Evolution from insulator (x=0.003) to metal (x=1) of the Eu2+ local environment in Ca1−xEuxB6

The local environment of Eu 2+ s 4 f 7 , S =7/2 d in Ca 1− x Eu x B 6 s 0.003 ł x ł 1.00 d is studied by means of electron spin resonance s ESR d . For x & 0.07 the resonances have Lorentzian line shape, indicating an insulating environment for the Eu 2+ ions. For x * 0.07, the lines broaden and become Dysonian in shape, suggesting a change to metallic environment for the Eu 2+ ions, anticipating the semimetallic character of EuB 6 . The broadening is attributed to a spin-ﬂip scattering relaxation process due to the exchange interaction between conduction and Eu 2+ 4 f electrons. High ﬁeld ESR measurements for x * 0.30 reveal narrower and anisotropic linewidths, which are attributed to magnetic polarons and Fermi surface effects, respectively. © 2005 American Institute of Physics . f DOI: 10.1063/1.1855612 g


I. INTRODUCTION
Ca 1−x R x B 6 ͑R = rare earths, specially La͒ has become the focus of extensive investigations since the reported weak ferromagnetism ͑WF͒ at high T ͑T c Ϸ 600-800 K͒. 1 Efforts were devoted, both, theoretically 2-4 and experimentally 1,5 to establish the origin of this WF in Ca 1−x La x B 6 and its relationship with the conducting nature of R doped CaB 6 . Studies of the de Haas-van Alphen effect, the plasma edge in optical spectroscopy and the electrical resistivity support a semimetallic character for CaB 6 , whereas NMR, angleresolved photoemission ͑ARPES͒, thermopower, and other resistivity measurements suggest that CaB 6 is a well defined semiconductor. High-resolution ARPES revealed an energy gap of ϳ1 eV between the valence and conduction bands and a carrier density of the order of ϳ5 ϫ 10 19 cm −3 for CaB 6 single crystals. Depending on the crystal growth method, CaB 6 can also show WF and self-doping due to defects. The data for Ca 0.995 La 0.005 B 6 are strongly sample dependent and doubts about the intrinsic nature of the WF in these systems have been raised. It has been suggested that CaB 6 is a ϳ1 eV gap semiconductor and that the intrinsic WF is hidden by the ferromagnetism ͑FM͒ of Fe and Ni impurities at the surface of the crystals. 6 In contrast to CaB 6 , EuB 6 is a well established semimetallic material that orders FM at T c Ϸ 15 K. 7 The substitution of Ca 2+ by Eu 2+ impurities breaks the translational invariance of the lattice and introduces localized split-off states from the valence/conduction band. The energy of such state lies in the gap of the semiconductor and its spatial extension is of the order of one unit cell. An impurity band forms when the Eu bound states overlap, leading to an insulator to metal transition when a percolative network of impurity bound states is formed. This transition is revealed by the electron spin resonance ͑ESR͒ line shape.
Probing the local environment of Eu 2+ via ESR sheds light on the magnetic/nonmagnetic and metallic/nonmetallic properties of Ca 1−x Eu x B 6 . We present systematic Eu 2+ ESR measurements in single crystals of Ca 1−x Eu x B 6 for 0.003 ഛ x ഛ 1.00. For EuB 6 ͑x = 1.00͒ the broad ESR linewidth, ⌬H, was attributed to a spin-flip scattering relaxation due to the exchange interaction between the Eu 2+ 4f and conduction electrons. 7 The observed H , T, and angle dependence of ⌬H is then intimately related to the formation of magnetic polarons and the Fermi surface of the conduction states.

II. EXPERIMENTS
Single crystals of Ca 1−x Eu x B 6 ͑0.003Շ x Շ 1.00͒ were grown as in Ref. 1. The structure and phase purity were determined by x-ray powder diffraction and the crystal orientation by Laue x-ray diffraction. Most of the ESR experiments were carried out on ϳ1 ϫ 0.5ϫ 0.3 mm 3 single crystals in a Bruker spectrometer using a X-band ͑9.48 GHz͒ TE 102 room-T cavity and a Q-band ͑34.48 GHz͒ cool splitring cavity, both coupled to a T controller using a helium gas flux system for 4.2Շ T Շ 300 K. The Eu 2+ concentration was obtained from Curie-Weiss fits of the susceptibility data.

III. RESULTS AND DISCUSSION
The room-T X-band ESR spectra for H in the ͑110͒ plane along the angle of minimum ⌬H, i.e., ϳ30°͑ϳ55°͒ away a͒  Fig. 1. The data show an increase of ⌬H as x increases. Around x Ϸ 0.07 there is a crossover from Lorentzian to Dysonian line shape with an A / B ratio of ϳ2.3 corresponding to a skin depth much smaller than the size of the crystals. 8 The Dysonian line shape suggests a metallic environment for the Eu 2+ ions, confirming an increasing semimetallic character of Ca 1−x Eu x B 6 as x increases.
The angular dependence of ⌬H measured at X-and Q-band frequencies in the ͑110͒, ͑100͒ and ͑001͒ planes at 300 K and 50 K is presented in Fig. 2 for x = 0.30. Note that ⌬H is smaller and more anisotropic for high H ͑Q band͒. Above 50 K the anisotropy is independent of T.
⌬H for the spectra of Fig. 1 measured at X and Q bands is shown in Fig. 3͑a͒. For x տ 0.30, with the Eu 2+ ions in the metallic environment, ⌬H becomes smaller at higher H ͑Q band͒. The larger anisotropy of ⌬H, Q,X ⌬H ͓001͔ − Q,X ⌬H min , for Q band than for X band is seen in Fig. 3͑b͒. Figure 3͑c͒ shows that the reduction, Q ⌬H min − X ⌬H min , is nearly x independent. This suggests that the dipolar interaction between Eu 2+ ions cannot be the responsible mechanism for the broadening of the resonance as x increases. 9 The ESR results of Fig. 1 for Eu 2+ in Ca 1−x Eu x B 6 show three different concentration regimes. For x Ͻ 0.07 the line shapes are Lorentzian, therefore, the local environment of the Eu 2+ sites is insulating. In this regime the spectra show partially resolved fine structure and an overall minimum of ⌬H at 30°away from the ͓001͔ direction in the ͑110͒ plane. 7 For 0.07ഛ x ഛ 0.10 the line shape starts to show an admixture of Lorentzian and Dysonian shape, i.e., it begins to display metallic character. For x ജ 0.30 the line shape is pure Dysonian, i.e., the local environment is metallic with conduction electron spin diffusion. 8 For small x, each Eu 2+ represents a charge neutral substitution that, as a consequence of the broken translational invariance, gives rise to a bound state in the gap of the semiconductor. The impurity states are localized within the extension of about a unit cell. As the number of impurity states increases with x, they start to overlap, form a band, and eventually yield a percolative network. The critical concentration for nearest-neighbor site percolation on a simple cubic lattice is x c = 0.307. 10 The percolation threshold is reduced to x c = 0.137 if next-to-nearest neighbors are included, which correspond to neighbors in the ͓110͔ directions. Third H and x dependence of the ESR ⌬H at room temperature: ͑a͒ minimum linewidth at X and Q bands, X,Q ⌬H min , ͑b͒ difference between the maximum and minimum linewidths, Q,X ⌬H ͓001͔ − Q,X ⌬H min , and ͑c͒ difference between the minimum linewidths, Q ⌬H min − X ⌬H min . The percolation regime of the Eu 2+ impurity bound states at 0.10Շ x Շ 0.30 is shown as a shaded area. neighbors are along the diagonals of the cube, but this direction is blocked for the wave functions because of the large B 6 2− anions. From our results in Fig. 1, it is reasonable to assume that the transition from insulator to metal occurs at x Ϸ 0.14. Hence, for x Ͻ x c Ϸ 0.14 the system is insulating. For x Ͼ x c , the system is metallic and the spin diffusion of the conduction electrons gives rise to a Dysonian line shape.
With increasing x the impurity band gradually smears the semiconducting gap and the system evolves to a semimetal for x =1͑EuB 6 ͒. 7 For x տ 0.30, ⌬H has an overall cubic anisotropy corresponding to the superposition of three tetragonal environments ͓⌬H min is at 55°in the ͑110͒, see Fig. 2͔. This differs from the case for x ഛ 0.07 where the local symmetry is genuinely cubic. There are two possible scenarios to explain these findings. First, the origin for the tetragonal symmetry may be associated with the Eu/Ca substitution. This scenario assumes that the crystal field of an Eu 2+ ion is determined by the nearest-neighbor cation ions. If a Eu ion is surrounded by five Eu and one Ca, the local symmetry is tetragonal. Since the Ca ion can be along any one of the axis, there is a superposition of tetragonal symmetries along the three directions. The overall spectrum is then cubic with inhomogeneous broadening. However, more than two Ca neighbors can give rise to a trigonal component in ⌬H, which was not observed. However, this mechanism does not account for the anisotropy observed in stoichiometric EuB 6 . 7 It would require a much larger number of Eu vacancies than the claimed for these samples to explain the tetragonal dependence of ⌬H. 11 The second possible scenario considers the relaxation of the Eu 2+ spins into the conduction electron bath and the concomitant spin diffusion. The conduction electrons occupy small ellipsoidal pockets centered at the X points of the Brillouin zone, i.e., at ͑± / a ,0,0͒ , ͑0, ± / a ,0͒, and ͑0,0, ± / a͒, 12 where a is the lattice constant. The drift of the diffusion is predominantly into the direction of the major axis of the ellipsoids, i.e., along one of the axes of the cube. Thus, each relaxation process gives rise to a tetragonal anisotropy of ⌬H. The superposition of the relaxation into the three directions is then expected. This mechanism explains why there is a tetragonal dependence in the metallic regime but not in the insulating one. The mechanism also applies to stoichiometric EuB 6 .
⌬H for EuB 6 was attributed to a homogeneous resonance with the main contribution to ⌬H involving spin-flip scattering relaxation due to the exchange interaction between the conduction and Eu 2+ 4f electrons. 7 The H , T, and angle de-pendence of ⌬H suggests that magnetic polarons and Fermi surface effects dominate the spin-flip scattering in EuB 6 . The second scenario is supported by the ESR and magnetoresistance data. Figures 2 and 3 show that the high-H spectra have narrower lines for x տ 0.30, indicating that the spin-flip mechanism is suppressed with field, which is consistent with the formation of polarons. This is similar to EuB 6 . The negative magnetoresistance observed in Ca 1−x Eu x B 6 for x տ 0.3 also supports the presence of magnetic polarons. 13

IV. CONCLUSIONS
The change in the line shape of the ESR spectra shows an evolution from insulating to semimetallic of the Eu 2+ local environment in Ca 1−x Eu x B 6 as a function of x. The crossover between these two regimes is approximately in the range 0.10Շ x Շ 0.30. For x տ 0.30 ⌬H shows: ͑i͒ a field narrowing, which is attributed to magnetic polarons, 7 and ͑ii͒ an overall cubic angular dependence corresponding to the superposition of three tetragonal components along the ͓001͔ axes, which is attributed to the relaxation mechanism and the Fermi surface. 7