Adventures in Frustrated Magnetism

Adventures in Frustrated Magnetism Jeremy P. Carlo Villanova University Jan. 22, 2014 St. Joseph’s University Physics Seminar Feb. 5, 2014

Outline • Magnetism in solids • Chemistry for magnet jocks • Magnetic frustration • Tools to measure magnetism: Neutron scattering, muon spin relaxation • Magnetism in face-centered cubic systems • Results / Conclusions

Magnetism in materials • Electrons have charge, and also “spin” • “Spin”  magnetic moment • May also have orbital magnetic moment • The key is… unpaired electrons… 3d 4d 5d 4f 5f

Magnetism in materials Fill according to Hund’s rules: • Why transition metals / lanthanides / actinides? • Number of orbitals per subshell s: 1 orbital p: 3 orbitals d: 5 orbitals f: 7 orbitals Example: 3d s p d f

Magnetism in materials • Simplest model: assume moments don’t interact with each other. • High temps: spins fluctuate rapidly and randomly, but can be influenced by an applied magnetic field H: U = -mH M= H = “susceptibility” • Paramagnetism: moments tend to align with field ( > 0) • Diamagnetism: moments tend to align against field ( < 0) • Temp dependence of : (T) = C / T “Curie Paramagnetism” • Real materials: moments do “talk” to each other “Exchange Interaction:” U = ̵ J S1  S2 • Then,(T) = C / (T - CW) “Curie-Weiss behavior”

Magnetism in materials • If the moments “talk” to each other with a nearest-neighbor interaction energy J, when kBT < J the interaction energy dominates over thermal fluctuations • Mean field theory: Torder |CW| • Unpaired spins may collectively align, leading to a spontaneous nonzero magnetic moment • Ferromagnetism (FM) (J, CW > 0) • Or they can anti-align: large localmagnetic fields in the material, but zero overall magnetic moment • Antiferromagnetism (AF) (J, CW< 0)

http://leadershipfreak.files.wordpress.com/2009/12/frustration.jpghttp://leadershipfreak.files.wordpress.com/2009/12/frustration.jpg

Geometric Frustration • Structural arrangement of magnetic ions prevents all interactions from being simultaneously satisfied; this inhibits development of magnetic order. f= |QCW| / Torder “frustration index” • So f >> 1 means that most of the interaction energy is cancelled out through frustration / competition! • Most common with AF correlations (QCW < 0) CW~ Weiss temperature (measure of strength of interactions) Torder~ actual magnetic ordering tempMFT result: f should be  1

Geometric Frustration http://en.wikipedia.org/wiki/File:Herbertsmithite-163165.jpg Herbertsmithite ZnCu3(OH6)Cl2 • In 2-D, associated with AF coupling on triangular lattices • edge-sharing triangles: triangular lattice • corner-sharing triangles: Kagome lattice • In a 3-D world , this usually means “quasi-2D systems“ composedof weakly-interacting layers:

Geometric Frustration • In 3-D, associated with AF couplingon tetrahedral architectures corner-sharing tetrahedra:pyrochlore lattice edge-sharing tetrahedra: FCC lattice

Geometric Frustration • What happens in frustrated systems? • Sometimes magnetic LRO at sufficiently low T << |Qw| • Sometimes a “compromise” magnetic state: e.g. “spin-ice,” “helimagnetism,” “spin glass” • Sometimes exquisite balancing between interactions prevents magnetic order to the lowest achievable temperatures: e.g. “spin-liquid,” “spin-singlet” • Extreme sensitivity to parameters! • Moment size, doping, ionic size / spacing, structural distortion, spin-orbit coupling… • Normally dominant terms in Hamiltonian may cancel, so much more subtle physics can contribute significantly!

Tools to measure magnetism A • Bulk probes • Susceptibility, Magnetization • Local probes • NMR, ESR, electron microscopy, Mossbauer , muon spin relaxation • Reciprocal-space (momentum) probes • X-ray, neutron diffraction • Spectroscopic (energy) probes • Inelastic x-ray/neutron scattering

X-Ray / Neutron Scattering Detector Scattered beam Momentum k’ Energy E’ Incoming beam Momentum: k Energy: E Sample Compare incoming and outgoing beams: Q = k – k’ “scattering vector” E = E – E’ “energy transfer” Represent momentum or energy Transferred to the sample

X-Ray / Neutron Scattering • How many neutrons are scattered at a given (Q,E) tells you the propensity for the sample to “accept” an excitation at that (Q,E). • Q-dependence: structure / spatial information “diffraction” • E-dependence: excitations from ground state “spectroscopy”

Neutron / X-Ray Diffraction Bragg condition: Constructive interference occurs when n = 2d sin Bonus: neutrons have a magnetic moment, so they reveal magnetic structure too! “Magnetic Bragg peaks”

Muon Spin Relaxation (SR): Probing Local Magnetic Fields Muons: “heavy electrons” or “light protons” Parity violation: muon beam is spin-polarized Muons act as local field “detectors”due to Larmor precession Polarized muon sources: TRIUMF, Vancouver BC PSI, Switzerland ISIS, UK (pulsed) KEK, Japan (pulsed)

Continuous-beam SR

Decay Asymmetry Muon spin at decay Detection: +→ e++ + e e = E / Emax normalized e+ energy

e+ detector U incoming muon counter sample e+ m+ detector time D 2.5 e+ detector D

e+ detector U incoming muon counter sample e+ m+ detector time D 2.5 e+ detector D U 1.7

e+ detector U incoming muon counter sample e+ m+ detector time D 2.5 e+ detector D U 1.7 D 1.2

e+ detector U incoming muon counter sample e+ m+ detector time D 2.5 e+ detector D U 1.7 D 1.2 D 9.0 + 106-107 more…

Histograms for opposing counters asy(t) = A0Gz(t) (+ baseline) a Total asymmetry ~0.2-0.3 Muon spin polarization function 135.5 MHz/T Represents muons in a uniform field

Outline • Magnetism in solids • Chemistry for magnet jocks • Magnetic frustration • Tools to measure magnetism: Neutron scattering, muon spin relaxation • Magnetism in face-centered systems • Results / Conclusions

Face-Centered Systems • Very, very common crystal structure“rock salt order” ~ NaCl • Tetrahedral Coordination + AF Correlations = Geometric Frustration

Example: Double perovskite lattice: • A2BB’O6 e.g. Ba2YMoO6 A: divalent cation e.g. Ba2+ B: nonmagnetic cation e.g. Y3+ B’: magnetic (s=½) cation e.g. Mo5+ (4d1) Magnetic ions: edge-sharing tetrahedral network

Nice thing about perovskites: can make them with almost any element in the periodic table! • Can study a variety of phenomena: colossal magnetoresistance, ferroelectrics, multiferroics, superconductivity, frustration… (Courtesy of J. Rondinelli)

Our survey • Goal: systematic survey of face-centered frustrated systems using mSR and neutron scattering.

Our double perovskite survey • We have been systematically surveying double perovskites in the context of GF, studying effects such as: • structural distortion (ideal cubic vs. distorted monoclinic/tetragonal) • Effects of ionic size / lattice parameter • Effects of moment size: s=3/2 s=1 s=1/2 • Effects of spin-orbit coupling: Larger moments More “classical” More amenable to bulk probes + neutrons Smaller moments More “quantum” More difficult to measure L-S J-J nd1 s=1/2 j=3/2 nd2 s=1 j=2 nd3 s=3/2 = j=3/2 Chen et al. PRB 82, 174440 (2010). Chen et al. PRB 84, 194420 (2011).

Comparison of Double Perovskite Systems: A “Family Portrait” • 4d3: (s=3/2 or jeff=3/2: L-S vs. J-J pictures) • Ba2YRuO6: cubic, AF LRO @ 36 K (f ~ 15) • La2LiRuO6: monoclinic, AF LRO @ 24 K (f ~ 8) • 5d2: (s=1 or jeff=2) • Ba2YReO6: cubic, spin freezing TG ~ 50 K (f ~ 12) • La2LiReO6: monoclinic, singlet ~ 50 K (f ~ 5) • Ba2CaOsO6: cubic, AF LRO @ 50 K (f ~ 2.5) • 4d1, 5d1: (s=1/2 or jeff=3/2) • Sr2MgReO6: tetragonal, spin freezing TG ~ 50 K (f ~ 8) • Sr2CaReO6: monoclinic, spin freezing TG ~ 14 K (f ~ 32) • La2LiMoO6: monoclinic, SR correlations < 20 K (f ~ 1) • Ba2YMoO6: cubic, singlet ~ 125K (f > 100)

Project 1: Neutron Scattering Studies of Ba2YMoO6 Neutron diffraction • Ba2YMoO6: Mo5+ 4d1 • Maintains ideal cubic structure; CW = -219K but no order found down to 2K: f > 100! XRD T = 297K l = 1.33 A Susceptibility T. Aharen et al. PRB 2010

Project 1: Neutron Scattering Studies of Ba2YMoO6 • However, heat capacity shows a broad peak • And NMR shows two signals,one showing the developmentof a gap at low temperatures • But mSR shows nothing…. T. Aharen et al. PRB 2010

Project 1: Neutron Scattering Studies of Ba2YMoO6 • Resolution comes from inelastic neutron scattering. • What’s happening? At low temps, neighboring moments pair up, to form “singlets.” • But no long range order! SEQUOIA Beamline Spallation Neutron Source Oak Ridge National Laboratory J. P. Carlo et al, PRB 2011

Project 2: Neutron Scattering Studies of Ba2YRuO6 Heat capacity • Ba2YRuO6: Ru5+ 4d3 • Much more “conventional” behavior qW = -571K T. Aharen et al. PRB 2009

Project 2: Neutron Scattering Studies of Ba2YRuO6 • Clear signs of antiferromagnetic order, but with f ~ 11-15. • Much more “conventional” behavior [100] magnetic Bragg peak J. P. Carlo et al. PRB 2013.

Project 2: Neutron Scattering Studies of Ba2YRuO6 • But the inelastic scattering dependence is much more exotic! J. P. Carlo et al. PRB 2013.

Project 2: Neutron Scattering Studies of Ba2YRuO6 • The ordered state is associated with the formation of a gap. • Interesting: Egap kBTorder • But why should such a gap exist? • Suggestive of exotic physics: relativistic spin-orbit coupling! J. P. Carlo et al. PRB 2013.

Project 3: Muon Spin Relaxation studies of Ba2CaOsO6 • Ba2YReO6 ~ Re5+, 5d2 ~spin glass ~ 50K • Ba2CaOsO6 ~Os6+, 5d2 orders at 50K, but is it similar to Ba2YReO6? • Isoelectronic, isostructural, lattice match, similar S-O coupling? C. M. Thompson et al. Submitted To PRB (2013).

Project 3: Muon Spin Relaxation studies of Ba2CaOsO6 • Long-livedprecession:sure sign ofLRO! C. M. Thompson et al. Submitted To PRB (2013).

Project 3: Muon Spin Relaxation studies of Ba2CaOsO6 • Precession notseenin “doppelganger”Ba2YReO6, but isseen in Ba2YRuO6! C. M. Thompson et al. Submitted To PRB (2013).

Summary • Frustration is widespread, and of great interest! • Very small differences in composition can lead to vastly different properties. Why? • Structural distortions / moment size / spin-orbit coupling • mSRand neutron scattering are “natural allies” • Ba2YMoO6: spin-singlet state; magnetic order is frustrated away! • Ba2YRuO6: conventional AF order, with a twist due to SOC? • Ba2YReO6: spin-glass, “filling the gap” from Ba2YMoO6 to Ba2YRuO6? • Ba2CaOsO6: how does it fit into the double perovskite “family tree?”

Neutron Diffraction (Q dependence) • Location of “Bragg peaks” reveal position of atoms in structure! Clifford G. Shull (1915-2001), Nobel Prize in Physics 1994

What about the energy dependence? • Tells us about excitations / time dependence • Phonons • Magnetism • To do this we need a way to discriminate between neutrons at different energies! • Triple-axis spectrometry (TAS) • Time-of-flight spectrometry (TOF)

Adventures in Frustrated Magnetism