Ternary borides Nb$_7$Fe$_3$B$_8$ and Ta$_7$Fe$_3$B$_8$ with Kagome-type iron framework

Two new ternary borides $TM$$_7$Fe$_3$B$_8$ ($TM$ = Nb, Ta) were synthesized by high-temperature thermal treatment of samples obtained by arc-melting. This new type of structure with space group $P$6/$mmm$, comprises $TM$ slabs containing isolated planar hexagonal [B$_6$] rings and iron centered $TM$ columns in a Kagome type of arrangement. Chemical bonding analysis in Nb$_7$Fe$_3$B$_8$ by means of the electron localizability approach reveals two-center interactions forming the Kagome net of Fe and embedded B, while weaker multicenter bonding present between this net and Nb atoms. Magnetic susceptibility measurements reveal antiferromagnetic order below $T_N$ = 240 K for Nb$_7$Fe$_3$B$_8$ and $T_N$ =265 K for Ta$_7$Fe$_3$B$_8$. Small remnant magnetization below 0.01 $\mu_B$/f.u. is observed in the antiferromagnetic state. The bulk nature of the magnetic transitions was confirmed by the hyperfine splitting of the M\"o{\ss}bauer spectra, the sizable anomalies in the specific heat capacity, and the kinks in the resistivity curves. The high-field paramagnetic susceptibilities fitted by the Curie-Weiss law show effective paramagnetic moments $\mu_{eff}$ about 3.1 $\mu_B$/Fe in both compounds. The temperature dependence of the electrical resistivity also reveals metallic character of both compounds. Density functional calculations corroborate the metallic behaviour of both compounds and demonstrate the formation of a sizable local magnetic moment on the Fe-sites. They indicate the presence of both antiferro- and ferromagnetic interactions.


Introduction
Transition-metal borides are remarkable for their physical, chemical and mechanical properties, in particular, combining refractory behavior, high hardness, chemical inertness, and metallic conductivity. [1][2][3][4][5][6][7] To exemplify a few well-known materials of high technological relevance, there are boridecontaining metallic glasses, 8 LaB 6 cathodes for electron microscopes, 9 and Nd 2 Fe 14 B-based permanent magnets. 10 On the other hand, soft magnetic properties particularly found in ferrous amorphous boron-containing alloys have led to several highly useful applications, such as electro-magnetic materials. 11,12 The structural complexity of electron-deficient boron and its compounds is caused by the intricate ways how their valence requirements are satisfied. [13][14][15] Therefore, in metal-borides this not only gives rise to the formation of one-, two-, or three-dimensional arrangements of covalently bonded boron atoms, [16][17][18][19][20][21] but also, due to complex structures, results in a multitude of physical interactions which can lead to superconductivity [22][23][24][25][26] or magnetism. [27][28][29][30][31] In a crystal structure, these interactions are governed by the spatial arrangement and coordination of the constituents which carry a magnetic moment. Accordingly, in borides phases with exotic and complex magnetic ground states can be expected and merit explorative research. To this purpose, we investigated the ternary TM-Fe-B (TM = Nb, Ta) systems which have been studied since 1960s. The hitherto known ternary compounds in these two systems are TMFeB, TM 2 FeB 2 , TM 3 Fe 3 B 4 and TaFeB 3 . [32][33][34][35] We attempted to synthesize TM 3 Fe 3 B 4 but failed. Instead, the analysis of samples with nominal compositions TM 3 Fe 3 B 4 revealed the appearance of new compounds TM 7 Fe 3 B 8 , which crystallize in a primitive hexagonal lattice. This new type of structure comprises TM slabs containing planar hexagonal boron rings and iron centered TM columns in a Kagome type of arrangement (see below). The interest in the Kagome lattices of magnetic ions is triggered by their strongly frustrated nature. No ordered antiferromagnetic magnetic configuration can be stabilized in such a geometry, and an exotic spin-liquid ground state is formed instead. 36,37 However, in order to suppress any ordering a two-dimensional isotropic next-neighbor coupling is the prerequisite. Systems with the Kagome-like arrangement of magnetic ions range from Cu 2+ minerals 38,39 to Ce-based intermetallic compounds, 40 but only few of them reveal the anticipated spin-liquid state at low temperatures. [41][42][43] Even subtle geometrical distortions or interactions beyond nearest neighbors are usually sufficient to alleviate the frustration and stabilize the magnetic order. 44,45 The majority of the kagome-lattice compounds reported so far are magnetic insulators. Kagome lattices in itinerant systems are by far more exotic, and no magnetic metals with the ideal kagome geometry have been reported to date. In the following, we fill this gap by investigating the TM 7 Fe 3 B 8 borides, where three-fold symmetry of the crystal structure ensures perfect frustration on individual triangles of the kagome lattice. However, these compounds are magnetically ordered with relatively high Néel temperatures. We suggest that strong interplane couplings arising from the geometrical proximity of the kagome planes may be instrumental in stabilizing the magnetically ordered state in these novel ternary Fecontaining borides.

Sample preparation
The following elements were used to prepare the samples: Ta

Powder and single-crystal X-ray diffraction
Powder X-ray diffraction (XRD) data were collected on a HUBER G670 imaging plate Guinier camera equipped with Co K 1 radiation ( = 1.78897 Å). Phase analysis and indexing were performed using the WinXPow program package. 46 Lattice parameters were refined by least-squares fitting with LaB 6 internal standard within the program package WinCSD. 47 TM 7 Fe 3 B 8 single crystals were selected from the samples with the nominal compositions TM 3 Fe 3 B 4 . Single crystal diffraction data were collected on a R-Axis Rapid or Rigaku AFC7 diffractometer equipped with Mercury CCD detectors (Mo K  radiation,  = 0.71073 Å). Absorption correction was made using a multi-scan procedure. The crystal structures were solved by a direct phase determination method and refined by a full-matrix least-squares procedure within the program package WinCSD. 47 Details on the single-crystal diffraction data collection and structural refinement are listed in Table 1.

Metallography
Pieces with several millimeters size were cut from the annealed samples for metallographic investigations. They were embedded in conductive resin and then subjected to a multistep grinding and polishing process to achieve highquality polished surfaces. The microstructures were investigated by optical microscopy (Axioplan2, Zeiss) as well as scanning electron microscopy (Philips XL 30 with a LaB 6 cathode, FEI). The chemical compositions were analyzed by means of energy dispersive X-ray spectroscopy (EDXS, Philips XL 30) and wavelength dispersive X-ray spectroscopy (WDXS, Cameca SX 100, W cathode, S-UTW-Si-(Li) detector). The determination of boron content by microprobe WDXS is challenging due to the general issue that the measured intensities are related to the mass concentrations, while boron is extremely light as compared to niobium, tantalum, and iron. Also, the very low energies of boron X-ray lines give rise to a strong influence of absorption effects. Therefore, completely detected intensities originating from the uppermost surface layer and its extending area are strongly influenced by the quality of the local area that is probed by the electron beam, and the energy and shape of the boron X-ray lines are influenced significantly by the local chemical environment and bonding situation of boron. under an acceleration voltage of 15 kV with dwelling time 3 seconds for each position. The intensity of B K 2 line was measured by applying the same acceleration voltage and current used for the Ta compound, however, due to the much weaker intensity of B K 2 line, dwelling time for each position was 1136 seconds.

Transmission electron microscopy (TEM) observations
Electron diffraction and high-resolution TEM (HRTEM) observations were both performed using a field-emission electron microscope JEM 2100F (JEOL, Japan) operating at 200 kV. HRTEM image simulations were carried out with program STEM_CELL. 50

Physical Properties
Magnetization at external magnetic fields  0 H ranging from 0.01 T to 7 T (temperature range 1.8 K-400 K) was measured in a SQUID magnetometer (MPMS XL-7, Quantum Design) on polycrystalline samples. The electrical resistance was recorded by a four contact method using low-frequency alternating current (ACT option, PPMS, Quantum Design) on small barshapes pieces in zero field and in a field  0 H = 9 T. Heat capacity was determined by a relaxation method (HC option, PPMS, Quantum Design) in fields  0 H of 0, 3, 6, and 9 T.
Mossbauer spectroscopy 57 Fe Mössbauer spectra were recorded at 294 K and 4.3 K. The measurements were performed with a standard constant acceleration spectrometer in transmission geometry in a continuous flow cryostat with the sample kept at helium atmosphere. The 57 CoRh source was mounted on the driving system and kept at room temperature. All center shift (CS) data are given relative to this source. Calibration of the velocity scale was carried out with α-Fe foils. The spectra were analysed by solving the full Hamiltonian including electrostatic and magnetic hyperfine interactions. Sample thickness was taken into account by the method of Mørup and Both. 51

Electronic structure calculations
The electronic structure of TM 7 Fe 3 B 8 was calculated within the framework of density functional theory (DFT) using the fullpotential code FPLO. 52 The local density approximation (LDA) to the exchange-correlation potential was chosen. 53 Reciprocal space was sampled by a fine k-mesh with 630 points in the symmetry-irreducible part of the first Brillouin zone for the crystallographic unit cell of TM 7 Fe 3 B 8 and 190 points for the supercell doubled along the c direction. Convergence with respect to the k-mesh was carefully checked. For the spinpolarized calculations, the highest crystallographic symmetry compatible with the magnetic ordering pattern was used in order to facilitate the convergence.

Chemical bonding analysis
Analysis of chemical bonding was performed for Nb 7 Fe 3 B 8 using the lattice parameters and atomic coordinates from the crystal structure refinement of single-crystal X-ray diffraction data (Tables 1 and 2). The TB-LMTO-ASA program package 54 was employed using the Barth-Hedin exchange potential 55 for the LDA calculations. The radial scalar-relativistic Dirac equation was solved to obtain the partial waves. 56 Addition of empty spheres was not necessary because the calculation within the atomic sphere approximation (ASA) includes corrections for the neglect of interstitial regions and partial waves of higher order. 57 The following radii of the atomic spheres were applied for the calculations r(Nb1) = 1.69 Å,  (1), respectively.

TEM investigation
The TEM study of Ta 7 Fe 3 B 8 confirmed the results of the crystal structure determined by the X-ray diffraction. The electron diffraction patterns along relevant zone axes are shown in Fig.  2. All five patterns can be well indexed in a hexagonal primitive lattice with the cell parameters obtained from powder XRD diffraction (Table 1). There are no superstructure reflections or diffuse reflections characteristic for disorder. The atomic arrangement in the TM 7 Fe 3 B 8 structure determined from single crystal diffraction (as shown in Fig. 4a) is proved by HRTEM observations (Fig. 3). For the image along [100] (Fig. 3a), the simulated image (the inset in Fig. 3a 8 ] tetragonal prisms and the second type of trigonal prisms. Such buildup of trigonal prims and tetragonal prims in TM 7 Fe 3 B 8 structures is observed in borides for the first time. This type of structure pattern was previously found in the crystal structure of BaFe 2 Al 9 . 64 Here the aluminum atoms are occupying the positions of TM2 and Fe, iron atoms are located at the B2 positions, barium is shifted by [00 1 / 2 ] in respect to Nb1 site, and the positions of B2 are not occupied: Ba 1 Al 6 Al 3 Fe 2  6 is equivalent to (TM1) 1 (TM2) 6 Fe 3 (B1) 2 (B2) 6 . Later another ordering variant for this atomic motif was discovered in Hf 5 Nb 5 Ni 3 P 5 : Hf 1 (Hf,Nb) 6 (Hf,Nb) 3 P 2 (Ni,P) 6 . 65 The structural motif of TM 7 (Fig. 4b), this atomic pattern plays important role in the magnetic behavior of these materials (cf. below).

Physical Properties
Magnetic Properties: The analysis of the magnetic properties of both TM 7 Fe 3 B 8 compounds is hampered by the presence of ferromagnetic impurities with high Curie temperatures. Fig. 6a shows the magnetic moment  per formula unit (in Bohr magnetons  B ) for two low fields. Magnetic ordering transitions are clearly visible for both compounds, at T N = 240 K for Nb 7  and their temperature derivatives d/dT are shown. Both compounds display metallic conduction with  300K ≈ 19  m for the Nb and ≈ 0.55  m for the Ta compound. While the former sample has an extraordinary large resistivity well above the Mott-Ioffe-Regel limit, the latter compound reaches only a value in the range typical for intermetallic compounds. For the Nb 7 Fe 3 B 8 a pronounced kink is visible at the magnetic transition. The kink at T N is weaker in the Ta compound. The derivatives d/dT indicate that for both compounds a contribution due to spin-disorder scattering of charge carriers is at work. Interestingly, the hump in d/dT of the Ta compound extends further to lower temperatures than that of Nb 7 Fe 3 B 8 . The high residual resistivities (RRR value = 3.0 and 2.4 for Nb and Ta-containing compounds, respectively) suggest that both samples have considerable amounts of point defects. Specific Heat Capacity: The isobaric specific heat c p (T) of the TM 7 Fe 3 B 8 compounds is shown in Fig. 8. The strongly bonded light boron atoms in these structures lead to high-frequency optical phonon modes. Therefore, the specific heat at room temperature is still well below the Dulong-Petit limit, i.e. c p ≤ 3nN A k B (n = number of atoms in the formula unit, N A = Avogadro constant, k B = Boltzmann constant). There are clear second-order anomalies at the weak ferromagnetic ordering transitions. The anomaly for the Ta compound is smaller than that for the Nb homologue. Interestingly, c p (T) of Ta 7 Fe 3 B 8 is well above that of the Nb compound at temperatures below ≈ 140 K, which may be expected from lower-lying phonon modes of the TM species (Ta has almost twice the atomic mass of Nb). The inset to Fig. 8 presents the low-T specific heats in a c p /T vs. T 2 representation. For temperatures below 10 K the c p (T) may be analyzed following the ansatz c p (T) = aT −2 + T + T 3 , where the first term captures the upturn towards the lowest temperatures (observed in the Ta compound only), T is the contribution from conduction electrons, and T 3 represents the Debye approximation of the lattice heat capacity. The Sommerfeld coefficients  are 32.9 and 38.0 mJ mol −1 K −1 for the Nb and Ta compound, respectively. The coefficients  correspond to initial Debye temperatures  D of 688 K and 640 K, respectively, the lower  D of the latter compound being due to the large atomic mass of tantalum. The origin of the upturn at the lowest T observed for Ta 7 Fe 3 B 8 is unclear. The application of magnetic fields  0 H of 3, 6, and 9 T leads to a progressive shift of entropy connected to this upturn to higher temperatures, however the involved entropy is very small compared to N A k B . This contribution is probably not due to hyperfine splitting of the nuclear multiplet of 181 Ta (I = 7/2), especially since no corresponding effect is observed for Nb ( 93 Nb with I = 9/2). Mössbauer Spectroscopy: Spectra of Nb 7 Fe 3 B 8 at 294 K and 4.3 K are shown in Fig. 9. The Mössbauer spectrum at 294 K shows a single line with small quadrupole splitting (Table 4). Magnetic hyperfine splitting is present at 4.3 K (Fig. 9) with a hyperfine field H hf less than one third of the value for pure α-Fe. The small line width (G/2) ( Table 4)   In order to gain further insight into the nature of the magnetic order in TM 7 Fe 3 B 8 , we analyzed nearest-neighbor exchange couplings by calculating total energies of several spin configurations. The following ordering patterns were considered: ferromagnetic order (I); ferromagnetic order in the ab plane and antiferromagnetic order along c (II); ferrimagnetic (up-up-down) order in the ab plane and ferromagnetic order along c (III). Note that we considered collinear spin configurations only. Therefore, a fully antiferromagnetic order in the ab plane is not possible given the frustrated nature of the kagome spin lattice. Our spin-polarized calculations revealed the lowest energy of configuration III that we further refer to as zero. The energies of the other two configurations are E I = +65.9 meV/f.u. and E II = +127.1 meV/f.u., respectively. This way, effective nearestneighbor exchange couplings are J ab = 16.5 meV/Fe and J c = 21.2 meV/Fe, where the positive and negative signs stand for the antiferromagnetic and ferromagnetic couplings, respectively, and we do not divide energies by S 2 because in itinerant magnets it is not a good quantum number. We conclude that the couplings in the ab plane are antiferromagnetic, while the coupling along c is ferromagnetic. Therefore, despite large Fe−Fe distances (cf. above), TM 7 Fe 3 B 8 are magnetically frustrated, as no collinear spin configuration satisfies the antiferromagnetic couplings in the Kagome net. It is worth noting that effective exchange couplings of +190 K and 247 K are comparable in magnitude to the Curie-Weiss temperature of 195 K in Nb 7 Fe 3 B 8 . However, both ferro-and antiferromagnetic interactions are observed.

Chemical bonding analysis in real space
A striking feature of the TM 7 Fe 3 B 8 crystal structure is the spatial separation of the TM atoms from the Fe and B ones forming separated planar nets perpendicular to the [001] direction at z = 0 and z = ½ respectively. The reasons for such atomic arrangement were evaluated by the real space analysis 1-11 | 9 of chemical bonding in Nb 7 Fe 3 B 8 employing electron localizability indicator ELI in its ELI-D representation 59 (Fig. 11). While the ELI-D distribution in the penultimate shell of boron atoms has a spherical shape as expected for a p element, the penultimate shells of niobium and iron atoms show strong inhomogeneity being the fingerprint of the participation of these electrons in the bonding interactions in the valence region. 60,72 In the valence region around B1 atoms reveal five ELI-D maxima (attractors). Three of them are located on the Fe−B contacts visualizing the 2c(Fe−B) bonds. The basins of the remaining two attractors are located above and below the boron nucleus being in contact with the core basins of three Nb atoms beside ones of B1. This arrangement reflects the four-center interaction. ELI-D reveals similar distribution around B2. According to the local symmetry, two of the attractors in the plane at z = ½ visualize the 2c(B−B) bonds, the third one shows mainly 2c(Fe−B) interaction. The basins of the attractors above and below the plane are not present, being united with that of the Fe−B interaction indicating here a delocalization of a 2c bond toward a multicenter one. Thus, the plane of Fe and B atoms at z = ½ with its Kagome topology mentioned above is formed mainly by two-center interactions. Between this plane and the niobium atoms at z = 0 the multicenter bonding is observed. Assuming that the multicenter bonding is weaker than the two-center interactions, such bonding picture should yield a pronounced cleavage of the material perpendicular to the [001] direction.

Conclusions
In this study, two new ternary borides TM 7 Fe 3 B 8 (TM = Nb, Ta) with Kagome-type iron sublattices were synthesized by arcmelting of the elements and subsequent annealing at 1500 °C. Their hexagonal primitive structure is an intergrowth of AlB 2type and CsCl-type slabs, involving [BTM 6 ] trigonal prisms and [FeTM 8 ] tetragonal prisms. The condensation of trigonal prisms results in the formation of hexagonal columns along caxis, hence, also forming isolated planar [B 6 ] rings in this structure. Metallic character of TM 7 Fe 3 B 8 is confirmed by temperature dependence of the electrical resistivity as well as by the sizable linear term in the specific heat for both compounds. Magnetic susceptibility measurements reveal predominantly antiferromagnetic order below T N = 240 K for Nb 7 Fe 3 B 8 and T N = 265 K for Ta 7 Fe 3 B 8 . The sextet in the Mößbauer spectra of Nb 7 Fe 3 B 8 , the sizable anomalies in the specific heat at T N , and the kinks in the resistivity curves confirm the bulk character of the magnetic transitions for both compounds. These transitions are related to the presence of sizable magnetic moments localized on the Fe atoms within the planar Kagometype iron sublattice. DFT calculations indicate metallic behaviour for both compounds and show that interactions in the ab plane are antiferromagnetic and thus subject to a strong geometrical frustration that should prevent Néel type magnetic ordering. On the other hand, strong interplane coupling (of any sign) can effectively suppress this frustration and trigger the formation of long-range-ordered states, 73 which is probably the case in TM 7 Fe 3 B 8 . However, the presence of remnant magnetization unanticipated in a regular Kagome antiferromagnet indicates a more complex nature of the magnetic order. Quantum-chemical analysis of the chemical bonding in Nb 7 Fe 3 B 8 within the electron localizability approach reveals five ELI-D maxima around B1, visualizing three in-layer Fe−B bonds and two interactions with core basins of three Nb atoms above and below, while only three maxima around B1, showing two B−B bonds and one Fe−B interaction. The analysis also indicates that the Kagome net of Fe and B is mainly formed by two-center interactions, whereas multicenter bonding between this net and Nb atoms is observed.