x 0.90) samples at zero applied mag-netic field. In order to obtain the magmag-netic contribution of each compound, we subtracted the phonon contribution from total specific heat for using the non-magnetic specific-heat data of the YNi3Ga9 sample. The observed peaks in the specific-heat data indicate the onset of the antiferromagnetic order. It is worth mentioning that these values are in agree-ment with those evaluated from the susceptibility data. In the
inset, one can see that the low-temperature (Cp=T) data for
YNi3Ga9increases linearly withT2. The solid line means the best fit to theCp=T¼ c þ bT2, with c ¼ 6.5(6) mJ/mol K2
and b¼ 1.1(2) mJ/mol K4. It is worth mentioning that the obtained c parameter can be used to evaluate the density of states at the Fermi level, gðEFÞ for a given compound. As
such, for using the c-e gas model, with c¼ ð2=3Þpk2gðE FÞ,
we have estimated the value of the electronic spin suscepti-bility, v¼ 2l2
BgðEFÞ, of the YNi3Ga9compound. This result is in good agreement with the temperature independent sus-ceptibility measured at high temperatures (Pauli susceptibil-ity) for all Gd1–xYxNi3Ga9compounds.
Figure 4 shows the evolution of the X-band (f 9.45 GHz) powder spectra of Gd3þ in Gd1-xYxNi3Ga9 measured at (a) T¼ 15 K, x ¼ 0.90 and (b) T 50 K, 0.0 <x < 0.80. The ESR spectra were fitted to Dysonian line shapes (solid red lines). These line shapes are characteristic of localized magnetic moments in a metallic host with a skin depth smaller than the size of the sample particles.
Figure 5 displays the temperature dependence of the Gd3þESR linewidth for Gd1xYxNi3Ga9(0 x 0.90) sam-ples. The thermal broadening of the linewidths was fitted using a linear behavior, DH¼ a þ bT, in the temperature
FIG. 2. Temperature dependence of the magnetic susceptibility for Gd1xYxNi3Ga9(0 x 0.90) samples, where vp(T) is the T-dependent term
of total susceptibility and v0is theT-independent susceptibility. The inset
showsTNand HCWas a function of the Y-concentration.
FIG. 3. Magnetic contribution to the specific heat for Gd1–xYxNi3Ga9
(0 x 0.90) samples at zero applied field. The inset shows the low-temperatureT2dependence ofC
p=T for the YNi3Ga9compound. The solid
line is the best fit to the data usingCp=T¼ c þ bT2.
FIG. 4. Concentration evolution (0 x 0.90) of the ESR spectra in Gd1xYxNi3Ga9measured at (a)T¼ 15 K for x ¼ 0.90 and (b) T 50 K for
0.0 <x < 0.80. The solid lines are the best fit of the resonance using a Dysonian lineshape.
range 50 <T < 300 K for 0 <x < 0.80 and 10 <T < 45 K for thex¼ 0.90 sample. On the other, the residual linewidth, a, is nearlyx-independent indicating that the Y-doping does not create a strong disorder in the system (see the inset of Fig. 5). It must be noted that the angular coefficients (b¼ DH/ DT) are Y-concentration-dependent. In TableII, we show the main parameters extracted from the ESR analysis.
Unlike L6¼ 0 rare earth based compounds, where the magnetic properties seem to be governed by both magnetic interactions and CF effects, such as in RNi3Ga4(R¼ Tb, Dy, Ho, and Er)19,24–27 for Gd-based compounds only magnetic interaction mechanisms must be considered. In this sense, the absence of CF effects can simplify the understanding of the magnetic interaction mechanisms which are believed to occur via Ruderman–Kittel–Kasuya–Yoshida (RKKY) interaction in intermetallic systems. TheT-dependence of vðTÞ and spe-cific heat data displayed in Figs. 2 and 3 show that TN is smoothly suppressed by Y-doping and extrapolates to zero at xc 0.80. As mentioned earlier, this critical concentration of
nonmagnetic impurities is close to the expected percolation threshold for 3D antiferromagnetic Heisenberg systems.4,20
As we have commented above, for T > 50 K, the ESR signal consists of a single Dysonian with an almost temperature-independentg-value which is attributed to Gd3þ ions in a metallic environment. Up tox¼ 0.8, the observed linearT-dependence of the Gd3þESR linewidth indicates a Korring-like relaxation mechanism in the temperature range 50 <T < 300 K, which is strongly concentration-dependent. This fact allows us to assume that the system is in the
“bottleneck” regime for this range of concentration. It is well-known that, for metallic systems in this regime, the increase of concentration of the resonating spins changes the relaxation process and the transferring of the absorbed microwave energy to the lattice occurs more slowly depend-ing on the level of resonatdepend-ing spins present in the sample. Nevertheless, within the accuracy of the measurements, the residual linewidths,a, were independent of the concentration indicating the negligible disorder induced by the Y-doping.
On the other hand, the ESR response of very diluted localized magnetic moments inside a metallic host can pro-vide information about the exchange constant,Jfce, between
the local moments and the conduction electrons, (c-e’s). In the simplest treatment of the exchange interaction,Jfce S.s,
between a localized 4f electron spin (S) on a solute atom (Gd3þ) and the freec-e’s spin (s) of the host metal, the ESR g-shift (Knight shift)28 and the thermal broadening of the linewidth (Korringa rate),29 when the “bottleneck” and “dynamic” effects are not present,30can be written as
Dg¼ Jfceð0Þ g Eð FÞ (1) and d DHð Þ dT ¼ kp gilB Jf2ceðqÞ g2ðEFÞ; (2)
whereJfce is the effective exchange interaction between the
Gd3þlocal moment and thec-e in the absence of c-e momen-tum transfer,31gðEFÞ is the “bare” density of states for one
spin direction at the Fermi surface, k is the Boltzmann con-stant, lB is the Bohr magneton, and gi is the ionicg factor
measured in insulators (g¼ 1.993(2)).17
Due the large linewidths observed for the concentrated Gd1xYxNi3Ga9 samples (x < 0.90) in the temperature range
where the Korringa rates were evaluated, we were not able to determine, within our experimental accuracy, a g-shift related theg-value of Gd3þin insulators (g¼ 1.993(2))17for thex < 0.90 samples, especially because the measured Gd3þ g-value in these cases was always much closer to 2.0 (see Table II). Besides, as one can see that the thermal broaden-ings are concentration-dependent, i.e., the “bottleneck” effect is present for these samples.
However, for the sample grown withx¼ 0.90 (and most likely for samples with higher Y-concentrations), theg-shift can be determined in the same temperature range of the observed Korringa relaxation. Furthermore, one should notice that this value of concentration is higher than the per-colation threshold observed for our set of samples for both TN and HCW, and in the Gd3þESR temperature dependent data. So, negligible Gd3þspin–spin interactions effects are expected.
Unfortunately, we are not able to observe the Gd3þ reso-nance for thex > 0.90 samples likely due the strong thermal broadening of the unbottleneck regime in the measured tem-perature range. In this way, the best we could do is to ana-lyze the sample grown with x¼ 0.90 as in the unbottleneck regime. So, in the simplest treatment of the exchange inter-action when conduction electron-electron correlations32,33
FIG. 5. Temperature dependence of the ESR linewidth for Gd1xYxNi3Ga9
(0 x 0.90) samples. The solid line means the best fit to DH ¼ a þ bT. In the inset, we show the residual lineshape as a function of Y-concentration.
TABLE II. Experimental parameters extracted from ESR experiments.
x a (G) b (G/K) g 0.00 830(30) 0.89 2.00(1) 0.15 780(30) 1.89 2.01(2) 0.30 760(30) 1.25 2.00(2) 0.50 730(30) 3.25 2.00(2) 0.70 780(30) 3.80 2.01(2) 0.80 820(30) 4.46 2.02(2) 0.90 840(30) 13.5 2.117(2)
and q-dependent exchange interaction, Jfce(q),31]are not
considered in the analysis of ESR data, it is expected that the following relation may hold:
d DHð Þ dT ¼ pk gilB Dg ð Þ2: (3)
For using Dg¼ 0.124(4), which was calculated in rela-tion to theg-value of Gd3þin a insulator environment,17 a thermal broadening of 570(40) Oe/K for the Gd3þresonance inGd0:10Y0:90Ni3Ga9 should be obtained. This value is much
larger than the one measured,b¼ 13.5(4) Oe/K. Therefore, we conclude that the approximations made in Eqs.(1) and (2)are not valid for this compound, and conduction electron-electron correlations33,34and q-dependent exchange interac-tion, Jfce(q),31 must be considered in the analysis of our
ESR data, whereJfce(q) is the Fourier transform of the
spa-tially varying exchange. In our analysis, we will only con-sider the contribution from a single c-e band, because the measured thermal broadenings of the linewidths were found to be much smaller than those expected for the measured g-shifts.34,35
As mentioned above, the electronic contribution to the heat capacity for the YNi3Ga9 compound yields c¼ 6.5(6)
mJ/mol K2. Assuming a free c-e gas model for YNi3Ga9;
c¼ ð2=3Þpk2
BgðEFÞ (where kB¼ 1.38 10–23 m2 kg/s2 K), we calculate a density of states at the Fermi level, gðEFÞ ¼ 1.35(2) states/eV mol spin. For this density of
states, one would expect an electronic-spin susceptibility, v¼ 2l2
BgðEFÞ, of 0.000107 emu/FU. That is of the order
of Pauli independent magnetic susceptibility measured for all studied compounds. Hence, one can assume that electron–electron correlations are not important in Gd0:10Y0:90Ni3Ga9. Taking into account only the wave-vector
dependence of the exchange interaction,Jfce(q),31 in Eqs.
(1)and(2), the exchange parameters should be replaced by Jfce(0) andJf2ce(q), respectively. At the Gd3þ site, the
g-shift probes the c-e polarization (q¼ 0) and the Korringa rate of the c-e momentum transfer (0 q 2kF) averaged over the Fermi surface.31 Using g(EF)¼ 1.35(2) states/eV mol spin, Dg¼ 0.124(4), and b ¼ 13.5(4) Oe/K, we found the exchange parameters between the Gd3þ local moment and the c-e in Gd0:10Y0:90Ni3Ga9 to be Jfce(0)¼ 90(10) meV
and hJ2 fceðqÞi
1=2
¼ 18(2) meV. Finally, as we have com-mented above, due the strong thermal broadening, we are not able to observe the Gd3þ ESR for samples with Y-concentration higher thanx¼ 0.90. So, as it was not possible to determine a “unbottleneck” limit of the Korringa rate, d(DH)=dT, where its value is concentration independent. As such, the above calculated exchange parameters must be taken as lower limits.
IV. CONCLUSIONS
In summary, we have grown single crystals of Gd1–xYxNi3Ga9(0 x 0.90) through a Ga self flux method. The X-ray data analyzed by the Rietveld method have con-firmed the formation of a single phase with a trigonal crystal structure (space group R32). A contraction of the unit cell
was observed as a function Y-doping. The effect of this dilu-tion in the T-dependence of the magnetic susceptibility and specific heat was to give rise to a continuous decrease in the Neel temperature extrapolating to zero atxc 0.80. The
T-dependence of Gd3þESR inGd1xYxNi3Ga9 presents a
sin-gle line with a nearly temperature independent g-value and a Korringa-like relaxation mechanism within a strong bottle-neck regime. From the Korringa rate, DH/DT 13.5(4) Oe/ K, and a g-shift value of 0.124(4) for the most diluted (x¼ 0.90) sample in the Gd0:10Y0:90Ni3Ga9 series, we have
extracted the exchange parameters between the Gd3þ local magnetic moments and the c-e in this compound, Jfce(q¼ 0) ¼ 90(10) meV and hJ2fceðqÞi
1=2
¼ 18(2) meV, which should be taken as lower limits for these parameters in this series.
ACKNOWLEDGMENTS
The authors thank the Brazilian agencies FAPITEC (PRONEX), CAPES, CNPq (Nos. 442230/2014-1, 3046449/ 2013-9, 309647/2012-6, 304649/2013-9, 157835/2015-4, and 455970/2014-9), FAPESP (2012/04870-7), and FAPEMIG-MG (APQ-02256-12) for the financial support.
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