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Magnetization, Structural and Nuclear Quadrupole Resonance Study of RuSr2EuCeCu2O10+d

We present the results from a magnetization, structural, and nuclear quadrupole resonance study of the ruthenate-cuprate, RuSr2R2-xCexCu2O10+d with x=1 and R=Eu. This compound is a superconductor for Ce doping in the range 0.4<=x<=0.8 and displays ferromagnetic order for 0.4<=x<=1.0. We show that the tilting and rotation of the RuO6 octahedra are essentially the same for x=1, x=0.6 and the superconducting antiferromagnet, RuSr2GdCu2O8. However, the moment per Ru in RuSr2EuCeCu2O10+d is comparable to that observed in RuSr2EuCu2O8. These results indicate that it is unlikely that the different magnetic order found in RuSr2R2-xCexCu2O10+d and RuSr2RCu2O8 (R=Y,Gd,Eu) is due to changes in structurally induced distortions of the RuO6 octahedra as found in the ruthenate compounds (e.g. Sr1-xCaxRuO3). We show that the Cu nuclear quadrupole resonance (NQR) data are similar to those observed in the single CuO2 layer superconductor, La1-xSrxCuO4, where the Cu spin-lattice relaxation rate is dominated by hyperfine coupling within the CuO2 layers and any additional hyperfine coupling from spin fluctuations in the RuO2 layers is small.


Introduction
The ruthenate-cuprates (RuSr 2 R 2-x Ce x Cu 2 O 10+δ and RuSr 2 RCu 2 O 8 , R=Y,Eu,Gd) are proving to be particularly interesting because they display magnetic order that is not seen in other ruthenate compounds (e.g. Sr 1-x Ca x RuO 3 and Sr 2 RRuO 6 ). These compounds were discovered by Bauernfeind, Widder and Braun [1,2] and they have been found to display weak ferromagnetic (RuSr 2 R 2-x Ce x Cu 2 O 10+δ [3]) or predominately antiferromagnetic (RuSr 2 RCu 2 O 8 [4,5,6]) order as well as the coexistence of superconductivity [7,8,9]. The ruthenate-cuprates contain CuO 2 layers as well as RuO 2 layers that magnetically order. A detailed measurement and characterization of the macroscopic and microscopic properties of the RuO 2 layers, the CuO 2 layers and their mutual interactions is a key ingredient for a consistent theoretical description of these materials.

Recent x -ray absorption near edge spectroscopy (XANES) studies on
RuSr 2 R 2-x Ce x Cu 2 O 10+δ and RuSr 2 RCu 2 O 8 have indicated that the average Ru valence is 4.6 [10] for RuSr 2 RCu 2 O 8 and 5.0 [11] or 4.95 [12] for RuSr 2 R 2-x Ce x Cu 2 O 10+δ . The appearance of a mixed Ru valence in the case of RuSr 2 RCu 2 O 8 has also been observed by nuclear magnetic resonance (NMR) measurements [13,14]. It is surprising that a mixed Ru valence is observed in RuSr 2 RCu 2 O 8 because a mixed Ru valence is not expected in, and has not been reported in, other ruthenate compounds. This may suggest that these materials display an intrinsic inhomogeneous distribution of charge and spin density. Furthermore, the Ru valence in RuSr 2 R 2-x Ce x Cu 2 O 10+δ is nearly the same as that from the antiferromagnetic insulator, Sr 2 RCuO 6 . Thus, there seems to be no direct correlation between the valence state of Ru and the observed magnetic ordering state, suggesting that more complicated models involving other physical parameters might be required.
There is also the question of the effect of Ce doping in RuSr 2 R 2-x Ce x Cu 2 O 10+δ . It has been found that there is no significant change in T c for 0.4≤x≤0.8 indicating that there is no change in the hole concentration on the CuO 2 planes [15]. Furthermore, there is no significant charge transfer to the RuO 2 planes for 0.5≤x≤1.0 [12]. It is believed, based on xray absorption spectroscopy measurements on a related compound (Pr 1.5 Ce 0.5 NbSr 2 Cu 2 O 10+δ [16]), that the Ce valence in RuSr 2 R 2-x Ce x Cu 2 O 10+δ is 4+ [11]. Thus, if all the carriers introduced by Ce doping appeared in the CuO 2 planes then it would be expected that an increase in the Ce concentration from 0.4 to 0.8 should correspond to a decrease in the hole concentration on the CuO 2 planes of 0.2. This change in hole concentration is large and it is comparable to the hole concentration range where superconductivity is observed in the high temperature superconducting cuprates (HTSC) (0.05≤p≤0.27). It has been suggested that the carriers introduced by Ce are partially compensated by an increase in the oxygen content [15].
It is not clear if the different magnetic order in the ruthenate-cuprates can be explained by the current theories that have been applied to Sr 1-x Ca x RuO 3 , which also has RuO 6 octahedra. In particular, the different magnetic order observed in Sr 1-x Ca x RuO 3 is believed to be due to changes in the bandwidth induced by the changes in the Ru-O-Ru bond lengths as well as tilting and rotations of the RuO 6 octahedra [17]. It is known that a rotation and tilting of the RuO 6 octahedra also occurs in RuSr 2 GdCu 2 O 8 where the rotations form coherent domains extending up to 20 nm and results in super-cell features [18]. One neutron powder diffraction study has shown that a rotation and tilting of the RuO 6 octrahedra also occurs in RuSr 2 Gd 1.4 Ce 0.6 Cu 2 O 10+δ [19]. However, it is not known if they occur for other Ce doping concentrations. This is especially pertinent because it is known that the magnetization at 1 T and the peak in the temperature-dependent magnetization data increase with increasing Ce concentration [15].
In this paper, we report the results from a magnetization, synchrotron x -ray diffraction and nuclear quadrupole resonance (NQR) study of RuSr 2 EuCeCu 2 O 10+δ with the aim to address the problems above. The techniques applied in this study provide insight into the macroscopic properties as probed by magnetization measurements as well as microscopic information concerning the atomic positions and bond angles or the local static and dynamic properties as seen by the 63,65 Cu nuclei. We show that this compound is a ferromagnet with a saturation moment at 6 T that is comparable to that observed in the antiferromagnetic superconductor, RuSr 2 EuCu 2 O 8 . Furthermore, the tilting and rotation angles are comparable to those observed in superconducting RuSr 2 GdCu 2 O 8 and RuSr 2 Gd 1.4 Ce 0.6 Cu 2 O 10+δ . We 4 was no evidence of impurity phases in the synchrotron x-ray spectra. A RuSr 2 EuCu 2 O 8 sample was prepared using the synthesis method described elsewhere [2,8]. X-ray diffraction measurements indicated that the sample was single phase. It is not possible to c-axis align RuSr 2 EuCeCu 2 O 10+δ or RuSr 2 EuCu 2 O 8 and hence the experiments were performed on unoriented ceramic samples or powders.
Synchrotron X-ray diffraction patterns were recorded at Station 9.1, Daresbury SRS (synchrotron radiation source), UK, which is a high-energy, high resolution monochromatic diffraction station for structure solution, time resolved and high pressure studies. The sample was placed in a 0.5 mm diameter borosilicate glass capillary mounted on the axis of the diffractometer about which it was spun at a frequency of approximately 1Hz to improve the powder averaging of the crystallites. Diffraction patterns were collected at room temperature with a step size of 0.01° and, in order to minimize absorption, a wavelength of 0.805521 Å was used. The high-angle parts of the pattern were scanned several times to improve the statistical quality of the data in these regions. Finally the counts from the detectors were normalized, summed and rebinned; the patterns were then refined by the Rietveld method using the GSAS program [20]. The full width at half maximum for this instrument in Debye -Scherrer geometry is ~ 0.03 -0.05º and the peaks are easily described by a Pseudo Voigt function.
The ac and dc magnetization measurements were made using a SQUID magnetometer. The remnant magnetic field from the superconducting magnet was ±0.6 mT.
The ac magnetization data was taken with an ac magnetic field of 5 µT and a frequency of 100 Hz. Room temperature thermopower measurements were made using the standard differential temperature technique. Electrical resistance measurements were made between 4 K and 300 K using the four terminal technique.
Cu NQR measurements were performed on a powder sample using a home built pulsed NQR spectrometer, described elsewhere [21]. The probe was placed in a continuous flow cryostat, which was encased in a µ-metal shield in order to reduce the magnetic field at the sample from stray magnetic fields and the earth's magnetic field. An inversion recovery pulse sequence was used to measure the spin-lattice relaxation rate, 1/T 1 , and a Hahn echo sequence was used to obtain the NQR spectra. In both cases the π/2 pulse width was 1 µs and the time between the π/2 pulse and the π pulse was 9-10 µs. The NQR spectra were obtained at discrete frequency steps and then adding the Fourier transformed spectra from the second half of the echo after phase correction.
In homogeneous materials the Cu NQR spin-lattice magnetization recovery for the inversion recovery pulse sequence is a mono-exponential and can be expressed as, where τ is the time between the first inversion pulse and the first pulse of the detection echo sequence. The additional factor of 3 is added in order to enable a direct comparison between the NQR and nuclear magnetic resonance (NMR) spin-lattice relaxation rates.

Results and Analyses
The unit cell of RuSr 2 R 2-x Ce x Cu 2 O 10+δ is plotted in figure 1.  [19] and RuSr 2 GdCu 2 O 8 [18]. The tilt and rotation of the RuO 6 octahedra are indicated in figure 1 by the multiple O(3) and O(1) positions.
The room temperature thermopower for the x=1 and R=Eu sample is 69 µV/K. A comparison with the room temperature thermopower values of the double CuO 2 layer HTSC [23] would indicate that the hole concentration of this sample is ~0.05 and it is on the insulator-superconductor boundary. However, the results from a recent study on single CuO 2 layer La 2-x Sr x CuO 4 would appear to suggest that the hole concentration is near 0.075 [24].
There is no evidence of superconductivity from the electrical resistance data (not shown) and the resistance increases with decreasing temperature.
There is also no evidence of superconductivity or a superconducting fraction in the ac susceptibility data plotted in figure 2. Rather, the main feature seen in the real part of the ac susceptibility, ' χ (solid curve, left axis), is a peak near 106 K which is associated with the magnetic ordering transition. The peak in the imaginary part of the ac susceptibility, ' ' χ , occurs at a slightly lower temperature of 100 K as can be seen in figure 2b. Similar peaks are seen in RuSr 2 RCu 2 O 8 but at a higher temperature of 132 K [8,25,26], as can be seen in figure   2a (dashed curve, right axis) for R=Eu. As mentioned above, the low-field magnetic order in RuSr 2 RCu 2 O 8 is predominately antiferromagnetic and the peak in ' χ occurs at essentially the same temperature as the magnetic ordering temperature [25], defined as temperature where dT dM / is a maximum negative value.
It is apparent in figure 3 that the low field magnetic ordering temperature in RuSr 2 EuCeCu 2 O 10+δ is 115 K, where we use the definition mentioned above. Here we plot the field-cooled and zero-field-cooled dc magnetization data from RuSr 2 EuCeCu 2 O 10+δ (solid curves, left axis) and RuSr 2 EuCu 2 O 8 (dashed curves, right axis) for an applied magnetic field of -2.5 mT. We find that the magnetic ordering temperature increases with increasing applied magnetic field as can be seen in the lower insert to figure 3, where the magnetic ordering temperature for an applied magnetic field of 6 T is 146 K. It can be seen that the peak in the zero-field-cooled dc magnetization, for an applied magnetic field of -2.5 mT, occurs at a lower temperature of 94 K. This can be contrasted with RuSr 2 RCu 2 O 8 where the peak in the dc magnetization for low applied fields occurs at essentially the same temperature as the temperature where dT dM / − from the field-cooled data is a maximum [25]. This peak is due to reorientation and growth of ferromagnetic domains and shifts to lower temperatures with increasing magnetic fields. For low temperatures, the domain wall pinning energy is greater than k B T. As the temperature is increased, the weakly pinned domain walls are free to move and hence the magnetization increases.
The higher magnetization observed in the field-cooled condition and for low applied magnetic fields and temperatures implies a magnetic irreversibility, which disappears for magnetic fields greater than ~ 0.2 T for RuSr 2 EuCeCu 2 O 10+δ but it is still evident for fields of up to 3 T in RuSr 2 RCu 2 O 8 . For low applied magnetic fields, the irreversibility occurs at a temperature that is 10 K greater than the magnetic ordering temperature. This can be seen in the upper insert to figure 3 for RuSr 2 EuCeCu 2 O 10+δ (solid curve, left axis) and RuSr 2 EuCu 2 O 8 (dashed curve, right axis). We note that the irreversibility temperature is close to the temperature where the onset of ac loss occurs as can be seen in figure 2b.
It is apparent in figure 4 that the magnetic field dependence of the magnetization is different for RuSr 2 EuCeCu 2 O 10+δ and RuSr 2 EuCu 2 O 8 . Here we plot the magnetization from RuSr 2 EuCeCu 2 O 10+δ (solid curve) and RuSr 2 EuCu 2 O 8 (dashed curve) at 5 K after subtracting the small van Vleck susceptibility from Eu 3+ , which will be discussed later. In particular, RuSr 2 EuCu 2 O 8 has a small remnant magnetization of ~0.035 µ B /Ru, which is slightly smaller than that found in an earlier study [25] [5,6,25]. In the case of RuSr 2 GdCu 2 O 8 , the remnant moment is significantly larger (0.14 µ B /Ru [8]) which has been attributed to coupling of the ferromagnetic component with the Gd 3+ moment [5]. The situation is more complicated because, although a recent theoretical study showed that the antiferromagnetic state is energetically favored over the antiferromagnetic state [27], a recent powder neutron diffraction study on RuSr 2 YCu 2 O 8 has found a significant ferromagnetic component of 0.28 µ B /Ru [28]. We note that it has been suggested that the high-field magnetic order in RuSr 2 EuCu 2 O 8 is ferromagnetic and hence there is a spin-flop transition [25].
The large remnant magnetization, in relation to the magnetization at 6 T, found in RuSr 2 EuCeCu 2 O 10+δ is consistent with ferromagnetic order although neutron diffraction measurements are required to precisely determine the nature of the magnetic order. Unlike RuSr 2 EuCu 2 O 8 , the magnetization from RuSr 2 EuCeCu 2 O 10+δ rapidly increases for magnetic fields of up to ~0.2 T after which the increase in the magnetization is more gradual. Similar behavior is also observed in the itinerant ferromagnetic metals, SrRuO 3 (T m =165 K [29]) and The first term is the Curie-Weiss contribution from the Ru moment where ϑ is the Curie-Weiss temperature. The second term is the van Vleck susceptibility from Eu 3+ ( 7 F 0 ). Similar to the high temperature susceptibility study on RuSr 2 EuCu 2 O 8 [33], we use a spin-orbit coupling constant of 303 cm -1 as measured in Eu 2 CuO 4 [35]. However, as we show below, the deduced Ru moment is not critically dependent on the value of the spin-orbit coupling constant. The van Vleck susceptibility from Eu 3+ is plotted in figure 5 ( We show by the solid curve in figure 5 that the susceptibility, after subtracting the Eu 3+ contribution, can be fitted to a Curie-Weiss function and a constant term. We find that the effective high-temperature moment is 2.6 µ B /Ru, θ =133 K and 0 χ =14×10 -5 . Note that varying the spin-orbit coupling constant from 250 cm -1 to 350 cm -1 does not significantly change the fitted parameters. While the effective high-temperature moment is greater than that expected for a t 2g 3 ground state and S=1/2 (1.73 µ B /Ru), it is considerably less than that expected for a t 2g 3 ground state and S=3/2 (3.87 µ B /Ru). Furthermore, θ is 18 K greater than the magnetic ordering temperature. The fitted value of 0 χ is significantly greater than ) (T χ in YBa 2 Cu 3 O 7 which gives an upper limit to the Pauli spin susceptibility and the diamagnetic term from the CuO 2 planes of ~4×10 -5 [36]. The remaining 0 χ is large but it is comparable to, or smaller than, the temperature independent susceptibility from Sr 2 YRuO 6 and SrRuO 3 [34].
We show in figure 6 that the synchrotron x-ray spectra can be refined to a I4/mmm space group where the atomic positions are given in  [13], could easily account for a broad spectral distribution of Cu NQR frequencies in zero field, especially as there is also magnetic disorder present due to ferromagnetic domain formation. We observe an enhancement of the Rabi precession frequency by a factor of 20, which is characteristic for ferromagnetic materials [43] and has also been observed in RuSr 2 GdCu 2 O 8 [13].
The room temperature 63 Cu NQR frequency is lower than that observed in La 2-x Sr x CuO 4 (>31.5 MHz [42] and nearly temperature independent), slightly less than that observed in optimally doped YBa 2 Cu 3 O 7-δ (31.2 MHz at 300 K [44]) and clearly greater than that observed in HgBa 2 CuO 4+δ (<24 MHz [45]). For these HTSC it has been found that there is a linear dependence of the Cu NQR frequency on hole concentration of the form,  [46].
We find that the 63 Cu NQR frequency in RuSr 2 EuCeCu 2 O 10+δ increases by ~1 MHz when the temperature is decreased from room temperature to 80 K as can be seen in the insert to figure 7. A temperature dependent increase in the Cu NQR linewidth is observed in fully loaded YBa 2 Cu 3 O 7-δ and it has been attributed to lattice effects [44]. However, the temperature dependent increase observed in RuSr 2 EuCeCu 2 O 10+δ is anomously large and increases dramatically for temperatures less than ~200 K as can be seen in the insert to figure   7. The origin of this increase is not clear. We speculate that it may be due to structurally induced changes that result either in charge transfer to the CuO 2 layer or changes in the charge distribution at the planar Cu site [46].
We show in figure 8 that the spin-lattice relaxation magnetization recovery can be fitted to equation (1) at, and above, room temperature (open circles). Here we plot (dashed curve) at 301.7 K and at 31.2 MHz. However, we find that the spin-lattice magnetization recovery at lower temperatures can not be fitted to a single exponential, as is apparent in figure 8 where we plot the spin-lattice magnetization recovery at 162.5 K and 31.2 MHz (crosses). The appearance of a spin-lattice magnetization recovery that can not be fitted to a single exponential indicates that there is a distribution of spinlattice relaxation rates.
The distribution of 1 63 / 1 T can not be due to impurity phases because the synchrotron x-ray diffraction data indicates that the sample is single phase. In the absence of a specific spin-lattice relaxation rate distribution function, we fit the spin-lattice magnetization recovery to the stretched exponential function used by other researchers [47][48][49]. This function can be written as for metallic and magnetic systems, which was originally derived by Moriya, is given by [51] where | ) ( | q A is the form factor containing onsite and transferred hyperfine coupling constants, γ n is the nuclear gyromagnetic ratio, and  and temperature as can be seen in figure 9b (plus symbols). 13 A linear decrease in T T 1 63 with decreasing temperature is also observed in La 2-x Sr x CuO 4 over the same temperature range [42]. Furthermore, the absolute values of T T 1 63 are within the range of those observed in La 2-x Sr x CuO 4 is can be seen by the lines in figure 10b for 0.075 Sr (dotted curve [42]) and 0.24 Sr (dashed curve [42]). However, they are significantly less that those observed in YBa 2 Cu 3 O 7-δ (~0.25 sK at 300 K [35,42]). The found that the spin-lattice magnetization could not be fitted to a single exponential below 300 K [42]. However, this was not reported by two other studies [41,50]. A systematic decrease of 1 63 / 1 T with increasing frequency has been reported in La 2-x Sr x CuO 4 in the same temperature region and it has been suggested that this is due to charge inhomogeneity [41].
This variation disappears on the overdoped side (p>0. 16). It is unlikely that the behavior mentioned above is due to a slowing down of spin or charge fluctuations in the CuO 2 layers reported by other studies on La 2-x Sr x CuO 4 because these effects are only expected to be observed below 100 K [47,51,55].
The simplest explanation for the Cu NQR data plotted in figures 7, 8 and 9 is that T T 1 63 in RuSr 2 EuCeCu 2 O 10+δ is dominated by hyperfine coupling within the CuO 2 layers and any additional hyperfine contribution from the spin fluctuations in the RuO 2 layers is small and therefore masked by the former. This interpretation is consistent with the known hyperfine coupling constants within the CuO 2 planes (37 T [56]) and if we assume that, like RuSr 2 GdCu 2 O 8 [13], the hyperfine coupling from Ru to Cu has an upper limit of 0.2 T. Thus, using equation (2) it can be shown that the origin of the inhomogeneity may be different from that observed in La 2-x Sr x CuO 4 . We note that La 2-x Sr x CuO 4 also has additional Cu A and Cu B sites which are believed to be due to 14 Cu sites with Cu-O-La or Cu-O-Sr apical oxygen bonds [42]. This is not expected in RuSr 2 EuCeCu 2 O 10+δ because the apical oxygen bond is Cu-O-Ru and Ru has a fixed valence near 5.

Conclusion
In conclusion, we find that RuSr 2 EuCeCu 2 O 10+δ ferromagnetically orders with a single transition temperature of 115 K. The magnetic ordering temperature is lower than that observed in the antiferromagnetic superconductors, RuSr 2 [19] and RuSr 2 GdCu 2 O 8 [18].     Also included is the estimated Eu 3+ contribution (dotted curve), the dc magnetization at 1 T after subtraction of the Eu 3+ contribution (dashed curve) and the best fit to the equation described in the text (solid curve).