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High-Temperature Ferromagnetism in CaB2C2

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Science  10 Aug 2001:
Vol. 293, Issue 5532, pp. 1125-1127
DOI: 10.1126/science.1061501

Abstract

We report a high Curie–temperature ferromagnet, CaB2C2. Although the compound has neither transition metal nor rare earth ions, the ferromagnetic transition temperature T c is about 770 Kelvin. Despite this high T c, the magnitude of the ordered moment at room temperatures is on the order of 10−4 Bohr magneton per formula unit. These properties are rather similar to those of doped divalent hexaborides, such as Ca1−xLaxB6. The calculated electronic states also show similarity near the Fermi level between CaB2C2 and divalent hexaborides. However, there is an important difference: CaB2C2 crystallizes in a tetragonal structure, and there are no equivalent pockets in the energy bands for electrons and holes—in contrast with CaB6. Thus, the disputed threefold degeneracy, specific to the cubic structure, in the energy bands of divalent hexaborides turns out not to be essential for high-temperature ferromagnetism. It is the peculiar molecular orbitals near the Fermi level that appear to be crucial to the high-T c ferromagnetism.

The search for magnets with high ferromagnetic transition temperatures (T c's) is not only of practical interest but is also of basic scientific interest, in identifying the mechanism. The origin of the high-T c ferromagnetism observed in doped hexaborides was initially attributed to electron correlations in the low-density electron gas (1), and much attention has been paid to the band structure of the divalent hexaborides (2, 3). It has been postulated that the presence of three equivalent valleys in the energy bands plays an important role in the formation of excitonic ferromagnetism (4–6). However, the fact that this has been observed only in this particular class of compounds has caused difficulty in identifying the mechanism of this phenomenon. This study reveals that the high-T c ferromagnetism is not a singular phenomenon but that a similar ferromagnetism appears in a tetragonal compound, CaB2C2, without the band degeneracy. Our observation may provide a route for preparation of new high-T c ferromagnets.

Powder samples of CaB2C2 were prepared from Ca shot (99%), amorphous powder boron (99%), and powder carbons (99%). The starting materials were mixed at the stoichiometric ratio Ca:B:C = 1: 2:2 in an argon glovebox, pressed into pellets, and placed in a wrapped tantalum tube. The pellets were then heated in two ways: (i) at 1050oC for 20 hours in 2000 atm of an argon atmosphere in a hot isostatic-pressing furnace, and (ii) at 1050oC for 30 hours in a vacuum quartz tube. In both cases, reddish-brown powders of CaB2C2 were obtained. Because the samples are sensitive to moisture, they were handled under an argon atmosphere.

In the x-ray diffraction patterns obtained (Fig. 1), most of the diffraction peaks can be indexed to the tetragonal structure, consistent with an earlier structural study (7) of CaB2C2. There are slight amounts of impurity phases of CaO and CaB6 in the sample, as seen in the corresponding weak intensity. The inset of Fig. 1 shows the two-dimensional network formed by boron (B) and carbon (C) atoms in CaB2C2. The Ca ions sit on each vertex and center of the square and sandwich each B-C layer. Depending on the stacking of B-C layers along the c axis, the crystal symmetry becomes either simple tetragonal (P4/mbm) lattices or body-centered tetragonal (I4/mcm) lattices. The latter has the sequence B-C-B-C- . . . along the c axis, whereas the former has B-B- . . . (and C-C- . . .) stacking. Experimentally, these two different structures can be distinguished only by observing a signal corresponding to the B-C superstructure along the c axis. Unfortunately, the x-ray scattering intensity is too weak to identify or disprove such a signal. Hence, the crystal structure of CaB2C2 has not yet been experimentally fixed. On the other hand, it has been established that related compounds RB2C2 with trivalent rare earth ion R haveP4/mbm (8, 9).

Figure 1

Powder x-ray diffraction patterns for CaB2C2. The inset shows the two-dimensional B-C network in CaB2C2; arb., arbitrary.

Magnetization measurements with a SQUID magnetometer (Fig. 2, inset) show the magnetization versus applied magnetic fields at T = 5 K. The diamagnetic contribution of the sample holder was independently measured by removing the sample, and this background has been subtracted. The magnetization shows a characteristic feature of ferromagnetism, with the saturation moment of 3.8 × 10−4 Bohr magneton (μB) per formula unit [or 2.1 electromagnetic units (emu) per mole of formula] at 1 T, which is comparable to that in divalent hexaborides (1). The observed hysteresis is consistent with ferromagnetism. The magnetization at room temperature is almost the same as that at T = 5 K. The magnetization as a function of temperature (Fig. 2) reveals that the Curie temperature T c is high and is estimated to be 770 K. The observed magnitude of the ferromagnetic moment is of the same order as that in CaB6, and the Curie temperature is different from the transition temperature reported for the doped CaB6 (1). These facts exclude the possibility that the observed ferromagnetism is due to the slight amount of CaB6 present as an impurity phase. Therefore, the observed ferromagnetism is intrinsic in the sample of CaB2C2.

Figure 2

Magnetization as a function of temperature in CaB2C2. The inset shows magnetization versus applied magnetic field.

The ferromagnetism observed here in CaB2C2 is very similar to that found in doped hexaborides. The unique band structures in the host divalent hexaborides seem to be important for the weak ferromagnetism (2–6). The conventional local density approximation (LDA) calculations predict that the host material CaB6 is a poor conductor that has a small overlap or a small gap between valence and conduction bands at the three X points in the Brillouin zone (2, 3). Recently, partial inclusion of a correlation effect in the Green's function description, known as the GW approximation, has pointed to a semiconducting band structure with a band gap of 0.8 eV in CaB6 (10). It is natural to inquire into the band structure of CaB2C2. The resistivity reported in (7) shows a semiconducting behavior with an energy gap of 0.2 eV. In deducing the intrinsic energy band structure from experiment, one should take notice of a possible self-doping effect caused by Ca deficiency, as in the case of hexaborides (11).

We performed the total energy calculation and found that theP4/mbm structure is more stable than theI4/mcm one, by using the full potential linear augmented plane wave method with the LDA. However, the difference is only about 8 milli-rydberg per formula unit if we use the experimentally observed lattice constants and the atomic positions in the layer. This difference is too small to definitely determine the crystal structure in the ground state. Thus, we investigated the electronic band structures for both P4/mbm andI4/mcm cases. The band structure forP4/mbm is semimetallic, with a small overlap (0.64 eV) between conduction and valence bands (Fig. 3). On the other hand, the I4/mcmstructure leads to a semiconducting electronic structure with a gap of 0.43 eV. Nevertheless, as in the case of CaB6(10), the inclusion of correlation effects may bring about a semiconducting gap even in the case of the P4/mbmstructure.

Figure 3

Energy band structure forP4/mbm CaB2C2 along the symmetry axes. E F denotes the Fermi level.

The overall features of the highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbital (LUMO) do not depend on the stacking of B-C layers. Figure 4 shows the schematic view of one of the HOMOs and the LUMO for the B-C network in CaB2C2. The HOMO wave function consists ofpx and py orbitals on boron and carbon sites within a B-C layer. This accounts for the very flat valence band along the Z-Γ direction in Fig. 3. On the other hand, the LUMO wave function consists of pz orbitals on boron and carbon sites and hybridizes well with thedxy orbital on Ca sites around the Z point. Hence, the bottom of the conduction band has larger dispersion. In the case of hexaborides, the cubic symmetry gives three equivalent X points. For each X point, four borons in the same plane composing a B6 cluster provide these orbitals. Therefore, in spite of the different compositions and crystal structures, there is a remarkable similarity between the orbitals in CaB2C2 and CaB6. In both cases, the valence bands are highly anisotropic. There is another common feature in the electronic structure: The dipole transition is forbidden between the HOMO and the LUMO. This selection rule is favorable for allowing the Coulomb and exchange interactions to work, because the screening is not effective (4).

Figure 4

Schematic view of (A) the LUMO and (B) the HOMO on the B-C network in CaB2C2. Red and blue indicate plus and minus inp wave functions, respectively, on boron and carbon sites. Large open spheres indicate Ca ions.

We emphasize that information on the wave functions in the real space is most reliable in the present band structure calculation. In contrast with the fine details in the energy band structure, which is rather sensitive to the parameters involved and to the way correlations are included, the real-space information applies to both crystal structures, P4/mbm andI4/mcm, and is insensitive to minute change of the lattice parameters. According to our calculation, the wave functions near the Fermi level of CaB2C2 have remarkable similarities to those in CaB6, except for the threefold degeneracy in the latter. Therefore, peculiar properties of the HOMO and the LUMO (Fig. 4) should play a crucial role in ferromagnetism in doped hexaborides and CaB2C2.

  • * To whom correspondence should be addressed. E-mail: jun{at}phys.aoyama.ac.jp

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