Martensitic Driving Forces

Phase Diagram In the previous section an overview over the structural, mag-netic and electronic properties of Ni-Mn-Ga based MSM alloys and their rele-vance for the martensitic phase transition was given. At this point the following question arises: What drives the martensitic transition and determines the mar-tensitic transformation temperature?

Several studies have addressed the phase diagram of Ni-Mn-Ga and related alloys by means of first-principles calculations (see, for example, [74, 81–83, 86, 111–114] and references therein). In a general approach the total energy at zero temperature is calculated as a function of the tetragonal distortionc/aat constant volume, which describes the tetragonal deformation of the austenitic phase with L21 structure (c/a = 1). All studies have demonstrated that the global minimum of the total energy landscape is located at a value ofc/a >1, in the region ofc/a ≈ 1.2−1.3 (see black data points in Fig. 2.19a), with a small local minimum (possibly) arising forc/a <1. These findings point to the fact that from theoretical calculations the NM tetragonal martensitic phase is the most stable configuration for Ni-Mn-Ga at zero temperature. The energy difference between the austenite and the non-modulated martensite phase

∆EA−N M is closely related toT_M. Comparisons with experimentally obtained T_Mshow that a larger∆EA−N M corresponds to a higherT_M[111].

The phase diagram for Mn-rich alloys calculated in this way is shown in Fig. 2.19b (M_S(∆E)). The overall agreement between theoretical and experi-mental values is satisfactory, howeverM_S(∆E)is systematically smaller than the experimental values. Additional information from the energetic scenario

Figure 2.19.: (a)Calculated total energy of Ni2MnGa for the ground state mag-netic moment of4.07µB/f.u.∆E¹and fixed spin moment value of3.60µB/f.u.

∆E². ∆E^α is plotted as a function of tetragonalityc/a and relative to its en-ergy minimum at c/a > 1. The calculation for the reduced magnetization of3.60µB/f.u.simulates the behavior for finite temperature. In addition, the phonon free energy at two different temperatures, F_ph¹ = F_ph(200K) and F_ph² =F_ph(300K), is shown. (Image taken from [112])(b)The theoretical phase diagram of Ni2Mn1+xGa1−x marked by the blue and violet circles and lines.

For comparison, the experimentally obtained data (orange circles and lines) is shown. The martensitic transformation temperatureM_S(∆E)is obtained from structural energy differences of total energy calculations that have been con-verted to a temperature scale.M_S(∆F_ph)refers to a calculation where also the phonon free energies where taken into account to approximateM_S. T_C^A(MC) andT_C^M(MC)refer to the Curie temperature of austenite and martensite, respec-tively, obtained from Monte Carlo calculations (Image taken from [115]).

involved in the structural transformation may be obtained when the phonon contributions to the free energy are taken into account [112, 114]. The phonon free energy as a function ofc/a for two different temperatures is shown in Fig. 2.19a. The temperature influence on the magnetization was also included by the calculation of the free energy∆E²for a reduced magnetization value of 3.60µ_B/f.u.From these calculations we can infer that the contributions from lat-tice vibrations help stabilize the austenitic phase (minimum ofF_ph atc/a= 1), while total energy favors martensite (minimum of∆Eatc/a≈1.25). This

com-2.3. Electronic Properties and instability of Ni-Mn-Ga petition governs the transition from austenite to martensite with decreasing temperature. The sum of different energy contributions shows that the MT oc-curs somewhere between200K and300K⁹. The transformation temperatures obtained from these calculations are shown in the phase diagram in Fig. 2.19b asM_S(∆F_ph). Moreover, Uijttewaalet al.have shown that additional contribu-tions from magnetic excitacontribu-tions further lower the MT temperature of Ni2MnGa [83]. Only the combined approach of including both vibrational as well as mag-netic excitations reproduces the complex sequence of phase transformations (martensite↔premartensite↔austenite) for stoichiometric Ni2MnGa as a func-tion of temperature.

Origin of the Martensitic Phase Transformation These results presented in the preceding paragraph have shown that electronic, vibrational and magnetic contributions and their competition have to be considered in order to access the phase transformation sequence and the phase diagram of Ni-Mn-Ga al-loys. The phase transformation sequence could be satisfactorily reproduced for the stoichiometric composition Ni2MnGa. However, it is obvious that the influence of chemical disorder for the off-stoichiometric or doped samples on the martensitic transformation can only with difficulty be taken taken into account.

For the case of the stoichiometric composition Ni2MnGa, however, the sit-uation is more simple. As already outlined in this section the origin of the premartensitic and martensitic transformation is related to a number of effects connected to the electronic properties of this system. The band Jahn-Teller ef-fect originating from a peak of Nid-states in the minority DOS which is moved aboveE_F when the system undergoes a structural transformation has been proposed as responsible for the structural instability of the austenitic phase [74, 81, 86, 95, 109, 114, 116]. This effect is closely related to Fermi surface nest-ing since these states form flat extended sheets on the FS [24, 26, 28, 85, 94]. In re-ciprocal space these sheets can be connected through a single wave vector along the[110]direction. The redistribution of states residing next to the Fermi energy

9 The experimental transformation temperature of stoichiometric Ni2MnGa is202K.

can gain sufficient energy to stabilize the modulated structural arrangement [117]. Only for near-stoichiometric compositions a modulated premartensitic phase is observed, which is indicated by a soft phonon mode in the austenitic phase. The wave vector of the soft phonon mode corresponds to modulation of the premartensite shuffle on the one hand and on the other hand to the nesting vector connecting the FS sheets [74, 79, 110, 113]. Due to FS nesting the elec-tron density correlation function is enhanced and, provided a selec-trong elecelec-tron- electron-phonon interaction, renormalizes the main shear electron-phonon mode, which leads to the observed dip in the phonon dispersion (Kohn anomaly) [114]. Recent experimental observations support a charge density wave ground state with the periodic lattice modulation driven by electronic instability [25–27]. In this context the character of the modulation in the premartensitic and the mar-tensitic phase of the stoichiometric Ni2MnGa was considered as a sinusoidal modulation of the undistorted lattice positions [17, 51, 117].

The overall picture of martensitic driving forces is getting more complex when considering the off-stoichiometric and doped samples. A number of dif-ferent martensitic phases were reported (see section 2.1) and the character of the modulation is still under debate for these type of Ni-Mn-Ga based alloys.

Meanwhile the interpretation of the 7M martensitic phase as a nanotwinned adaptive structure is widely accepted [29–31, 67, 70, 117]. However, there is an ongoing debate about the nature of the 5M martensitic phase in the context of the adaptive phase concept. Also the driving forces for the martensitic insta-bility and their temperature behavior in off-stoichiometric and doped samples have not been resolved yet.

The role of the chemical disorder and the influence is difficult to implement in theoretical calculations, which is why only few works have been carried out [82, 109, 111, 113, 118–120]. Experimental studies of the electronic structure for this group of Ni-Mn-Ga alloys are almost completely missing [101]. Calcu-lations of the electronic structure of off-stoichiometric and doped alloys have demonstrated a change in the DOS near the Fermi energy compared to the stoichiometric composition Ni2MnGa [109, 111, 113]. It has been pointed out, that the position of the peak in the DOS related to the Jahn-Teller instability

2.3. Electronic Properties and instability of Ni-Mn-Ga with respect to the Fermi level is influenced by the composition and doping elements. Siewertet al.argued that band Jahn-Teller effect becomes less pro-nounced for the off-stoichiometric compositions and consequently should be regarded only as an accompanying feature, and not as the origin, of the mar-tensitic transformation in Ni-Mn-Ga composition range which supports the formation of 7M modulated martensite [113]. Calculations of the evolution of the Fermi surfaces of Ni2Mn1+xGa1−xdemonstrated that the nesting behavior prevails in the alloys with extra Mn [82]. This means that charge susceptibility and Kohn anomaly are still enhanced in off-stoichiometric alloys and extra valence electrons of Mn atoms only increase the volume of the FS. In contrast, calculations performed by Siewertet al.contradict these [113]. They claim that the FS plain sheets which are connected to the nesting features partly vanish as the valence electron concentratione/ais increased for Ni2MnGa. Recent in-vestigations emphasize the importance of the complex magnetic behavior as a martensitic driving force arising from competing ferro- and antiferromagnetic interactions with increasing chemical disorder in the super cell [82, 113, 115].

The antiferromagnetic tendencies have their origin in the magnetic interaction of nearest neighbor Mn-Mn pairs in off-stoichiometric (Mn-rich)¹⁰ composi-tions. The possible influence of magnetism on phase diagrams, the topology of the FS and the formation of modulated martensitic phases was recently discussed by Entelet al.[82, 115].

In summary, the existing investigations identify the Ni-Mn-Ga alloy as a sys-tem with competing vibrational, electronic and magnetic interactions which were all identified as important for the microscopic origin of the martensitic transformation. The individual contributions of the different properties and their dependency on temperature, composition and chemical disorder are still

10The magnetic Mn-Mn interaction becomes of antiferromagnetic type if one of the Mn atoms resides on the regular Mn site of the L21unit cell and the other Mn atom occupies the regular Ni or Ga sublattice. This causes the nearest-neighbor distance to shrink and leads to antiferro-magnetic interaction between these Mn-Mn pairs (See 2.2.1). This situation occurs not only for Mn-rich sample composition but also for doped and off-stoichiometric samples when atoms occupy the Mn sublattice and displace the Mn atoms from their regular places (see for instance [109] an references therein).

elusive. In order to bring more clarity in this discussion more experimental studies are missing in first place. The study of structural, electronic and mag-netic properties as a function of composition and temperature for both the austenitic and the martensitic phase can help to solve the puzzling issue of driving forces of the martensitic instability in Ni-Mn-Ga Heusler alloys.

Part II.

Methodology

Chapter 3.

Experimental Techniques

In this chapter a broad range of experimental techniques used for the character-ization of film and bulk sample will be presented. The most import ones, which were implemented under ultra high vacuum (UHV) conditions (base pressure:

10⁻¹⁰−10⁻¹¹mbar), will be discussed in detail: scanning tunneling microscopy and spectroscopy (STM/STS) and several methods of the photoemission spec-troscopy family: X-ray photoemission specspec-troscopy (XPS), ultraviolet photoe-mission spectroscopy (UPS) and angle-resolved photoephotoe-mission spectroscopy (ARPES). Other measurement techniques, which were used rather frequently (LEED), and also standard analysis methods (SQUID magnetometry, XRD and SEM) will be introduced only briefly.