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Magnetic structure of Ho2CoGa8 determined by X-ray resonant magnetic scattering
ARTICLE IN PRESS Physica B 404 (2009) 3289–3292
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Magnetic structure of Ho2 CoGa8 determined by X-ray resonant magnetic scattering C. Adriano , C. Giles, L.N. Coelho, G.A. Faria, P.G. Pagliuso Instituto de F´ısica ‘‘Gleb Wataghin’’, UNICAMP, C. P. 6165, 13083-970 Campinas, SP, Brazil
a r t i c l e in fo
PACS: 71.20.Lp 71.27.þa 75.25.þz 75.50.Ee Keywords: Intermetallic compound Ho2CoGa8 X-ray magnetic scattering (XRMS)
abstract We report the low temperature magnetic structure of the Ho2 CoGa8 intermetallic compound studied by X-ray magnetic scattering technique at the Brazilian Synchrotron Light Laboratory. We found that below TN ¼ 5:1 K, Ho2 CoGa8 has a commensurate antiferromagnetic structure with a propagation vector ~ Z ¼ ð12 ; 12 ; 12Þ and preliminary analysis indicated that the Ho magnetic moment points along the c-axis. The magnetic structure of this compound was obtained by measuring the strong dipolar resonant peak at the L3 edge using polarization analysis. The magnetic structure and properties Ho2 CoGa8 are found to be consistent with the general trend already seen for the Nd-, Tb-, and the Ce-based compounds from the Rm Mn In3mþ2n family (R ¼ rare earth; M ¼ Co, Rh, or Ir; m ¼ 1; 2; n ¼ 0; 1). & 2009 Elsevier B.V. All rights reserved.
1. Introduction The isostructural intermetallic compounds of the family Rn MX3nþ2 (with R ¼ rare earth or actinides, M ¼ transition metal, X ¼ In, Ga and n ¼ 1; 2) show a wide range of interesting electronic and magnetic properties with a tunable variety of ground states such as antiferromagnetism (AFM), unconventional superconductivity (USC), non-Fermi Liquid (NFL), and Fermi liquid (FL) behaviors [1–3]. Many members of this family can have their states changed just by doping, applying pressure or magnetic fields [4–7]. Also by changing the structure from the cubic ðRX3 Þ material to the monolayer member with n ¼ 1 ðRMX5 Þ or to the bilayer one ðR2 MX8 Þ we observe the evolution of some interesting physical properties. Within the rare earth materials with X ¼ In and M ¼ Co, Rh and Ir, many different ground states can be attained by changing R, like heavy fermion behavior and USC for R ¼ Ce, AFM for R¼Nd, Sm, Gd, Tb and paramagnetic metals for R ¼ La, Pr. Within the actinides, interesting properties also occur for M ¼ Co, X ¼ Ga like AFM for R ¼ Np and USC for R ¼ Pu with TC ¼ 15 K [8,9]. Systematic investigation of the Rn MX3nþ2 class of materials show that these compounds usually follow the microscopic Ruderman–Kittel–Kasuya–Yosida (RKKY) magnetic interaction, crystalline electrical field (CEF) effects, and the hybridization between 4f-electrons and conduction electrons of structurally related materials. To contribute with these investigations, we are
Corresponding author.
E-mail address: cadriano@ifi.unicamp.br (C. Adriano). 0921-4526/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2009.07.127
studying some Ga-based compounds with R ¼ rare earth and M ¼ Co [10]. In this work, we report measurements using X-ray resonant magnetic scattering (XRMS) technique in Ho2 CoGa8 intermetallic compound to determine the magnetic structure and to check if the CEF trends observed for Rm MIn3mþ2 series also apply to the Ga-based compounds. This technique has proven to be a valuable tool in unraveling features of the microscopic magnetic structure not available to other conventional techniques.
2. Experiment Single crystalline samples of Ho2 CoGa8 were grown by gallium flux technique as described previously [11]. The tetragonal structure (space group P4/mmm No. 123) and unit cell parameters a ¼ 4:219ð5Þ A˚ and c ¼ 10:99ð5Þ A˚ were confirmed by X-ray powder diffraction and are in good agreement with the results found by Joshi et al. [10]. Magnetization, specific heat and electrical resistivity measurements of these samples have been reported in a previous work [12]. For the X-ray magnetic scattering experiments, a crystal was selected and prepared with polished (1 0 0) flat surface, and size of approximately 4 3 2 mm3. The preferred crystal growth direction of this compound is columnar along the ½0 0 l direction and the (0 0 1) facet is relatively large. However, in rare cases, we can also obtain crystal plates with the ½h 0 0 direction and a large (1 0 0) facet. The mosaic spread of the sample was found to be o0:053 by a rocking curve (y scan) on a four circle X-ray diffractometer. XRMS studies were performed at the bending magnet XRD2 beamline [13] of the Brazilian Synchrotron Light Laboratory
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(LNLS) in Campinas, Brazil. The XRD2 beamline uses a double crystal Si (111) monochromator, with sagital focusing and a Rh-coated mirror cylindrically bent to focus the beam to a 0.6 mm (vertical) 2.0 mm (horizontal) spot, yielding an incident flux of 3 1010 photons=s around 8 keV with an energy resolution of DE=E5 104 . The sample was cooled in a closed-cycle He cryostat (with a base temperature of 1.7 K using a Joule–Thomson stage), installed on a HUBER four-circle diffractometer in the vertical scattering plane, with the c-axis parallel to the beam. This configuration allowed s-polarized scattering geometry for the experiment.
3. Results and discussions The magnetic structure of the Ho2 CoGa8 was investigated by XRMS technique using polarization analysis. The central result of this paper is the observation of resonant magnetic scattering peaks at the L3 absorption edge of Ho (8071 eV). Resonances at the magnetic peaks were observed at the dipolar and quadrupolar energies at temperatures below TN ¼ 5:1 K at reciprocal lattice points forbidden for charge scattering and consistent with an antiferromagnetic commensurate structure with propagation vector ð12 ; 12 ; 12Þ. The observation of a commensurate structure differs from the results found for pure metallic Ho by Gibbs et al. [14] where they observed an incommensurate magnetic structure due to the spiral antiferromagnetic structure of pure Ho. The transition temperature where the magnetic peaks fade away is in agreement with those found by macroscopic property measurements reported before [12]. The polarization analysis performed at the magnetic peaks Z ¼ ð12 ; 12 ; 12Þ propagation vector is compatible with what is with ~ expected from a dipolar resonance polarization dependence as described by Hill and McMorrow [15]. In order to carry out these analyses a polarization analyzer setup was placed in the 2y arm of the diffractometer. The polarization analyzer crystal suitable to the Ho L3 edge energy is a graphite crystal with the (0 0 6) reflection at a Bragg angle of yA ¼ 43:43 . The deviation from the ideal value ð453 Þ results in a leakage from one channel to another. Fig. 1 shows the intensity as a function of the yA angle of the analyzer crystal for s2s0 and s2p0 polarization channels for the peak ð52 ; 12 ; 12Þ at 2 K and photon energy of 8071 eV.
Fig. 1. Angular scan of the analyzer crystal through the magnetic peak ð52 ; 12 ; 12Þ of the Ho2 CoGa8 compound at 2 K for s2p0 (closed circles) and s2s0 (open circles) polarization channels at the Ho L3 absorption edge.
The results shown in Fig. 1 are consistent with a dipolar resonant magnetic scattering peak where all the intensity is found in the s2p0 channel (closed circles) and no intensity is found in the s2s0 channel (open circles). The intensity observed in the small peak of the s2s0 channel is consistent with the leakage. To study the temperature dependence of the magnetic phase sweeps of the temperature were performed at the Ho L3 edge from 2 to 5:2 K. Fig. 2 shows the temperature dependence of the ð32 ; 12 ; 12Þ magnetic reflection at an incident photon energy of 8071 eV and measured at s2p0 channel. Fig. 2 shows the square root of the integrated intensity which is proportional to the magnetization of Ho in the compound. A squared Lorentzian peak shape was used to fit longitudinal y22y scans in order to obtain the integrated intensities of the reflection peak. As the temperature increases, the peak intensity gradually decreases and disappears above TN ¼ 5:1 K. A fitting using a power-law expression ð1 T=TN Þ2b for a second-order phase transition (denoted by a solid line in the inset of Fig. 2) within the temperature range of 3% below TN gives a magnetic transition temperature TN ¼ 5:1 K and a critical order exponent b ¼ 0:29ð2Þ for the Ho magnetic sublattice. This value of b is compatible with a three-dimensional Heisenberg system and the smooth decrease in intensity in the crossover to the paramagnetic phase is consistent with a second-order phase transition. The energy line shapes for the polarization channel s2p0 of the ð52 ; 12 ; 12Þ and ð72 ; 12 ; 52Þ peaks at the L3 edge of Ho at T ¼ 2 K are shown in Fig. 3. Both line shapes demonstrate a characteristic resonance enhancement of the magnetic peak but at two different energies. For the peak ð52 ; 12 ; 12Þ (open triangles) the maximum enhancement is observed at 8076 eV which is only few eV larger than the L3 edge, revealing the electric dipolar character ðE1Þ of this transition (from 2p3=2 to 5d states). An interesting result is that the energy line shape changes according to the magnetic peak measured. The curve in Fig. 3 for the peak ð72 ; 12 ; 52Þ (closed squares) shows a small maximum at the same energy 8076 eV, characterizing the ðE1Þ transition and another peak at the energy 8068 eV. This second peak seen for the ð72 ; 12 ; 52Þ is the quadrupolar ðE2Þ transition from the 2p3=2 to a 4f intermediate states. The quadrupolar transition of Ho3þ at 8068 eV was seen
Fig. 2. Squared root of the intensity as a function of temperature for Ho2 CoGa8 measured with longitudinal ðy22yÞ scans at the ð32 ; 12 ; 12Þ peak at 2 K and 8076 eV for s2p0 polarization channel around the L3 absorption edge of Ho. The inset shows in detail the critical region around the transition at the Ne el temperature and the solid line is a power-law fit to the data within the temperature range of approximately 3% below TN .
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Fig. 3. Energy line shape curve of the magnetic peaks ð52 ; 12 ; 12Þ (open triangles) and ð72 ; 12 ; 52Þ (closed squares) measured for s2p0 polarization channel at the L3 absorption edge of Ho ion at T ¼ 2 K.
also by Gibbs et al. [14] for pure metallic Ho, Nandi et al. for HoMnO3 [16] and Beutier et al. for HoMn2 O5 [17]. The energy line shape exhibits a long asymmetry tail to lower energies, this behavior was observed also for pure Ho [14] and some other light rare-earth (Nd [18] and Sm [19]) where it is believed to arise from interference between the non-resonant and resonant magnetic scattering. The results confirm the magnetic origin of the ð12 ; 12 ; 12Þ reflections due to the existence of an AFM structure that duplicate the chemical cell in all three directions. Since the tetragonal structure of Ho2 CoGa8 contains two magnetic Ho3þ ions per unit cell in the c-direction, this means that two possibilities of an AFM coupling can take place along the c-axis: Model 1 (sequence þ þ ) or Model 2 (sequence þ þ ) where the symbols þ and represent the relative orientation of the magnetic moment of a holmium atom with respect to its neighbour. To completely determine the magnetic structure of this compound we have to determine the coupling along the caxis and the direction of the magnetic moment. For collinear magnetic structures, the polarization dependence of the X-ray magnetic scattering assumes a simple form for dipolar resonances [15], and the intensities of magnetic Bragg peaks are proportional XRES Þ: to the magnetic form factor ðfnE1 2 X 1 ~ ~ XRES ~ ^ ~0 ^0 ^ iQ Rn f ð k; e ; k ; e ; z Þe ð1Þ Ip ; n nE1 m sinð2yÞ n where m is the absorption correction for asymmetric reflections, ~ ¼ k~0 ~ k is the wave-vector transfer, ~ k 2y is the scattering angle, Q ~ 0 0 ^ and k (e^ and e ) are the incident and scattered wave (polarization) vectors, respectively. ~ R n is the position of the nth atom in the lattice, and z^ n is the moment direction at the nth site. To calculate the ~ R n positions in Eq. (1), just the l-Miller indices are important since the Ho atoms are located in the c-direction of the unit cell. The sum is over the n resonant ions in the magnetic unit cell. The resonant scattering amplitude contains both dipole ðE1Þ and quadrupole ðE2Þ contributions. However for the determination of the magnetic structure in this work we have used the second term of the E1 transition (just for s2p0 polarization channel) which produces magnetic peaks [15]. The magnetic structure of Ho2 CoGa8 can thus be resolved by comparing the intensities of the magnetic Bragg reflections with those calculated using Eq.(1) [19–21].
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Fig. 4. Integrated intensities of the magnetic peaks (crosses) (l ¼ 12 at the left column and l ¼ 52 at the right column) plotted as a function of Q, compared to the calculated intensities for Model 1 (triangles) and Model 2 (circles) and with the moment direction along a-direction (upper plots (a) and (b)) and c-direction (lower plots (c) and (d)).
Seven magnetic peaks were measured and used in our model, for which four peaks have l ¼ 12 : ð32 ; 12 ; 12Þ; ð52 ; 12 ; 12Þ; ð52 ; 32 ; 12Þ and ð72 ; 12 ; 12Þ and three peaks have l ¼ 52 : ð52 ; 32 ; 52Þ; ð72 ; 12 ; 52Þ, and ð72 ; 32 ; 52Þ. Fig. 4 shows the normalized intensities of the experimental data (crosses), plotted as a function of the ~ , together with the calculated data reciprocal space vector Q using Eq. (1) considering four different cases: (1) Model 1 with the magnetic moment aligned along the a-direction; (2) Model 2 with the magnetic moment aligned along the a-direction; (3) Model 1 with the magnetic moment aligned along the c-direction; and (4) Model 2 with the magnetic moment aligned along the c-direction. Comparing the experimental data in Fig. 4 with the four different calculations proposed above using Eq. (1), these preliminary results suggest that the moment direction is in the c-direction. However, we could not determine the relative orientation of the Ho magnetic moment inside the magnetic unit ~ values cell. The main point is that magnetic peaks at different Q seem to follow different antiferromagnetic couplings within the unit cell. As can be seen from Fig. 4, Model 1 conveniently fits the magnetic peaks with indices l ¼ 12, while Model 2 conveniently fits the peaks with l ¼ 52. We can gain more insight into this apparent strange result if we recall that the energy line shapes shown in Fig. 3 are also different for the two sets of data, the dipolar resonance seen at 8076 eV decreases at the ð72 ; 12 ; 52Þ peak as compared to the ð52 ; 12 ; 12Þ peak. It is well known that the dipolar resonance probes the 5d magnetism and that the quadrupolar resonance probes the 4f magnetism of Ho. It is also well known that the 5d shell has a larger spatial extent than the 4f shell and consequently the 5d form factor falls off more rapidly at higher wave-vector transfer [22]. This sensitivity to the shell selectivity of the long range magnetic order can only be gained by X-ray magnetic scattering and is not possible with neutron scattering studies in a model-independent fashion. We believe that further X-ray magnetic scattering experiments on this compound should unravel the different contributions of the 5d and 4f magnetism of Ho in the Ho2 CoGa8 compound. Comparing the results obtained in this work with the general trend observed for the Rm Mn In3mþ2n family (R¼rare earth; M¼Co, Rh, or Ir; m ¼ 1; 2; n ¼ 0; 1), Ho2 CoGa8 seems to follow the same behavior seen for R¼Nd, Tb [23], since the magnetic moment of this compound is in the c-axis and the AFM ordering temperature
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for the HoCoGa5 parent ðTN ¼ 9:5 KÞ is larger than the TN for Ho2 CoGa8 . Since HoCo3 grows in a hexagonal crystal structure [24] it cannot be used as a parent cubic compound, preventing further comparison of Ho-based Ga compounds. In order to check the rule for Ga-based compounds, more experiments are desired to determine the magnetic structure of the other members of the family.
4. Conclusions In summary, we have studied the magnetic structure of Ho2 CoGa8 compound using resonant magnetic X-ray scattering at the Ho L3 edge. The results obtained so far show that Ho2 CoGa8 has a commensurate AFM order below TN ¼ 5:1 K with propagaZ ¼ ð12 ; 12 ; 12Þ. The calculations proposed suggest that the tion vector ~ magnetic moment is pointing at the c-direction. The differences in the energy line shape curves reveal a possible Q dependence of the dipolar resonance due to the different contribution of the 5d magnetic form factor. Further experiments with X-ray resonant magnetic scattering will be performed aiming to clarify the magnetic coupling in the magnetic unit cell. References [1] J.D. Thompson, R. Movshovich, Z. Fisk, F. Bouquet, N.J. Curro, R.A. Fisher, P.C. Hammel, H. Hegger, M.F. Hundley, M. Jaime, P.G. Pagliuso, C. Petrovic, N.E. Phillips, J.L. Sarrao, J. Magn. Magn. Mater. 226–230 (2001) 5. [2] P.G. Pagliuso, R. Movshovich, A.D. Bianchi, M. Nicklas, N.O. Moreno, J.D. Thompson, M.F. Hundley, J.L. Sarro, Z. Fisk, Physica B 312–313 (2002) 129. [3] A. Bianchi, R. Movshovich, I. Vekhter, P.G. Pagliuso, J.L. Sarrao, Phys. Rev. Lett. 91 (2003) 257001. [4] P.G. Pagliuso, N.O. Moreno, N.J. Curro, J.D. Thompson, M.F. Hundley, J.L. Sarrao, Z. Fisk, A.D. Christianson, A.H. Lacerda, B.E. Light, A.L. Cornelius, Phys. Rev. B 66 (2002) 054433.
[5] L. Mendonc-a-Ferreira, T. Park, V. Sidorov, M. Nicklas, E.M. Bittar, R. Lora-Serrano, E.N. Hering, S.M. Ramos, M.B. Fontes, E. Baggio-Saitovich, H. Lee, J.L. Sarrao, J.D. Thompson, P.G. Pagliuso, Phys. Rev. Lett. 101 (2008) 017005. [6] L.D. Pham, T. Park, S. Maquilon, J.D. Thompson, Z. Fisk, Phys. Rev. Lett. 97 (2006) 056404. [7] A.L. Cornelius, P.G. Pagliuso, M.F. Hundley, J.L. Sarrao, Phys. Rev. B 64 (2001) 144411. [8] J.L. Sarrao, L.A. Morales, J.D. Thompson, B.L. Scott, G.R. Stewart, F. Wastin, J. Rebizant, P. Boulet, E. Colineau, G.H. Lander, Nature (London) 420 (2002) 297. [9] A. Hiess, A. Stunault, E. Colineau, J. Rebizant, F. Wastin, R. Caciuffo, G.H. Lander, Phys. Rev. Lett. 100 (2008) 076403. [10] D.A. Joshi, R. Nagalakshmi, S.K. Dhar, A. Thamizhavel, Phys. Rev. B 77 (2008) 174420. [11] Z. Fisk, J.P. Remeika, Handbook on the Physics and Chemistry of Rare Earths, vol. 12, Elsevier, North-Holland, Amsterdam, 1989, p. 53. [12] C. Adriano, L. Mendonc- a-Ferreira, E.M. Bittar, P.G. Pagliuso, J. Appl. Phys. 103 (2008) 07B712. [13] C. Giles, F. Yokaichiya, S.W. Kycia, L.C. Sampaio, D.C. Ardiles-Saravia, M.K.K. Franco, R.T. Neuenschawander, J. Synchrotron Rad. 10 (2003) 430. ¨ [14] D. Gibbs, G. Grubel, D.R. Harshman, E.D. Isaacs, D.B. McWhan, D. Mills, C. Vettier, Phys. Rev. B 43 (1991) 5663. [15] J.P. Hill, D.F. McMorrow, Acta Crystallogr. Sect. A Found. Crystallogr. A 52 (1996) 236. [16] S. Nandi, A. Kreyssig, J.W. Kim, J.Q. Yan, J.C. Lnag, D. Haskel, R.J. McQueeney, A.I. Goldman, Phys. Rev. Lett. 100 (2008) 217201. [17] G. Beutier, A. Bombardi, C. Vecchini, P.G. Padaelli, S. Park, S.-W. Cheong, L.C. Chapon, Phys. Rev. B 77 (2008) 172408. [18] J.P. Hill, A. Vigliante, D. Gibbs, J.L. Peng, L. Greene, Phys. Rev. B 52 (1995) 6575. [19] C. Adriano, R. Lora-Serrano, C. Giles, F. de Bergevin, J.C. Lang, G. Srajer, C. Mazzoli, L. Paolasini, P.G. Pagliuso, Phys. Rev. B 76 (2007) 104515. ¨ [20] R. Lora-Serrano, C. Giles, E. Granado, D.J. Garcia, E. Miranda, O. Aguero, L. Mendonc- a Ferreira, J.G.S. Duque, P.G. Pagliuso, Phys. Rev. B 74 (2006) 214404. [21] D. Mannix, P.C. de Camargo, C. Giles, A.J.A. de Oliveira, F. Yokaichiya, C. Vettier, European Phys. J. B 20 (2001) 19. [22] A. Stunault, K. Dumesnil, C. Dufour, C. Vettier, N. Bernhoef, Phys. Rev. B 65 (2002) 064436. [23] P.G. Pagliuso, D.J. Garcia, E. Miranda, E. Granado, R. Lora Serrano, C. Giles, J.G.S. Duque, R.R. Urbano, C. Rettori, J.D. Thompson, M.F. Hundley, J.L. Sarrao, J. Appl. Phys. 99 (2006) 08P703. [24] A. Czopnik, Phys. Status Solidi A 147 (1995) K35.
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Magnetic structure of Ho2 CoGa8 determined by X-ray resonant magnetic scattering C. Adriano , C. Giles, L.N. Coelho, G.A. Faria, P.G. Pagliuso Instituto de F´ısica ‘‘Gleb Wataghin’’, UNICAMP, C. P. 6165, 13083-970 Campinas, SP, Brazil
a r t i c l e in fo
PACS: 71.20.Lp 71.27.þa 75.25.þz 75.50.Ee Keywords: Intermetallic compound Ho2CoGa8 X-ray magnetic scattering (XRMS)
abstract We report the low temperature magnetic structure of the Ho2 CoGa8 intermetallic compound studied by X-ray magnetic scattering technique at the Brazilian Synchrotron Light Laboratory. We found that below TN ¼ 5:1 K, Ho2 CoGa8 has a commensurate antiferromagnetic structure with a propagation vector ~ Z ¼ ð12 ; 12 ; 12Þ and preliminary analysis indicated that the Ho magnetic moment points along the c-axis. The magnetic structure of this compound was obtained by measuring the strong dipolar resonant peak at the L3 edge using polarization analysis. The magnetic structure and properties Ho2 CoGa8 are found to be consistent with the general trend already seen for the Nd-, Tb-, and the Ce-based compounds from the Rm Mn In3mþ2n family (R ¼ rare earth; M ¼ Co, Rh, or Ir; m ¼ 1; 2; n ¼ 0; 1). & 2009 Elsevier B.V. All rights reserved.
1. Introduction The isostructural intermetallic compounds of the family Rn MX3nþ2 (with R ¼ rare earth or actinides, M ¼ transition metal, X ¼ In, Ga and n ¼ 1; 2) show a wide range of interesting electronic and magnetic properties with a tunable variety of ground states such as antiferromagnetism (AFM), unconventional superconductivity (USC), non-Fermi Liquid (NFL), and Fermi liquid (FL) behaviors [1–3]. Many members of this family can have their states changed just by doping, applying pressure or magnetic fields [4–7]. Also by changing the structure from the cubic ðRX3 Þ material to the monolayer member with n ¼ 1 ðRMX5 Þ or to the bilayer one ðR2 MX8 Þ we observe the evolution of some interesting physical properties. Within the rare earth materials with X ¼ In and M ¼ Co, Rh and Ir, many different ground states can be attained by changing R, like heavy fermion behavior and USC for R ¼ Ce, AFM for R¼Nd, Sm, Gd, Tb and paramagnetic metals for R ¼ La, Pr. Within the actinides, interesting properties also occur for M ¼ Co, X ¼ Ga like AFM for R ¼ Np and USC for R ¼ Pu with TC ¼ 15 K [8,9]. Systematic investigation of the Rn MX3nþ2 class of materials show that these compounds usually follow the microscopic Ruderman–Kittel–Kasuya–Yosida (RKKY) magnetic interaction, crystalline electrical field (CEF) effects, and the hybridization between 4f-electrons and conduction electrons of structurally related materials. To contribute with these investigations, we are
Corresponding author.
E-mail address: cadriano@ifi.unicamp.br (C. Adriano). 0921-4526/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2009.07.127
studying some Ga-based compounds with R ¼ rare earth and M ¼ Co [10]. In this work, we report measurements using X-ray resonant magnetic scattering (XRMS) technique in Ho2 CoGa8 intermetallic compound to determine the magnetic structure and to check if the CEF trends observed for Rm MIn3mþ2 series also apply to the Ga-based compounds. This technique has proven to be a valuable tool in unraveling features of the microscopic magnetic structure not available to other conventional techniques.
2. Experiment Single crystalline samples of Ho2 CoGa8 were grown by gallium flux technique as described previously [11]. The tetragonal structure (space group P4/mmm No. 123) and unit cell parameters a ¼ 4:219ð5Þ A˚ and c ¼ 10:99ð5Þ A˚ were confirmed by X-ray powder diffraction and are in good agreement with the results found by Joshi et al. [10]. Magnetization, specific heat and electrical resistivity measurements of these samples have been reported in a previous work [12]. For the X-ray magnetic scattering experiments, a crystal was selected and prepared with polished (1 0 0) flat surface, and size of approximately 4 3 2 mm3. The preferred crystal growth direction of this compound is columnar along the ½0 0 l direction and the (0 0 1) facet is relatively large. However, in rare cases, we can also obtain crystal plates with the ½h 0 0 direction and a large (1 0 0) facet. The mosaic spread of the sample was found to be o0:053 by a rocking curve (y scan) on a four circle X-ray diffractometer. XRMS studies were performed at the bending magnet XRD2 beamline [13] of the Brazilian Synchrotron Light Laboratory
ARTICLE IN PRESS 3290
C. Adriano et al. / Physica B 404 (2009) 3289–3292
(LNLS) in Campinas, Brazil. The XRD2 beamline uses a double crystal Si (111) monochromator, with sagital focusing and a Rh-coated mirror cylindrically bent to focus the beam to a 0.6 mm (vertical) 2.0 mm (horizontal) spot, yielding an incident flux of 3 1010 photons=s around 8 keV with an energy resolution of DE=E5 104 . The sample was cooled in a closed-cycle He cryostat (with a base temperature of 1.7 K using a Joule–Thomson stage), installed on a HUBER four-circle diffractometer in the vertical scattering plane, with the c-axis parallel to the beam. This configuration allowed s-polarized scattering geometry for the experiment.
3. Results and discussions The magnetic structure of the Ho2 CoGa8 was investigated by XRMS technique using polarization analysis. The central result of this paper is the observation of resonant magnetic scattering peaks at the L3 absorption edge of Ho (8071 eV). Resonances at the magnetic peaks were observed at the dipolar and quadrupolar energies at temperatures below TN ¼ 5:1 K at reciprocal lattice points forbidden for charge scattering and consistent with an antiferromagnetic commensurate structure with propagation vector ð12 ; 12 ; 12Þ. The observation of a commensurate structure differs from the results found for pure metallic Ho by Gibbs et al. [14] where they observed an incommensurate magnetic structure due to the spiral antiferromagnetic structure of pure Ho. The transition temperature where the magnetic peaks fade away is in agreement with those found by macroscopic property measurements reported before [12]. The polarization analysis performed at the magnetic peaks Z ¼ ð12 ; 12 ; 12Þ propagation vector is compatible with what is with ~ expected from a dipolar resonance polarization dependence as described by Hill and McMorrow [15]. In order to carry out these analyses a polarization analyzer setup was placed in the 2y arm of the diffractometer. The polarization analyzer crystal suitable to the Ho L3 edge energy is a graphite crystal with the (0 0 6) reflection at a Bragg angle of yA ¼ 43:43 . The deviation from the ideal value ð453 Þ results in a leakage from one channel to another. Fig. 1 shows the intensity as a function of the yA angle of the analyzer crystal for s2s0 and s2p0 polarization channels for the peak ð52 ; 12 ; 12Þ at 2 K and photon energy of 8071 eV.
Fig. 1. Angular scan of the analyzer crystal through the magnetic peak ð52 ; 12 ; 12Þ of the Ho2 CoGa8 compound at 2 K for s2p0 (closed circles) and s2s0 (open circles) polarization channels at the Ho L3 absorption edge.
The results shown in Fig. 1 are consistent with a dipolar resonant magnetic scattering peak where all the intensity is found in the s2p0 channel (closed circles) and no intensity is found in the s2s0 channel (open circles). The intensity observed in the small peak of the s2s0 channel is consistent with the leakage. To study the temperature dependence of the magnetic phase sweeps of the temperature were performed at the Ho L3 edge from 2 to 5:2 K. Fig. 2 shows the temperature dependence of the ð32 ; 12 ; 12Þ magnetic reflection at an incident photon energy of 8071 eV and measured at s2p0 channel. Fig. 2 shows the square root of the integrated intensity which is proportional to the magnetization of Ho in the compound. A squared Lorentzian peak shape was used to fit longitudinal y22y scans in order to obtain the integrated intensities of the reflection peak. As the temperature increases, the peak intensity gradually decreases and disappears above TN ¼ 5:1 K. A fitting using a power-law expression ð1 T=TN Þ2b for a second-order phase transition (denoted by a solid line in the inset of Fig. 2) within the temperature range of 3% below TN gives a magnetic transition temperature TN ¼ 5:1 K and a critical order exponent b ¼ 0:29ð2Þ for the Ho magnetic sublattice. This value of b is compatible with a three-dimensional Heisenberg system and the smooth decrease in intensity in the crossover to the paramagnetic phase is consistent with a second-order phase transition. The energy line shapes for the polarization channel s2p0 of the ð52 ; 12 ; 12Þ and ð72 ; 12 ; 52Þ peaks at the L3 edge of Ho at T ¼ 2 K are shown in Fig. 3. Both line shapes demonstrate a characteristic resonance enhancement of the magnetic peak but at two different energies. For the peak ð52 ; 12 ; 12Þ (open triangles) the maximum enhancement is observed at 8076 eV which is only few eV larger than the L3 edge, revealing the electric dipolar character ðE1Þ of this transition (from 2p3=2 to 5d states). An interesting result is that the energy line shape changes according to the magnetic peak measured. The curve in Fig. 3 for the peak ð72 ; 12 ; 52Þ (closed squares) shows a small maximum at the same energy 8076 eV, characterizing the ðE1Þ transition and another peak at the energy 8068 eV. This second peak seen for the ð72 ; 12 ; 52Þ is the quadrupolar ðE2Þ transition from the 2p3=2 to a 4f intermediate states. The quadrupolar transition of Ho3þ at 8068 eV was seen
Fig. 2. Squared root of the intensity as a function of temperature for Ho2 CoGa8 measured with longitudinal ðy22yÞ scans at the ð32 ; 12 ; 12Þ peak at 2 K and 8076 eV for s2p0 polarization channel around the L3 absorption edge of Ho. The inset shows in detail the critical region around the transition at the Ne el temperature and the solid line is a power-law fit to the data within the temperature range of approximately 3% below TN .
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Fig. 3. Energy line shape curve of the magnetic peaks ð52 ; 12 ; 12Þ (open triangles) and ð72 ; 12 ; 52Þ (closed squares) measured for s2p0 polarization channel at the L3 absorption edge of Ho ion at T ¼ 2 K.
also by Gibbs et al. [14] for pure metallic Ho, Nandi et al. for HoMnO3 [16] and Beutier et al. for HoMn2 O5 [17]. The energy line shape exhibits a long asymmetry tail to lower energies, this behavior was observed also for pure Ho [14] and some other light rare-earth (Nd [18] and Sm [19]) where it is believed to arise from interference between the non-resonant and resonant magnetic scattering. The results confirm the magnetic origin of the ð12 ; 12 ; 12Þ reflections due to the existence of an AFM structure that duplicate the chemical cell in all three directions. Since the tetragonal structure of Ho2 CoGa8 contains two magnetic Ho3þ ions per unit cell in the c-direction, this means that two possibilities of an AFM coupling can take place along the c-axis: Model 1 (sequence þ þ ) or Model 2 (sequence þ þ ) where the symbols þ and represent the relative orientation of the magnetic moment of a holmium atom with respect to its neighbour. To completely determine the magnetic structure of this compound we have to determine the coupling along the caxis and the direction of the magnetic moment. For collinear magnetic structures, the polarization dependence of the X-ray magnetic scattering assumes a simple form for dipolar resonances [15], and the intensities of magnetic Bragg peaks are proportional XRES Þ: to the magnetic form factor ðfnE1 2 X 1 ~ ~ XRES ~ ^ ~0 ^0 ^ iQ Rn f ð k; e ; k ; e ; z Þe ð1Þ Ip ; n nE1 m sinð2yÞ n where m is the absorption correction for asymmetric reflections, ~ ¼ k~0 ~ k is the wave-vector transfer, ~ k 2y is the scattering angle, Q ~ 0 0 ^ and k (e^ and e ) are the incident and scattered wave (polarization) vectors, respectively. ~ R n is the position of the nth atom in the lattice, and z^ n is the moment direction at the nth site. To calculate the ~ R n positions in Eq. (1), just the l-Miller indices are important since the Ho atoms are located in the c-direction of the unit cell. The sum is over the n resonant ions in the magnetic unit cell. The resonant scattering amplitude contains both dipole ðE1Þ and quadrupole ðE2Þ contributions. However for the determination of the magnetic structure in this work we have used the second term of the E1 transition (just for s2p0 polarization channel) which produces magnetic peaks [15]. The magnetic structure of Ho2 CoGa8 can thus be resolved by comparing the intensities of the magnetic Bragg reflections with those calculated using Eq.(1) [19–21].
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Fig. 4. Integrated intensities of the magnetic peaks (crosses) (l ¼ 12 at the left column and l ¼ 52 at the right column) plotted as a function of Q, compared to the calculated intensities for Model 1 (triangles) and Model 2 (circles) and with the moment direction along a-direction (upper plots (a) and (b)) and c-direction (lower plots (c) and (d)).
Seven magnetic peaks were measured and used in our model, for which four peaks have l ¼ 12 : ð32 ; 12 ; 12Þ; ð52 ; 12 ; 12Þ; ð52 ; 32 ; 12Þ and ð72 ; 12 ; 12Þ and three peaks have l ¼ 52 : ð52 ; 32 ; 52Þ; ð72 ; 12 ; 52Þ, and ð72 ; 32 ; 52Þ. Fig. 4 shows the normalized intensities of the experimental data (crosses), plotted as a function of the ~ , together with the calculated data reciprocal space vector Q using Eq. (1) considering four different cases: (1) Model 1 with the magnetic moment aligned along the a-direction; (2) Model 2 with the magnetic moment aligned along the a-direction; (3) Model 1 with the magnetic moment aligned along the c-direction; and (4) Model 2 with the magnetic moment aligned along the c-direction. Comparing the experimental data in Fig. 4 with the four different calculations proposed above using Eq. (1), these preliminary results suggest that the moment direction is in the c-direction. However, we could not determine the relative orientation of the Ho magnetic moment inside the magnetic unit ~ values cell. The main point is that magnetic peaks at different Q seem to follow different antiferromagnetic couplings within the unit cell. As can be seen from Fig. 4, Model 1 conveniently fits the magnetic peaks with indices l ¼ 12, while Model 2 conveniently fits the peaks with l ¼ 52. We can gain more insight into this apparent strange result if we recall that the energy line shapes shown in Fig. 3 are also different for the two sets of data, the dipolar resonance seen at 8076 eV decreases at the ð72 ; 12 ; 52Þ peak as compared to the ð52 ; 12 ; 12Þ peak. It is well known that the dipolar resonance probes the 5d magnetism and that the quadrupolar resonance probes the 4f magnetism of Ho. It is also well known that the 5d shell has a larger spatial extent than the 4f shell and consequently the 5d form factor falls off more rapidly at higher wave-vector transfer [22]. This sensitivity to the shell selectivity of the long range magnetic order can only be gained by X-ray magnetic scattering and is not possible with neutron scattering studies in a model-independent fashion. We believe that further X-ray magnetic scattering experiments on this compound should unravel the different contributions of the 5d and 4f magnetism of Ho in the Ho2 CoGa8 compound. Comparing the results obtained in this work with the general trend observed for the Rm Mn In3mþ2n family (R¼rare earth; M¼Co, Rh, or Ir; m ¼ 1; 2; n ¼ 0; 1), Ho2 CoGa8 seems to follow the same behavior seen for R¼Nd, Tb [23], since the magnetic moment of this compound is in the c-axis and the AFM ordering temperature
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for the HoCoGa5 parent ðTN ¼ 9:5 KÞ is larger than the TN for Ho2 CoGa8 . Since HoCo3 grows in a hexagonal crystal structure [24] it cannot be used as a parent cubic compound, preventing further comparison of Ho-based Ga compounds. In order to check the rule for Ga-based compounds, more experiments are desired to determine the magnetic structure of the other members of the family.
4. Conclusions In summary, we have studied the magnetic structure of Ho2 CoGa8 compound using resonant magnetic X-ray scattering at the Ho L3 edge. The results obtained so far show that Ho2 CoGa8 has a commensurate AFM order below TN ¼ 5:1 K with propagaZ ¼ ð12 ; 12 ; 12Þ. The calculations proposed suggest that the tion vector ~ magnetic moment is pointing at the c-direction. The differences in the energy line shape curves reveal a possible Q dependence of the dipolar resonance due to the different contribution of the 5d magnetic form factor. Further experiments with X-ray resonant magnetic scattering will be performed aiming to clarify the magnetic coupling in the magnetic unit cell. References [1] J.D. Thompson, R. Movshovich, Z. Fisk, F. Bouquet, N.J. Curro, R.A. Fisher, P.C. Hammel, H. Hegger, M.F. Hundley, M. Jaime, P.G. Pagliuso, C. Petrovic, N.E. Phillips, J.L. Sarrao, J. Magn. Magn. Mater. 226–230 (2001) 5. [2] P.G. Pagliuso, R. Movshovich, A.D. Bianchi, M. Nicklas, N.O. Moreno, J.D. Thompson, M.F. Hundley, J.L. Sarro, Z. Fisk, Physica B 312–313 (2002) 129. [3] A. Bianchi, R. Movshovich, I. Vekhter, P.G. Pagliuso, J.L. Sarrao, Phys. Rev. Lett. 91 (2003) 257001. [4] P.G. Pagliuso, N.O. Moreno, N.J. Curro, J.D. Thompson, M.F. Hundley, J.L. Sarrao, Z. Fisk, A.D. Christianson, A.H. Lacerda, B.E. Light, A.L. Cornelius, Phys. Rev. B 66 (2002) 054433.
[5] L. Mendonc-a-Ferreira, T. Park, V. Sidorov, M. Nicklas, E.M. Bittar, R. Lora-Serrano, E.N. Hering, S.M. Ramos, M.B. Fontes, E. Baggio-Saitovich, H. Lee, J.L. Sarrao, J.D. Thompson, P.G. Pagliuso, Phys. Rev. Lett. 101 (2008) 017005. [6] L.D. Pham, T. Park, S. Maquilon, J.D. Thompson, Z. Fisk, Phys. Rev. Lett. 97 (2006) 056404. [7] A.L. Cornelius, P.G. Pagliuso, M.F. Hundley, J.L. Sarrao, Phys. Rev. B 64 (2001) 144411. [8] J.L. Sarrao, L.A. Morales, J.D. Thompson, B.L. Scott, G.R. Stewart, F. Wastin, J. Rebizant, P. Boulet, E. Colineau, G.H. Lander, Nature (London) 420 (2002) 297. [9] A. Hiess, A. Stunault, E. Colineau, J. Rebizant, F. Wastin, R. Caciuffo, G.H. Lander, Phys. Rev. Lett. 100 (2008) 076403. [10] D.A. Joshi, R. Nagalakshmi, S.K. Dhar, A. Thamizhavel, Phys. Rev. B 77 (2008) 174420. [11] Z. Fisk, J.P. Remeika, Handbook on the Physics and Chemistry of Rare Earths, vol. 12, Elsevier, North-Holland, Amsterdam, 1989, p. 53. [12] C. Adriano, L. Mendonc- a-Ferreira, E.M. Bittar, P.G. Pagliuso, J. Appl. Phys. 103 (2008) 07B712. [13] C. Giles, F. Yokaichiya, S.W. Kycia, L.C. Sampaio, D.C. Ardiles-Saravia, M.K.K. Franco, R.T. Neuenschawander, J. Synchrotron Rad. 10 (2003) 430. ¨ [14] D. Gibbs, G. Grubel, D.R. Harshman, E.D. Isaacs, D.B. McWhan, D. Mills, C. Vettier, Phys. Rev. B 43 (1991) 5663. [15] J.P. Hill, D.F. McMorrow, Acta Crystallogr. Sect. A Found. Crystallogr. A 52 (1996) 236. [16] S. Nandi, A. Kreyssig, J.W. Kim, J.Q. Yan, J.C. Lnag, D. Haskel, R.J. McQueeney, A.I. Goldman, Phys. Rev. Lett. 100 (2008) 217201. [17] G. Beutier, A. Bombardi, C. Vecchini, P.G. Padaelli, S. Park, S.-W. Cheong, L.C. Chapon, Phys. Rev. B 77 (2008) 172408. [18] J.P. Hill, A. Vigliante, D. Gibbs, J.L. Peng, L. Greene, Phys. Rev. B 52 (1995) 6575. [19] C. Adriano, R. Lora-Serrano, C. Giles, F. de Bergevin, J.C. Lang, G. Srajer, C. Mazzoli, L. Paolasini, P.G. Pagliuso, Phys. Rev. B 76 (2007) 104515. ¨ [20] R. Lora-Serrano, C. Giles, E. Granado, D.J. Garcia, E. Miranda, O. Aguero, L. Mendonc- a Ferreira, J.G.S. Duque, P.G. Pagliuso, Phys. Rev. B 74 (2006) 214404. [21] D. Mannix, P.C. de Camargo, C. Giles, A.J.A. de Oliveira, F. Yokaichiya, C. Vettier, European Phys. J. B 20 (2001) 19. [22] A. Stunault, K. Dumesnil, C. Dufour, C. Vettier, N. Bernhoef, Phys. Rev. B 65 (2002) 064436. [23] P.G. Pagliuso, D.J. Garcia, E. Miranda, E. Granado, R. Lora Serrano, C. Giles, J.G.S. Duque, R.R. Urbano, C. Rettori, J.D. Thompson, M.F. Hundley, J.L. Sarrao, J. Appl. Phys. 99 (2006) 08P703. [24] A. Czopnik, Phys. Status Solidi A 147 (1995) K35.