Gd concentration dependence of the spin reorientation critical ﬁeld

ESR measurements of the microwave absorption signal associated with weak ferromagnetism in single crystals of Eu 2 (cid:50) x Gd x CuO 4 are presented for X band (cid:126) 9.5 GHz (cid:33) and L band (cid:126) 1.2 GHz (cid:33) as a function of the Gd concentration. The strong absorption observed at low magnetic ﬁelds was interpreted, for samples with low Gd concentration, as due to a ﬁeld-induced spin reorientation transition occurring at a critical ﬁeld H c , coincident with the in-plane magnetic anisotropy effective ﬁeld H eff y . For larger x the Cu-Gd magnetic interaction needs to be considered leading to smaller H c values. Our measurements show that for Gd concentrations in the range 0 (cid:60) x (cid:60) 1 the experimental data can be very well ﬁtted with parameters derived from previous measurements. This fact indicates that these compounds have nearly the same in-plane anisotropy effective ﬁeld, in spite of the small changes in lattice parameters. For x (cid:53) 2 lattice distortions increase causing an H c larger than the expected one. © 1996 American Institute of Physics. (cid:64) S0021-8979 (cid:126) 96 (cid:33) 03008-X (cid:35)


I. INTRODUCTION
The rate earth cuprates RE 2 CuO 4 ͑REϭPr,..., Tm͒, parent compounds of the so-called n-type high T C superconductors, crystallize in the tetragonal Nd 2 CuO 4 TЈ structure. 1 Pr 2 CuO 4 has the largest a lattice parameter which decreases monotonically for the heavier RE compounds due to the smaller rare earth ion size. 2 This lattice reduction causes a distortion of the CuO 2 planes for Eu 2 CuO 4 ͑aϭ3.910 Å͒ and heavier compounds, consisting of a displacement of the inplane oxygens ͓called O͑1͔͒ from its centrosymmetrical position. These displacements seem to be ordered, and several superstructures have been found in single crystals with diffraction techniques. 2,3 Copper moments order antiferromagnetically ͑AF͒ below room temperature for the whole series. However, coincident with the boundary for lattice distortions, a weak ferromagnetic ͑WF͒ component in the magnetization develops, that was attributed to a canting of the copper moment away from a perfect AF alignment. 4 Several experimental techniques have been used to characterize the WF behavior. Among them, microwave absorption proved to be very useful to elucidate the magnetic behavior of the compounds near the WF boundary. 5 X-and Q-band experiments in Eu 2 CuO 4 single crystals, slightly doped with Gd, have shown that the WF moment lays in the CuO 2 plane pointing parallel to an easy axis defined by the field cooling ͑FC͒ magnetic field and coincident with a ͓110͔ crystallographic direction ͓͑110͔ FC ͒. When the external field is applied perpendicular to this axis a field-induced spin reorientation transition occurs at a critical field H c . 5 More recently 6 it was shown that, for samples with larger amounts of Gd, the interaction between the WF ordered Cu lattice and the Gd paramagnetic ͑PM͒ lattice must be taken into account in order to explain several anomalies found in the EPR spectra. In this article we present the Gd concentration dependence of H c obtained from X-band measurements. We also discuss the L-band results within the proposed model.

II. MODEL
The following expression for the magnetic free energy of the coupled PM-WF system was proposed: 6 m WF and M Gd are the Cu-WF and Gd-PM magnetizations, 2K eff y m WF ϭ H eff y and 2K eff z m WF ϭ H eff z are in-plane and out-ofplane magnetic anisotropy fields, Ј is the Cu-Gd coupling constant and Gd ϭxC/(Tϩ⌰) is the Gd molar magnetic susceptibility. This effective free energy describes the equilibrium and the low-energy excitations of the system. The resonance modes can be obtained solving a 6ϫ6 dynamical matrix for m WF and M Gd . Two modes are obtained: a highenergy WF-like mode, and a low-energy PM-like one.
In Fig. 1 we show both modes, as calculated for Ј Gd ϭ0 ͑dashed curves͒ and Ј Gd 0 ͑solid curves͒. For Ј Gd ϭ0 a softening of the WF mode would occur at a critical field H c ϭH eff y , coincident with the field-induced spin reorientation transition when H is applied perpendicular to the easy axis ͑i.e., ϭ90°͒. Note that for X and L bands a resonance absorption is expected only for ϭ90°. For Ј Gd 0 the critical field is reduced by a factor 1 ϩ Ј Gd giving and the WF mode does not soften to zero. This would imply that no resonance arising from the WF ordered Cu lattice should be observed at X and L bands. However, a maximum in the microwave absorption may be expected due to nonresonant loses as described in Ref. 5. In addition an energy gap opens in the PM-like mode for Hϭ0 given by Due to the temperature dependence of Gd (T) the gap tends to zero for Tϭ0 K and increases for TϾ0 because other parameters are only weakly temperature dependent. 6 For TϾT N the energy gap becomes zero again. Because of the anticrossing of the coupled modes an ''anomaly'' is also predicted in the PM-like branch which softens to zero at H c .

III. RESULTS AND DISCUSSION
Eu 2Ϫx Gd x CuO 4 single crystals were grown following standard flux techniques in Pt crucibles. 7 In all cases crystals grew in the shape of small platelets with the c crystallographic axis perpendicular to the axis. EPR measurements were made in a Bruker ESP 300 spectrometer at X band ͑9.5 GHz͒ and L band ͑1.2 GHz͒ between 120 and 300 K.
Although the softening of the WF mode at H c is not complete for ϭ90°͑see Fig. 1͒, originating a strong reduction in the intensity of the WF line at the X band, it could still be clearly detected in all samples due to nonresonant loses. 5 In L band, however, no line was found for samples with low Gd content (0рxр0.2) indicating that the gap was large enough to prevent even the observation of nonresonant losses. We have determined the Gd concentration dependence of H c , coincident with the X-band resonance field of the WF line, at Tϭ120 K and with HЌ[110] FC . The experimental data, presented in Fig. 2, were fitted using Eq. ͑2͒ in the range 0рxр1. We obtain the following values for the in-plane anisotropy effective field and the Cu-Gd coupling constant: H eff y ϭ 425(5) G and Јϭ1.2͑1͒ϫ10 5 G/͑ ␤ /Cu-atom͒. These are consistent with the values found in Refs. 5 and 8 ͑for samples slightly doped with Gd͒ and in Ref. 9, respectively. Note that the experimental data can be explained with a single value of the in-plane anisotropy field for all compounds (0рxр1), although the lattice size varies and consequently the displacement of the oxygen ions might change. We did not include the value measured for Gd 2 CuO 4 in the fit because it was proposed 10 that for this compound Eq. ͑2͒ should be corrected due to the presence of a metamagnetic-like transition at low fields. In Ref. 10 the value of H eff y for xϭ2 was estimated, from dc magnetization measurements, to be Ϸ1200 G at Tϭ120 K. This value is nearly three times larger than the one measured for samples with lower Gd concentrations 8 probably due to the larger lattice distortions. Correspondingly, the measured H c value is almost three times larger than that predicted assuming a constant H eff y ͑see Fig. 2͒. In Fig. 3 we show the EPR spectra of Gd 2 CuO 4 mea- sured at L band for Tϭ250 K. The PM mode in absence of coupling to the Cu lattice would occur at PM /␥ Gd ϭ410 G. Due to the large linewidth of the Gd 3ϩ EPR line in Gd 2 CuO 4 measured at X band 4 ͑⌬H pp Ϸ1500 G͒ a superposition of the absorptions occurring at negative and positive fields would cause a strongly asymmetric signal with a broad minimum at Ϸ750 G. Surprisingly a narrow and very intense line is observed at a lower field, H r Ϸ100 G. The origin of this absorption may be explained looking at the behavior of the PM-like mode in Fig. 1. From the X-band results we estimate the energy gap of the PM-like mode at Tϭ120 K, ͑ PM /␥ Gd ͒ Hϭ0 Ϸ300 G, lower than the L-band frequency L /␥ Gd ϭ410 G. Thus the microwave absorption should occur at fields lower than that corresponding to gϭ2. When the temperature is increased H r moves to lower fields ͑see Fig.  4͒ and the line disappears at Tϭ265 K, i.e., 20 K below T N . As we have mentioned above, the value of the energy gap of the PM-like mode is expected to increase as T rises and hence Tϭ265 K would indicate the temperature where PM equals L .
In this description the reduced linewidth of the PM-like absorption may be associated with coupled excitations. In fact, a strong mixture of modes is expected especially when an anticrossing of modes occurs at H c .
In summary, we have analyzed the variation of the spin reorientation critical field, H c ϭ H eff y /(1 ϩ Ј Gd ), as a function of Gd concentration. We have found that the decrease of H c for increasing x may be explained ͑in the range 0рxр1͒ in terms of the magnetic coupling between the Cu-WF and the Gd-PM lattices. We have also discussed the origin of the absorption line measured at L band and suggested that it is due to the PM-like branch of the PM-WF coupled modes.

ACKNOWLEDGMENT
One of us, A. B., acknowledges support from CONICET ͑Argentina͒ through a post-doctoral fellowship.