Mitglied der HelmholtzGemeinschaft Firstprinciples calculation of Hubbard U
Mitglied der Helmholtz-Gemeinschaft First-principles calculation of Hubbard U parameters for half-metallic ferromagnets Ersoy Şaşıoğlu, Christoph Friedrich, and Stefan Blügel Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany March 13, 2013
Motivation Half metallic ferromagnets (DFT-LSDA) Ni. Mn. Sb de Groot et al. , Phys. Rev. Lett. 50, 2024 (1983). Applications (GMR, TMR, spin transistor) Co 2 Mn. Si Mg. O Fe 25 Co 75 March 13, 2013 217% TMR effect at RT (753% at 2 K) Tsunegi et. al. , Appl. Phys. Lett. , 93 112506 (2008). Folie 2
Motivation Half metallic ferromagnets (LDA+DMFT) Ni. Mn. Sb DFT-LSDA+DMFT Correlation effects (electron-magnon interaction) Chioncel et al. , Phys. Rev. B 68, 144425 (2003). magnon March 13, 2013 Folie 3
Hubbard U from Constrained RPA Fully screened Coulomb interaction W m‘ EF m March 13, 2013 Folie 4
Hubbard U from Constrained RPA Partially screened Coulomb interaction: Hubbard U r space r d space d r d EF d d r r F. Aryasetiawan, et al. , Phys. Rev. B 74, 125106 (2006) March 13, 2013 Folie 5
Hubbard U from Constrained RPA c. RPA for disentangled and entangled bands Sr. VO 3 ( ) Cr. As ( ) r space d space r space well-defined ? ? ? not well-defined Hubbard-U Fully screened E. Sasioglu, C. Friedrich, and S. Blügel, Phys. Rev. B 83, 121101(R) (2011). March 13, 2013 Folie 6
FLAPW Realization (c. RPA) Full-Potential Linearized Augmented Plane Wave (www. flapw. de) DFT part GW part FLEUR SPEX Projection of U(r, r‘) onto Wannier basis Wannier 90 March 13, 2013 Folie 7
Results Half metallic ferromagnets VAs Cr. As Mn. As Fe. Mn. Sb Co. Mn. Sb Ni. Mn. Sb Co 2 Cr. Al Co 2 Cr. Si Co 2 Mn. Al Co 2 Mn. Si Co 2 Fe. Al Co 2 Fe. Si 2. 8 1. 6 1. 4 1. 3 1. 6 2. 5 1. 3 1. 4 1. 3 1. 6 1. 3 2. 5 1. 4 1. 3 1. 4 2. 8 1. 3 1. 8 2. 5 March 13, 2013 Folie 8
Results Hubbard U for half metallic ferromagnets VAs Cr. As Mn. As UV =2. 0 e. V UCr =1. 7 e. V UMn=1. 7 e. V U ~ 1. 7 - 2. 0 e. V March 13, 2013 Fe. Mn. Sb Co. Mn. Sb Ni. Mn. Sb UFe=2. 2 e. V UMn=3. 1 e. V UCo=2. 3 e. V UMn=2. 8 e. V UNi =2. 7 e. V UMn=2. 7 e. V U ~ 2. 2 - 3. 1 e. V Co 2 Cr. Al Co 2 Mn. Al Co 2 Fe. Al UCr =2. 8 e. V UCo=3. 7 e. V UMn=3. 2 e. V UCo=3. 4 e. V UFe =3. 4 e. V UCo=3. 0 e. V U ~ 2. 8 - 3. 7 e. V Folie 9
Results Hubbard U for half metallic ferromagnets: Effect of the sp element Co 2 Cr. Al Co 2 Mn. Al Co 2 Fe. Al UCr =2. 8 e. V UCo=3. 7 e. V UMn=3. 2 e. V UCo=3. 4 e. V UFe =3. 4 e. V UCo=3. 0 e. V U ~ 2. 8 - 3. 7 e. V March 13, 2013 Co 2 Cr. Si Co 2 Mn. Si Co 2 Fe. Si UCr =2. 7 e. V UCo=3. 8 e. V UMn=3. 1 e. V UCo=3. 3 e. V UFe =3. 4 e. V UCo=3. 1 e. V U ~ 2. 7 - 3. 8 e. V Folie 10
Results Hubbard U for half metallic ferromagnets: Different screening channels Compound Orbital U(d d) U(pd pd) Cr. As Cr-3 d 1. 7 4. 7 Ni. Mn. Sb Ni-3 d 2. 7 4. 3 Mn-3 d 2. 7 3. 9 Co-3 d 3. 3 4. 6 Mn-3 d 3. 1 4. 4 Co 2 Mn. Si March 13, 2013 Folie 11
Results LSDA+DMFT study of half metallic ferromagnets Cr. As Chioncel et al. , Phys. Rev. B 71, 085111 (2005). Ni. Mn. Sb Chioncel et al. , Phys. Rev. B 68, 144425 (2003). Co 2 Mn. Si Chioncel et al. , Phys. Rev. Lett. 100, 086402 (2008). UCr =2 e. V JCr=0. 9 e. V UMn =3 e. V JMn=0. 9 e. V UCo =3 e. V JCo=0. 9 e. V UMn =3 e. V JMn=0. 9 e. V c. RPA: UCr =1. 7 e. V JCr=0. 6 e. V UNi =2. 7 e. V JNi =0. 7 e. V UMn =2. 7 e. V JMn=0. 6 e. V UCo =3. 3 e. V JCo=0. 7 e. V UMn =3. 1 e. V JMn=0. 6 e. V March 13, 2013 Folie 12
Conclusions c. RPA: Hubbard U for half metallic ferromagnets VAs Cr. As Mn. As U ~ 1. 7 - 2. 0 e. V Fe. Mn. Sb Co. Mn. Sb Ni. Mn. Sb U ~ 2. 2 - 3. 1 e. V Co 2 Cr. Al Co 2 Mn. Al Co 2 Fe. Al U ~ 2. 8 - 3. 7 e. V Acknowledgments March 13, 2013 Folie 13
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Hubbard U from Constrained RPA New parameter-free approach using Wannier functions Maximally localized Wannier functions d space (9 bands) Unitary transformation matrix d character of the bands within the window d character of band m for wave vector k in d space Weight factor for transition of electrons in d space Weighted polarization function in d space March 13, 2013 E. Sasioglu, C. Friedrich, and S. Blügel, Phys. Rev. B 83, 121101(R) (2011). Folie 15
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