Magnetic phase transition and Magnetic phase transition and spin fluctuations in the geometrically frustrated spin fluctuations in the geometrically frustrated antiferromagnetic antiferromagnetic spinel spinel CdCr CdCr 2 2 O O 4 4 : : An experiment using the SPINS An experiment using the SPINS cold cold - - neutron triple axis spectrometer neutron triple axis spectrometer Supervisors Supervisors Jae Jae - - Ho Chung, Ho Chung, Hye Hye - - Jung Kang & William Ratcliff II Jung Kang & William Ratcliff II NIST Center for Neutron Research NIST Center for Neutron Research Summer School on Methods and Applications of Neutron Spectroscopy NIST Center for Neutron Research, June 25-29, 2007 Group A Group A Ken Desmond, Jason Ken Desmond, Jason Haraldsen Haraldsen , Rafael Jaramillo, , Rafael Jaramillo, Xianglin Xianglin Ke Ke , , Jong Jong Keun Keun Park, Park, Cuihuan Cuihuan Wang, Wang, Shao Shao - - Chun Wang, and Ben White Chun Wang, and Ben White
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Magnetic phase transition and Magnetic phase transition and spin fluctuations in the geometrically frustrated spin fluctuations in the geometrically frustrated
antiferromagnetic antiferromagnetic spinelspinel CdCrCdCr22OO44::An experiment using the SPINS An experiment using the SPINS
SupervisorsSupervisorsJaeJae--Ho Chung, Ho Chung, HyeHye--Jung Kang & William Ratcliff IIJung Kang & William Ratcliff II
NIST Center for Neutron ResearchNIST Center for Neutron Research
Summer School on Methods and Applications of Neutron Spectroscopy NIST Center for Neutron Research, June 25-29, 2007
Group AGroup AKen Desmond, Jason Ken Desmond, Jason HaraldsenHaraldsen, Rafael Jaramillo, , Rafael Jaramillo, XianglinXianglin KeKe, , JongJong
KeunKeun Park, Park, CuihuanCuihuan Wang, Wang, ShaoShao--Chun Wang, and Ben WhiteChun Wang, and Ben White
CdCrCdCr22OO44 : Cr: Cr3+3+ (3(3dd33, , SS =3/2)=3/2)Magnetic Cr3+ ions form a lattice of corner-shared tetrahedraSimilar lattices are found in spinel (AB2O4) B-sites or pyrochlores (A2B2O7)
Magnetic exchange energy between a pair of spins is H = Jij Si·Sj. If Jij > 0, then Si and Sjwill become antiparallel to each other.
frustrated
?
??
?
unfrustrated
CdCr2O4ZnCr2O4
But CdCr2O4 eventually orders at very low temperatures. How?
Magnetic phase transition in Magnetic phase transition in CdCrCdCr22OO44
Magnetic susceptibilityχ = dM/dH
M: magnetization of the materialH: applied magnetic field
susceptibility inverse susceptibility
Indication of the strength of the antiferromagnetic interaction
- Provides a flexible choice of highresolution or high intensity
Looking for the degenerate ground states in Looking for the degenerate ground states in the geometrically frustrate phasethe geometrically frustrate phase
Using simulations, we can try to determine the magnetic structure by comparing to the collected data.
Simple calculation of magnetic Simple calculation of magnetic neutron scattering intensityneutron scattering intensity
Magnetic neutron scattering cross sectionMagnetic neutron scattering cross section
But if we consider only up and down spins for But if we consider only up and down spins for diffuse quasidiffuse quasi--elastic scattering, all we need is elastic scattering, all we need is the following simple equation:the following simple equation:
)( ˆ''ˆ
)}(exp{)()()~~(),( where,
),(dd
d
'''
,''
'''
*
',,
22
λλβα
λλλ
βαβααβ
ωωωδλλλλ
δω
ωωσ
hhh −+×
−⋅−=
=Ω
∑ ∑∑∑
dlld
dllddl
,dldd
i
fo
SS
iffpQQS
Skk
r
RRQQQQ
Q
1or,1
factorformmagnetic:)()(2
−=
∝ ⋅∑σ
σ fefI i RQR
RR QQ
QQ--dependence along the (h,0,0) and dependence along the (h,0,0) and (0,k,0) crystal configurations(0,k,0) crystal configurations
T = 15 K
Experimental Data Theoretical Simulation
QQ--dependence along the (h,h,0) and dependence along the (h,h,0) and (0,0,l) crystal configurations(0,0,l) crystal configurations
T = 10 K
Experimental Data Theoretical Simulation
Low Temperature
Magnon Excitations
High Temperature
Short Range Quasi-elastic Spin Fluctuation
Temperature DependenceTemperature Dependence
Magnetic Fluctuation
Lifetime ~ 3 ps
T = 1.4 K
T = 10 K
SummarySummaryUsing the TripleUsing the Triple--Axis Spectrometer, we studied the Axis Spectrometer, we studied the magnetic phase transitions in CdCrmagnetic phase transitions in CdCr22OO44, which is a , which is a spinelspinelwith with antiferromagneticantiferromagnetic interactions between Crinteractions between Cr3+3+ ions on ions on B sites.B sites.
We examined the QWe examined the Q--dependence on different crystal dependence on different crystal planes.planes.
Using a theoretical simulations, we were able to Using a theoretical simulations, we were able to determine the basic magnetic structure.determine the basic magnetic structure.
Through the use of temperature dependence, we were Through the use of temperature dependence, we were able to find that the discovered peaks are consistent with able to find that the discovered peaks are consistent with magnetic excitations.magnetic excitations.
The examination of the line width for the quasiThe examination of the line width for the quasi--elastic elastic fluctuation shows the lifetime to be on the fluctuation shows the lifetime to be on the picopico--second second scale.scale.
AcknowledgementsAcknowledgementsYamaliYamali Hernandez and Antonio Hernandez and Antonio FaraoneFaraone
JaeJae--Ho Chung, Ho Chung, HyeHye--Jung Kang and William Ratcliff IIJung Kang and William Ratcliff II
M.C. M.C. RheinstRheinstäädterdter and C.L. and C.L. BroholmBroholm
Dave Team (Larry Dave Team (Larry KnellerKneller and others)and others)