Suppression of magnetic excitations near the surface of the topological Kondo insulator SmB6

1.1 MB·

by  P. K. Biswas

Suppression of magnetic excitations near the surface of the topological Kondo
insulator SmB
6
P. K. Biswas,1,2,∗ M. Legner,3 G. Balakrishnan,4 M. Ciomaga Hatnean,4 M. R. Lees,4
D. McK. Paul,4 E. Pomjakushina,5 T. Prokscha,1 A. Suter,1 T. Neupert,6 and Z. Salman1,†
1Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
2ISIS Pulsed Neutron and Muon Source, STFC Rutherford Appleton Laboratory,
Harwell Campus, Didcot, Oxfordshire, OX11 0QX, United Kingdom
3Institut fu¨r Theoretische Physik, ETH Zu¨rich, 8093 Zu¨rich, Switzerland
4Department of Physics, University of Warwick, Coventry, CV4 7AL, UK
5Laboratory for Scientific Developments and Novel Materials,
Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
6Physik-Institut, Universita¨t Zu¨rich, Winterthurerstrasse 190, 8057 Zu¨rich, Switzerland
7
1 We present a detailed investigation of the temperature and depth dependence of the magnetic
0 propertiesof3DtopologicalKondoinsulatorSmB ,inparticularnearitssurface. Wefindthatlocal
6
2 magnetic field fluctuations detected in the bulk are suppressed rapidly with decreasing depths, dis-

n appearingalmostcompletelyatthesurface. Weattributethemagneticexcitationstospinexcitons
a in bulk SmB6, which produce local magnetic fields of about ∼1.8mT fluctuating on a time scale
J of ∼60ns. We find that the excitonic fluctuations are suppressed when approaching the surface

4 on a length scale of 40–90nm, accompanied by a small enhancement in static magnetic fields. We
associate this length scale to the size of the excitonic state.

]
l
e PACSnumbers: 71.27.+a,74.25.Jb,75.70.-i,76.75.+i
-
r
t
s Introduction—TopologicalInsulators(TIs)areaclass the in-gap states disappear completely at a much higher
t. ofquantummaterialsthatarecharacterizedbyafullyin- temperature [10], or that they gradually transform from
a
sulating gap in the bulk and robust metallic topological 2D to 3D nature with increasing temperature [23, 24].
m
surface states. It was suggested that these are promising The magnetic properties of bulk SmB have been ex-
6
d- materials for electronic spin manipulation [1]. Theoret- tensivelystudiedusingmagnetizationmeasurements[17],
n ical studies predicted that the prototypical Kondo insu- inelastic neutron scattering [22, 25–27], nuclear mag-
o lator SmB6 belongs to this new class of materials [2–5]. netic resonance (NMR) [28–31] and muon spin relax-
c This was later supported by transport [6–9] and angle- ation (µSR) [32]. These measurements detected mag-
[ resolved photoemission spectroscopy (ARPES) [10–12] netic excitations at energies below the bulk gap. How-
1 measurements. Xu et al. have also revealed that the ever, magnetic ordering in the bulk of SmB was ruled
6
v surface states of SmB6 are spin polarized [13], where out by magnetization [17] and µSR measurements down
5 the spin is locked to the crystal momentum, respecting to 20mK [32] (except under high pressure [33]). In con-
5 time reversal and crystal symmetries. At high tempera- trast, low temperature magnetotransport measurements
9
tures, Kondoinsulatorsbehaveashighlycorrelatedmet- indicate magnetic ordering at the surface of SmB below
0 6
als, while at low temperature they are insulators due to 600mK, which was attributed to ferromagnetic [34] or
0
. the formation of an energy gap at the Fermi level [14– possibly glassy [35] ordering. This ordering is claimed
1 16]. The opening of a gap at low temperature is at- to involve Sm3+ magnetic moments which were detected
0
tributed to the hybridization between the localized f- usingx-rayabsorptionspectroscopy(XAS)atthesurface
7
1 electrons and the conduction d-electrons. In SmB6, the of SmB6 [36].
resistivity increases exponentially as the temperature is
: Although various theoretical [2–5] and experimental
v decreased, as expected for a normal insulator. However,
[6–13] studies have now established compelling evidence
i
X as the temperature is decreased below 4K, the resistiv- that SmB is a topological Kondo insulator, a number
6
ity saturates at a finite value (a few Ωcm) [17, 18]. This
r of open questions remain unanswered. In particular, the
a behavior was attributed to extended states [19], whose
source of the magnetic excitations mentioned above is
nature was revealed recently by transport experiments,
still unclear. It was suggested that an excitonic state
identifying them with metallic surface states [6–9] and
is responsible for these fluctuations [15, 26, 27, 37]. In
supporting predictions of the nontrivial topological na-
this context, it is also important to understand the in-
ture of SmB . ARPES measurements reveal a Kondo
6 terplaybetweenthesemagneticexcitationsandthetopo-
gap of ∼20meV in the bulk and identify the low-lying
logicalsurfacesatesinordertoelucidatethesourceofre-
bulkin-gapstatesclosetotheFermilevel[10–12,20,21].
portedmagneticorderingatthesurfaceofSmB [34,35].
6
These in-gap states have been associated with magnetic
In this paper, we address these important aspects us-
excitations[15,20,22]andfoundtodisappearasthetem-
ing depth-resolved low-energy µSR (LE-µSR) measure-
perature is raised above 20–30K [11, 22]. Other ARPES
ments on single-crystal samples of SmB . We detect a
6
resultssuggestthatthetransitionisverybroadandthat
clear signature of fluctuating local magnetic fields ap-
2
pearing below ∼15K, similar to our previous bulk mea- (cid:2)(cid:1)(cid:4)(cid:6)
(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:9)(cid:4)(cid:6)(cid:1)(cid:13)(cid:20)(cid:15)(cid:1)(cid:2)(cid:11)(cid:26)(cid:23)(cid:22)(cid:3)
surements [32]. The typical size of the fluctuating field (cid:2)(cid:1)(cid:4)(cid:2)
(cid:7)
(cid:4) (cid:9)(cid:4)(cid:10)(cid:1)(cid:12)
inthebulkis∼1.8mTwithacorrelationtimeof∼60ns. (cid:2)(cid:6) (cid:2)(cid:1)(cid:3)(cid:6)
(cid:3) (cid:7)(cid:5)(cid:1)(cid:12)
Moreover,wefindthatthemagnitudeand/orfluctuation (cid:3) (cid:2)(cid:1)(cid:3)(cid:2)
tsiumrfeacoef,thoveseermaalegnngetthicsficealldesodfe4cr0e–a9s0esnmgr,adpuosaslilbylnyedairstahpe- (cid:1)(cid:5)(cid:7) (cid:2)(cid:1)(cid:2)(cid:6) (cid:2)(cid:16)(cid:3)
(cid:2)(cid:1)(cid:2)(cid:2)
pearing completely at the surface of SmB . We propose
6 (cid:2)(cid:1)(cid:4)(cid:6)
thatexcitonicstatesareresponsibleforthesefluctuating (cid:1)(cid:1)(cid:1)(cid:6)(cid:9)(cid:4)(cid:8)(cid:1)(cid:22)(cid:20)(cid:15)
(cid:2)(cid:1)(cid:4)(cid:2)
(cid:7)
magnetic fields. In contrast, we detect an enhancement (cid:4)
(cid:2)(cid:6) (cid:2)(cid:1)(cid:3)(cid:6)
of static magnetic fields near the surface, which may be (cid:3)
(cid:3) (cid:2)(cid:1)(cid:3)(cid:2)
attributed to an increasing number of Sm3+ moments at (cid:7)
the surface of SmB6 [36]. (cid:1)(cid:5) (cid:2)(cid:1)(cid:2)(cid:6) (cid:2)(cid:17)(cid:3)
(cid:2)(cid:1)(cid:2)(cid:2)
Experimental details — µSR measurements were per-
(cid:2)(cid:1)(cid:4)(cid:6)
formed using the LEM [38, 39] and DOLLY spectrome- (cid:1)(cid:1)(cid:1)(cid:1)(cid:9)(cid:1)(cid:22)(cid:20)(cid:15)
(cid:2)(cid:1)(cid:4)(cid:2)
ters at PSI, Switzerland. In these measurements, 100% (cid:4)(cid:7)
(cid:2)(cid:6) (cid:2)(cid:1)(cid:3)(cid:6)
spinpolarizedpositivemuonsareimplantedintothesam- (cid:3)
(cid:3) (cid:2)(cid:1)(cid:3)(cid:2)
ple. The evolution of the spin polarization, which de-
(cid:7)
pends on the local magnetic fields, is monitored via the (cid:1)(cid:5) (cid:2)(cid:1)(cid:2)(cid:6) (cid:2)(cid:18)(cid:3)
anisotropic beta decay positron which is emitted prefer- (cid:2)(cid:1)(cid:2)(cid:2)
(cid:2)(cid:1)(cid:4)(cid:6)
entiallyinthedirectionofthemuon’sspinatthetimeof
(cid:1)(cid:1)(cid:1)(cid:1)(cid:6)(cid:4)(cid:10)(cid:1)(cid:22)(cid:20)(cid:15)
decay. Using appropriately positioned detectors one can (cid:7) (cid:2)(cid:1)(cid:4)(cid:2)
(cid:4)
measuretheasymmetry,A(t),ofthebetadecayalongthe (cid:3)(cid:2)(cid:6) (cid:2)(cid:1)(cid:3)(cid:6)
initial polarization direction. A(t) is proportional to the (cid:3) (cid:2)(cid:1)(cid:3)(cid:2)
(cid:7)
time evolution of the spin polarization of the ensemble (cid:1)(cid:5) (cid:2)(cid:1)(cid:2)(cid:6)
(cid:2)(cid:19)(cid:3)
of implanted spin probes [40]. Conventional µSR exper-
(cid:2)(cid:1)(cid:2)(cid:2)
iments use surface muons with implantation energy of (cid:2) (cid:4) (cid:5) (cid:7) (cid:8) (cid:3)(cid:2)
m
4.1MeV, resulting in a stopping range in typical density (cid:14)(cid:21)(cid:24)(cid:20)(cid:1)(cid:2) (cid:25)(cid:3)
solidsfrom0.1mmto1mm. Thuslimitingtheirapplica-
FIG. 1. (Color online) ZF-µSR spectra obtained at different
tion to studies of bulk properties, i.e., they cannot pro-
temperatures and implantation energies. The solid lines are
vide depth-resolved information or study extremely thin
fits to Eq. (1).
film samples. Depth-resolved µSR measurement can be
performed at the LEM spectrometer using muons with
tunable energies in the 1–30keV range, corresponding
time scale of µSR). A clear change in the shape of the
to implantation depths of 10–200nm. All the µSR data
asymmetry is detected upon cooling (from Gaussian to
reported here were analyzed using the MUSRFIT pack-
Lorentzian),whichindicatestheappearanceofadditional
age [41].
dilute local magnetic fields and a change in the internal
The studied single crystals of SmB samples were
6 field distribution [44]. Since the dipolar fields from nu-
grownusingthefloating-zonemethod[42]. LE-µSRmea-
clearmomentsdonotchangewithtemperature,weargue
surements were performed on a mosaic of 6 disc shaped
that the appearance of additional dilute local magnetic
single crystals, aligned with their [100] axis normal to
fields is most probably due to electronic magnetic mo-
the surface, and glued on a silver backing plate. The
bulk µSR measurements reported here were performed
on one of these single crystals.
(cid:6)
Results — Figure 1(a) shows typical zero field (ZF) (cid:12)(cid:4) (cid:5)(cid:4)(cid:8)(cid:1)(cid:16)(cid:12)(cid:10)
µSR asymmetries, measured at two different tempera- (cid:13)
(cid:2)(cid:5)
tures,aboveandbelowthe“critical”temperature∼15K, (cid:3) (cid:5) (cid:7)(cid:1)(cid:16)(cid:12)(cid:10)
(cid:7)(cid:1)
i.e.,wherestronglocalmagneticfieldfluctuationsappear (cid:8)(cid:10)(cid:11)
in bulk SmB6 [32]. These are compared in Fig. 1(b–d) (cid:15)(cid:16)(cid:14) (cid:4) (cid:5)(cid:7)(cid:4)(cid:6)(cid:1)(cid:16)(cid:12)(cid:10)
to LE-µSR measurements at the same temperatures and (cid:9)(cid:1)
(cid:13)
three different muon implantation energies, E. The cor- (cid:15)(cid:10)
(cid:15)
respondingmuonstoppingprofilesinSmB6 forthediffer- (cid:6)(cid:17)(cid:14) (cid:3)
ent energies, which were calculated using a Monte Carlo
program TRIM.SP [43], are shown in Fig. 2. At 20K we
(cid:1)
observe a Gaussian-like muon spin damping for all four (cid:1) (cid:3)(cid:1) (cid:4)(cid:1) (cid:5)(cid:1) (cid:6)(cid:1) (cid:2)(cid:1)(cid:1)
different energies. This type of damping is attributed to (cid:9)(cid:21)(cid:19)(cid:20)(cid:20)(cid:15)(cid:18)(cid:13)(cid:1)(cid:11)(cid:12)(cid:20)(cid:21)(cid:14)(cid:1)(cid:2)(cid:18)(cid:17)(cid:3)
randomly oriented static magnetic fields [40], which re-
flect the Gaussian field distribution typically produced FIG. 2. (Color online) Muon implantation profiles in SmB6,
by dipolar fields from nuclear moments (static on the calculated using TRIM.SP for various implantation energies.
3
ments in SmB which are dynamic in nature within the energies, though it becomes less pronounced as we ap-
6
µSR time scale [32]. Most importantly, however, we find proach the surface. Although a gradual slowing down is
thatthedifferencebetweenthelowandhightemperature observedforallimplantationenergies, ourresultsclearly
asymmetriesbecomeslesspronouncedwithdecreasingE, show that the nature of magnetic fluctuations strongly
i.e., as we approach the surface of the SmB . As we dis- depends on depth. In Fig. 4 we plot λ at ∼4.5K and σ
6
cussbelow,thisindicatesthatthesizeand/orfluctuation as a function of the muon implantation depth in SmB .
6
timeoftheobservedmagneticfieldsatlowtemperatures The relaxation rate λ decreases rapidly with decreasing
decreases gradually with decreasing depth. depthandmaybeextrapolatedtoλ→0atthesurfaceof
We turn now to a quantitative analysis of our µSR SmB6 (dashed line). This is accompanied by an increase
data. Following the same analysis procedure used pre-
vcaionusbleyfifottredthweeblluulksinmgeaasuGraeumsesinatns K[3u2b],oa-TlloyZaFbespreeclatrxa- (cid:6)(cid:5)(cid:9)(cid:1)(cid:15)(cid:14)(cid:12)(cid:8)(cid:1)(cid:15)(cid:14)(cid:12) (cid:6)(cid:8)(cid:5)(cid:7)(cid:1)(cid:15)(cid:14)(cid:12) (cid:13)(cid:18)(cid:16)(cid:15)
ation function multiplied by a stretched exponential de-
(cid:2)(cid:1)(cid:6) (cid:2)(cid:1)(cid:5)(cid:4)(cid:7)
cay function,
(cid:26) (cid:27) (cid:2)(cid:1)(cid:5)
A(t)=A0 31 + 23(cid:0)1−σ2t2(cid:1)e−σ22t2 e−(λt)β +Abg, (cid:4)(cid:6)(cid:17)(cid:3) (cid:2)(cid:1)(cid:4) (cid:2)(cid:1)(cid:5)(cid:2)(cid:2) (cid:11)(cid:10)(cid:19)(cid:3)
(1) m(cid:1)(cid:2) (cid:1)(cid:2)
l (cid:2)(cid:1)(cid:4)(cid:8)(cid:7)s
whereA istheinitialasymmetry,βisthestretchparam-
0 (cid:2)(cid:1)(cid:3)
eter, andA isanon-relaxingbackgroundcontribution.
bg
σ is the width of static field distribution, e.g., due to
(cid:2)(cid:1)(cid:2) (cid:2)(cid:1)(cid:4)(cid:7)(cid:2)
nuclear moments, while λ is the muon spin relaxation (cid:2) (cid:7)(cid:2) (cid:3)(cid:2)(cid:2) (cid:3)(cid:7)(cid:2) (cid:4)(cid:2)(cid:2)(cid:2)(cid:2) (cid:3)(cid:2)(cid:2)(cid:2)(cid:2)(cid:2)
(cid:4)(cid:11)(cid:14)(cid:10)(cid:5)(cid:12)(cid:15)(cid:5)(cid:15)(cid:9)(cid:13)(cid:12)(cid:1)(cid:6)(cid:7)(cid:14)(cid:15)(cid:8)(cid:1)(cid:2)(cid:12)(cid:11)(cid:3)
rates due to the presence of dynamic local fields. Note,
A = 0 in the bulk µSR measurements, but it is non-
bg FIG. 4. (Color online) The relaxation rates λ at ∼ 4.5K
zero in the LE-µSR measurements due to muons miss- (red, left axis) and σ (blue, right axis) as a function of muon
ing the sample and landing in the silver backing plate. implantation depth in SmB . The dashed lines are guides to
6
Forconsistencywiththebulk-µSRdataanalysis[32], we the eye and the dotted vertical lines indicate the different E
values.
(cid:1)(cid:14)(cid:27)(cid:21)(cid:20)(cid:1) in σ with decreasing depth. The value of σ in the bulk
(cid:2)(cid:1)(cid:6)
(cid:1)(cid:6)(cid:9)(cid:4)(cid:8)(cid:1)(cid:20)(cid:19)(cid:17)(cid:1)(cid:5)(cid:1)(cid:13)(cid:6)(cid:2)(cid:6)(cid:11)(cid:3)(cid:1)(cid:23)(cid:22) is consistent with what we expect from (predominantly
(cid:1)(cid:9)(cid:1)(cid:20)(cid:19)(cid:17)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:5)(cid:1)(cid:7)(cid:12)(cid:2)(cid:13)(cid:3)(cid:1)(cid:23)(cid:22)
boron) nuclear magnetic moments in this system [32].
(cid:1)(cid:6)(cid:4)(cid:10)(cid:1)(cid:20)(cid:19)(cid:17)(cid:1)(cid:1)(cid:1)(cid:5)(cid:1)(cid:6)(cid:6)(cid:2)(cid:10)(cid:3)(cid:1)(cid:23)(cid:22)
(cid:2)(cid:1)(cid:5)
Therefore, the observed increase near the surface must
(cid:4)(cid:5)(cid:6)(cid:3) beduetoadditionalsourcesofrelativelysmallandstatic
(cid:2)(cid:1)(cid:4) magneticfields. Thismaybeduetoanincreasedconcen-
m(cid:1)(cid:2)
l trationofSm3+momentsnearthesurfaceofSmB6which
(cid:2)(cid:1)(cid:3) wasobservedinXASmeasurements[36]. Theincreasein
σ mayhinttoapossiblemagneticorderingatthesurface
of SmB , such as that reported below 600mK [34, 35].
(cid:2)(cid:1)(cid:2) 6
(cid:2) (cid:7) (cid:3)(cid:2) (cid:3)(cid:7) (cid:4)(cid:2) (cid:4)(cid:7) (cid:5)(cid:2) However, this cannot be fully confirmed since it is not
(cid:16)(cid:19)(cid:22)(cid:24)(cid:19)(cid:25)(cid:18)(cid:26)(cid:27)(cid:25)(cid:19)(cid:1)(cid:2)(cid:15)(cid:3) possible to reach the required low temperatures in LE-
µSR measurements.
FIG. 3. (Color online) Temperature dependence of the dy-
Note that λ reflects the spin lattice relaxation rate of
namicmuonspinrelaxationrateλfordifferentmuonimplan-
the muon spin in ZF, which is proportional to ∆B2τ,
tation energies. The solid lines are guides to the eye.
where ∆B is the size of the fluctuating local field sensed
by the implanted muons and τ is its correlation time.
maintain A , σ and A as globally common variables
0 bg Therefore, the observed decrease in λ at lower implan-
for all temperatures at a particular muon implantation
tation energies may be attributed to a decrease in ∆B
energy. Similarly, we also keep the value obtained from
and/or τ as we approach the surface of SmB . To evalu-
bulk measurements, β = 0.72(1), fixed for all temper- 6
atethesizeof∆B andτ wemeasuretheasymmetryasa
atures and implantation energies. Figure 3 shows the
functionoflongitudinalmagneticfield,i.e.,appliedalong
obtained λ values from the fit as a function of tempera-
the direction of initial muon spin polarization. The field
ture for each implantation energy/depth. We observe a
dependence of λ follows [44–46],
large increase in λ below ∼15K in the bulk-µSR data
with a pronounced peak at ∼4.5K which we attribute 2τ(γ∆B)2
to gradual slowing down in the dynamics of the local λ= , (2)
1+(τγB )2
0
magnetic fields at low temperatures [32]. As expected
from our qualitative discussion above, we observe simi- where γ = 2π×135.5MHz/T is the gyromagnetic ratio
lar increase in λ below ∼15K for all other implantation of the muon and B is the applied magnetic field. The
0
4
(cid:1)
duetotheantiferromagneticcorrelationsintheregionof
(cid:2)(cid:1)(cid:4)(cid:2)
the exciton yields an average value of ∼0.01µ for the
B
magnetic moments, where µ is the Bohr magneton.
B
(cid:2)(cid:1)(cid:3)(cid:7) In addition, we can use a simple hydrogen model for
the exciton, describing it as a bound state of an electron
(cid:4)(cid:5)(cid:6)(cid:3)(cid:2)(cid:1)(cid:3)(cid:2) andahole,inordertorelatethesizetothereducedmass
m(cid:1)(cid:2) (cid:1) µex of the electron–hole pair via d = a0(cid:15)rme/µex. Here,
l a is the Bohr radius and (cid:15) is the dielectric constant of
0 r
(cid:2)(cid:1)(cid:2)(cid:7)
SmB ,whichisestimatedbetween(cid:15) ∼600[48]and1500
6 r
[49]. Ourmeasurementsthenimplyareducedmassofthe
(cid:2)(cid:1)(cid:2)(cid:2)(cid:2) (cid:3)(cid:2)(cid:2) (cid:4)(cid:2)(cid:2) (cid:5)(cid:2)(cid:2) (cid:6)(cid:2)(cid:2) (cid:7)(cid:2)(cid:2) orderofthebareelectronmassme,suggestingthateither
electrons, holes, or both are relatively light compared to
(cid:4)(cid:8)(cid:7)(cid:9)(cid:6)(cid:1)(cid:2)(cid:10)(cid:5)(cid:3)
reported values for the effective mass in SmB of m∗ ∼
6
100m [48]. Note that within this model, the observed
FIG. 5. (Color online) The relaxation rate λ at 1.8K as a e
functionofappliedfield[32]. Thesolidlineisthefitdescribed decrease in λ near the surface is primarily due to the
in the text. absence of exitonic states and associated magnetic fields
in this region.
Conclusions — In conclusion, we observe fluctuating
experimental results, which were measure in the bulk of magnetic fields appearing only below ∼15K in the bulk
SmB6 at 1.8K, fit well to Eq. (2) (see Fig. 5) giving of SmB6. Using LE-µSR measurements we find that
∆B =1.8(2)mTandτ =60(10)ns[47]. Hereweassume thesefieldsarerapidlysuppressedwithdecreasingdepth
that we are in the fast fluctuations limit, τγ∆B (cid:28) 1, andprobablydisappearcompletelyatthesurface. Weat-
whichisconsistentwiththevaluesobtainedfromthefit. tribute these fluctuating fields to excitonic states, whose
extent is limited to the bulk of SmB and disappears
6
Discussion — Wenow discussourdata assumingbulk
within∼60nmofitssurface. Anestimateof∼0.01µ for
B
excitons as a source for the observed magnetic fluctua-
the average magnitude of magnetic moments is obtained
tions. The excitons are believed to be of antiferromag-
from the distribution of fluctuating magnetic fields. We
netic nature with a wavelength of the order of a few lat-
also observe a slight increase in the distribution width
tice constants [15, 27]. The observed decay length of
of static magnetic fields near the surface of SmB , hint-
6
magneticfluctuationsnearthesurface(40–90nm)should
ing to the appearance of additional magnetic moments
then be interpreted as the coherence length or “size” of
in this region. Our results reveal a complex magnetic
the excitons. This size is much larger than the ordering
behavior near the surface of the 3D topological Kondo
wavelength so that the exciton can be thought of as a
insulator SmB . We expect that the magnetic nature of
6
fluctuating region with antiferromagnetic correlations.
thenearsurfaceregionofSmB mayhavesignificantim-
6
Themeasuredvalue∆B ∼1.8mTforthewidthofthe plications on the topological surface states at very low
distribution of magnetic fields can be used to estimate temperatures.
themagnitudeofthefluctuatingmagneticmoments. We This work was performed at the Swiss Muon Source
assume that the muons stop at a random position inside (SµS), Paul Scherrer Institute (PSI, Switzerland). The
the cubic unit cell of SmB with a lattice constant of work was supported, in part, by the EPSRC, United
6
4.13˚A. Calculating the distribution of magnetic fields Kingdom grant no. EP/I007210/1.
∗ [email protected] and J. Paglione, Phys. Rev. X 3, 011011 (2013).
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