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

coldcold--neutron triple axis spectrometerneutron triple axis spectrometer

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

: normal antiferromagnet: strong frustrationNCW

NCW

T

T

>>Θ

≅Θ

H

SPINS cold neutron triple axis SPINS cold neutron triple axis spectrometerspectrometer

Why SPINS for this study? Because SPINS

- Precisely access desired Q and hω

- Covers hω in the range between 0.1 to 10 meV

- Perform diffraction measurement

- 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)

Julie KeyserJulie Keyser