Transcript Adventures in Frustrated Magnetism

Adventures in Frustrated
Magnetism
Jeremy P. Carlo
Villanova University
Jan. 22, 2014 St. Joseph’s University Physics Seminar
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
7/17/2015 8:55 PM
2
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
7/17/2015 8:55 PM
3
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
7/17/2015 8:55 PM
4
Magnetism in materials
Total Spin
3
• Why transition metals / lanthanides / actinides?
2.5
• Number of orbitals per subshell
Fill2 according to Hund’s rules:
s: 1 orbital
1.5
p: 3 orbitals
1
d: 5 orbitals
0.5
f: 7 orbitals
0
0
Example: 3d
s
7/17/2015 8:55 PM
d
2
4
6
8
10
12
Number of 3d electrons
p
f
5
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,
7/17/2015 8:55 PM
(T) = C / (T - CW)
“Curie-Weiss behavior”
6
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 local
magnetic fields in the material, but zero
overall magnetic moment
– Antiferromagnetism (AF)
7/17/2015 8:55 PM
(J, CW < 0)
7
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
7/17/2015 8:55 PM
8
http://leadershipfreak.files.wordpress.com/2009/12/frustration.jpg
7/17/2015 8:55 PM
9
Geometric Frustration
• Structural arrangement of magnetic ions prevents all interactions from
being simultaneously satisfied; this inhibits development of magnetic
order.
f = |CW| / Torder
“frustration index”
CW ~ Weiss temperature
(measure of strength of interactions)
Torder ~ actual magnetic ordering temp
MFT result: f should be  1
• So f >> 1 means that most of the interaction energy is cancelled out
through frustration / competition!
• Most common with AF correlations (CW < 0)
7/17/2015 8:55 PM
10
Geometric Frustration
http://en.wikipedia.org/wiki/File:Herbertsmithite-163165.jpg
• In 2-D, associatedHerbertsmithite
with
AF coupling on ZnCu3(OH6)Cl2
triangular lattices
• edge-sharing triangles:
triangular lattice
•
corner-sharing triangles:
Kagome lattice
• In a 3-D world , this usually means
“quasi-2D systems“ composed
of weakly-interacting layers:
7/17/2015 8:55 PM
11
Geometric Frustration
• In 3-D, associated with AF coupling
on tetrahedral architectures
corner-sharing tetrahedra:
pyrochlore lattice
edge-sharing tetrahedra:
FCC lattice
7/17/2015 8:55 PM
12
Geometric Frustration
• What happens in frustrated systems?
– Sometimes magnetic LRO at sufficiently low T << |w|
– 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!
7/17/2015 8:55 PM
13
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
7/17/2015 8:55 PM
14
Tools to measure magnetism
• Bulk probes
A
– 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
7/17/2015 8:55 PM
15
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”
7/17/2015 8:55 PM
Represent momentum or energy
Transferred to the sample
16
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”
7/17/2015 8:55 PM
17
Neutron / X-Ray Diffraction
Bragg condition:
Constructive interference occurs when
n = 2d sin
7/17/2015 8:55 PM
Bonus: neutrons have a magnetic moment, so
they reveal magnetic structure too!
“Magnetic Bragg peaks”
18
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)
7/17/2015 8:55 PM
19
7/17/2015 8:55 PM
20
Continuous-beam SR
7/17/2015 8:55 PM
21
Decay Asymmetry
Muon spin
at decay
Detection:
+ → e+ + + e
e = E / Emax normalized e+ energy
7/17/2015 8:55 PM
22
e+ detector U
incoming
muon counter
sample
e+
+
detector
e+ detector D
7/17/2015 8:55 PM
D
time
2.5
23
e+ detector U
incoming
muon counter
sample
e+
+
detector
e+ detector D
7/17/2015 8:55 PM
time
D
2.5
U
1.7
24
e+ detector U
incoming
muon counter
sample
e+
+
detector
e+ detector D
7/17/2015 8:55 PM
time
D
2.5
U
1.7
D
1.2
25
e+ detector U
incoming
muon counter
sample
e+
+
detector
e+ detector D
time
D
2.5
U
1.7
D
1.2
D
9.0
+ 106-107 more…
7/17/2015 8:55 PM
26
Histograms for
opposing counters
asy(t) = A0 Gz(t)
Total asymmetry
~0.2-0.3
Muon spin
polarization
function
(+ baseline)
a
135.5 MHz/T
Represents
muons in a
uniform field
7/17/2015 8:55 PM
27
7/17/2015 8:55 PM
28
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
7/17/2015 8:55 PM
29
Face-Centered Systems
• Very, very common crystal structure
“rock salt order” ~ NaCl
• Tetrahedral Coordination
+
AF Correlations
=
Geometric Frustration
7/17/2015 8:55 PM
30
• 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
7/17/2015 8:55 PM
31
• Nice thing about perovskites: can make them
with almost any element in the periodic table!
(Courtesy of
J. Rondinelli)
• Can study a variety of phenomena: colossal
magnetoresistance, ferroelectrics, multiferroics,
superconductivity, frustration…
7/17/2015 8:55 PM
32
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
7/17/2015 8:55 PM
33
Our survey
• Goal: systematic survey of face-centered
frustrated systems using SR and neutron
scattering.
7/17/2015 8:55 PM
34
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:
– Effects of spin-orbit coupling:
s=3/2
nd1
nd2
nd3
7/17/2015 8:55 PM
s=1
Larger moments
More “classical”
More amenable to
bulk probes + neutrons
L-S
s=1/2
s=1
s=3/2 =
s=1/2
Smaller moments
More “quantum”
More difficult
to measure
J-J
j=3/2 Chen et al. PRB 82,
174440 (2010).
j=2
j=3/2 Chen et al. PRB 84,
194420 (2011).
35
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,
• La2LiReO6: monoclinic,
• Ba2CaOsO6: cubic,
spin freezing TG ~ 50 K (f ~ 12)
singlet ~ 50 K (f ~ 5)
AF LRO @ 50 K (f ~ 2.5)
– 4d1, 5d1: (s=1/2 or jeff=3/2)
•
•
•
•
Sr2MgReO6: tetragonal,
Sr2CaReO6: monoclinic,
La2LiMoO6: monoclinic,
Ba2YMoO6: cubic,
7/17/2015 8:55 PM
spin freezing TG ~ 50 K (f ~ 8)
spin freezing TG ~ 14 K (f ~ 32)
SR correlations < 20 K (f ~ 1)
singlet ~ 125K (f > 100)
36
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
= 1.33 A
Susceptibility
T. Aharen et al. PRB 2010
7/17/2015 8:55 PM
37
Project 1: Neutron Scattering Studies
of Ba2YMoO6
• However, heat capacity shows a broad peak
• And NMR shows two signals,
one showing the development
of a gap at low temperatures
T. Aharen et al. PRB 2010
• But mSR shows nothing….
7/17/2015 8:55 PM
38
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
7/17/2015 8:55 PM
39
Project 2: Neutron Scattering Studies
Heat capacity
of Ba2YRuO6
• Ba2YRuO6: Ru5+
4d3
• Much more “conventional” behavior
W = -571K
7/17/2015 8:55 PM
T. Aharen et al. PRB 2009
40
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
7/17/2015 8:55 PM
J. P. Carlo et al. PRB 2013.
41
Project 2: Neutron Scattering Studies
of Ba2YRuO6
• But the inelastic scattering dependence is much more exotic!
J. P. Carlo et al. PRB 2013.
7/17/2015 8:55 PM
42
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.
7/17/2015 8:55 PM
43
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?
C. M. Thompson
et al. Submitted
To PRB (2013).
• Isoelectronic, isostructural, lattice match, similar S-O
coupling?
7/17/2015 8:55 PM
44
Project 3: Muon Spin Relaxation
studies of Ba2CaOsO6
• Long-lived
precession:
sure sign of
LRO!
C. M. Thompson
et al. Submitted
To PRB (2013).
7/17/2015 8:55 PM
45
Project 3: Muon Spin Relaxation
studies of Ba2CaOsO6
• Precession not seen
in “doppelganger”
Ba2YReO6, but is
seen in Ba2YRuO6!
C. M. Thompson
et al. Submitted
To PRB (2013).
7/17/2015 8:55 PM
46
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
• SR and 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?”
7/17/2015 8:55 PM
47
7/17/2015 8:55 PM
48
Neutron Diffraction (Q dependence)
– Location of “Bragg peaks” reveal position of atoms
in structure!
Clifford G. Shull (1915-2001), Nobel Prize in Physics 1994
7/17/2015 8:55 PM
49
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)
7/17/2015 8:55 PM
50