Abstract:
In this paper we present an overview of various features of the structure of L10 magnetic phase. We discuss the various microstructural features which occur in these materials due to the changes in symmetry (translational and orientational domains) as well as the relationship between the crystal symmetry and features such as the thermodynamic order of the disorder to order phase transition. We also show the various ways that the magnetic moments of the elements align themselves in these alloys producing ferromagnetic and antiferromagnetic materials. Finally we discuss the way that the atomic order, composition and magnetic order affect the Curie temperatures of the FePd L10 alloys.
Crystallographic information
The fcc and L10 structures are shown in Fig. 1. The fcc structures have all their faces and their corner sites occupied by the same atoms, or in the case of an alloy, the probability of each site being occupied by a specific type of atom is the same. L10 is a crystallographic derivative structure of the fcc structure and has two of the faces occupied by one type of atom and the corner and the other face occupied with the second type of atom. If the two types of atoms were randomly arranged the structure would be fcc. Derivative structures are ordered variants of a parent structure and are usually low temperature phases, since their configuration entropy is lower that that of the disordered fcc alloy parent phase. On atomic ordering, the symmetry of the structure decreases. For the case of fcc to L10, the decrease is in both translational symmetry and point group symmetry; see below for further discussion.
There are several ways of denoting the L10 structure. The Strukturbericht designation L10 is that given in the ‘‘Structure Reports’’ series of the early 20th century [1]. The prototype structure is CuAu I. The prototype is an actual phase that is either the first to be discovered or is an important phase with the structure that it denotes. Pearson [2] has combined Bravais lattice information and unit cell information in a notation which lists the crystal system (c for cubic, t for tetragonal, etc.), the Bravais Lattice (P for primitive, F for face centered, etc.) with the number of atoms in the unit cell. For the L10 structure the Pearson symbol is either tP4 (if the unit cell shown in Fig. 1b is used) or tP2 (if the smaller unit cell with lattice parameters c 0 = c and a 0 = a p2/2 is used). The space group of the L10 structure is P4/mmm. An important crystallographic feature of the L10 structure is its c/a ratio. Since this structure is based on a cubic one, if we use the unit cell shown in Fig. 1, c/a 1. For most structures c/a is less than one, TiAl being the well known exception. If the two atom unit cell is used, the c/a ratio is about p2. It should be pointed out that even if the values of a and c were equal, the symmetry of the unit cell is tetragonal since there is no threefold axis and only one fourfold axis (along the caxis of the L10 structure). The ordering of the atoms on specific sites has lowered the overall symmetry of the structure.
Another important aspect of the structure is the number and type of near neighbors. Since the distortion is small we can say that in the L10 structure there are 12 near neighbors (along the h110i directions) and six next near neighbors (along the h100i directions) as in its parent fcc structure. For the L10 structure, each atom has eight opposite near neighbors and 4 similar near neighbors. (The opposite near neighbor bonds have a slightly smaller distance than the same near neighbor bonds for c/a < 1). Each atom also has six similar next-near neighbors. For energy calculations it is necessary to include at least the second nearest neighbors, as there is at least one other structure with the same number and type of first neighbors, namely the A2B2 structure that has the space group I 41 a md [3].
The positions of the atoms in the unit cell are summarized in Table 1. For the P4/mmm space group the 2(e) sites in general do not have the full space group symmetry. However, in the case of the four atom unit cell of the L10 structure, both types of atoms do have the site symmetry of 4/mmm. The unit cell shown in Fig. 1b is actually a base centered tetragonal one. However, since base centered tetragonal cells can be redrawn as primitive tetragonal cells, to keep the number of Bravais lattices to a minimum, it has been decided by the International Crystallography community to designate all lattices with base centered tetragonal unit cells as primitive cells.
Magnetic ordering
Both ferromagnetic and anti-ferromagnetic phases with the L10 structure are known to exist. It would be possible for a phase with the L10 structure to be ferrimagnetic, but no unambiguous example could be found at the time this paper was written. The ferromagnetic phases have their easy axis along the high symmetry axis of the structure, namely the [0 0 1] direction. From the point of view of magnetic symmetry this lowers the point group of the paramagnetic L10 phase from 4/mmm10 (order 32 in magnetic symmetry) to 4/mm0 m0 in the magnetic symmetry notation, which is of order 16. The lowering of the symmetry by a factor of two is the reason for the existence of two magnetic domains in uniaxial materials. The ordering of the spins in anti-ferromagnetic phases is less certain. There are various possible arrangements, summarized in Fig. 5 [17].
In Fig. 5a, only one of the elements is assumed to have a magnetic moment associated with it. The spins on a (0 0 1) plane are either directed up or down. The symmetry of this arrangement remains 4/mmm, showing that there is only one antiferromagnetic domain with respect to the orientation of spins. However, in this case there are two translational domains which could in principle arise due to the loss of translational symmetry during the magnetic ordering. These domains will have very large interfacial energy because they will put parallel spins as near neighbors. In Fig. 5b both elements are assumed to have a moment, but of different magnitude. Again the spins are thought to cancel in the (0 0 1) planes, but this time the direction of the spins is thought to be along the [1 0 0] direction of the unit cell. This lowers the symmetry to mm0 m0 (the m being perpendicular to the [1 0 0]-axis). Thus in transforming from a paramagnetic L10 phase to this antiferromagnetic structure the symmetry is lowered from 4/mmm10 (order 32 in magnetic symmetry) to mm0 m0 (order 8 in magnetic symmetry). Four domains are possible, two with their spins along the [1 0 0] direction and two with their spins along the [0 1 0] direction. Translational domains also exist for this structure, and once again will be of high interfacial energy. Fig. 5c shows a third possibility of the alignment of the magnetic spins, this time along the face diagonals of the (0 0 1) planes. This orientation of the spins results in the same magnetic point group symmetry as in b. It should be pointed out that the near neighbor spins pointing to one another makes this structure highly energetic from the point of view of dipolar interaction energy.
Both ferromagnetic and anti-ferromagnetic phases with the L10 structure are known to exist. It would be possible for a phase with the L10 structure to be ferrimagnetic, but no unambiguous example could be found at the time this paper was written. The ferromagnetic phases have their easy axis along the high symmetry axis of the structure, namely the [0 0 1] direction. From the point of view of magnetic symmetry this lowers the point group of the paramagnetic L10 phase from 4/mmm10 (order 32 in magnetic symmetry) to 4/mm0 m0 in the magnetic symmetry notation, which is of order 16. The lowering of the symmetry by a factor of two is the reason for the existence of two magnetic domains in uniaxial materials. The ordering of the spins in anti-ferromagnetic phases is less certain. There are various possible arrangements, summarized in Fig. 5 [17].
In Fig. 5a, only one of the elements is assumed to have a magnetic moment associated with it. The spins on a (0 0 1) plane are either directed up or down. The symmetry of this arrangement remains 4/mmm, showing that there is only one antiferromagnetic domain with respect to the orientation of spins. However, in this case there are two translational domains which could in principle arise due to the loss of translational symmetry during the magnetic ordering. These domains will have very large interfacial energy because they will put parallel spins as near neighbors. In Fig. 5b both elements are assumed to have a moment, but of different magnitude. Again the spins are thought to cancel in the (0 0 1) planes, but this time the direction of the spins is thought to be along the [1 0 0] direction of the unit cell. This lowers the symmetry to mm0 m0 (the m being perpendicular to the [1 0 0]-axis). Thus in transforming from a paramagnetic L10 phase to this antiferromagnetic structure the symmetry is lowered from 4/mmm10 (order 32 in magnetic symmetry) to mm0 m0 (order 8 in magnetic symmetry). Four domains are possible, two with their spins along the [1 0 0] direction and two with their spins along the [0 1 0] direction. Translational domains also exist for this structure, and once again will be of high interfacial energy. Fig. 5c shows a third possibility of the alignment of the magnetic spins, this time along the face diagonals of the (0 0 1) planes. This orientation of the spins results in the same magnetic point group symmetry as in b. It should be pointed out that the near neighbor spins pointing to one another makes this structure highly energetic from the point of view of dipolar interaction energy.
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