Making the Invisible Visible: Probing Antiferromagnetic Order in Novel Materials

Making the Invisible Visible: Probing Antiferromagnetic Order in Novel Materials Elke Arenholz Lawrence Berkeley National Laboratory Antiferromagnetic contrast in X-ray absorption Ni in NiO Neel Temperature of Cr 2 O 3 XMLD XA Antiferromagnetic domains in NiO 850 860 870 photon energy (ev) 1

Magnetic Materials Characterization Wish List + Sensitivity to antiferromagnetic and ferromagnetic order + Element specificity = distinguishing Fe, Co, Ni, + Sensitivity to valence state = distinguishing Fe 2+, Fe 3+, + Sensitivity to site symmetry, e.g. tetrahedral, T d; octahedral, O h + Nanometer spatial resolution + Ultra-fast time resolution Soft X-Ray Spectroscopy and Microscopy 2

Soft X-Ray Spectroscopy ( h 400-1000eV, 1-2nm) X-ray absorption (arb. units) Source Electron Storage Ring e.g. ALS BL4.0.2, BL6.3.1 Monochromator Sample electron yield I e / I 0 6 4 2 0 770 780 790 800 photon energy (ev) Endstation EY_TM.opj 3

X-Ray Absorption Typical Detection Modes transmitted intensity I t / I 0 electron yield I e / I 0 1.0 0.9 0.8 0.7 0.6 770 780 790 800 photon energy (ev) 6 4 2 0 770 780 790 800 photon energy (ev) EY_TM.opj EY_TM.opj photons absorbed electrons generated J. Stöhr, H.C. Siegmann, Magnetism (Springer) Electron yield: + Absorbed photons create core holes subsequently filled by Auger electron emission + Auger electrons create low-energy secondary electron cascade through inelastic scattering + Emitted electrons probability of Auger electron creation absorption probability 4

X-Ray Absorption Fundamentals Experimental Concept: Monitor X-ray absorption of samples as function of photon energy depending on details of electronic structure E valence states Charge state of absorber Fe 2+, Fe 3+ Symmetry of lattice site of absorber: O h, T d Sensitive to magnetic order Absorption probability: X-ray energy, X-ray polarization, experimental geometry 2p 3/2 L 3 2p 1/2 L 2 Core level Atomic species of absorber Fe, Co, Ni,. 5

X-Ray Magnetic Circular Dichroism (XMCD) + XMCD probes ferromagnetic order + Circularly polarized X-ray excite electrons with one spin orientation into empty d-states + Unequal spin-up and spin-down populations in exchange split valence shell acts as detector for spin of excited electrons + Calculate transition probabilities from filled 2p 3/2 and 2p 1/2 states to empty states in d-band for circularly polarized X rays using Fermi s golden rule XA (arb. units) XMCD (arb. units) 1.0 0.5 0.0 0.0-0.2-0.4 + Magnitude of XMCD depends on - 3d magnetic moment - degree of circular photon polarization, P circ - geometry Co L 3 L 2 I XMCD = I I 770 780 790 800 photon energy (ev) FeCo_GaAs_XMCD.opj 7

X-Ray Linear Dichroism (XLD) XA (arb. units) O Cu L 3 La 1.85 Sr 0.15 CuO 4 Cu E L 2 C. T. Chen et al. PRL 68, 2543 (1992) X-Ray Linear Dichroism: 920 940 960 photon energy (ev) + Difference in X-ray absorption for different linear polarization direction relative to crystalline and/or spin axis. + Due to the anisotropic charge distribution about absorbing atom caused by bonding and/or magnetic order. + Search Light Effect : Absorption of linear polarized X rays proportional to density of empty valence states in direction of electric field vector E. + Theory: Calculate angular dependent transition matrix elements! 8

X-Ray Magnetic Linear Dichroism (XMLD) Isotropic d electron charge density No polarization dependence XA (arb. units) 1.0 0.5 L 3 antiferromagnetic NiO CoNiO_4.0.2_Ni_XMLD.opj Magnetically aligned system Spin-orbit coupling distorts charge density Polarization dependence! L S XMLD (arb. units) 0.0 0.05 0.00-0.05 L 3 = 0 = 45 850 855 860 865 870 875 photon energy (ev) [001] [001] + I XMLD = I I m 2, m 2 = expectation value of square of atomic magnetic moment + XMLD allows investigating ferri- and ferromagnets as well as antiferromagnets + XMLD spectral shape and angular dependence are determined by magnetic order and lattice symmetry 9

X-Ray Absorption Fundamentals Experimental Concept: Monitor reduction in x-ray flux transmitted through sample as function of photon energy E valence states Charge state of absorber Fe 2+, Fe 3+ Symmetry of lattice site of absorber: O h, T d Sensitive to magnetic order Absorption probability: X-ray energy, X-ray polarization, experimental geometry 2p 3/2 L 3 2p 1/2 L 2 Core level Atomic species of absorber Fe, Co, Ni,. 10

Element-Specificity Cu valence states 2p 3/2 L 3 2p 1/2 L 2 core level Intensity of L 3,2 resonances is proportional to number of d states above the Fermi level, i.e. number of holes in the d band. 11

X-ray Absorption Valence State Influence of the charge state of the absorber N. Telling et al., Appl. Phys. Lett. 95, 163701 (2009) J.-S. Kang et al., Phys. Rev. B 77, 035121 (2008) 12

X-Ray Absorption Lattice Symmetry x- ray absorption TiO 2 Rutile Influence of lattice site symmetry at the absorber O h Anatase TiO 2 D 2h G. Van der Laan Phys. Rev. B 41, 12366 (1990) 13

X-Ray Magnetic Circular Dichroism (XMCD) 1.0 CoFe 2 O 4 H XA (arb. units) 0.5 L 3 Fe Co L 2 L 3 L 2 0.0 circularly polarized XMCD (arb. units) Fe 3+, T d 0.0 Fe 3+, O h -0.2 Fe 2+,O Co 2+ h 700 710 720 730 780 790 800 photon energy (ev) CoFe2O4.opj + XMCD provides magnetic information resolving elements Fe, Co, valence states: Fe 2+, Fe 3+, lattice sites: octahedral, O h, tetrahedral, T d, 14

X-Ray Magnetic Linear Dichroism (XMLD) 1.0 // CoFe 2 O 4 XMLD (arb. units) XA (arb. units) 0.5 0.0 0.02 0.00-0.02 // 700 710 720 730 780 790 800 photon energy (ev) + I XMLD = I I m 2, m 2 = expectation value of square of atomic magnetic moment + XMLD allows investigating ferri- and ferromagnets as well as antiferromagnets + XMLD spectral shape and angular dependence are determined by magnetic order and lattice symmetry Fe L 3 L 2 // Co L 3 L 2 = 0 = 45 CoFe2O4_110_Sept.opj H H [001] 15

Fe 3 O 4 - Fe L 3,2 XMLD Calculated XMLD spectra for three Fe sites Fe 2+ O h, Fe 3+ T d, and Fe 3+ O h and spectrum for stoichiometric 1:1:1 ratio for magnetic moments along and 110 direction Fe moments along [100] axis Fe moments along [110] axis E. Arenholz et al., PRB 74, 094407 (2006) 16

(Ga,Mn)As - Mn L 3,2 XMLD experimental spectra Calculated spectra A. A. Freeman et al., PRB 73, 233303 (2006) + Strong Mn XMLD! + Strong dependence on rotation of magnetization and polarization directions with respect to crystalline axes. + Experimental result well reproduced by atomic multiplet calculations for d 5 configuration in cubic crystal field 17

Ni Fe 2 O 4 and NiO - Ni L 3,2 XMLD E. Arenholz et al., PRL 98, 197201 (2007) + XMLD angular dependence = Linear combination of two fundamental spectra, I 0 and I 45, with distinct spectral features. I 0 : Ni moments along [100] axis I 45 : Ni moments along [110] axis + Fundamental spectra have same spectral shapes for ferromagnet and antiferromagnet + Spectra well reproduced using atomic multiplet theory while angular dependence derived considering symmetry of crystal electric field. 18

Characterizing a Planar Domain Wall wall angle H XMCD, XA (arb. units) 1.0 0.5 0.0 L 3 Co FM AFM L 2 L 3 L 2 Co/NiO Co NiO Ni x50 770 780 790 850 860 870 photon energy (ev) CoNiO_6.3.1.opj XA (arb. units) XMLD (arb. units) 2 1 0.0-0.2 NiO Co/NiO 868 870 872 photon energy (ev) H Co XMCD (arb. units) 10 0-10 Ni L 2 ratio 1.2 1.1 1.0 0.9 50 o 40 o 30 o 20 o E H 10 o E H o 0 Co H -0.5 0.0 0.5 field (T) 0.0 0.2 0.4 0.6 applied field (T) NiO A. Scholl et al., Phys. Rev. Lett. 92, 247201 (2004) 19

Characterize Anisotropy of AFMs XMLD (%) Direct Measurement of rotatable and pinned CoO Spins in Fe/CoO bilayers CoO Fe H Fe CoO CoO 20 J. Wu et al., PRL 104, 217204 (2010)

Magnetic Coupling At Interfaces Fe L 3,2 XMLD (arb. units) XA (arb. units) XMCD (arb. units) XA (arb. units) XMLD (arb. units) 1.0 0.5 0.0 0.0-0.2 1.0 0.5 0.0 0.1 0.0-0.1 Mn XMCD 640 650 photon energy (ev) Fe XMLD 710 720 photon energy (ev) XA (arb. units) XMLD (arb. units) 1.0 0.5 0.0 0.2 0.0-0.2 H H LSMO LSFO expt. H 710 720 photon energy (ev) calc. Perpendicular coupling at LSMO/LSFO interface La 0.7 Sr 0.3 MnO 3 (LSMO) ferromagnet La 0.7 Sr 0.3 FeO 3 (LSFO) antiferromagnet Mn L 3,2 XMCD (arb. units) Fe L 3,2 XMLD (arb. units) 1.0 0.5 0.0 1.0 0.5 0.0 0 100 200 300 400 temperature (K) E. Arenholz et al., Appl. Phys. Lett. 94, 072503 (2009) 1.0 0.5 0.0 21

Magnetic Microscopy 10-50 nm spatial resolution J. Stöhr, H.C. Siegmann, Magnetism (Springer) 22

Imaging Magnetic Domains Using X-Rays i070725_046_047_div.jpg i070725_049_050_div.jpg i070725_046.jpg i070725_050.jpg left circ. A right circ. B XMCD, XA (arb. units) 1.0 0.5 0.0 Co/NiO(001) 780 790 800 photon energy (ev) 070727_Co_XMCD.opj A / B E. Arenholz et al., Appl. Phys. Lett. 93, 162506 (2008) + Images taken with left and right circularly polarized x-rays at photon energies with XMCD, i.e. Co L 3 edge, provide magnetic contrast and domain images. 23

Magnetic Coupling At Co/NiO Interface x rays Co XMCD Ni XMLD 5 m + Taking into account the geometry dependence of the Ni XMLD signal Perpendicular coupling of Co and NiO moments at the interface. probing in-plane 5 m E. Arenholz et al., Appl. Phys. Lett. 93, 162506 (2008) 24

Magnetic Vortices + First direct observation of vortex state in antiferromagnetic CoO and NiO disks in Fe/CoO and Fe/NiO bilayers using XMCD and XMLD. + Two types of AFM vortices: - conventional curling vortex as in ferromagnets - divergent vortex, forbidden in ferromagnets - thickness dependence of magnetic interface coupling conventional curling vortex divergent vortex J. Wu et al., Nature Phys. 7, 303 (2011) 25

Control AFM domains with patterning/strain E. Folven et al., PRB 84, 220410(R) (2011) + Antiferromagnetic easy axes in LaFeO 3 layer along in-plane 110 and 100 crystalline axes. + Extended antiferromagnetic domains stabilized selectively for nanowires through strain. LaFeO 3 26

Scanning Soft X-ray Microscopy for Magnetism Research New Luminescence Detection Mode: + X rays transmitted through thin films to substrate converted to visible light and detected closely behind sample. Transmission geometry for epitaxial thin film with substrate functioning as scintillator. Microscope Characteristics: + Characterization of epitaxial films + <10 nm spatial resolution + Flexible sample geometries + Magnetic and electric fields + Variable temperatures + Elemental, magnetic, electronic and orbital contrast + Access to transition metal L 2,3 edges and rare earth M 4,5 edges 27

Probing antiferromagnetic order with soft X-rays J. Wu et al., PRL 104, 217204 (2010) XMLD XA NiONi in NiO Antiferromagnetic contrast in X-ray absorption Impact of external parameters on antiferromagnetic order 850 860 870 photon energy (ev) Antiferromagnetic domains 28

Magnetic Neutron Scattering Neutrons carry no charge but do carry s = 1/2 magnetic moment Neutrons only couple to electrons in solids via magnetic interactions Neutron scattering powerful tool for study of magnetic materials n g = 1.913 n = - g N s nuclear magneton e ħ/2m n Pauli spin operator NIST NIST Center for Neutron Research: https://www.nist.gov/ncnr ORNL Spallation Neutron Source: https://neutrons.ornl.gov/sns ORNL High Flux Isotope Reactor: https://neutrons.ornl.gov/hfir 29

Magnetic Neutron Scattering Neutrons scatter off: n e - e - Magnetic field from orbital motion of electrons Magnetic field from spin 1/2 of electron Magnetic Peak Intensity: I V m 2 5 µ B Fe 25 1 µ B2 V Neutrons scatter off samples with a specific + Change in momentum: Q = k i k f + Change in energy: ħw = ħ 2 k i2 /2m - ħ 2 k f2 /2m k i Q k f H 30

Neutron Diffraction Bragg s Law ki ki θ 2θ d θ θ kf kf Defining Q = 4π sinθ / λ give Q = 2π / d nλ = 2d sin(θ) n = 1 λ = 2d sinθ + Periodic structures exhibit intense scattering at angles corresponding to constructive interference of the neutron wave + Bragg peak corresponds to a real space period of d = 2π / Q of - Nuclear Structure - Magnetic Structure Ferromagnetism Antiferromagnetism Complex Spin Structures Typical neutron energy: 2 80 mev Corresponding wavelength: 1 6 Å 31

Polarized Measurements Polarized Beam Diffraction + We may polarize the neutron beam and look for magnetic scattering events. + Magnetic peaks will appear in the spin flip channel. + Nonmagnetic (Nuclear) peaks appear in the non spin-flip channel. CaMnO 3 G-type perovskite AFM n Scattering! n Non-Spin-Flip n Scattering! n Peak is clearly magnetic in nature, with no indications of a nuclear contribution. Spin-Flip 32

Polarization Analysis Magnetic Sensitivity: Non-spin flip ( or ): M H M Spin-flip ( or ): M H k i Q k f H Both Cases: M Q M n Scattering! n Non-Spin-Flip n Scattering! n Spin-Flip 33

Cr 2 O 3 Moment Orientation M Q 006: out-of-plane, T independent 204: in-plane, T dependent Moments are in-plane! 34

Cr 2 O 3 Neel Temperature Intensity scales with volume: 1 µm 10 mm 10 mm 35

(Eu,Sr)MnO 3 Neel Temperature Intensity scales with volume: 16 nm 5 mm 5 mm (NIST NCNR record low volume) 36

Neutron Reflectometry: Depth Profile + CaMnO 3 Antiferromagnetic Insulator + CaRuO 3 - Paramagnetic metal (CaRuO 3 ) 3 /(CaMnO 3 ) 17 x10 CaMnO 3 : m = 17 CaRuO 3 : n = 3 X-Ray Reflectometry: + Strong total thickness fringes + Strong superlattice Bragg peaks + High interfacial quality (σ 1 unit cell) 37 A. Grutter et al., Nano Lett. 16, 5647 (2016)

AFM Correlations in Superlattices + CaMnO 3 Antiferromagnetic Insulator + CaRuO 3 - Paramagnetic metal (CaRuO 3 ) 3 /(CaMnO 3 ) 17 x10 CaMnO 3 : m = 17 CaRuO 3 : n = 3 Neutron Reflectometry + Depth dependence of nuclear and magnetic scattering length density + Shows ferromagnetic layer 1 unit cell thick at interfaces 38

Neutron Reflectometry: Depth Profile + Measure nuclear depth profile + Magnetic depth profile (in plane) Compare Data Calculate Reflectometry Model Iterative Convergence 39 A. Grutter et al., Nano Lett. 16, 5647 (2016)

NIST Web Fitting Tools Brian Maranville and Brian Kirby, NIST, NCNR Summer School, June 2016 40

Neutron Reflectometry: Depth Profile Neutron Reflectometry + Depth dependence of nuclear and magnetic scattering length density + Shows magnetic layer 1 unit cell thick at interfaces 41 A. Grutter et al., Nano Lett. 16, 5647 (2016) 41

Neutron Reflectometry and X-ray Magnetic Dichroism 42 A. Grutter et al., Nano Lett. 16, 5647 (2016) 42

Planning Your Neutron Scattering Experiment Reflectometry Samples: Typically Signal Limited (not Signal/Noise Limited) Larger Samples 5 5 mm 2 minimum 10 10 mm 2 desirable Larger is usually better Diffraction Samples: Mimimum Volume ~ 0.4 nanoliters Preferred Volume ~5 nanoliters Thinner Substrates Remove substrate backing (In) Temperature ranges: 4.2-400 K Standard closed cycle refrigerator < 100 mk in-situ dilution fridge > 400 K High temperature CCRs Magnetic and Electric Field Ranges: Reflectometers 3 T Most other beamlines 9 T Bias voltage (up to 5 kv) Contact: alexander.grutter@nist.gov 43

Planning Your X-ray Spectroscopy/Microscopy Experiment Spectroscopy Samples: + Typically: 5mm x 5mm; Smaller possible (0.5mm x 0.5mm) and larger possible (10mm x 10)mm + Electron yield probes predominantly surface near sample region (5-10nm) + Transmission microscopy probes entire film thickness (ideally 25-50nm) Temperature ranges: 7-700 K Different sample holders Magnetic and Electric Field Ranges: ALS BL4.0.2: 4T in any direction ALS BL6.3.1: 2T parallel to X-ray beam Bias voltage (up to 500 V) Microscopy Samples: + PEEM: Sufficiently conducting samples + Transmission microscopy: Sufficiently thin samples Contact: earenholz@lbl.gov 44