Anomalous Hall effect
I have a general interest in all aspects of Magnetotransport, but I particularly focus on the
roles played by topology and transport spin polarization in the anomalous Hall effect. The
anomalous Hall effect is a remarkable area of solid-state physics where even the underlying
physical origin has been hotly disputed since the 1950s. Our experimental work builds on the
resonant topological anomalous Hall mechanism and the associated power law scaling
between anomalous Hall and longitudinal conductivity that was predicted by Onoda et al.,
[PRL 97, 126602 (2006)], to identify the underlying materials parameter that control the
anomalous Hall. This strategy is illustrated in the two case studies below in CrO21 and
Co2MnSi.2
Coexistence of Universal and Topological Anomalous Hall Effects in Dirty-Limit metal
CrO2 thin films1
We find that the carriers in films studied here are hole-like, the hole mobility correlating with
film thickness and the residual resistivity ratio governed by carrier mobility not carrier
density. CrO2 has the band features required for the resonant mechanism and by growing a
series of films with systematically increasing structural defect concentration, or dirtiness, at a
given temperature, we are able to isolate the universal Hall scaling. CrO2 also exhibits a
topological Hall term that is controlled by the concentration of purely magnetic defects, and
above 100K we observe coexistence of the universal and topological terms with an apparent
deviation from the exponent 1.6. We note that both these terms are intrinsic, and yet one
increases and the other is suppressed by the concentration of certain defects, Furthermore
both have a quantum topological aspect and we observe coexistence of topological
singularities in real and momentum-space in CrO2. An additional observation relates to spin
polarisation of the carriers. We have previously reported that the transport spin polarization
of these films is not sensitive to the morphological changes in this series of films at 4.2K and
that Pt (4.2K) is high and close to 90%. The results presented here support this view,
moreover we see no signature to suggest a strong temperature dependence of Pt. This null
result is encouraging for spintronic applications suggesting that the spin polarisation is robust
in this system up to room temperature. The requirements to engineer this effect in other
systems are spin-orbit splitting of magnetic defects, strong coupling of carriers to local
magnetic moments and possibly half-metallicity. As these conditions are met in the
manganite system it is possible that the manganites would display similar tunability of
properties.
Figure 1: Measured Saturation anomalous Hall conductivity vs. Temperature (symbols).
Dashed line: Universal fit, AHU,
Topological fit, AHTop,
calc
calc
(T) = 1.1*10-7(Ωm)0.6 (xx(T))
1.6
. Dotted line:
(T) =[μ0MS(T).(xx(T))2].(A/T)exp(EC/kBT). Solid line: Total fit:
AHCalc(T) = AHU, calc(T) + AHTop, calc(T).
Temperature Insensitivity of the Spin Polarization in Co2MnSi films on GaAs (001)2
The sputtered Co2MnSi films on GaAs (001) have large residual resistivities as a result of
temperature independent defect scattering, which is the dominant scattering mechanism up to
room temperature. This temperature independent extrinsic regime allows much more
information about the spin polarization to be extracted from the anomalous Hall conductivity,
which is sensitive to both spin polarization and scattering mechanism, than is usually the
case. We observe that the anomalous Hall conductivity, and hence the spin polarization, is
robust up to room temperature in all the Co2MnSi films, and its absolute value decreases as
the thickness decreases and the loss of manganese into the interface reaction layer becomes
more significant. This temperature independence in the Hall conductivity of the thinner films
is surprising given the decreasing saturation magnetisation. This may arise because the
magnetisation measurement is sensitive to the whole volume, whereas the transport only
samples the conducting region, and the faceted morphology of the reaction zone in these
films does not provide a good conduction path. The importance of the temperature
independent extrinsic regime for the anomalous Hall analysis is illustrated by comparison
with an MBE grown NiMnSb film on GaAs (001) with low antisite disorder. The residual
resistivity is far smaller in the NiMnSb film, there is less defect scattering, and there is a
change in the dominant scattering mechanism between 10K and room temperature. This
particular difference is a result of the different growth methods, not of a difference between
the materials. At all temperatures the ordinary Hall constant is far greater, and the anomalous
Hall constant far smaller than in the Co2MnSi films, and it is quite strongly temperature
dependent. Furthermore, the anomalous Hall constant varies with the square of the resistivity
in Co2MnSi, whereas it is nearly linear in resistivity in the NiMnSb film. These observations
indicate that the higher structural quality of the NiMnSb film results in a lower carrier
density, higher mobility and reduced impurity scattering than in the “dirty metal” Co2MnSi
films. The temperature dependent anomalous Hall conductivity of the MBE grown NiMnSb
could be attributed to either the changing scattering mechanism, or decreasing spin
polarization with increasing temperature.
Figure 2: Saturation anomalous Hall conductivity vs temperature for Co2MnSi:GaAs and
NiMnSb:GaAs films.
1
W. R. Branford, K. A. Yates, E. Barkhoudarov, J. D. Moore, K. Morrison, F. Magnus,
Y. Miyoshi, P. M. Sousa, O. Conde, A. J. Silvestre, and L. F. Cohen, Phys. Rev. Lett.
102, 227201 (2009).
2
W. R. Branford, L. J. Singh, Z. H. Barber, A. Kohn, A. K. Petford-Long, W. Van
Roy, F. Magnus, K. Morrison, S. K. Clowes, Y. V. Bugoslavsky, and L. F. Cohen,
New Journal of Physics 9, 42 (2007).