Possible martensitic transformation in Pd2MnTi and Pt2MnTi: First-principles investigation
PPossible martensitic transformation in Pd MnTi andPt MnTi: First-principles investigation
L. Feng
Department of Physics, Taiyuan University of Technology, 030024, Taiyuan, Republicof China
Abstract:
The martensitic transformation in all- d -metal Heusler alloys Pd MnTi andPt MnTi have been investigated based on first-principles investigations. Thecalculated results indicate that the martenstic transformation have great possibility tooccur in both Pd MnTi and Pt MnTi. The energy differences between the cubic andtetragonal phases are 215.12 meV and 329.45 meV for Pd MnTi and Pt MnTi,respectively. The analysis of the electronic structure of cubic and tetragonal phasesalso support this conclusion. The magnetic properties are also investigated for the twocompounds.
Key words: all- d -metal; martensitic transformation; Heusler alloy; first-principles Introduction:
Magnetic shape memory alloys have many applications, such asmagnetic-field-induced martensitic transformation, magneto-induced strain,magnetocaloric effect, exchange bias and so on. Most magnetic shape memory alloysare Heusler alloys. And it has been found that, in these magnetic shape memory alloys, p - d covalent hybridization plays an important role in atomic ordering, lattice structurestability and long-range magnetic ordering. Recently, all- d -metal Heusler alloys havedrawn great interest in the field of the magnetic material [1-5]. Generally, thechemical formula of Heusler alloys is X YZ, in which X and Y are transition metals,and Z is main group element. And when the Z is also transition metal, all- d -metalHeusler is obtained. It has already known that the p - d interaction have great influenceon the electronic structure and the stability of the Heusler alloy. What will happenwhen the d - d interaction replace the p-d interaction. The work by E. K. Liu et. al hasindicated that the martensitic transformation can still occur in Ni-Mn-Ti Heusler alloy[1]. In addition, the physical effects related to magnetism and martensiticransformation are also observed, such as magnetocaloric effect [2, 3],magnetoresistance effect [4], and so on. Thus, this discovery opens up a new field ofmagnetic materials. Since Pd and Pt belong to the same group as Ni in the chemicalperiodic table, it is worth studying whether the martensitic transformation can occurin Pd-Mn-Ti and Pt-Mn-Ti. In this work, we have investigated the possibility ofoccurrence for the martensitic transformation in Pd MnTi and Pt MnTi Heusler alloysusing first-principles calculations. The electronic structure and the magnetic propertyhave also given out. Based on these results, these two compounds might besynthesized and studied experimentally.2. Computational detailsThe calculations are performed by Cambridge Serial Total Energy Package(CASTEP) code [6]. The Perdew-Wang generalized gradient approximation [7] isused to describe the exchange correlation energy. The ultrasoft pseudopotentials [8]are used to describe the interactions between ion cores and valence electrons. For thepseudopotentials used, the electronic configurations with core level correction arePd(4 d ), Pt(5 d s ), Mn(3 d s ) and Ti(3 d s ), respectively. The cut-off energy ofthe plane wave basis set is 500 eV for all of the cases. The scheme for generatingk-points is Monkhorst-Pack method, and k-points are set as 20 × ×
20 and 18×18×10in the irreducible Brillouin zone of cubic and the tetragonal phases, respectively. Theconvergence criterion for the calculations is selected as the total energy differencewithin 10 -6 eV/atom.3. Results and discussions.3.1 Crystal structure. ig. 1 Atomic configuration of Pd MnTi and Pt MnTi with L2 and Hg CuTi structureFig. 2 Total energy of Pt MnTi as a function of lattice parameter
Both L2 structure and Hg CuTi structure are considered to determine the groundstate, as shown in Fig. 1. In L2 structure, Pt(Pd) atoms occupy A (0, 0, 0) and C (1/2,1/2, 1/2) sites, and Ti and Mn atoms occupy B (1/4, 1/4, 1/4)and D (3/4, 3/4, 3/4) sites,respectively. For Hg CuTi structure, however, Pt(Pd) atoms occupy A (0, 0, 0) and B(1/4, 1/4, 1/4) sites, while Mn and Ti atoms occupy C (1/2, 1/2, 1/2) and D (3/4, 3/4,3/4) sites. To obtain the ground state of the austenitic phase of Pd MnTi and Pt MnTi,both the ferromagnetic (FM) and antiferromagnetic (AFM) of L2 structure andHg CuTi structure are calculated. As a result, for Pd MnTi, we obtain the AFM resultseven though we set the initial magnetic structure to be parallel (FM). while forPt MnTi, we obtain the FM results even though we set the initial magnetic structure tobe antiparallel (AFM). For both the L2 structure and the Hg CuTi structure, themagnetic state is more stable than the paramagnetic state (PM) (as shown in Fig. 2). Itcan also be found that, for Pt MnTi, the total energy of the ferromagnetic state in theL2 structure is the lowest, which indicates that the stable structure of the austeniticphase of Pt MnTi is the ferromagnetic L2 structure. And the stable structure of theaustenitic phase of Pd MnTi is the antiferromagnetic L2 structure. And the latticeparameters for Pd MnTi and Pt MnTi are 6.30 Å and 6.32 Å, respectively. ig. 3 (a) Variation of the total energy of Pd MnTi with c / a ; (b)Variation of the total energy ofPt MnTi with c / a In order to investigate the possibility of occurrence for the martensitictransformation, the volume-conserving tetragonal distortion has been conducted forPd MnTi and Pt MnTi. It means that we keep the cell volume constant and change the c/a ratio of the tetragonal phase. And the total energy of all the tetragonal phases withdifferent c/a ratio. Here, the c and a are the lattice parameter of the distortedtetragonal phase. The variation of the total energy of Pd MnTi with c/a ratio hasshown in Fig. 3(a). It can be found that there are two minimums for the energy curveof Pd MnTi. And one minimum locates at c/a =0.86 and the other one locates at c/a =1.36. In addition, the energy of the tetragonal phase with c/a =1.36 is the lowest.The energy differences between the two minimums and the energy of the cubic phaseare 50 meV/ f.u. and 200 meV/ f.u.
Based on the a large amount of simulation andexperimental results, a empirical rule has been obtained to predict the martensitictransformation of the Heusler alloy: the distortion degree is in the appropriate range of1.2-1.4 and the difference between the cubic phase and the tetragonal phase is largeenough to overcome the resistance of the structure distortion. For example, thecalculated results for Ni MnGa indicate that the c/a ratio of the predicted tetragonalphase is 1.26. And the energy difference between the cubic and tetragonal phase is 32meV/ f.u. [9]. Obviously, the situation in Pd MnTi is conforms to the empirical rule.And the martensitic transformation has great possibility to occur in Pd MnTi. Similaranalysis also applies to Pt MnTi. The variation of the total energy of Pt MnTi with c/a ratio has shown in Fig. 3(b). It can be found that there are also two minimums for thenergy curve of Pt MnTi. And one minimum locates at c/a =0.86 and the other onelocates at c/a =1.35. In addition, the energy of the tetragonal phase with c/a =1.35 is thelowest. The energy differences between the two minimums and the energy of thecubic phase are 125 meV/ f.u. and 325 meV/ f.u.
Thus, the martensitic transformationhas great possibility to occur in Pt MnTi. In addition, if the magnetic momentdifference between the tetragonal structure with c/a<1 and the tetragonal structurewith c/a>1 is large, then the magnetic field driven strain might also be realized.3.2 Electronic structure
Fig. 4 (a) DOS of cubic phase of Pd MnTi; (b) DOS of tetragonal phase of Pd MnTi
In order to explain the reasons for the phase transition from the perspective ofelectronic structure, the total and partial density of states of both cubic and tetragonalphases of Pd MnTi have also been drawn in Fig. 4. We have already known that the p - d hybridization has a great impact on the stability of the cubic phase of Heuslercompounds. From the DOS images, we can find that the d - d hybridization also has avery significant impact on the stability of the cubic phase of Heusler compounds.Thus, Ti plays the same role as the main group elements in this system. The detailedanalysis is as follows: For the cubic structure, in the spin-up channel, the density ofstates in the vicinity of the Fermi level is considerable, which brings instability to thecubic phase. And it can be found that these electronic states mainly comes from theTi- d electrons. In addition, there is a obvious peak above the Fermi level at 1.18eV,which is the hybridization peak of Pd- d and Ti- d electrons. While in the tetragonalphase, in the spin-up channel, the density of state in the vicinity of the Fermi level isreatly reduced and becomes very flat, and the peak which is corresponding to thepeak located at 1.18 eV in the cubic phase moves down to 0.86 eV and becomes veryweak. In the spin-down channel, the overall density of the electronic states in thevicinity of Fermi level in the tetragonal phase is weakened compared with the cubicphase. However, the small packets near the Fermi level in the spin down channelmight also bring instability to the tetragonal phase, so it might imply the possibility todistort from the tetragonal structure to the modulation structure. Fig. 5 (a) DOS of cubic phase of Pt MnTi; (b) DOS of tetragonal phase of Pt MnTi
The analysis of the electronic structure of Pt MnTi is similar to that of Pd MnTi.The total and partial density of states of both cubic and tetragonal phases ofPt MnTi have been drawn in Fig. 5. For the cubic structure, in the spin-up channel,the density of states in the vicinity of the Fermi level is also considerable, whichbrings instability to the cubic phase. And it can be found that these electronic statesmainly comes from the Pt- d and Ti- d electrons. In addition, there is a obvious peakabove the Fermi level at 1.13eV, which is the hybridization peak of Pt- d and Ti- d electrons. While in the tetragonal phase, in the spin-up channel, the density of state inthe vicinity of the Fermi level is greatly reduced and becomes very flat, and the peakwhich is corresponding to the peak located at 1.13 eV in the cubic phase moves downto 0.89 eV and becomes very weak. In the spin-down channel, the overall density ofthe electronic states in the vicinity of Fermi level in the tetragonal phase is alsoweakened compared with the cubic phase. And the small packets near the Fermi levelin the spin down channel might also imply the possibility to distort from theetragonal structure to the modulation structure.3.3 Magnetic property Fig. 6 Variation of the total and atomic magnetic moment of (a) Pd MnTi and (b) Pt MnTiwith c/a ratio.
The magnetic property of Pd MnTi and Pt MnTi have also been investigated.Table 1 has summarized the total and atomic magnetic moment of the cubic andtetragonal phases of Pd MnTi. The magnetic moment of Mn change from 4.62 B incubic phase to 4.24 B in the tetragonal phase. And the magnetic moment of Ti issmall and negative (-0.20 B ) in the cubic phase while it become large (-0.92 B ) in thetetragonal phase. Thus, both the cubic phase and the tetragonal phase areferrimagnetic. And Fig. 6 (a) has drawn the variation of the total and atomic magneticmoment of Pd MnTi. It can be found that the magnetic moment of cubic phase is thelargest, and the magnetic moment of tetragonal phase decreases with the degree ofdistortion. The magnetic moment of Pd is very small, which can be almost ignored.And Ti and Mn atoms are coupled antiferromagnetically. The variation of themagnetic moment of Mn is moderate, and the variation of the magnetic moment of Tiis very significant. Thus, the variation of the total magnetic moment of Pd MnTi ismainly caused by the variation of the magnetic moment of Ti. This is very differentfrom the variation of the magnetic moment of the main group element in thetraditional Heusler compounds. The main group elements in the traditional Heuslercompounds only have a very small magnetic moment, and the variation of theirmagnetic moment with the degree of distortion almost can be ignored. able 1 Lattice parameter and magnetic moment of Pd MnTi, M t , M Mn , M Ti and M Pd represent thetotal magnetic momont, the magnetic moment of Mn, Ti and Pd, respectively.Pd MnTi a (Å) c (Å) c/a M t ( ) M Mn ( B ) M Ti ( B ) M Pd ( B )austenite 6.30 6.30 1.00 4.35 4.62 -0.20 -0.04martensite 5.68 7.73 1.36 3.42 4.24 -0.92 0.04 Table 2 has summarized the total and atomic magnetic moment of cubic andtetragonal phases of Pt MnTi. It can be found that the magnetic moment of Mnchange from 4.48 B in cubic phase to 4.14 B in the tetragonal phase. And themagnetic moment of Ti is very small and positive (0.08 B ) in the cubic phase while itbecome considerable and negative (-0.66 B ) in the tetragonal phase. Thus, the cubicphase is ferromagnetic and the tetragonal phase is ferrimagnetic. And Fig. 6 (b) hasalso drawn the variation of the total and atomic magnetic moment of Pt MnTi. It canbe found that the magnetic moment of cubic phase is the largest, and the magneticmoment of tetragonal phase decreases with the degree of distortion. The magneticmoment of Pt is very small, which can be almost ignored. In most case, Ti and Mnatoms are coupled antiferromagnetically. The variation of the magnetic moment ofMn is moderate, and the variation of the magnetic moment of Ti is very significant.Thus, the variation of the total magnetic moment of Pt MnTi is also mainly caused bythe variation of the magnetic moment of Ti.
Table 2 Lattice parameter and magnetic moment of Pt MnTi, M t , M Mn , M Ti and M Pt represent thetotal magnetic momont, the magnetic moment of Mn, Ti and Pt, respectively.Pt MnTi a (Å) c (Å) c/a M t ( ) M Mn ( B ) M Ti ( B ) M Pt ( B )cubic 6.32 6.32 1.00 4.63 4.48 0.08 0.04tetragonal 5.72 7.72 1.35 3.63 4.14 -0.66 0.08
4. ConclusionsThe martensitic transformation in the new all- d -metal Heusler alloys Pd MnTiand Pt MnTi have been investigated based on first-principles investigations. Thecalculated results indicate that the martenstic transformation have great possibility tooccur in both Pd MnTi and Pt MnTi. The energy differences between the cubic andtetragonal phases are 215.12 meV and 329.45 meV for Pd MnTi and Pt MnTi,respectively. The electronic structure analysis indicate that phase stability has beenreatly enhanced by the tetragonal distortion. The austenitic phase of Pd MnTi andPt MnTi are ferrimagnetic and ferromagnetic, respectively. And the total magneticmoment of austenitic phase of Pd MnTi and Pt MnTi are 4.62 and 4.48 B ,respectively. Acknowledgement:
This work is supported by the National Natural Science Foundation of China GrantNo. 51301119, the Natural Science Foundation for Young Scientists of Shanxi inGrant No. 2013021010-1, and Scientific and the Technological Innovation Programsof Higher Education Institutions in Shanxi in Grant No. 201802023.