Annual Report 2011 / 2012 - E21 - Technische Universität München

10 E21 Annual Report 2011/2012
Vibrating-Coil Magnetometry of the Spin Liquid Properties of Tb 2 Ti 2 O 7
S. Legl 1 , C. Krey 1 , S.R. Dunsiger 1 , H.A. Dabkowska 2 , J.A. Rodriguez 3, 4 , G.M. Luke 3 ,
C. Pfleiderer 1
1 Physik-Department E21, Technische Universität München, D-85748 Garching, Germany.
2 Brockhouse Institute for Materials Research, McMaster University, Hamilton, Ontario L8S 4M1, Canada
3 Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada
4 Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institut, 5232 Villigen, Switzerland
Magnetic pyrochlore oxides, A 2 B 2 O 7 , can be ideal examples
of geometric frustration. In the pyrochlores Ho 2 Ti 2 O 7
and Dy 2 Ti 2 O 7 a strong easy-axis (Ising)-anisotropy along
the local [111] axis on the rare earth site within the unit
cell, together with net ferromagnetic interactions, are the
most important preconditions for the emergence of spin ice
behavior, which has been modelled theoretically with enormous
success. An unresolved question concerns the consequences
of reducing the strength of the local Ising anisotropy.
An exciting theory [1] postulates a “quantum spin ice
(QSI)ßcenario, when quantum fluctuations renormalize the
interactions. Striking magnetization plateaux are predicted,
like those observed in Ho 2 Ti 2 O 7 and Dy 2 Ti 2 O 7 , for a magnetic
field strictly along a global [111] axis [2]. Tb 2 Ti 2 O 7 is an
ideal model system of such a scenario. At high temperatures
Tb 2 Ti 2 O 7 exhibits a Curie-Weiss susceptibility with a large
effective moment µ eff = 9.6µ B Tb −1 and a negative Curie-
Weiß temperature Θ CW characteristic of antiferromagnetic
interactions. However, µSR, ac susceptibility, and Neutron
Spin Echo (NSE) established strong spin dynamics down to
20 mK without long-range magnetic order, known as cooperative
paramagnetism. The origin of the reported coexisting
magnetic glassiness remains unclear and may be either intrinsic
or due to defects. Taken together, the nature of the
spin liquid state in Tb 2 Ti 2 O 7 and the proposal of QSI are
hence unresolved.
M (µ B Tb -1 )
0.12
0.09
0.06
T*
T*
[111]
[100]
[110]
µ 0 H=0.01 T
fc-fh
zfc-fh
T*
0.03
0 0.5 1.0 1.5
T (K)
Figure 1: Temperature dependence of the magnetization of
Tb 2Ti 2O 7 in an applied magnetic field of 10 mT. Below T ∗ ∼
200mK a distinct difference between data recorded under zerofield
cooling (zfc) and field-cooling (fc) emerges. Curves are shifted
for clarity.
We address this by measuring the magnetization of a
Tb 2 Ti 2 O 7 single-crystal at TUM using a bespoke vibratingcoil
magnetometer (VCM) for temperatures down to ∼
0.04K and magnetic fields up to 5 T [3, 4]. The Tb 2 Ti 2 O 7
single crystal was grown at McMaster University by optical
float-zoning. The single-crystalline disc used was oriented
such that the face was perpendicular to [111] within ∼ 1 ◦ .
The sample was approximated as an ellipsoid with a demagnetising
factor N = 0.34. We observe magnetic history
dependence below T ∗ ∼ 0.2K reminiscent of the classical
spin ice systems Ho 2 Ti 2 O 7 and Dy 2 Ti 2 O 7 . Figure 1 illustrates
the temperature dependence of the magnetization in an
applied field of 10mT, where data for [100] and [110] have
been shifted by 0.03µ B Tb −1 and 0.06µ B Tb −1 , respectively
for clarity. With decreasing temperature the magnetization
increases with a positive curvature consistent with the
paramagnetic properties at high temperatures. In all field
directions, the curves display a cusp in the zfc-fh and fcfh
data. The shape of the cusp, the absolute difference of
zfc-fh and fc-fh data and the qualitative temperature dependence
of the data provide strong evidence of the emergence
of intrinsic magnetic glassiness below T ∗ which is essentially
isotropic. The glassiness also suggests that the spin freezing
is not specific to classical spin ice.
experiment
2.0
A µ 0 H || [111]
1.5
M (µ B Tb -1 )
B
dM dB int
-1
1.0
0.5
0
30
20
10
µ 0 H*
0
0 0.05 0.10
B int (T)
0.043 K
0.07 K
0.15 K
0.3 K
0.46 K
0.6 K
0.9 K
1.4 K
theory
µ 0 H || [111]
T=0.02 K
J=0.167
J=0.2
0
0 0.05 0.10 0.15
µ 0 H (T)
Figure 2: Experimental and theoretical low-field magnetization of
Tb 2Ti 2O 7 for the[111] axis. (A) Magnetic field dependence of the
magnetization of Tb 2Ti 2O 7 in small fields at various temperatures.
(B) Numerical derivative of the data shown in panel (A). (C)
Theoretically predicted magnetization for a QSI in Tb 2Ti 2O 7 as
reported in Ref. [1]. (D) Derivative of the theoretical data shown
in panel (C).
It is importnat to note that this plot does not display a
point of inflection of M(B). Instead, dM/dB has a broad
maximum only. Data for [110] and [100] (not shown) are
similar to the [111] axis. For comparison we reproduce in
Figure 2(C) and (D) theoretical calculations of the magnetization
and their first derivatives at 20 mK for two different
J, J = 0.167 (“quantum spin ice“(QSI)) and J = 0.2
(“all-in/ all-out“(AIAO)) [1]. The difference between the
QSI and AIAO concerns the marked change in the slope
of dM/dB at low field (< 0.05 T) from negative to
positive for QSI and AIAO structures, respectively. Taken
together we find no evidence of the magnetization plateaux
in Tb 2 Ti 2 O 7 expected of QSI and fluctuation-induced
ferromagnetic interactions. Instead, our data are in semiquantitative
agreement with the theoretical predictions of
AIAO-antiferromagnetism, suggesting that the spin liquid
state in Tb 2 Ti 2 O 7 may be viewed as an incipient AIAO antiferromagnet.
References
[1] H.R. Molavian and M.J.P. Gingras, Journal of Physics: Condensed
Matter 21, 172201 (2009).
[2] C. Krey et al., Phys. Rev. Lett. 108, 257204 (2012).
[3] S. Legl et al., Phys. Rev. Lett. 109, 047201 (2012).
[4] S. Legl et al., Rev. Sci. Instr. 81, 043911 (2010).
2.0
1.5
1.0
0.5
0
100
50
C
M (µ B Tb -1 )
D
dM d(µ 0 H) -1