Magnetic Frustration on a Kagomé Lattice in R_3Ga_5SiO_14 Langasites with R = Nd, Pr

In the R3Ga5SiO14 compounds, the network R of rare earth cations form well separated planes of corner sharing triangles topologically equivalent to a kagomé lattice. Powder samples and single crystals with R = Nd and Pr were prepared and magnetostatic measurements were performed under magnetic field up to 10 T in the temperature range from 1.6 K to 400 K. Analysis of the magnetic susceptibility at the high temperatures where only the quadrupolar term of the crystal electric field prevails, suggests that the Nd and Pr magnetic moments can be modeled as coplanar elliptic rotators perpendicular to the three fold axis of the crystal structure that interact antiferromagnetically. Nonetheless, a disordered phase that can be ascribed to geometric frustration persists down to the lowest temperature which is about 25 times smaller than the energy scale for the exchange interactions. PACS numbers: 61.66-f, 75.50-y, 75.30-Gw, 75.10.Dg Submitted to: J. Phys.: Condens. Matter Magnetic Frustration on a Kagomé Lattice in R3Ga5SiO14 Langasites 2 The langasite series, the prototype of which is the La3Ga5SiO14 compound (LGS), hence the acronym, belongs to a vast family of materials having the Ca3Ga2Ge4O14 type structure [1]. These materials rapidly attracted a strong interest because they show piezoelectric properties with better electro-mechanical coupling and weaker impedance than quartz or lithium niobate and tantalate [2]. They can be grown as high quality large single crystals, mainly by the Czochralski method, and are now used in surface acoustic wave filters in telecommunication devices and high temperature sensors. Crystallizing in a non centrosymmetric structure they exhibit quadratic non linear optical and electrooptical properties which are also intensively investigated [3]. On the other hand, probably because the interest was focused on the striking piezoelectric properties, the magnetic behaviors of these materials have not been studied until now, although several compounds contain arrays of magnetic cations. We report herein the magnetostatic properties of Nd3Ga5SiO14 (NGS) and Pr3Ga5SiO14 (PGS), which are isostructural to LGS. Inspection of the crystal structure and analysis of the magnetic susceptibility show that these provide us with a rare opportunity for a thorough investigation of geometric frustration in kagomé magnets, all the more as large single crystals can be grown. Geometric frustration is currently attracting strong attention for the numerous novel phenomena it might generate [4]. It is classically featured by macroscopic degeneracies which prevent magnetic order to set up, thus allowing for new states of matter and unconventional excitations to come out [5]. Unfortunately the materialization of these generally meets with difficulties because of secondary interactions (next neighbors or antisymmetric exchange and magnetoelastic interactions) or structural and stoichiometric imperfections, which induce ordering at low temperatures. Within the temperature range we considered, this is not the case with NGS and PGS. Langasite type compounds crystallize in the trigonal space group P321, with lattice parameters a = b = 8.07 Å and c = 5.06 Å (for NGS). The structure given in Table 1 for NGS and shown in Fig.1 contains four crystallographically non-equivalent cation sites, and the general formula can be written as A3BC3D2O14. The A site (3e at (≈ 0.42 0 0)) is 8-coordinated by oxygen anions forming a distorted square antiprism. The B site (1a at (0 0 0)) is octahedrally coordinated. The A and B site coordination polyhedra share edges to form a layer at z = 0. The C site (3f at (≈ 0.76 0 1/2)) and the D site (2d at (1/3 2/3 ≈ 0.53)) are both in tetrahedral coordination, the C site being larger than the D one. The CO4 and DO4 tetrahedra share corners to form a layer centered at z = 1 2 , and are also connected to the (A, B) cation layers above and below via corner sharing. In the NGS and PGS compounds [2], the rare earth trivalent cations occupy the large A sites, while the Ga cations occupy the B, C and half of the D sites. The Si cations are localized in the remaining half of the D sites. In Fig.2, the structural arrangement of the magnetic rare earth cations in NGS and PGS is outlined. It is formed by planes of corner sharing triangles perpendicular to the c-axis and separated from each other by the layer of tetrahedral C and D sites. The triangles are equilateral by symmetry, being centered by a 3-fold axis passing through the O1 and the mixed D Magnetic Frustration on a Kagomé Lattice in R3Ga5SiO14 Langasites 3 Table 1. Structural parameters for Nd3Ga5SiO14 determined by single crystal Xray diffraction on a Bruker-Nonius kappaCCD diffractometer (AgKα radiation) on a sphere of 0.1 mm radius, cut from a crystal grown by the floating zone technique. Data refined using the SHELX software [6]. R1= 0.0273, wR2 = 0.0495, GooF = 1.059. Cell parameters a = 8.066(1) Å, c = 5.062 Å. The Ga3/Si3 site is half occupied by each cation. Atom Site X Y Z Ueq(Å ) Nd 3e 0.41809(2) 0 0 0.00856(2) Ga1 1a 0 0 0 0.01092(9) Ga2 3f 0.76479(4) 0 1/2 0.00887(8) Ga3/Si3 2d 1/3 2/3 0.5350(2) 0.00706(8) O1 2d 2/3 1/3 0.8042(8) 0.0158(6) O2 6g 0.5341(4) 0.8514(3) 0.6916(6) 0.0201(4) O3 6g 0.2236(4) 0.0771(4) 0.7610(5) 0.0194(4) sites, and the intercationic distances are 4.18 Å for NGS and 4.21 Å for PGS. Exchange interactions are mediated by the O1 and O2 oxygen anions. For NGS, the Nd-O1-Nd angle is 110 with two equal Nd-O1 distances at 2.554 Å, and the Nd-O2-Nd angle is 106.5 with two Nd-O2 distances at 2.38 Å and 2.83 Å. Because of the lack of hexagonal symmetry, this is not an ideal kagomé lattice but considering only the shortest atom bridging interactions we get the same overall topology. Powders of the NGS and PGS compounds have been prepared by solid state reactions of stoichiometric amounts of high purity oxides at 1420C in air. X-ray powder diffraction patterns indicated that the samples were single phase and Rietveld refinements confirmed the crystal structures reported in Ref. [2]. Single crystals of size up to 40 mm in length by 5 mm in diameter were grown by the floating zone method using an image furnace, under a 99% Ar + 1% O2 atmosphere, at a growth rate of 10 mm/h [7]. Although it does not allow to grow very large crystals, this technique has the advantage of preventing a crucible pollution due to long crystal growth times at high temperature necessary for the Czochralsky or Brigman techniques. Moreover the size of the grown crystal is large enough to allow probing the spatially resolved dynamic spin-spin correlations by inelastic triple axis neutron scattering [8]. The unit cell and crystallographic orientations were checked using Laue photographs. The structure of a small piece of a NGS crystal was re-determined using single crystal X-ray diffraction with a kappaCCD x-ray diffractometer using AgKα radiation. The results are in grood agreement with those listed in Table 1 and those reported in [2]. We shall emphasize that to the accuracy of the experiment, the Nd site is fully occupied and no substitution of another cation for Nd is detected. The magnetostatic properties of NGS and PGS were investigated on single crystals under magnetic field up to 10 T in the temperature range from 1.6 K to 400 K on a purpose-built magnetometer using the anti-Helmholz two-coil axial extraction method Magnetic Frustration on a Kagomé Lattice in R3Ga5SiO14 Langasites 4 Figure 1. Polyhedral representation of the langasite structure. Two consecutive layers are shown. The four different cation sites are indicated. Figure 2. Atomic arrangement of Nd3Ga5SiO14 projected along the c-axis. The full lines linking the Nd cations enhance the magnetic net topologically equivalent to a kagomé lattice. Magnetic Frustration on a Kagomé Lattice in R3Ga5SiO14 Langasites 5 0 100 200 300 400 0 2x10 4x10 6x10 8x10 0 2 4 6 8 10 0.0 0.5 1.0 1.5 0 20 40 60 0.0 5.0x10 1.0x10 1.5x10 0.0 0.1 0.2 0.3 0.4 0.5 1/ (m 3 /m ol e f.u .) 1 H=1 T H // c H c T (K) Tcross=33 K M ( B /N d) H (T) T=100 K T=1.6 K M /M at Figure 3. Magnetostatic data measured on a NGS single crystal under magnetic field parallel (‖) and perpendicular (⊥) to the three fold axis ~c. Top : Magnetic isotherms at 1.6 K and 100 K. Bottom : Thermal variation of the inverses 1/χ‖ and 1/χ⊥ of the magnetic susceptibilities. The dashed lines stand for high temperature linear extrapolations for each field direction. Inset : zoom on the cross-over of 1/χ‖ and 1/χ⊥. and on a commercial Quantum Design MPMS SQUID magnetometer. We show in Fig.3 the magnetic isotherms measured on NGS at 1.6 K and 100 K when the magnetic field is applied parallel (‖) and perpendicular (⊥) to the three fold axis ~c of the crystal structure. We also give details of the thermal variation of the inverses 1/χ‖ and 1/χ⊥ of the initial magnetic susceptibilities deduced from the initial slope of the magnetic isotherms measured at different temperatures and from the thermal variation of the magnetization measured under a magnetic field of 1 T for the same two field orientations with respect to the ~c axis. Similar measurements on PGS are displayed in Fig.4. A large uniaxial magnetocrystalline anisotropy is evidenced in both compounds in the whole temperature range of the measurements with the ~c axis as the magnetization axis at low temperature changing to a hard axis on increasing the temperature at about 33 K in NGS and 127 K in PGS. A smaller magnetocrystalline anisotropy in the plane perpendicular to the ~c axis exists which however dwindles out rapidly on increasing the temperature. Analysis of the magnetic susceptibility can easily be performed at high temperature (T) by limiting the expansion of the quantum statistical average of the component of Magnetic Frustration on a Kagomé Lattice in R3Ga5SiO14 Langasites 6 0 2 4 6 8 10 0.0 0.5 1.0 0 50 100 150 200 250 300 350 0 2x10 4x10 6x10 8x10 0.0 0.1 0.2 0.3 H (T) T=300 K T=1.6 K