SECTOR SALUD

A material development typically begins with the discovery of a new interesting com- pound, which is subsequently studied and improved over time to yield better properties. This process becomes a bottleneck in a world of fast developing technology, which has a constant need for tailored functional materials. The high-throughput computational approach (HTA) [5] takes a different perspective. Modern computers and DFT codes can offer a fast and cost-effective characterization of the material properties. In this way a large portion of the chemical space can be explored much faster than before. The goal of the HTA is to characterize an entire family of compounds at once using a completely automatized process. The properties are stored in a searchable database so that the material screening can be performed as a post-processing step. The problem of material discovery then becomes a data-mining problem. In general, one needs to define search criteria, namely to identify the crucial material properties and the range of permissible values, which can be obtained from the database and used to identify interesting mate- rials. This is often a challenging and non-trivial task. A more in-depth discussion of the related problems is deferred to Chapter 4. Here we are able to utilize a simple search criteria to select potentially interesting magnetic materials.

Finding a new permanent magnet requires a number of criteria to be satisfied. These are derived from both the underlying physics and the application requirements. Due to the availability of the data, we will focus solely on the family of full Heusler alloys [29]. These will serve as a testing ground to assess the feasibility of the high-throughput approach. Although the high-throughput and the combinatorial investigations are becoming ever more widespread, we know of only two works, namely Drebov et al. [134] and Sanvito et al. [132], where the discovery of permanent magnets was the main objective of the high-throughput search. The work of Drebov et al. focused on a number of rare-earth transition metal structures, for which the Curie temperature and the magneto-crystalline anisotropy was determined. The work of Sanvito et al. was a data-mining oriented inves- tigation, where the perspective candidates were selected from a pre-computed database of materials, using descriptors. The Curie temperature was estimated using a regression technique and a couple of new magnets were synthesized, clearly demonstrating the ad- vantage of performing anab initiothermodynamic stability analysis. The work presented here can be understood as a combination of the two aforementioned approaches. We combine the data-mining candidate selection withab initio DFT techniques, in order to achieve an accurate characterization of the magnetic properties, namely the anisotropy and the Curie temperature. These parameters are then used for further selection. In this way we incorporate the competitive advantages of the aforementioned methods. The

main search criteria that we employ to identify viable candidate materials are discussed below.

Thermodynamic stability - entails calculating all possible decomposition paths for a given compound. In other words a full phase diagram needs to be calculated. Obviously, the effort scales combinatorially with the number of atomic species in the unit cell. This is an incredibly demanding computational task. Nevertheless, the AFLOW database [135] implements just such a protocol [8, 132], offering robust stability estimates for the ma- terials. We note that the temperature effects and, in the case of the magnetic materials, the full phase-space of spin configurations, are not taken into account here. In the latter case this means that an error associated with the magnetic order needs to be consid- ered, typically between ∼ 100 meV and 400 meV per formula unit. These values are sufficiently large to affect the accuracy of the stability assessment. Since the AFLOW database is not yet completed, a complete stability analysis is not possible for all mate- rials at this point. A computationally cheaper but less robust estimate of the stability is given by the enthalpy of formation calculated with respect to decomposition into the most stable elemental phases. Although it can not tell us, which materials will exhibit a full thermodynamic stability, it can be used to eliminate materials that are likely un- stable. This leads to a significant reduction of the potential candidates. In addition a relative stability of different Heusler phases can be compared using this method. This approach was used, for example, in Chapter 3.

Tetragonal crystal structure - guarantees that the magneto-crystalline anisotropy is not quenched, as discussed in section 1.1.4.1. This criterion represents another computa- tional challenge. Since the calculations in the AFLOW database are performed for cubic Heusler cells, additional structural relaxation needs to be performed for the mag- netic systems. In this case an interplay between the crystal structure, namely the c/a ratio of the tetragonal unit cell and the magnetic moment may lead to different energy minima. Both these mechanisms tend to reduce the Fermi level DOS and thus, to lower the kinetic energy. Ab initio calculations need to be used here in order to establish what is the lowest energy structure. Here we do not perform such calculations, instead we identify the lowest energy structures from the data available in the Materials Mine database [31, 133]. The database provides both the enthalpy of formation, calculated with respect to the decomposition into elemental phases, magnetic moments and the c/aratio for each structure. We will therefore make this database our default source of data.

Saturation Magnetization - needs to be high enough in order to achieve a high energy product and to prevent the magnet from undergoing spontaneous demagnetization. The target values for the magnetization are in the range 1 MA m−1 to 1.5 MA m−1 [28]. In

screening

I)

II)

Tc

III)

MAE

tetragonal magnetic stable

Figure 2.1: Protocol for the high-throughput screening of permanent magnets. The procedure is broken down into three steps (I - III). We start from a full database of Heusler alloys [31]. The screening criteria are then applied, i.e. we look for stable magnetic materials with a tetragonal ground-state structure. This is illustrated as a two step data reduction. In the second step we calculate the Curie temperature, TC,

for the candidate materials. The materials with aTC<500 K are filtered out. Finally,

we proceed by calculating the magnetic anisotropy energy (MAE).

the case of the Heusler alloys, this roughly corresponds to 6µBf.u.−1 to 9µBf.u.−1. However, slightly lower values should be expected for the Heusler alloys. Here we will consider any magnet that exhibits a magnetic moment > 0.5µBf.u.−1. In effect we aim at considering all tetragonal magnetic materials. In doing so we wish to achieve two objectives. The first is to provide the best magnets for the application and the second, to create a large enough dataset, which can be used to study the trends in the magneto-crystalline anisotropy, with respect to the composition, the structure, etc. Critical temperature - guarantees that the magnet will maintain its properties at elevated temperatures. This quantity is not available in any of the databases and should be estimated via direct calculation for the ground state structure.

Magneto-crystalline anisotropy - is required in order for a magnet to qualify for real- world use. A minimum value required in practical applications is Ku > 500 kJ m−3.

However, here we will target a value of 1 MJ m−3, since the former one is close to the established numerical precision of the calculation method. Similarly to the case of the critical temperature, this quantity needs to be calculated for candidate materials explicitly. However, due to a high sensitivity of this quantity to the experimental growth conditions, it is unclear if it can be used as a reliable descriptor.