collin broholm- magnetic surprises on a triangular lattice
TRANSCRIPT
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
1/27
Magnetic Surprises on a Triangular Lattice
Collin BroholmJohns Hopkins University & NIST
Introduction Frustration
Neutron Scattering Triangular Lattice AFM
Theoretical Status Experimental Status
Triangular lattice systems Neel (RbFe(MoO4)2) Glassy (NiGa2S4)
Conclusions
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
2/27
11/15/05 Rutgers Seminar 2
Collaborators
RbFe(MoO4)2G. GasparovicM. KenzelmannS. ParkA. SmirnovL. N. Demianets
A. Ya. ShapiroG. LawesA. P. Ramirez
NiGa2S4S. NakatsujiY. NambuH. TonomuraO. SakaiC. Stock
S. JonasY. QiuY. MaenoJ. Chung
La4Cu3MoO12Y. Qiu
S. IshiwataM. AzumaM. TakanoR. BewleyW. J. L. Buyers
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
3/27
11/15/05 Rutgers Seminar 3
Frustrated Condensed Matter
Lattice symmetry established by chemical bonding (large energyscales) can frustrate weaker magnetic interactions
Frustrated
Frustration produces classically degenerate states of matter witha potential for emergent quantum properties
Satisfied
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
4/27
11/15/05 Rutgers Seminar 4MACS spectrometer under construction at NIST
MACS spectrometerunder construction at NIST
pi pf
Q
"!
RR'RR
RRQ
Q )(S)0(
1
2
1
),( ''
tSeNedt
iti FE[EF
T[ JS
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
5/27
11/15/05 Rutgers Seminar 5
z=3/4 CuMoO plane
La4Cu3MoO12: A lattice of spin-1/2 trimers
Magnetic susceptibility Crystal Structure
(Azuma et. al., PRB 62 R3588)
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
6/27
11/15/05 Rutgers Seminar 6
Frustrated quantum spin triangles
133221 SSSSSS ! JH
J
J J
J2
3
J2
3
133322211 SSSSSS ! JJJH
J1
J3
J2
22
3 J
J
H
2
132
322
2121 JJJJJJJ !H
JH
YimingQiu etal. PRB 2005
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
7/27
11/15/05 Rutgers Seminar 7
Spectroscopy of spin trimers
Transition to quartet
YimingQiu etal. PRB 2005
70 K
10 K
0.0
0.1
0.0
0.1
0.2
JH
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
8/27
11/15/05 Rutgers Seminar 8
Magnetic Ordering of Composite spin-1/2
002
1!Q
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
9/27
11/15/05 Rutgers Seminar 9
Strongly fluctuating spin trimer AFM
YimingQiu etal. PRB 2005
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
10/27
11/15/05 Rutgers Seminar 10
Neutron Scattering
Exact two-spinon
cross-section
Stoneetal. (2003).
Karbach etal. 2000
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
11/27
11/15/05 Rutgers Seminar 11
Frustrated Linkage of Triangles
Triangular lattice Kagome lattice
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
12/27
11/15/05 Rutgers Seminar 12
A brief status of Triangular lattice research
Theory RVB state proposed (Anderson 1973) Classical Heisenberg model has 120o LRO at T=0
(Huse, Rutenberg) S=1/2 model has LRO for T=0 (Huse, Singh)
Finite temperature KT transition (Kawa
mura
&Miyashita) RVB state in Ising model (Moessner and Sondhi)
Experiments Spin-1/2 insulators generally have some form of
dimerization and no LRO Spin-1/2 (ET)2Cu2(CN)3 close to MIT shows no spin
order. It superconducts under pressure Spin-1/2 anisotropic system has de-confined
excitations in a field (Cs2CuCl4)
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
13/27
11/15/05 Rutgers Seminar 13
RbFe(MoO4)2: spin-5/2 triangular AFM
J
J1
J2J
Kenzelmann, Gasparovic etal. (2005)
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
14/27
11/15/05 Rutgers Seminar 14
Field Dependent Long Range Order
120o structure Field dependent
Incommensurate
stacking Spins in
triangular plane Moment reduced
to 75(1)% Incommensurate
state isferroelectric!
Kenzelmann, Gasparovic etal. (2005)
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
15/27
11/15/05 Rutgers Seminar 15
NiGa2S4 : Spin-1 Triangular Lattice AFM
J11 x 97o2 x 2.42
J22 x 100o2 x 2.42 1 x 3.21
J32 x 138.5o
2 x 2.421 x 3.63
Nakatsuji et
al. Science (2005)
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
16/27
11/15/05 Rutgers Seminar 16
No phase transition as T/5CW 0
5CW=80 K so AFM Cusp in G for T7 K
No conventionalphase transition
Two maxima in C/T Finite T entropy
plateau
Nakatsuji etal. (2005)
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
17/27
11/15/05 Rutgers Seminar 17
Spin freezing without C(T) anomaly
Single crystal
Nakatsuji etal. (2005)
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
18/27
11/15/05 Rutgers Seminar 18
Short range magnetic correlations
2 * 22
2
0 22 2
/ 1 2 cos2
d g Ar F Q N
d
W O TE
O
! ; s
q q
m Q m Q c
Q q
Surprises:
1
2 120oQ Q}
1 25(3)O !
Nakatsuji etal. (2005)
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
19/27
11/15/05 Rutgers Seminar 19
Single crystals confirm 2D Incom. SRO
0.155(1)L !1 16(1)O
! FM inter-plane correlationsPlanar spin structure
1 16 6 1
C. Stock etal. (2005)
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
20/27
11/15/05 Rutgers Seminar 20
Excitations from low T state
Early dispersion relation
What is clear so far:
Spin wave like modes at low T
A slow low E mode throughout zone
+ A highly dispersive mode
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
21/27
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
22/27
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
23/27
11/15/05 Rutgers Seminar 23
Frozen spin structure
120o structure on 2asuper-lattice (colors)
Incommensuratemodulation
Spins in triangularplane Moment reduced to
75(8)% Weak ferromagnetic
inter-plane correlations
Nakatsuji etal. (2005)
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
24/27
11/15/05 Rutgers Seminar 24
J1-J3 model on triangular lattice?
0LL!Q J1=0
J1=-0.2J3
Accounts for no peak incommensurability
Plausible given likelyexchange paths
Further confirmationneeded
1 13 3 0
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
25/27
11/15/05 Rutgers Seminar 25
Thought on quantum glassy phase
Not conventional disordered glass: Coherent wave propagation No forward scattering
Impurities involved but unlikely todefine short length scale
Puddles of AFM around impurities inisolated singlet ground state system
Gapped triplet sector gapless singletsector pinned by impurities
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
26/27
11/15/05 Rutgers Seminar 26
Conclusions Glassy phases endemic to real spin systems near quantum
critical point Distinguishing characteristics of glassy phase
Coherent modes despite short range spin-correlations Absence of forward scattering Gapless triplet spectrum
RbFe(MoO4)2 120o structure for sufficient inter-plane coupling Competing interplane interactions yield incommensurate
ferroelectric phase NiGa2S4
spin-1 system with potential for J1-J3 model Glassy incommensurate phase at low T suggest weakinterlayer coupling and weak or absent 2D Neel order
Double peak structure in C(T) indicates a gapped phasemay be present in this problem
e
-
8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice
27/27
11/15/05 Rutgers Seminar 27
Future plans
RbFe(MoO4)2 Explore multiferroic properties in particular electricfield induced handedness of magnetic state
Establish exchange constants through spin wavemeasurements
NiGa2S
4 Carrier doping may be possible. Effects of uni-axial stress and pressure Spin wave measurements to determine hamiltonian Increase disorder (Zn, S)
Theoretical issues: Spin-1 triangular lattice AFM: spin liquid? J1-J3 triangular lattice model: entropy plateau? Phenomenology of glassy quantum magnetism