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Ambient-pressure 99Ru NMR in URu2Si2: internal-field anisotropy
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 272–276 (2004) e59–e60
Ambient-pressure 99Ru NMR in URu2 Si2: internal-field anisotropy O.O. Bernala,*, M.E. Moroza, H.G. Lukefahrb, D.E. MacLaughlinc, J.A. Mydoshd, A.A. Menovskye, C. Ortiza,1 a
Physics and Astronomy Department, California State University, 5151 State University Drive, Los Angeles, CA 90032, USA b Physics Department, Whittier College, Whittier, CA 90601, USA c Physics Department, University of California, Riverside, CA 92521, USA d Max-Planck-Institute for Chemical Physics of Solids, Dresden 01187, Germany e Kamerlingh Onnes Laboratorium, Leiden University, The Netherlands
Abstract Ambient-pressure 99 Ru NMR spectra and lineshape parameters in URu2 Si2 as functions of temperature and magnetic field orientation reveal local internal field distributions at the 99 Ru sites below the hidden-order transition temperature T0 B17 K: The fields are anisotropic and larger in the ab-plane. We discuss our experiments within the framework of orbital antiferromagnetism, which predicts anisotropic field distributions at the Ru sites. r 2003 Elsevier B.V. All rights reserved. PACS: 71.27.+a; 75.30.Mb; 76.60.Cq; 76.60.Jx Keywords: Hidden order; URu2 Si2 ; Heavy fermion
The nature of the hidden-order (HO) state in URu2 Si2 below T0 B17 K continues to be a matter of investigation [1,2]. It is now widely accepted that the state of small-moment antiferromagnetism below T0 at ambient pressure can be understood as being due to an inhomogeneous coexistence of t1% antiferromagnetic ( and (AF) domains with mB0:25 mB =U and xB200 A; paramagnetic HO regions [2]. Our previous 29 Si NMR measurements uncovered the presence of internal field distributions at the 29 Si sites for the HO state, i.e., below T0 [3]. One possible source of internal fields consistent with the thermodynamic behavior of the system is a distribution of orbital AF (OAF) currents around uranium plaquettes [4]. At the silicon sites, the rms field is of the correct size ðB10 GÞ; consistent with a gap in *Corresponding author. Tel.: +1-323-343-2138; fax: +1323-343-2497. E-mail address: [email protected] (O.O. Bernal). 1 Permanent address: Universidad Pedagogica y Tecnologica de Colombia (UPTC), Tunja, Colombia.
the spin excitation spectrum of 110 K [1]. To obtain the correct symmetry, however, the distribution of currents in this model needs to be fine tuned to produce an isotropic value of the rms field at the silicon positions. The fine-tuning of the current distribution for the 29 Si sites, actually allows the model to predict that the size of the internal field distributions will be anisotropic at the 99 Ru positions. Here we report preliminary results for the anisotropy in the internal field distributions at the 99 Ru sites in URu2 Si2 : Although the effect sought after is field independent (related to the HO phase as for the 29 Si NMR study [3]), it is also small and can be overwhelmed by the paramagnetism of the U ions. This would suggest to look for it at the lowest possible applied fields where the U paramagnetism contribution can be made as small as desired. However, there are two impediments to reducing the field below about 3 T and still obtaining usable data. The first is the small 99 Ru gyromagnetic ratio; for fields o3 T 99 Ru Zeeman frequencies are o5 MHz; and the signal is forbiddingly weak. The
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.11.159
ARTICLE IN PRESS O.O. Bernal et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e59–e60
e60
(a)
Linewidth (G)
H⊥c 150
150
100
100
URu2Si2
Γ10
λ10 50
0
(b)
H || c
URu2Si2
50 Γ2
λ2 0
5 10 15 Temperature (K)
0
(c)
0
5 10 15 Frequency (MHz)
Fig. 1. (a) NMR Spectra vs. T for H>c; curves: powerLorentzian fits; circles: data. (b) Squares: l2 ðTÞ; circles: l10 ðTÞ; curves: s ¼ 12 mean-field function. (c) G2 and G10 vs. frequency as indicated; triangles: T ¼ 20 K; circles: T ¼ 12 K; fits: one (lines) and two (curves) width components added in quadrature—see [3].
second impediment is the second-order quadrupole broadening of the 99 Ru line, which dominates the linewidth below these frequencies. In Fig. 1(a) we plot field-swept spectra relative to the average field for applied field H>c and different temperatures above and below T0 : Unlike the case of 29 Si [3], the lineshape of the spectra cannot be fit using a single Lorentzian function. We use instead the ‘‘power Lorentzian’’ ðp1=½a2 þ H 2 b Þ: From the fits (smooth curves in Fig. 1(a)), we use a and b to obtain the spectral linewidths at half ðG2 Þ and tenth ðG10 Þ maximum. [Gn ; the linewidth at a given height fraction 1=n; is simply G2n ¼ a2 ðn1=b 1Þ:] Below T0 these parameters contain
paramagnetic and quadrupolar components, which are both essentially temperature-independent for H>c; and an HO component l that vanishes above T0 : We obtain l by subtracting the linewidth measured at high temperatures T > T0 from the measured linewidth for ToT0 ; as was done for the 29 Si data [3]. The results are plotted in Fig. 1(b). l follows a mean-field like behavior very similar to the one found for 29 Si [3]. To look for the anisotropy of the effect, we plot G2 and G10 as functions of frequency Fig. 1(c) at T ¼ 20 K > T0 and T ¼ 12 KoT0 for a field Hjjc and frequencies where quadrupole effects can be neglected. Without the complication of the T-dependent effect of the U paramagnetism which is dominant for this geometry, the frequency dependence of G at constant T can be fit to one (two) independent width component(s) above (below) T0 : Within 10–15% we obtain for l> ðT ¼ 0 KÞ: > jj l2 B30 G; l> 10 B145 G: For l ðT ¼ 12 KÞ the values jj jj are l2 B14 G; l10 B63 G: Extrapolation for the latter orientation to T ¼ 0 K using a mean-field function yields values 23% higher (i.e., ljj2 B17 G and ljj10 B77 G at T ¼ 0 K). Thus we find anisotropy in the lineshape, and a field strength greater in the ab plane. Such observations need to be explained by any model of HO. For the OAF [4], anisotropy is expected at the 99 Ru sites. Although the details of the prediction are not yet known, the difference in relative position of the Ru (vertical) and Si (diagonal) ions with respect to the U–U bond currents would be consistent with the type of anisotropy we observe. This work was supported by NSF/DMR 0203524 (CSULA) and 0102293 (UC Riverside), and by an award from the Research Corporation (CSULA, Whittier).
References [1] T.T.M. Palstra, et al., Phys. Rev. Lett. 55 (1985) 2727; W. Schlabitz, et al., Z. Phys. B 62 (1986) 171; C. Broholm, et al., Phys. Rev. Lett. 58 (1987) 1467. [2] K. Matsuda, et al., Phys. Rev. Lett. 87 (2001) 087203; H. Amitsuka, et al., Physica B 312–313 (2002) 390; M. Jaime, et al., Phys. Rev. Lett. 89 (2002) 287201; J. Mydosh, et al., Acta Phys. Polonica B 34 (2003) 659. [3] O.O. Bernal, et al., Phys. Rev. Lett. 87 (2001) 196402. [4] P. Chandra, et al., Nature (London) 417 (2002) 831.
Journal of Magnetism and Magnetic Materials 272–276 (2004) e59–e60
Ambient-pressure 99Ru NMR in URu2 Si2: internal-field anisotropy O.O. Bernala,*, M.E. Moroza, H.G. Lukefahrb, D.E. MacLaughlinc, J.A. Mydoshd, A.A. Menovskye, C. Ortiza,1 a
Physics and Astronomy Department, California State University, 5151 State University Drive, Los Angeles, CA 90032, USA b Physics Department, Whittier College, Whittier, CA 90601, USA c Physics Department, University of California, Riverside, CA 92521, USA d Max-Planck-Institute for Chemical Physics of Solids, Dresden 01187, Germany e Kamerlingh Onnes Laboratorium, Leiden University, The Netherlands
Abstract Ambient-pressure 99 Ru NMR spectra and lineshape parameters in URu2 Si2 as functions of temperature and magnetic field orientation reveal local internal field distributions at the 99 Ru sites below the hidden-order transition temperature T0 B17 K: The fields are anisotropic and larger in the ab-plane. We discuss our experiments within the framework of orbital antiferromagnetism, which predicts anisotropic field distributions at the Ru sites. r 2003 Elsevier B.V. All rights reserved. PACS: 71.27.+a; 75.30.Mb; 76.60.Cq; 76.60.Jx Keywords: Hidden order; URu2 Si2 ; Heavy fermion
The nature of the hidden-order (HO) state in URu2 Si2 below T0 B17 K continues to be a matter of investigation [1,2]. It is now widely accepted that the state of small-moment antiferromagnetism below T0 at ambient pressure can be understood as being due to an inhomogeneous coexistence of t1% antiferromagnetic ( and (AF) domains with mB0:25 mB =U and xB200 A; paramagnetic HO regions [2]. Our previous 29 Si NMR measurements uncovered the presence of internal field distributions at the 29 Si sites for the HO state, i.e., below T0 [3]. One possible source of internal fields consistent with the thermodynamic behavior of the system is a distribution of orbital AF (OAF) currents around uranium plaquettes [4]. At the silicon sites, the rms field is of the correct size ðB10 GÞ; consistent with a gap in *Corresponding author. Tel.: +1-323-343-2138; fax: +1323-343-2497. E-mail address: [email protected] (O.O. Bernal). 1 Permanent address: Universidad Pedagogica y Tecnologica de Colombia (UPTC), Tunja, Colombia.
the spin excitation spectrum of 110 K [1]. To obtain the correct symmetry, however, the distribution of currents in this model needs to be fine tuned to produce an isotropic value of the rms field at the silicon positions. The fine-tuning of the current distribution for the 29 Si sites, actually allows the model to predict that the size of the internal field distributions will be anisotropic at the 99 Ru positions. Here we report preliminary results for the anisotropy in the internal field distributions at the 99 Ru sites in URu2 Si2 : Although the effect sought after is field independent (related to the HO phase as for the 29 Si NMR study [3]), it is also small and can be overwhelmed by the paramagnetism of the U ions. This would suggest to look for it at the lowest possible applied fields where the U paramagnetism contribution can be made as small as desired. However, there are two impediments to reducing the field below about 3 T and still obtaining usable data. The first is the small 99 Ru gyromagnetic ratio; for fields o3 T 99 Ru Zeeman frequencies are o5 MHz; and the signal is forbiddingly weak. The
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.11.159
ARTICLE IN PRESS O.O. Bernal et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e59–e60
e60
(a)
Linewidth (G)
H⊥c 150
150
100
100
URu2Si2
Γ10
λ10 50
0
(b)
H || c
URu2Si2
50 Γ2
λ2 0
5 10 15 Temperature (K)
0
(c)
0
5 10 15 Frequency (MHz)
Fig. 1. (a) NMR Spectra vs. T for H>c; curves: powerLorentzian fits; circles: data. (b) Squares: l2 ðTÞ; circles: l10 ðTÞ; curves: s ¼ 12 mean-field function. (c) G2 and G10 vs. frequency as indicated; triangles: T ¼ 20 K; circles: T ¼ 12 K; fits: one (lines) and two (curves) width components added in quadrature—see [3].
second impediment is the second-order quadrupole broadening of the 99 Ru line, which dominates the linewidth below these frequencies. In Fig. 1(a) we plot field-swept spectra relative to the average field for applied field H>c and different temperatures above and below T0 : Unlike the case of 29 Si [3], the lineshape of the spectra cannot be fit using a single Lorentzian function. We use instead the ‘‘power Lorentzian’’ ðp1=½a2 þ H 2 b Þ: From the fits (smooth curves in Fig. 1(a)), we use a and b to obtain the spectral linewidths at half ðG2 Þ and tenth ðG10 Þ maximum. [Gn ; the linewidth at a given height fraction 1=n; is simply G2n ¼ a2 ðn1=b 1Þ:] Below T0 these parameters contain
paramagnetic and quadrupolar components, which are both essentially temperature-independent for H>c; and an HO component l that vanishes above T0 : We obtain l by subtracting the linewidth measured at high temperatures T > T0 from the measured linewidth for ToT0 ; as was done for the 29 Si data [3]. The results are plotted in Fig. 1(b). l follows a mean-field like behavior very similar to the one found for 29 Si [3]. To look for the anisotropy of the effect, we plot G2 and G10 as functions of frequency Fig. 1(c) at T ¼ 20 K > T0 and T ¼ 12 KoT0 for a field Hjjc and frequencies where quadrupole effects can be neglected. Without the complication of the T-dependent effect of the U paramagnetism which is dominant for this geometry, the frequency dependence of G at constant T can be fit to one (two) independent width component(s) above (below) T0 : Within 10–15% we obtain for l> ðT ¼ 0 KÞ: > jj l2 B30 G; l> 10 B145 G: For l ðT ¼ 12 KÞ the values jj jj are l2 B14 G; l10 B63 G: Extrapolation for the latter orientation to T ¼ 0 K using a mean-field function yields values 23% higher (i.e., ljj2 B17 G and ljj10 B77 G at T ¼ 0 K). Thus we find anisotropy in the lineshape, and a field strength greater in the ab plane. Such observations need to be explained by any model of HO. For the OAF [4], anisotropy is expected at the 99 Ru sites. Although the details of the prediction are not yet known, the difference in relative position of the Ru (vertical) and Si (diagonal) ions with respect to the U–U bond currents would be consistent with the type of anisotropy we observe. This work was supported by NSF/DMR 0203524 (CSULA) and 0102293 (UC Riverside), and by an award from the Research Corporation (CSULA, Whittier).
References [1] T.T.M. Palstra, et al., Phys. Rev. Lett. 55 (1985) 2727; W. Schlabitz, et al., Z. Phys. B 62 (1986) 171; C. Broholm, et al., Phys. Rev. Lett. 58 (1987) 1467. [2] K. Matsuda, et al., Phys. Rev. Lett. 87 (2001) 087203; H. Amitsuka, et al., Physica B 312–313 (2002) 390; M. Jaime, et al., Phys. Rev. Lett. 89 (2002) 287201; J. Mydosh, et al., Acta Phys. Polonica B 34 (2003) 659. [3] O.O. Bernal, et al., Phys. Rev. Lett. 87 (2001) 196402. [4] P. Chandra, et al., Nature (London) 417 (2002) 831.