Noncubic symmetry in Ca 1− x Eu x B 6 „ 0.15 › x Ï 1.00 … : An electron-spin-resonance study

The Eu 2+ (cid:1) 4 f 7 , S =7/2 (cid:2) g value in Ca 1− x Eu x B 6 (cid:1) 0.15 (cid:1) x (cid:2) 1.00 (cid:2) was measured by means of electron spin resonance at two frequencies (cid:1) ﬁelds (cid:2) , 9.4 (cid:1)(cid:3) 3.4 kOe (cid:2) and 34.4 GHz (cid:1)(cid:3) 12.1 kOe (cid:2) . The g value was found to be anisotropic and magnetic-ﬁeld dependent. The amplitude of the anisotropy increases at low temperatures. The observed angular and temperature dependences of the g value suggest tetragonal symmetry caused, presumably, by a distortion along a direction perpendicular to the largest crystal face, the (cid:4) 001 (cid:5) direction. Due to the platelet shape of the samples, part of the anisotropy of the g value can also be attributed to demagnetization effects. The g values decrease at higher ﬁelds, which is interpreted in terms of a two-band model involving an exchange interaction between the localized Eu 2+ 4 f 7 electrons with conduction Eu 2+ 5 d -like electrons and B 2 p -like holes. ©

Over the past decades the cubic hexaboride compounds RB 6 ͑R = rare/alkaline earths, space group 221, Pm3m͒ have been the subject of intensive studies, both experimental and theoretical, due to their variety of exotic effects and interesting physical properties such as ferromagnetism, weak ferromagnetism, metal-insulator transition, large negative magnetoresistance, quadrupolar ordering, Jahn-Teller effect, superconductivity, heavy fermion, fluctuating valence, and Kondo lattice behaviors. [1][2][3][4][5][6][7][8][9][10][11][12][13] Among them the semimetal EuB 6 is particularly interesting because of the formation of magnetic polarons, changing the magnetic and transport properties, and the two transitions observed at T c1 = 15.3 K and T c2 = 12.7 K. 4,6,14 The one at T c1 is believed to correspond to the percolation transition of the polarons and is accompanied by a semimetal to metal transition, while below T c2 all Eu 2+ spins participate in the ferromagnetic ͑FM͒ longrange order.
In previous reports 15, 16 we have studied the evolution from insulator ͑x =0͒ to semimetal ͑x = 1.00͒ in Ca 1−x Eu x B 6 by measuring the Eu 2+ ͑4f 7 , S =7/2͒ electron-spin-resonance ͑ESR͒ linewidth ͑⌬H͒. Due to the broken translational invariance in an alloy, each Eu 2+ ion introduces a bound state in the gap of the insulator CaB 6 . Our results indicate that at x Ϸ 0.15 the bound states percolate leading to a metallic environment with a spin-flip relaxation process involving magnetic polarons and the symmetry of the Fermi surface. x Ϸ 0.15 corresponds to the site percolation of random nearestand next-to-nearest-neighbor bonds. Note that the next-to-next-to-nearest-neighbor bonds ͓͑111͔ direction͒ are blocked for the propagation of the wave functions by the large B 6 anions.
In the present work we report on the field dependence of the Eu 2+ ͑4f 7 , S =7/2͒ ESR g shift and its angular dependence. We explain the field dependence of the g shift in terms of the exchange interaction between the localized Eu 2+ 4f 7 electrons with the conduction Eu 2+ 5d-like electrons and B 6 2− 2p-like holes. We attribute the angular dependence of the g value and its T dependence to a tetragonal distortion along the directions perpendicular to the ͑001͒ natural growth faces of the crystal. The distortion is believed to arise from the surface of the crystal and propagates deep into the crystal. This effect, which is present only in the metallic phase, is enhanced by the crystalline field splitting of the 5d electrons at low temperatures. Due to the platelet shape of the samples, part of the anisotropy of the g value can also be attributed to demagnetization effects.
Platelet ͑ϳ1.2ϫ 0.9ϫ 0.2 mm 3 ͒ single crystals of Ca 1−x Eu x B 6 ͑0.003Շ x ഛ 1.00͒ were grown, as described in Ref. 2. The structure and phase purity were checked by x-ray powder diffraction and the crystal orientation determined by Laue x-ray diffraction. The faces of natural growth of the crystals are called ͑001͒ planes and are relevant to the g value anisotropy investigation. The ESR experiments were performed in a Bruker spectrometer using an X-band ͑9.48 GHz͒ TE 102 room-T cavity and a Q-band ͑34.48 GHz͒ cool split-ring cavity, both coupled to a T controller using a helium gas flux system for 4.2Շ T Շ 300 K. The ESR spectra were analyzed in terms of Dyson's theory for the resonance line shape. 17 In the pertinent range of T, the resistivity of our crystals changes from ϳ0.5 to ϳ 5 m⍀ cm, which corresponds to microwave ͑X and Q bands͒ penetration skin depths of about 5 -25 m. M͑T , H͒ measurements for 2 Շ T Շ 300 K were taken in a Quantum Design superconducting quantum interference device-reciprocating sample option ͑SQUID-RSO͒ dc magnetometer. The Eu 2+ concentration in our crystals was determined from Curie-Weiss fits to the susceptibility data. The experimental data presented in this work were obtained on the same samples used in our previous work. 15,16 The high quality of the crystals was determined by magnetoresistance and heat-capacity measurements. 15,16 Figures 1 and 2 present the angular dependence of the g value for the plateletlike crystals measured at the X and Q bands in the ͑110͒, ͑100͒, and ͑001͒ planes at ϳ297 and ϳ55 K for x = 0.30 and x = 1.00, respectively. Similar results were obtained for the x = 0.60 crystal ͑not shown here͒. The ͑001͒ plane coincides with the largest crystal face. The data show the following features: ͑i͒ The angular dependence of the g value displays a surprising tetragonal symmetry with the twofold axis being perpendicular to the largest crystal face, 18 in spite of the overall cubic symmetry found for the anisotropy of the linewidth ͑see Figs. 6 and 7 in Ref. 16͒; ͑ii͒ the amplitude of the g value anisotropy, g Ќ − g ʈ , is nearly H and x independent; ͑iii͒ this amplitude increases at low T; and ͑iv͒ the g value decreases with H.
The reduction in the positive g shift ͑⌬g = g − 1.988͒ at high fields ͑see Q-band data in Figs. 1 and 2͒ may be under-stood in terms of a two-band model 19,20 involving the exchange interaction between the localized Eu 2+ 4f 7 electrons with ͑i͒ the conduction Eu 2+ 5d-like electrons and ͑ii͒ the B 2p-like holes. 21 The exchange interaction with the 5d-like electrons is assumed to be of atomic type, J at e Ͼ 0, and that with the B 2p-like holes of covalent origin, J cv h Ͻ 0. The magnitudes of the exchange constants have been estimated in Ref. 21 to be ͉J at e ͉Ϸ100 meV and ͉J cv h ͉Ϸ5 meV. The latter is expected to be small because of the almost ionic bond nature of the crystal. Thus, the g shift can be written as ⌬g = ⌬g e + ⌬g h = ͓J at e ͑0͒͗s z e ͘ + J cv h ͑0͒͗s z h ͔͘ / ͑ B H͒, where J at e ͑0͒ and J cv h ͑0͒ are the q = 0 component ͑zero-momentum transfer between electrons͒, 22 and ͗s z e ͘ and ͗s z h ͘ are the spin polarizations of the electrons and holes, respectively. The semimetal is not compensated, since it contains more electrons in the conduction band than holes in the valence band ͑B 6 defi-ciency͒. Since ͉J at e ͉ ӷ ͉J cv h ͉, the g shift is dominated by the electrons and necessarily positive. For low fields the g shift is then given by ⌬g / g = J at e ͑0͒ F e + J cv h ͑0͒ F h , where F e and F h are the carrier densities of electrons and holes at the Fermi level, respectively. As the field increases, the atomiclike 5d-electrons spin polarize and ⌬g Ϸ J at e ͑0͒͗s z e ͘ / ͑ B H͒ decreases with H, as observed in Figs. 1 and 2.
The unexpected tetragonal symmetry revealed by the angular dependence of the g value, shown in Figs. 1 and 2 for x տ 0.30, is H and x independent within the accuracy of our experiments. The data were also taken at T ӷ T c1 , i.e., at temperatures where the magnetic short-range order is small. Since the ESR signal in plateletlike crystals mainly arises  from the Eu 2+ ions within the microwave skin depth of the two largest crystal faces, the g value anisotropy must be caused by a tetragonal distortion within the microwave skin depth of the crystal with the fourfold symmetry axis along the ͓001͔ direction ͑see Figs. 1 and 2͒. A strong demagnetization due to the platelet shape of the sample would give rise to a similar effect.
Moreover, since the g value anisotropy is almost the same for X and Q bands, the distortion should be nearly uniform over a distance of the order of the the skin depth of the corresponding microwaves. Thus, the distortion, presumably arising at the surface, must penetrate deeply into the crystal. The amplitude of the g value angular dependence also increases at lower T, which is consistent with an increasing distortion as T is lowered.
A possible explanation of this symmetry reducing distortion of the lattice is the following. The binding energy of the crystal is predominantly ionic and given by the Madelung sum of the Coulomb interaction between all the ions. For the bulk, choosing a Eu 2+ as the origin, this sum can be viewed as a sum over shells of equidistant ͑measured from the ori-gin͒ ions. These shells have alternating charges, thus leading to effective ͑radial͒ dipolar contributions. Since the Coulomb interaction falls off only as the inverse of the distance, a very large number of shell pairs will contribute to the binding energy. At a distance z from the surface of the crystal only spherical shells of radius less than z are complete. Shells of radius larger than z are incomplete in the direction of the surface. Hence, the dipoles contributing to the binding energy at distances larger than z in the direction of the surface are missing. This imbalance introduces an axial symmetry and has as a consequence, an elongation of the lattice spacing in the ͓001͔ direction. Hence, the crystal has effectively a tetragonal symmetry with ͓001͔ being the fourfold axis. This distortion affects the crystalline splitting of the 5d electrons and via the exchange J at e induces a g value anisotropy of Eu 2+ in the metallic phase. Since the carrier density increases as T is lowered, the anisotropy should increase with decreasing T.
In summary, we have reported the field, angular, and temperature dependences of the g value in the ESR of Ca 1−x Eu x B 6 for 0.30Շ x ഛ 1.00. The observed field-reduced g shift was interpreted in terms of an exchange interaction between the localized Eu 2+ 4f 7 electrons with two types of conduction electrons ͑two-band model͒, Eu 2+ 5d-like electrons and B 2p-like holes. The tetragonal angular dependence of the g value and its temperature dependence were associated with a crystal distortion within ͑or beyond͒ the microwave skin depth, with the tetragonal axis perpendicular to the crystal ͑001͒ faces. It should be stressed that the anisotropy of the g value appears to be at variance with x-ray and neutron-scattering measurements, where a departure from cubic symmetry was not observed. However, a small lattice distortion amplified by the 5d-electron crystalline field could lead to an effect measurable by ESR but too small to be detected by x rays and neutrons. 7 Demagnetization effects due to the shape of the sample can also contribute to the anisotropy of the g value.
The support of this work by FAPESP, CNPq, National Science Foundation, and U.S. Department of Energy is acknowledged.