Structural and Composition Effects on Electronic and Magnetic

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Structural and Composition Effects on Electronic and Magnetic Properties in Thermoelectric Mn Co Ge Materials 1-x-y

1+x

1+y

Konstanze R. Hahn, Elie Assaf, Alain Portavoce, Sylvain Bertaina, and Ahmed Charai J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b04863 • Publication Date (Web): 07 Nov 2017 Downloaded from http://pubs.acs.org on November 14, 2017

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The Journal of Physical Chemistry

Structural and Composition Effects on Electronic and Magnetic Properties in Thermoelectric Mn1−x−y Co1+xGe1+y Materials Konstanze R. Hahn,∗ Elie Assaf, Alain Portavoce, Sylvain Bertaina, and Ahmed Chara¨ı Aix-Marseille University, Faculté des Sciences de Saint-Jérôme, IM2NP, CNRS, Case 142, 13397 Marseille, France E-mail: [email protected]

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Abstract In this study, structural, electronic and magnetic properties of MnCoGe alloys with several composition (stoichiometric and Mn-depleted) have been investigated using first-principles calculations based on density functional theory. Their stability in the orthorhombic and hexagonal structure has been determined for different spinconfigurations. In all materials, the ferromagnetic orthorhombic phase is most stable, however, variation of the composition can lead to a decrease of the energy difference between the equilibrium orthorhombic and hexagonal structure. The magnetic moment is primarily found on the Mn atoms leading to a decrease of the total magnetic moment with decreasing amount of Mn. Using the Boltzmann transport model and the electronic density of states, the spin Seebeck coefficient has been estimated. At room temperature it is found to be highest in stoichiometric MnCoGe in the orthorhombic crystal structure.


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Introduction Depletion of natural resources such as fossil fuels that are still widely used for energy production demand the development of alternative and more energy efficient technologies. In this respect, a promising alternative to traditional cooling technologies based on vaporcompression is magnetic refrigeration utilizing the magnetocaloric effect (MCE). 1 The MCE was first observed in 1881 by Warburg 2 and physically explained in 1918 3 paving the way to magnetic refrigeration applications. 4,5 The first materials, however, had production temperatures far below room temperature and were thus not ideal for application in refrigeration devices of normal households. In 1988, Fert 6 and Gr¨ unberg 7 observed the spin-dependent electron transport and discovered the giant magnetoresistance which is related to enhanced magnetocaloric effects. The MCE can be improved when magnetic and structural transition coincide (magnetostructural coupling) as it has been shown recently in several materials such as LaFeSi, 8,9 Gd5 Si4−x Ge 10,11 and MnFeP(As,Ge). 12,13 Another interesting family of MCE materials in this respect are MnXGe alloys where X refers to ferromagnetic transition metals Co, Ni and Fe. 14 However, in the stoichiometric composition, the transformation temperature lies above the Curie temperature, 15–17 thus magnetostructural coupling is absent. Stoichiometric MnCoGe undergoes structural transformation from the low-temperature orthorhombic TiNiSi-type structure to the hexagonal Ni2 In-type structure at a temperature of ∼420 K while magnetic transition occurs at 275 K 18 and 345 K 19,20 in the hexagonal and in the orthorhombic phase, respectively. Nevertheless, previous studies have shown a significant dependence of the transition temperature on stoichiometry, 20,21 chemical composition 22 and applied pressure. 23,24 Substitution of Co with Fe atoms, for example, has yielded a decrease in the structural transformation temperature leading to a magnetostructural transition. 25 Coincidence of the magnetic and structural transition temperatures has been as well achieved by B- and Cr-doping of MnCoGe leading to a giant MCE. 22,26 Similarly, theoretical studies predicted a change in 3 ACS Paragon Plus Environment


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structural and magnetic transition temperatures in vacancy induced MnCo1−x Ge materials 20 and the effect has been confirmed experimentally. 17 Furthermore, changes in the composition of MnCoGe-based materials have shown antiferromagnetic behavior in the hexagonal phase at certain compositions. 27 Recently, a detailed experimental study has systematically evaluated such effects of the alloy composition on the structural and magnetic properties in Co-Mn-Ge thin films. 28 Here, we have used theoretical methods based on density functional theory (DFT) for the investigation of Mn1−x−y Cox Gey alloys evaluating the structure and composition dependent material properties. In particular, the stability of the orthorhombic and hexagonal phase with a non-magnetic, a ferromagnetic and an antiferromagnetic spin-configuration has been evaluated in MnCoGe with stoichiometric and three non-stoichiometric, Mn-depleted compositions. The magnetic moment of these systems has been determined. From the spin-dependent density of states the spin-Seebeck coefficient has been estimated using the Boltzmann transport equation.

Computational Methods The DFT calculations of this study are based on planewaves basis sets and pseudopotentials as implemented in the Quantum Espresso program package. 29 Exchange and correlation interactions are modeled within the generalized-gradient approximation (GGA) using the Perdew-Burke-Ernzerhof (PBE) functional. Kohn-Sham equations have been solved considering spin-polarization and an energy cut-off of 60 and 240 Ry has been applied for the wave function basis set and the charge density, respectively. Ultrasoft pseudopotentials 30 have been used to describe Mn and Co atoms with 15 and 9 valence electrons, respectively. The pseudopotential of Mn has been generated for the 2+ ionization state, thus the effective number of valence electrons is 13. A projected-augmented wave (PAW) pseudopotential has been used for Ge atoms with 4 valence electrons. All


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pseudopotentials have been tested on the crystalline structure of the pure metals and on the Mn5 Ge3 alloy. Stoichiometric MnCoGe and three compositions of non-stoichiometric MnCoGe, denoted as Mn0.75 Co1.125 Ge1.125 , Mn0.75 CoGe1.25 and Mn0.688 Co1.062 Ge1.25 , have been investigated in the bulk crystal of the orthorhombic (space group Pnma) and the hexagonal (space group P63 /mmc) phase (Figure 1). Simulation cells consisted of 48 atoms. In the non-stoichiometric systems Mn0.75 Co1.125 Ge1.125 , Mn0.75 CoGe1.25 and Mn0.688 Co1.062 Ge1.25 respectively 4, 4 and 5 Mn atoms have been substituted randomly by Co and/or Ge atoms. The orthorhombic and hexagonal structure of all compositions have been optimized for a non-magnetic (NM), a ferromagnetic (FM) and an anti-ferromagnetic (AFM) spin-configuration. For the ferromagnetic phase of stoichiometric MnCoGe the lattice parameters are optimized to ao =5.80 ˚ A, bo =3.895 ˚ A and co =7.026 ˚ A in the orthorhombic crystal and to ah =4.104 ˚ A and ch =5.233 ˚ A in the hexagonal structure in agreement with previous studies. 19,31

a

b

Pnma

Mn

Mn

c

P63/mmc

Co

c

Ge

Co

Ge

a

b

a

Figure 1: Unit cell of (a) orthorhombic (space group Pnma) and (b) hexagonal (space group P63 /mmc) MnCoGe. Purple, blue and green spheres indicate Mn, Co and Ge atoms, respectively.

Spin-dependent electron transport that gives rise to the giant magnetocaloric effect can be attributed to different chemical potentials and transport properties in the majority and minority spin channels of magnetic materials. Different scattering rates and densities result in dissimilar conductivity of electrons in the two spin channels when a temperature gradient 5 ACS Paragon Plus Environment


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is applied to a ferromagnetic material. This behavior has been denoted as the spin Seebeck effect implying the definition of separate spin Seebeck coefficients for spin-up and spin-down electrons in magnetic materials. The different transport properties of electrons with diverse spins generate a spin voltage which is described as the difference in chemical potential of spin-up and spin-down electrons (∆ (µ↑ − µ↓ )) 32,33 and it is proportional to the temperature gradient according to

∆ (µ↑ − µ↓ ) = eSS ∆T.

(1)

The meaning of the term ”spin Seebeck effect” used in literature is not clearly defined. Throughout this paper, we will refer to the spin Seebeck effect as the analog to the charge Seebeck effect and the spin Seebeck coefficient is defined as the absolute value of the difference between the spin-dependent Seebeck coefficients calculated separately in each of the two spin channels.

Sspin

1 ∆ (µ↑ − µ↓ ) = = e ∆T

1 ∂µc↑ ∂µc↓ − = |S ↑ − S ↓ | e ∂T ∂T

(2)

The spin-dependent Seebeck coefficients and the resulting spin Seebeck coefficient can be estimated using the semi-classical Boltzmann transport theory with the constant scattering time approximation where transport coefficients are calculated from the electronic band structure and the symmetry of the superlattice. Within this approach, the conductivity tensor is obtained according to

σαβ (i, k) = e2 τi,k vα (i, k) vβ (i, k) ,

(3)

where e is the electronic charge, τi,k is the relaxation time and vα,β are the α and β components, respectively, of the group velocity for an electron in band i. From the tensor, the distribution of the conductivity can be calculated by


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σαβ (ε) =

1 X δ (ε − εi,k ) σαβ (i, k) N i,k dε

where N is the number of sampled k-points.

(4)

This description of the conductivity

distribution allows for the determination of the temperature-(T ) and chemical-potential(µ)dependent transport coefficients according to Z ∂fµ (T, ε) 1 σαβ (ε) − dε, σαβ (T, µ) = Ω ∂ε Z 1 ∂fµ (T, ε) ναβ (T, µ) = σαβ (ε) (ε − µ) − dε eT Ω ∂ε

(5) (6)

where f is the Fermi-Dirac distribution. Finally, the Seebeck coefficient can be calculated by Sij = Ei (∇j T )−1 = σ −1

αi

ναj

(7)

In this work, results of the DFT calculations have been fed into the BoltTraP code 34 to calculated the Seebeck coefficients based on the method described above. With this method, only the electronic contribution to the Seebeck coefficient is considered and electron-phonon interactions are neglected. The effect of phonon-scattering can be introduced by the so-called phonon drag term. 35 The phonon contribution dominates in particular at temperatures below the Debye temperature while the electronic contribution dominates at higher temperatures. Introduction of the phonon-drag contribution was not feasible for this study and since we are mostly interested in the behavior of the materials around room temperatures and higher (>300 K) it has been neglected. At the temperatures studied it can still have a notable influence on the Seebeck coefficient. However, the phonon-drag contribution adds up to the normal Seebeck effect. 36 The presented results therefore give a lower limit of the Seebeck coefficient.



Results and Discussion Crystal structure Stoichiometric MnCoGe is found to be most stable in the orthorhombic phase with an FM spin-configuration (Figure 2a) in agreement with the experimental results for MnCoGe at room temperature. 15,37–39 In the FM configuration, a decrease of the crystal volume by 3.7% is calculated when the symmetry changes from orthorhombic to hexagonal supporting previous studies reporting a volume change by ca. 3.9%. 39,40 It has to be noted that in the

a

NM Pnma

b

1.2NM P63/mmc

MnCoGe

1.0

FM Pnma 1.0FM P63/mmc

0.8

0.8AFM P63/mmc

NM Pnma NM P63/mmc

0.6

FM Pnma FM P63/mmc

0.4

AFM Pnma AFM P63/mmc

0.2

0.6 0.4 0.2

0.0

0.0 36

1.2

Mn0.75Co1.125Ge1.125

AFM Pnma

E−E0 [eV]

E−E0 [eV]

1.2

38

40

3

42

V [Å ]

c

36 NM Pnma

d

1.2NM P63/mmc

Mn0.75CoGe1.25

FM Pnma

1.0

1.0FM P63/mmc

0.8 38

0.8AFM P63/mmc

38

3

40

42

V [Å ]

Mn0.688Co1.062Ge1.25

AFM Pnma

3

40

42

E−E0 [eV]

E−E0 [eV]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.6 V [Å ] 0.4 0.2

0.6 0.4 0.2

0.0

0.0 36

38

3

40

42

36

V [Å ]

38

3

40

42

V [Å ]

Figure 2: Total energy of (a) MnCoGe, (b) Mn0.75 Co1.125 Ge1.125 , (c) Mn0.75 CoGe1.25 and (d) Mn0.688 Co1.062 Ge1.25 as a function of the unit cell volume V (per MnCoGe unit) in the orthorhombic (Pnma, solid lines) and hexagonal (P63 /mmc, dotted lines) crystal structure with different spin-configurations NM (orange) and FM (green). non-magnetic case, the hexagonal phase is found to be more stable (by 0.05 eV) than the orthorhombic one. In the antiferromagnetic configuration, the two crystal phases are almost 8 ACS Paragon Plus Environment

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equi-energetic (∆E=0.006 eV, Figure 3). 0.10

0.02

−0.02 0.10

a 37

AFM P63mmc

0.06

0.06

E−E0 [eV]

E−E0 [eV]

0.04

0.02 0.00

0.00 38 −0.02 39

MnCoGe 373

40

V [Å ]

38

41

39

42

−0.02

V [Å3]

b

37 40 41 0.10 FM Pnma

AFM Pnma 0.08

0.06

0.06

38 42

39

3

40

41

42

V [Å ]

AFM P63mmc

0.04 0.02

−0.02

Mn0.75Co1.125Ge1.125

FM P63/mmc

0.08

0.00

AFM Pnma AFM P63/mmc

0.04

0.02

E−E0 [eV]

E−E0 [eV]

0.04

FM Pnma FM P63/mmc

FM P63/mmc

AFM Pnma 0.08

0.08

0.06

0.00

0.10 FM Pnma

0.10

0.08

E−E0 [eV]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.02 0.00

c 37

0.04

Mn0.75CoGe1.25 38

39

3

40

41

42

−0.02

d 37

Mn0.688Co1.062Ge1.25 38

V [Å ]

39

3

40

41

42

V [Å ]

Figure 3: Total energy of (a) MnCoGe, (b) Mn0.75 Co1.125 Ge1.125 , (c) Mn0.75 CoGe1.25 and (d) Mn0.688 Co1.062 Ge1.25 as a function of the unit cell volume V (per MnCoGe unit) in the orthorhombic (Pnma, solid lines) and hexagonal (P63 /mmc, dotted lines) crystal structure with an FM (green) and an AFM (blue) spin configuration. The change of the internal energy with volume has been fitted to the Murnaghan equation of states 41 to determine the equilibrium energy, volume and bulk modulus. In both the orthorhombic and the hexagonal crystal structure, the bulk modulus of the NM configuration is larger than the one of the magnetic FM and AFM configurations (Table 1). All non-stoichiometric configurations calculated here are most stable in the ferromagnetic orthorhombic phase similar to stoichiometric MnCoGe with a slightly larger equilibrium volume (0.7-2.1%). At the same time, the bulk modulus is reduced (Table 1) in particular in the case of Mn0.75 CoGe1.25 and Mn0.75 Co1.125 Ge1.125 indicating a somewhat larger compress9 ACS Paragon Plus Environment


AFM

FM

Table 1: Optimized lattice parameters a, b and c and bulk modulus BM in orthorhombic (Pnma) and hexagonal (P63 /mmc) MnCoGe with different composition and spin-configuration (NM, FM, AFM).

NM

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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MnCoGe Mn0.75 Co1.125 Ge1.125 Mn0.75 CoGe1.25 Mn0.688 Co1.062 Ge1.25 MnCoGe Mn0.75 Co1.125 Ge1.125 Mn0.75 CoGe1.25 Mn0.688 Co1.062 Ge1.25 MnCoGe Mn0.75 Co1.125 Ge1.125 Mn0.75 CoGe1.25 Mn0.688 Co1.062 Ge1.25

ao [˚ A] bo [˚ A] 5.792 3.892 5.778 3.929 5.488 4.015 5.679 4.012 5.747 3.897 5.578 4.016 5.717 4.012 5.706 4.009 5.518 3.832 5.475 3.876 5.370 3.928 5.550 3.960

Pnma co [˚ A] 7.043 7.038 7.354 7.087 7.103 7.028 7.089 7.075 6.941 7.035 7.196 6.982

BMo [GPa] 149 142 128 131 139 135 130 132 200 188 182 177

P63 /mmc ˚ ah [A] ch [˚ A] BMh [GPa] 4.106 5.235 136 4.133 5.188 135 4.190 5.162 121 4.187 5.145 126 4.098 5.295 150 4.141 5.176 143 4.199 5.152 127 4.191 5.142 132 4.083 4.957 210 4.109 4.978 197 4.135 5.019 184 4.163 4.946 187

ibility. As a result of asymmetric repulsive and attractive interactions between the atoms of the non-stoichiometric systems the ratio between the lattice parameters changes. This is most notable in the Mn0.75 CoGe1.25 system where ao becomes smaller by 5.2% while bo and co increase by 3.2% and 4.4%, respectively, with respect to stoichiometric MnCoGe. Details of the crystal structure of all configurations in the orthorhombic and hexagonal phase and with different spin-configurations are reported in Table 1.


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Electronic structure of MnCoGe The density of states of stoichiometric MnCoGe has been evaluated of the orthorhombic and the hexagonal phase both for non-magnetic and ferromagnetic spin configurations (Figure 4). The density of states of the NM configuration in both crystal phases is in good agreement with previous studies where the electronic structure has been calculated using the self-consistent Korringa-Kohn-Rostoker method. 42 In both the orthorhombic and the hexagonal structure, the states around the Fermi level responsible for the conducting nature of the material are primarily located on the Mn atoms. 42

a

c

P63/mmc

DOS [a.u.]

DOS [a.u.]

Pnma

FM NM

FM NM

d PDOS [a.u.]

b PDOS [a.u.]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Mn Co Ge

-15

Mn Co Ge

-10

-5

E-EF [eV]

0

5

-15

-10

-5

E-EF [eV]

0

5

Figure 4: Total density of states near the Fermi level of stoichiometric MnCoGe in (a) the orthorhombic and (c) the hexagonal phase with a non-magnetic (dotted line) and a ferromagnetic (solid line) spin-configuration. The projected density of states on the Mn, Co and Ge atoms, respectively, is shown for the ferromagnetic phase of (b) orthorhombic and (d) hexagonal MnCoGe. In the ferromagnetic spin-configuration, however, the occupied states are shifted to lower energies in the majority spin channel and the unoccupied states in the minority spin channel



to higher energies similar to the electronic structure in ferromagnetic Mn5 Ge3 . 43 This leads to a significant decrease of the density around the Fermi level indicating a loss of electrical conductivity in the ferromagnetic material. The density of states (Figure 4 b,d) projected on Ge atoms demonstrate that Ge plays a minor role for the electronic and magnetic structure around the Fermi level in both crystal structures. A high density of occupied states close to the Fermi level (∆E ≈ 3eV) is observed both on Mn and Co atoms. The projected density of states further indicates that the magnetic moment is mostly carried by Mn atoms while minor asymmetric spin occupation is found on Co atoms. This is slightly more pronounced in the orthorhombic phase (Figure 4b,d). In the non-stoichiometric systems, a broadening of the states is observed with decreasing Mn content (Figure 5). In particular, the Mn-type states of the spin up channel at around 3 eV below the Fermi level in the Pnma phase is remarkably reduced in Mn0.75 CoGe1.25 and Mn0.688 Co1.062 Ge1.25 . It is further noticed that in particular in the spin down channel of the Pnma crystals, the states on the upper edge of the valence band are shifted closer to the Fermi level leading to a rather metallic characteristic of the DOS. Pnma Pnma

P6P6 3/mmc /mmc

DOS

3

DOS

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MnCoGe Mn0.75Co1.125Ge1.125 Mn0.75CoGe1.25 Mn0.688Co1.062Ge1.25

-15

-10


-5

E-EF [eV]

0

5

-15

-10

-5

E-EF [eV]

0

5

Figure 5: Total density of states near the Fermi level of all systems in (a) the orthorhombic and (b) the hexagonal phase with a ferromagnetic spin-configuration.


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Stability A stable hexagonal phase of MnCoGe thin films at room temperature has been observed in experiments carried out in our laboratory. 44 The reason for the hexagonal phase to be stable at room temperature, however, is not resolved yet. This in mind, we have analyzed the differences in the thermodynamic equilibrium of the hexagonal and the orthorhombic phase of MnCoGe with various compositions. For this, the energy difference ∆Eh−o (=EP63 /mmc − EPnma ) between the equilibrium point of the orthorhombic and the hexagonal phase with a ferromagnetic spin-configuration has been calculated. Results are shown in Figure 6. In stoichiometric MnCoGe, ∆Eh−o is largest with 0.035 eV (per MnCoGe unit). It is smaller for all non-stoichiometric configurations, most notably in Mn0.75 Co1.125 Ge1.125 with an energy difference below 0.01 eV. It is even smaller if we consider a possible change of the magnetic structure to AFM (∆E=0.003 eV). This indicates that already small perturbations can lead to a change from the orthorhombic to the hexagonal phase and possibly also a transition from FM to AFM. Experimental studies have observed an antiferromagnetic phase of hexagonal Co7−x Mnx Ge6.1 with x≤2.8. 27 There, it has been suggested that the antiferromagnetic behavior is promoted by Co-Co and Co-Mn interactions. In fact, we have found the AFM structure to be most probable in the Mn0.75 Co1.125 Ge1.125 system which has the highest Co content. In the mentioned experiments of our laboratory, Mn, Co and Ge have been deposited on Si(111) substrates by simultaneous magnetron sputtering. Using this method, formation of small Mn clusters has been observed which leads to a depletion of Mn in the MnCoGe layers. All thin films are found to be stable in the hexagonal phase even after annealing. From the results of the calculations, however, we find the orthorhombic structure to be favored in the Mn-depleted bulk materials. In thin films, perturbations can result from surface strain which is not present in the bulk phase. This can possibly lead to a volume change in the crystal. The equilibrium volume of the hexagonal phase in stoichiometric FM MnCoGe is by 3.7% smaller with respect to the orthorhombic equilibrium volume. The volume difference 13 ACS Paragon Plus Environment


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in Mn0.75 Co1.125 Ge1.125 is slightly larger (3.9%). In Mn0.75 CoGe1.25 and Mn0.688 Co1.062 Ge1.25 it is slightly smaller with 3.1% and 3.3% (Figure 6). Even though the changes are quite small it indicates that an altered composition of MnCoGe materials can possibly result in a facilitated change of the crystal phase when the material is exposed to pressure and thus to volume change. Additional perturbation in the unordered structure of the real material can result from the formed Mn clusters and it can be considered that the hexagonal phase is favored by the deposition on the Si(111) substrate. The calculations carried out here are focused on thermodynamic properties. Kinetic properties such as the activation energy for a phase change from orthorhombic to hexagonal are not considered. However, the results give an idea of the difference in the two equilibrium points and it can be assumed that smaller energy differences facilitate the phase change and reduce the transition temperature. The pressure effect on the stability of the systems has been investigated based on the Murnaghan equation. 41 In the Murnaghan equation of states, pressure and volume of a solid crystal are related according to B0 P (V ) = 0 B0

"

V V0

−B00

# −1

(8)

where B0 is the bulk modulus, B00 its derivative with respect to pressure and V0 the equilibrium volume. Equation 8 with the parameters of the most stable ferromagnetic Pnma phase has been used to estimate the pressure that has to be applied to overcome the volume difference between the equilibrium of the ferromagnetic Pnma phase and the equilibrium of the other configurations that have been investigated here. The highest pressure to reach the equilibrium volume of the ferromagnetic P63 phase has to be applied in Mn0.75 Co1.125 Ge1.125 with a value of 62 kbar similar to stoichiometric MnCoGe (61.5 kbar, Table 2). The required pressure in Mn0.75 CoGe1.25 and Mn0.688 Co1.062 Ge1.25 is about 25% smaller (44 and 47 kbar, repsectively).


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EP63/mmc-EPnma [eV]

0.04

a

MnCoGe

0.03 Mn0.688Co1.062Ge1.25

0.02

Mn0.75CoGe1.25

0.01 -3.0

ΔVP63/mmc-Pnma [%]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-3.2

Mn0.75Co1.125Ge1.125

b

0.4

0.6 0.8 Mn0.75CoGe1.25 content (1-x-y) Mn0.688Co1.062Mn Ge1.25

1

-3.4 -3.6 MnCoGe

-3.8 Mn0.75Co1.125Ge1.125

-4.0 0.4

0.6

0.8 Mn content (1-x-y)

1

Figure 6: (a) Energy difference between hexagonal (EP63 /mmc ) and orthorhombic (EPnma ) MnCoGe as a function of the Mn content and (b) change of volume (∆VP63 /mmc−Pnma = V0,P63 /mmc − V0,Pnma /V0,Pnma ) required to move from the orthorhombic to the hexagonal phase. Changes in the magnetic configuration from NM to AFM are found to be most favorable. In fact, the volume has to be expanded applying negative pressures from -2.8 to -4.8 kbar in MnCoGe, Mn0.75 CoGe1.25 and Mn0.688 Co1.062 Ge1.25 . A pressure of 21.4 kbar is required in Mn0.75 Co1.125 Ge1.125 . More results are shown in Table 2.

Magnetic Properties Magnetic stability of a system can be characterized by the Curie temperature TC where the material undergoes a transition from a ferromagnetic to a paramagnetic spin-configuration. At room temperature, stoichiometric MnCoGe in the orthorhombic phase is ferromagnetic and changes to a paramagnetic configuration at a transition temperature of 345 K. 19,20 In



Table 2: Estimated pressure that has to be applied to overcome the volume difference between the equilibrium of the most stable ferromagnetic Pnma phase and other crystal and magnetic configurations.

configuration Pnma P63 /mmc Pnma P63 /mmc Pnma P63 /mmc

NM AFM FM

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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MnCoGe ˚ V0 [A] P [kbar] 39.7 – 38.2 61.5 39.8 -2.9 38.5 48.4 36.7 139.3 35.8 194.7

Mn0.75 Co1.125 Ge1.125 V 0 [˚ A] P [kbar] 39.9 – 38.4 62.0 39.4 21.4 38.4 59.6 37.3 112.3 36.4 162.7

Mn0.75 CoGe1.25 V 0 [˚ A] P [kbar] 40.5 – 39.2 44.0 40.6 -4.2 39.3 40.9 38.0 98.0 37.1 137.2

Mn0.688 Co1.062 Ge1.25 V0 [˚ A] P [kbar] 40.4 – 39.0 47.3 40.5 -2.8 39.1 45.4 38.4 75.8 37.1 135.7

the hexagonal phase, a smaller TC of 275 K is reported. 18 To get an estimation of the magnetic stability in the MnCoGe systems investigated here, the energy difference between the ferromagnetic and the non-magnetic configuration at the equilibrium volume of the FM phase has been determined. In stoichiometric MnCoGe it is calculated to be 0.876 eV and 0.751 eV in the orthorhombic and the hexagonal phase, respectively (Figure 7). The smaller energy difference for the transition in the hexagonal phase is in agreement with the smaller transition temperature found experimentally. In all non-stoichiometric configurations the energy difference decreases with respect to stoichiometric MnCoGe suggesting that these materials exhibit a smaller Curie temperature. Based on these results the lowest TC is expected in Mn0.688 Co1.062 Ge1.25 where the energy difference is calculated to be 0.52 and 0.45 eV for the orthorhombic and the hexagonal phase, respectively (Figure 7). Similarly, decrease of TC has been observed experimentally in MnCo0.95 Gex . 17 As depicted in Figure 7, the energy difference (and correspondingly TC ) tend to decrease with decreasing Mn content. This is also in line with preliminary studies on the materials produced in our laboratory showing a tendency of TC to decreasing with decreasing Mn content and vice versa, increasing TC with increasing Mn content. The absolute magnetic moment in stoichiometric MnCoGe is found to be 4.33 µB (per MnCoGe unit) and 3.86 µB in the orthorhombic and the hexagonal crystal structure, respec16 ACS Paragon Plus Environment

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0.9 MnCoGe (TC=345 K)

Pnma P63/mmc

0.8

MnCoGe (TC=275 K)

0.7

Mn0.75Co1.125Ge1.125

TC

ENM-EFM [eV]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.6

Mn0.75CoGe1.25 Mn0.688Co1.062Ge1.25

0.5

Mn0.75Co1.125Ge1.125 Mn0.75CoGe1.25 Mn0.688Co1.062Ge1.25

0.4 0.4

0.6

0.8 Mn content (1-x-y)

1

Figure 7: Energy difference between non-magnetic (ENM ) and ferromagnetic (EFM ) MnCoGe as a function of the Mn content in the orthorhombic (triangles up) and hexagonal (triangles down) structure. tively. The larger magnetic moment in orthorhombic MnCoGe is consistent with previous studies 20,42 and can be explained by the narrower 3d bandwidth and the increased exchange splitting between majority and minority bands as a result of the larger Mn-Mn distance. The primary carriers of the magnetic moment in both the orthorhombic and the hexagonal phase are Mn atoms with µ of 3.28 µB and 3.09 µB , respectively (Table 3), in agreement with the literature. 20,42 A notable contribution to the total magnetic moment results also from the Co atoms with 0.66 µB an 0.46 µB , respectively (Table 3). It has been matter of dispute whether the lower magnetic moment in the hexagonal structure is attributed to the vanishing moment on Co atoms 42 or rather the reduced moment on Mn atoms. 18 Our results show a reduced but not vanishing moment on both Mn and Co atoms in the hexagonal structure, thus supporting the latter position. A decrease of the absolute magnetic moment with decreasing Mn content is observed (Figure 8) similar to the trend of the energy difference between FM and NM phase (Figure 7). This is in agreement with the reduced Mn content which are the main carriers of the magnetic moment. Only marginal changes in the magnetic moment on Mn atoms is observed in the 17 ACS Paragon Plus Environment


4.5 Pnma P63/mmc

MnCoGe

4.0

µabs [µB/UC]

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MnCoGe Mn0.75Co1.125Ge1.125

3.5 Mn0.75CoGe1.25 Mn0.75Co1.125Ge1.125

3.0

Mn0.688Co1.062Ge1.25 Mn0.75CoGe1.25 Mn0.688Co1.062Ge1.25

0.6

0.7 0.8 0.9 Mn content (1-x-y)

1

Figure 8: Absolute magnetic moment in ferromagnetic MnCoGe as a function of the Mn content in the orthorhombic (triangles up) and hexagonal (triangles down) structure. non-stoichiometric configurations (≤3%, Table 3). Instead, notable variations are observed in the magnetic moments on Co atoms. In the orthorhombic phase it decreases by up to 23% in the alloys where both Co and Ge content are increased (Mn0.75 Co1.125 Ge1.125 and Mn0.688 Co1.062 Ge1.25 ). In the hexagonal phase, on the other hand, it is reduced by 26% in Mn0.75 CoGe1.25 and Mn0.688 Co1.062 Ge1.25 . The reduced magnetic moment on Co atoms with reduced Mn content indicates that the asymmetric spin distribution on Co is induced by the magnetic moment on Mn atoms. To examine the effect of the Mn-Mn interatomic distance on the magnetic moment of the materials, the absolute magnetic moment in the different systems has been determined as a function of the unit cell volume which corresponds directly to the Mn-Mn distance. As shown in Figure 9, the magnetic moment increases linearly with increasing average Mn-Mn distance (of nearest neighbors) in line with the increasing magnetic moment with increasing Mn-Mn distance stated in literature. 20,42 For different chemical compositions, this trend is only valid considering the magnetic 18 ACS Paragon Plus Environment

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P63 /mmc

Pnma

Table 3: Total and absolute magnetic moment in µB per MnCoGe unit in the ferromagnetic phase of orthorhombic (Pnma) and hexagonal (P63 /mmc) MnCoGe alloys and magnetic moment on the Mn, Co and Ge atoms, respectively.

4.5

MnCoGe Mn0.75 Co1.125 Ge1.125 Mn0.75 CoGe1.25 Mn0.688 Co1.062 Ge1.25 MnCoGe Mn0.75 Co1.125 Ge1.125 Mn0.75 CoGe1.25 Mn0.688 Co1.062 Ge1.25

total 3.81 3.06 3.00 2.69 3.48 2.85 2.56 2.43 4.5

Pnma

4.0

4.0

3.5

3.5

µabs [µB/UC]

µabs [µB/UC]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3.0

Co 0.66 0.57 0.67 0.51 0.46 0.46 0.34 0.34

Ge -0.08 -0.06 -0.06 -0.07 -0.07 -0.05 -0.06 -0.05

P63/mmc

3.0

MnCoGe Mn0.75Co1.125Ge1.125 2.5 Mn0.75CoGe1.25 Mn0.688Co1.062Ge1.25

2.5 2.0

µ [µB /UC] absolute Mn 4.33 3.28 3.51 3.28 3.41 3.19 3.08 3.22 3.86 3.09 3.20 3.07 2.94 3.03 2.79 3.03

35

36

37

38

39

40

41

2.0

35 42

36

37

V [Å3]

38

39

40

41

42

V [Å3]

Figure 9: Absolute magnetic moment µabs per MnCoGe unit (UC) as a function of the unit cell volume V in the orthorhombic (Pnma) and the hexagonal (P63 /mmc) crystal. moment in the two structural phases in general (Figure 10), i.e. the Mn-Mn interatomic distance in all hexagonal structures is smaller with respect to the orthorhombic structure resulting in a smaller magnetic moment. However, no distinct correlation between MnMn distance and magnetic moment on Mn atoms is noticeable when comparing magnetic moments and Mn-Mn distance separately in either of the two structural phases (Figure 10). This indicates that heteroatomic interactions are more relevant for exchange splitting and in consequence of the magnetic properties than just the interatomic Mn-Mn distance.



Pnma P63/mmc

3.3

Mn0.75Co1.125Ge1.125 MnCoGe

µMn [µB/UC]

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Mn0.688Co1.062Ge1.25

3.2

Mn0.75CoGe1.25

3.1

MnCoGe Mn0.75Co1.125Ge1.125 Mn0.75CoGe1.25

3.0

Mn0.688Co1.062Ge1.25

2.6

2.7

2.8

2.9 dMn−Mn [Å]

3.0

3.1

Figure 10: Average magnetic moment µM n on the Mn atom as a function of the nearest neighbor Mn-Mn bond length in ferromagnetic MnCoGe with different compositions in the orthorhombic (triangles up) and hexagonal (triangles down) structure.


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Spin Seebeck effect The Seebeck coefficient has been estimated for all compositions in the FM configuration of the orthorhombic and the hexagonal phase. It has been determined separately for each spin channel using the BoltzTraP toolbox and the spin Seebeck coefficient has then been calculated as the difference between majority and minority spin channel (Sspin =|S↑ − S↓ |). The spin-dependent Seebeck coefficient has been analyzed as a function of the chemical potential µ close to the Fermi energy (µF ) at 200, 300 and 500 K (Figure 11). As expected, the Seebeck coefficient shows different behavior in the two spin channels. In all phases of the different systems, the Seebeck coefficient in both majority (spin up) and minority (spin down) spin channel varies significantly with the chemical potential. One exception is S of the majority spin channel in orthorhombic Mn0.688 Co1.062 Ge1.25 at high temperature (500 K, Figure 11c). There, an almost constant value around 25 µV/K is observed. In the orthorhombic and the hexagonal crystal the value of the Seebeck coefficient varies for most of the systems between -50 and 50 µV/K. These values are relatively low compared to good bulk thermoelectric materials that are around 150-250 µV/K. 45 However, it has to be noted that the phonon drag effect has not been considered in the calculations and can possibly lead to a higher value of the Seebeck coefficient. Higher values are found in orthorhombic stoichiometric MnCoGe in the minority spin channel (Figure 11a). Here, the Seebeck coefficient changes sign from 70 µV/K (hole doping) to -90 µV/K (electron doping). Such discontinuity of S is usually found in semicoductors at the Fermi level. 46 In the orthorhombic stoichiometric MnCoGe it can possibly be explained by a small band gap in the minority spin of the Co-type states at ca. 0.1 eV below the Fermi energy (Figure 4). More significant is the discontinuity of S in the minority spin channel of orthorhombic Mn0.75 Co1.125 Ge1.125 . The change from positive to negative values is found directly at the Fermi energy and the maximum values around the discontinuity reach up to 200 µV/K at a temperature of 200 K. In the majority spin-channel, values are significantly smaller and 21 ACS Paragon Plus Environment


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no semiconducting-type behavior is found. Similar behaviors of the spin-dependent Seebeck coefficient have been found previously in half-metallic SrTiO3 /SrRuO3 superlattices 46 indicating that the orthorhombic Mn0.75 Co1.125 Ge1.125 has half-metallic character. No indication of a band gap in the total DOS has been observed in the minority spin channel of ferromagnetic orthorhombic Mn0.75 Co1.125 Ge1.125 (Figure 5). Analysis of the band structure along the high-symmetric k-point path Γ -X-S-Y-Γ -Z-U-R-T, however, showed a band gap in the minority spin channel of ca. 0.1 eV (Figure S2). No such band gap is observed in any of the other systems and crystal structures (Figure S1, S3-S8). The remarkable increase of the Seebeck coefficient in the minority spin channel of FM orthorhombic Mn0.75 Co1.125 Ge1.125 can thus been attributed to the formation of a small band gap leading to a half-metallic character of this system. Further investigation of the Seebeck coefficient in orthorhombic Mn0.75 Co1.125 Ge1.125 has been done focusing on the pressure effect. Figure 12 shows the spin-dependent Seebeck coefficient of orthorhombic Mn0.75 Co1.125 Ge1.125 applying a pressure of up to 163 kbar. The discontinuity of the Seebeck coefficient in the minority spin channel shifts towards smaller chemical potentials with increasing pressure. Furthermore, the maximum value of the Seebeck coefficient is decreased. This suggests that the thermoelectric properties of such a half-metallic material can be controlled and varied applying an external pressure. The temperature-dependent spin Seebeck coefficient of all materials is shown in Figure 13. It only gives a rough estimation of the temperature dependence of S since its value is taken at the Fermi energy and as presented in Figure 11 S significantly varies with the chemical potential. Nevertheless, it is an indication of the temperature effect on the Seebeck coefficient as has been shown in several studies previously. 47,48 Except for orthorhombic Mn0.75 Co1.125 Ge1.125 as discussed above, the Seebeck coefficient tends to increase with increasing temperature. In the Pnma phase, the maximum value is reached around 250 K. This is similar in the P63 /mmc phase of Mn0.75 Co1.125 Ge1.125 and Mn0.75 CoGe1.25 while in stoichiometric MnCoGe and Mn0.688 Co1.062 Ge1.25 it increases further


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with increasing temperature up to 500 K. The general trend shows a higher Sspin in the orthorhombic phase compared to the hexagonal one. This can possibly result from the smaller density of states around the Fermi energy in the ferromagnetic orthorhombic structures (Figure 5) leading to semiconducting-like characteristics.



100

300

a

MnCoGe 200

b

Mn0.75Co1.125Ge1.125

50

S [µV/K]

S [µV/K]

100 0

0 -100

-50 -200

200 K 300 K 500 K

Pnma 100

50

S [µV/K]

S [µV/K]

0

0

-50

-50

P63/mmc -100 -0.4 100

-0.3

-0.2

c

P63/mmc

spin up spin down -0.1

0.0

0.1

µ-µF [eV]Mn

0.2

-100 0.4 -0.4 100

0.3

-0.2


0.0

0.1

µ-µMn F [eV]

0.2

0.3

0.4

0.688Co1.062Ge1.25

S [µV/K]

50

0

-50

0

-50 200 K 300 K 500 K

Pnma 100

200 K 300 K 500 K

Pnma 100

50

S [µV/K]

50

0

-50

0

-50

P63/mmc -100 -0.4

-0.3

d

0.75CoGe1.25

50

S [µV/K]

200 K 300 K 500 K

Pnma

-300

50

S [µV/K]

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-0.3

-0.2


0.0

0.1

µ-µF [eV]

0.2

0.3

P63/mmc -100 0.4 -0.4

-0.3

-0.2


0.0

0.1

µ-µF [eV]

0.2

0.3

0.4

Figure 11: Seebeck coefficient of the spin up (solid lines) and spin down (dotted lines) channels in orthorhombic (Pnma) and hexagonal (P63 /mmc) MnCoGe with different compositions at a temperature of 200, 300 and 500 K. Note the different scale in (b) Mn0.75 Co1.125 Ge1.125 .


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200 0 kbar 12 kbar 35 kbar 61 kbar 109 kbar 163 kbar

S [µV/K]

100

0

-100

spin up spin down

-200 -0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

EF [eV]

Figure 12: Seebeck coefficient of the spin up (solid lines) and spin down (dotted lines) channels in orthorhombic (Pnma) Mn0.75 Co1.125 Ge1.125 at different pressures.

120

40 MnCoGe Pnma Mn0.75Co1.125Ge1.125 Mn0.75CoGe1.25 Mn0.688Co1.062Ge1.25

100 80

35 30

Sspin [µV/K]

Sspin [µV/K]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


60 40

P63/mmc

25 20 15 10

20 0 100


5 200

300

400

500

0 100

200

T [K]

300

400

500

T [K]

Figure 13: Spin Seebeck coefficient (Sspin =|S↑ − S↓ |) as a function of the temperature in orthorhombic (Pnma) and hexagonal (P63 /mmc) MnCoGe with different compositions.



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Conclusions Thermoelectric Mn1−x−y Co1+x Ge1+y has been studied by DFT calculations. In all systems, the orthorhombic FM phase is found to be most stable, however, smaller energy differences are found between the orthorhombic and the hexagonal equilibrium phase in nonstoichiometric compositions, indicating a facilitated phase transition. The crystal volume of the hexagonal phase is found to be smaller by 3-4% in agreement with previous studies and varies slightly with the composition of the MnCoGe alloy. In both the orthorhombic and the hexagonal phase, the energy difference between the FM and the NM state has been calculated where the one in the hexagonal phase is found to be smaller in line with the smaller Curie temperature reported in the literature. The decrease of the energy difference with decreasing Mn content indicates a decrease of the Curie temperature in Mn depleted compounds. With increasing crystal volume, and thus increasing Mn-Mn distance, the absolute magnetic moment in the materials increases linearly as a result of enhanced exchange splitting between majority and minority channels. This trend is confirmed by the lower magnetic moment in the hexagonal phase where the Mn-Mn distance is smaller compared to the orthorhombic phase. However, no correlation between magnetic moment on Mn atoms and Mn-Mn distance is found with altering composition within one crystal phase. Considering this and the decrease of the absolute magnetic moment with decreasing Mn content it can be concluded that the magnetic moment of these materials primarily depends on the magnetic moment on Mn atoms. It is therefore expected that MnCoGe alloys with higher Mn content exhibit a higher magnetic moment and possibly show a higher magnetocaloric effect. In general, the spin Seebeck coefficient of the ferromagnetic materials has been found to be higher in the orthorhombic phase. This can possibly be related to the smaller density of states around the Fermi energy in the orthorhombic structures compared to the hexagonal ones leading to a small band gap and a semiconducting-type behavior of the spin-dependent 26 ACS Paragon Plus Environment

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Seebeck coefficient. This is in particularly true for Mn0.75 Co1.125 Ge1.125 , where the Seebeck coefficient of the minority spin channel reaches values up to 200 µV/K at a temperature of 200 K. It can possibly related to a small band gap of 0.1 eV found in the band structure of the minority spin channel. In conclusion, these results prove a possible way to direct the crystal phase and magnetic properties in MnCoGe alloys by small changes in their chemical composition.

Acknowledgement This work is financially supported by the A*MIDEX foundation.

Computational time

was provided by the HPC resources of Aix-Marseille Université financed by the project Equip@Meso (ANR-10-EQPX-29-01) of the program ”Investissements d‘Avenir” supervised by the Agence Nationale de la Recherche.

References (1) Russek, S. L.; Zimm, C. B. Potential for Cost Effective Magnetocaloric Air Conditioning Systems. Int. J. Refrig. 2006, 29, 1366–1373. (2) Warburg, E. Magnetische Untersuchungen. Ann. Phys. 1881, 249, 141–164. (3) Weiss, P.-E.; Piccard, A. Sur un Nouveau Phénomène Magnétocalorique. C. R. Acad. Sci. 1918, 166, 352. (4) Giauque, W. F. A Thermodynamic Treatment of Certain Magnetic Effects. A Proposed Method of Producing Temperatures Considerably Below 1◦ Absolute. J. Am. Chem. Soc. 1927, 49, 1864–1870. (5) Giauque, W. F.; MacDougall, D. P. Attainment of Temperatures Below 1◦ Absolute by Demagnetization of Gd2 (SO4 )3 ·8H2 O. Phys. Rev. 1933, 43, 768–768. 27 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(6) Baibich, M. N.; Broto, J. M.; Fert, A.; Van Dau, F. N.; Petroff, F. Giant Magnetoresistance of (001)Fe/(001)Cr Magnetic Superlattices. Phys. Rev. Lett. 1988, 61, 2472–2475. (7) Binasch, G.; Gr¨ unberg, P.; Saurenbach, F.; Zinn, W. Enhanced Magnetoresistance in Layered Magnetic Structures with Antiferromagnetic Interlayer Exchange. Phys. Rev. B 1989, 39, 4828–4830. (8) Hu, F.-x.; Shen, B.-g.; Sun, J.-r.; Cheng, Z.-h.; Rao, G.-h.; Zhang, X.-x. Influence of Negative Lattice Expansion and Metamagnetic Transition on Magnetic Entropy Change in the Compound LaFe11.4 Si1.6 . Appl. Phys. Lett. 2001, 78, 3675–3677. (9) Yan, A.; M¨ uller, K.-H.; Gutfleisch, O. Structure and Magnetic Entropy Change of Melt-spun LaFe11.57 Si1.43 Ribbons. J. Appl. Phys. 2005, 97, 036102. (10) Pecharsky, V. K.; Gschneidner, Jr., K. A. Giant Magnetocaloric Effect in Gd5 (Si2 Ge2 ). Phys. Rev. Lett. 1997, 78, 4494–4497. (11) Gschneidner, K. A.; Pecharsky, V. K.; Tsokol, A. O. Recent Developments in Magnetocaloric Materials. Rep. Prog. Phys. 2005, 68, 1479–1539. (12) Tegus, O.; Br¨ uck, E.; Buschow, K. H. J.; de Boer, F. R. Transition-Metal-Based Magnetic Refrigerants for Room-Temperature Applications. Nature 2002, 415, 150–152. (13) Yan, A.; M¨ uller, K.-H.; Schultz, L.; Gutfleisch, O. Magnetic Entropy Change in MeltSpun MnFePGe (invited). J. Appl. Phys. 2006, 99, 08K903. (14) Br¨ uck, E.; Tegus, O.; Cam Thanh, D.; Trung, N. T.; Buschow, K. A Review on Mn Based Materials for Magnetic Refrigeration: Structure and Properties. Int. J. Refrig. 2008, 31, 763–770. (15) Lin, S.; Tegus, O.; Br¨ uck, E.; Dagula, W.; Gortenmulder, T.; Buschow, K. Structural and Magnetic Properties of MnFe1−x Cox Ge Compounds. IEEE T. Magn. 2006, 42, 3776–3778. 28 ACS Paragon Plus Environment

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(16) Ba˚ zela, W.; Szytula, A.; Todorović, J.; Tomkowicz, Z.; Zi¸eba, A. Crystal and Magnetic Structure of NiMnGe. Phys. Status Solidi A 1976, 38, 721–729. (17) Liu, J.; Skokov, K.; Gutfleisch, O. Magnetostructural Transition and Adiabatic Temperature Change in MnCoGe Magnetic Refrigerants. Scripta Mater. 2012, 66, 642–645. (18) Kanomata, T.; Ishigaki, H.; Sato, K.; Sato, M.; Shinohara, T.; Wagatsuma, F.; Kaneko, T. NMR Study of

55

Mn and

59

Co in MnCoGe. J. Magn. Soc. Jpn. 1999,

23, 418–420. (19) Niziol, S.; Bombik, A.; Ba˚ zela, W.; Szytula, A.; Fruchart, D. Crystal and Magnetic Structure of Cox Ni1−x MnGe System. J. Magn. Magn. Mater. 1982, 27, 281–292. (20) Wang, J.-T.; Wang, D.-S.; Chen, C.; Nashima, O.; Kanomata, T.; Mizuseki, H.; Kawazoe, Y. Vacancy Induced Structural and Magnetic Transition in MnCo1−x Ge. Appl. Phys. Lett. 2006, 89, 262504. (21) Fang, Y.; Yeh, C.; Chang, C.; Chang, W.; Zhu, M.; Li, W. Large Low-Field Magnetocaloric Effect in MnCo0.95 Ge1.14 Alloy. Scripta Mater. 2007, 57, 453–456. (22) Trung, N. T.; Biharie, V.; Zhang, L.; Caron, L.; Buschow, K. H. J.; Br¨ uck, E. From Single- to Double-first-order Magnetic Phase Transition in Magnetocaloric Mn1−x Crx CoGe Compounds. Appl. Phys. Lett. 2010, 96, 162507. (23) Niziol, S.; Zach, R.; Senateur, J.; Beille, J. Pressure Dependence of the Magnetic Transition Temperature of the CoMnGe1−x Six System. J. Magn. Magn. Mater. 1989, 79, 333–337. (24) Caron, L.; Trung, N. T.; Br¨ uck, E. Pressure-tuned Magnetocaloric Effect in Mn0.93 Cr0.07 CoGe. Phys. Rev. B 2011, 84, 020414. (25) Zeng, J.; Wang, Z.; Nie, Z.; Wang, Y. Crystal Structural Transformation Accompanied by Magnetic Transition in MnCo1−x Fex Ge Alloys. Intermetallics 2014, 52, 101–104. 29 ACS Paragon Plus Environment


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(26) Trung, N. T.; Zhang, L.; Caron, L.; Buschow, K. H. J.; Br¨ uck, E. Giant Magnetocaloric Effects by Tailoring the Phase Transitions. Appl. Phys. Lett. 2010, 96, 172504. (27) Hori, T.; Shiraishi, H.; Kato, H.; Kido, G.; Nakagawa, Y. Magnetic Properties of M7−x Mnx Ge6 (M = Co, Fe). J. Magn. Magn. Mater. 1992, 104-107, 2043–2044. (28) Salomon, S.; Hamann, S.; Decker, P.; Savan, A.; Meshi, L.; Ludwig, A. Combinatorial Synthesis and High-throughput Characterization of the Thin Film Materials System Co-Mn-Ge: Composition, Structure, and Magnetic Properties. Phys. Status Solidi A 2015, 212, 1969–1974. (29) Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I. et al. QUANTUM ESPRESSO: A Modular and Open-Source Software Project for Quantum Simulations of Materials. J. Phys.Condens. Mat. 2009, 21, 395502. (30) Vanderbilt, D. Soft Self-Consistent Pseudopotentials in a Generalized Eigenvalue Formalism. Phys. Rev. B 1990, 41, 7892–7895. (31) Szytula, A.; Pdziwiatr, A.; Tomkowicz, Z.; Ba˚ zela, W. Crystal and Magnetic Structure of CoMnGe, CoFeGe, FeMnGe and NiFeGe. J. Magn. Magn. Mater. 1981, 25, 176–186. (32) Uchida, K.; Takahashi, S.; Harii, K.; Ieda, J.; Koshibae, W.; Ando, K.; Maekawa, S.; Saitoh, E. Observation of the Spin Seebeck Effect. Nature 2008, 455, 778–781. (33) Bauer, G. E. W.; Saitoh, E.; van Wees, B. J. Spin Caloritronics. Nat. Mater. 2012, 11, 391–399. (34) Madsen, G. K.; Singh, D. J. BoltzTraP. A Code for Calculating Band-Structure Dependent Quantities. Comput. Phys. Commun. 2006, 175, 67–71. (35) Mahan, G. D.; Lindsay, L.; Broido, D. A. The Seebeck Coefficient and Phonon Drag in Silicon. J. Appl. Phys. 2014, 116, 245102. 30 ACS Paragon Plus Environment

Page 30 of 33

Page 31 of 33

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(36) Zhou, J.; Liao, B.; Qiu, B.; Huberman, S.; Esfarjani, K.; Dresselhaus, M. S.; Chen, G. Ab Initio Optimization of Phonon Drag Effect for Lower-Temperature Thermoelectric Energy Conversion. P. Natl. A. Sci. USA 2015, 112, 14777–14782. (37) Liu, E. K.; Zhu, W.; Feng, L.; Chen, J. L.; Wang, W. H.; Wu, G. H.; Liu, H. Y.; Meng, F. B.; Luo, H. Z.; Li, Y. X. Vacancy-tuned Paramagnetic/Ferromagnetic Martensitic Transformation in Mn-poor Mn1−x CoGe Alloys. Europhys. Lett. 2010, 91, 17003. (38) Niziol, S.; Weselucha, A.; Ba˚ zela, W.; Szytula, A. Magnetic Properties of the Cox Ni1−x MnGe System. Solid State Commun. 1981, 39, 1081–1085. (39) Johnson, V. Diffusionless Orthorhombic to Hexagonal Transitions in Ternary Silicides and Germanides. Inorg. Chem. 1975, 14, 1117–1120. (40) Kanomata, T.; Ishigaki, H.; Suzuki, T.; Yoshida, H.; Abe, S.; Kaneko, T. MagnetoVolume Effect of MnCo1−x Ge (0 ≤ x ≤ 0.2). J. Magn. Magn. Mater. 1995, 140-144, 131–132. (41) Murnaghan, F. D. The Compressibility of Media under Extreme Pressures. P. Natl. A. Sci. USA 1944, 30, 244–247. (42) Kaprzyk, S.; Niziol, S. The Electronic Structure of CoMnGe with the Hexagonal and Orthorhombic Crystal Structure. J. Magn. Magn. Mater. 1990, 87, 267–275. (43) Slipukhina, I.; Arras, E.; Mavropoulos, P.; Pochet, P. Simulation of the Enhanced Curie Temperature in Mn5 Ge3 Cx Compounds. Appl. Phys. Lett. 2009, 94, 192505. (44) Portavoce, A.; Assaf, E.; Alvarez, C.; Bertoglio, M.; Clerac, R.; Hoummada, K.; Alfonso, C.; Charai, A.; Pilone, O.; Hahn, K. R. et al. Ferromagnetic MnCoGe Thin Films Elaborated via Magnetron Sputtering and Non-Diffusive Reaction. submitted (45) Tritt, T. M.; Subramanian, M. A. Thermoelectric Materials, Phenomena, and Applications: A Bird’s Eye View. MRS Bull. 2006, 31, 188–198. 31 ACS Paragon Plus Environment


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(46) Garc´ıa-Fernández, P.; Verissimo-Alves, M.; Bilc, D. I.; Ghosez, P.; Junquera, J. FirstPrinciples Modeling of the Thermoelectric Properties of SrTiO3 /SrRuO3 Superlattices. Phys. Rev. B 2012, 86, 085305. (47) Miao, N.; Xu, B.; Bristowe, N. C.; Bilc, D. I.; Verstraete, M. J.; Ghosez, P. FirstPrinciples Study of the Thermoelectric Properties of SrRuO3 . J. Phys. Chem. C 2016, 120, 9112–9121. (48) Reshak, A. H.; Knight, S.; Teubert, J.; Heimbrodt, W.; Shuai, Z.; Wang, D.; Shuai, Z.; Huang, Y.-S.; Xie, L. Thermoelectric Properties of Highly-Mismatched Alloys of GaNx As1−x from First- to Second-Principles Methods: Energy Conversion. RSC Adv. 2016, 6, 72286–72294.


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TOC Graphic 300 200

S [µV/K]

100 0 -100 -200

100 K 300 K 500 K

Pnma

-300

50

S [µV/K]

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P63/mmc -100 -0.4 -0.3 -0.2 -0.1

spin up spin down 0.0

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µ-µF [eV]


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Structural and Composition Effects on Electronic and Magnetic

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