X-ray magnetic dichroism, magneto-optic Kerr effect
and transverse transport
in non-collinear antiferromagnets
K.Chadova1, S. Wimmer1, J. Minár1,2, S. Mankovsky1, D. Ködderitzsch1, and H. Ebert1
1) LMU München, Dept. Chemie / Phys. Chemie, D-81377 München, Germany
2) University of West Bohemia, Pilsen, Czech Republic
Outline
Outline
●●
Linear
Linear response
response && symmetry
symmetry
●●
Application
Application to
to Mn
Mn33IrIr
●●
Symmetry
Symmetry analysis
analysis
●●
Electrical
Electrical conductivity
conductivity
●●
Optical
Optical conductivity
conductivity
●●
X-ray
X-ray absorption
absorption spectra
spectra
Financial Support:
SFB 689
Spinphänomene in
reduzierten Dimensionen
Discussions with
A. Yaresko (MPI-FKF Stuttgart)
are gratefully acknowledged
Introduction & motivation
●
Unconventional – e.g. non-collinear, uncompensated, frustrated –
forms of magnetism are (still) an active field of research:
●
Mn3Ir: Chen, Niu, and MacDonald, PRL 112, 017205 (2014)
●
Mn3Ge: Kübler and Felser, EPL 108, 67001 (2014)
●
Nd2Mo2O7 (pyrochlore): Yoshii et al., JPSJ 69, 3777 (2000) (expt.)
Tomizawa & Kontani, PRB 80, 100401(R) (2009); PRB 82 104412 (2010)
AFM/FM interfaces (exchange-bias)
●
●
2015/10/06
(theor.)
●
Co/FeMn: Kuch et al., PRL 92, 017201-1 (2004); Nat. Mater. 5, 128 (2006)
●
Co(-Fe)/Mn-Ir(111): Takahashi et al., JAP 110, 123920 (2011)
●
Mn/Fe(100): Grazioli et al., PRL 95, 117201 (2005)
Apart from academic interest
●
technological importance (e.g. use of Mn3Ir in spintronics devices)
●
test systems for various applications of SPRKKR program package
Internen SFB689 Workshop, Frauenchiemsee 2015
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Linear response – Kubo formalism
Response in B caused by coupling to perturbation in A
R. Kubo, M. Yokota, and S. Nakajima, J. Phys. Soc. Jpn. 12, 1203 (1957)
R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957)
Example – electrical current
symmetric part:
longitudinal charge conductivity
Anisotropic Magnetoresistance (AMR)
● antisymmetric part:
transverse, anomalous Hall effect (AHE)
●
2015/10/06
Internen SFB689 Workshop, Frauenchiemsee 2015
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Mn3Ir
●
Cu3Au structure
●
in (hypothetical) AFM state:
moments in (111) plane (Kagome lattice)
●
Along <112> directions
●
Magnetic SG: R3m' (166.5.1331)
●
Used as material for pinning layers
●
Prediction of AHE
●
2015/10/06
●
●
based on analysis of electronic structure
Chen, Niu, and MacDonald, PRL 112, 017205 (2014)
●
shape of conductivity tensor derived much earlier,
based exclusively on symmetry arguments
Kleiner, PR 142, 318 (1966)
XMCD signal and MOKE should be observable as well
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Mn3Ir – transport results
●
●
Electrical conductivity
●
predicted tensor shape (MLG 3m'):
●
numerical results based on
Kubo-Bastin formalism confirm prediction
●
AHC of ~275 Ohm-1 cm-1 agrees with previous results
(Chen et al.: 218 Ohm-1 cm-1); comparable in size to Fe, Co, Ni.
spin-polarized conductivities
●
●
2015/10/06
predicted tensor shapes vs. numerical results
work in progress
Mn3Ir1-xPtx and Mn3Pt1-xRhx alloys
Internen SFB689 Workshop, Frauenchiemsee 2015
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Mn3Ir – optical conductivity & Kerr angle
Mn3Ir
bcc Fe
2015/10/06
●
results in line with symmetry predictions
●
same tensor shape as bcc Fe, comparable magnitudes
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X-ray absorption formalism
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One-electron approximation to Fermi's Golden Rule
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Electron-photon interaction operator
●
electric current density operator
Absorption coefficient in terms of Green function
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Relation to transport effects
●
2015/10/06
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XMCD (
) ↔ AHE
●
XMLD (
) ↔ AMR
Construction of spectra as sum of site-resolved absorption coefficients
●
only magnetic atoms taken into account
●
wavevectors
along high symmetry directions → connection to
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Mn3Ir – XAS results I
2015/10/06
●
spectra by superposition of site-resolved abs. coeffs.
obtained suppressing internal symmetrisation
●
incidence
: [111] vs. direction of
(polar geometry)
●
almost identical total absorption
●
in both cases XMCD (larger for polar geometry)
Experimental work is in progress in C.Back's group
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Mn3Ir – XAS results II
XMLD
XMCD
2015/10/06
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Mn3Ge
●
●
Space group P63/mmc (194)
Mn2
Mn atoms couple antiferromagnetically
on Kagome lattices (stacked along [0001])
●
●
magnetic moments in {0001}
Ge1
Ge1
Mn1
Ge1
Mn5
Ge2
Ge1
Mn3
Ge1
Ge1
Mn6
Mn4
Mn1
Mn2
Mn2
Mn3
Mn2
Mn1
Ge1
various triangular configurations discussed
Zhang et al. JPCM 25, 206006 (2013), Kübler and Felser, EPL 108, 67001 (2014)
AFM1
2015/10/06
Ge1
Mn1
AFM2
AFM3
●
AHC predicted by Kübler and Felser (for AFM3 & AFM4)
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Excluded for AFM1 (“...bipartite lattice...”)
Internen SFB689 Workshop, Frauenchiemsee 2015
AFM4
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Mn3Ge – transport results
●
Electrical conductivity
predicted tensor shapes (MSGs determined using FINDSYM)
●
AFM1
MSG Am'm'2
MLG m'm'm
AFM2
P-6'2c'
6'/m'mm'
AFM3
Pm'
2'/m'
●
numerical results confirm prediction in all cases
●
Comparison to results obtained by Kübler & Felser [1]
AFM4
Am'm'2
m'm'm
●
Discrepancies for AFM1 (no AHE) & AFM4 (2 different AHCs)
●
AFM2 not considered in [1]
●
Agreement for AFM3
●
Self-consistently obtained FM structure of [1] not considered here
[1] Kübler & Felser, EPL 108, 67001 (2014)
2015/10/06
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Mn3Ge – XAS results for AFM1
XMLD
z
x
XMCD
2015/10/06
Internen SFB689 Workshop, Frauenchiemsee 2015
AFM1
Am'm'2
m'm'm
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Conclusions & Outlook
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Conclusions
●
Symmetry analysis allows predicting occurrence of effects
●
Applied to ω-dependent conductivity in non-collinear AFMs
●
Independent verification by first-principles calculations
●
Numerical results for AHE and MOKE in Mn3Ir (& Mn3Ge) consistent
●
●
2015/10/06
●
Agreement with Chen et al. for AHE in Mn3Ir
●
Optical conductivity & MOKE comparable (shape & size) to bcc Fe
Occurrence of XMCD and XMLD predicted
Outlook
●
Uncompensated/frustrated magnetism (e.g. pyrochlore)
●
Surfaces/Interfaces (FM|AFM, exchange-biased systems)
→ e.g. Co(-Fe)/Mn-Ir(111): Takahashi et al., JAP 110, 123920 (2011)
●
Spin-polarized conductivities → SW et al., PRB 92, 041101(R) (2015)
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