How strongly correlated is MnSi?

0.68 MB·English

by  F. Carbone

How strongly correlated is MnSi?
F. Carbone1, M. Zangrando2, A. Brinkman1, A. Nicolaou2, F. Bondino2, E.
Magnano2, A.A. Nugroho4,5, F. Parmigiani2,3, Th. Jarlborg1, D. van der Marel1
1D´epartement de Physique de la Mati`ere Condens´ee,
Universit´ee de Gen`eve, CH-1211 Gen`eve 4, Switzerland
2Laboratorio Nazionale TASC-CNR, Basovizza S.S. 14, Km 163.5, 34012 Trieste, Italy
3INFM, Dipartimento di Matematica e Fisica, UCSC, Via dei Musei 41, 25121 Brescia, Italy
6
4Materials Science Centre, University of Groningen, 9747 AG Groningen, The Netherlands
0
5Jurusan Fisika, Institut Teknologi Bandung, Indonesia
0
2 (Dated: September9, 2005)

n We present an experimental study of the electronic structure of MnSi. Using X-ray Absorption
a Spectroscopy, X-ray photoemission and X-ray fluorescence we provide experimental evidence that
J MnSi has a mixed valence ground state. We show that self consistent LDA supercell calculations

3 cannot replicate the XAS spectra of MnSi, while a good match is achieved within the atomic
2 multiplettheoryassumingamixedvalencegroundstate. Wediscusstheroleoftheelectron-electron
interactionsinthiscompoundandestimatethatthevalencefluctuationsaresuppressedbyafactor

] of 2.5, which means that the Coulomb repulsion is not negligible.
l
e
-
r
t Traditionally the magnetism of MnSi is considered as rayphotoelectronspectroscopy(XPS)andX-rayfluores-
s weakly itinerant[1, 2], i.e. the spin-polarization is mod- cence spectroscopy (XFS), we provide the experimental
.
t
a eledasarelativeshiftofbandsofdelocalizedBloch-states evidence that MnSi has a mixed valence ground state
m forthetwospin-directions. AtambientpressureMnSior- which cannot be described by the standard LDA ap-
- ders heli-magnetically below TC=29.5 K, and becomes proach. We will show that the electron-electron corre-
d ferromagnetic in a magnetic field exceeding 0.6 Tesla. lations are not negligible, the value of U/W is estimated
n
The Hall effect and the negative magneto-resistance[3] tobearound0.4,whereUaretheonsiteCoulombrepul-
o
in the ferromagnetic phase agree well with the theory sion and W is the bandwidth; we think that most likely
c
[ of spin-fluctuations in itinerant ferromagnetism[1]. Also the observed deviations from the usual itinerant picture

the inelastic neutron scattering data can be interpreted are due to the suppression of valence fluctuations in the
1
inthisframework[4]. Thesaturationmomentofthemag- ground state of the material.
v
9 netically ordered phase is 0.4 µB per Mn atom. On the The crystal structure of MnSi is generated by the cu-
0 other hand, ab initio calculations based on the the Lo- bic B20 structure [11, 12]. The unit cell contains 4
5 cal Density Approximation (LDA) indicate a tendency Mn atoms at crystallographically equivalent positions.
1
0 of the Mn-atoms to form a moment close to 1 µB if the The sub-lattice of transition metal atoms, displayed in
6 real lattice constant for MnSi (4.558 ˚A) is used[5, 6]. A Fig. 1, reveals that the basic structural element is
0 fit of the susceptibility in the paramagnetic phase to a an equilateral triangle of 3 Mn atoms. The structure
t/ Curie-Weiss law gives 2.2 µB per Mn atom[7]. is corner-sharing: Each Mn-atom connects 3 triangles,
a
Recently, several properties of MnSi have been dis- whichoccurwith4differentorientationsalongthebody-
m
covered which had not been anticipated on the basis of diagonals of the cubic unit cell. The singly connected
-
d the itinerant model and which remain to be fully under- loops of the structure shown in Fig. 1 contain an
n stood: Above 14.6 kbar the materialenters a phase with odd number of bonds. The structural similarity to the
o partialheli-magnetic orderalong the (1,1,0)direction[8], pyrochlore[13, 14], Kagome[15, 16], Gadolinium Gallium
c where the electrical resistivity is proportional to T3/2 Garnet[17], and the β-Mn lattices[18, 19] is a peculiarity
:
v in contradiction to standard notions of a Landau Fermi thathasbeenoverlookedsofar. Thismightplayarolein
Xi liquid[9]. A further indication of anomalous low en- the formation of the helical magnetic structure observed
ergy scale properties follows from the non-Drude in- below 29 K.
r
a frared optical conductivity at ambient pressure[10], pro- MnSi high quality single crystals were grown by the
portional to (iω)−1/2. Above TC the resistivity is de- floating zone technique starting from 4N purity Mn and
scribed by the formula[10] ρ=ρsatT/(T0+T) which for 5N purity Si. All samples were characterized by x-ray
T ≫ T0 = 180K approaches the Mott-Ioffe-Regel limit, diffraction, EDX elemental analysis and electrical resis-
ρsat =287µΩcm. The rapid rise towards saturation cor- tivity. The residual resistivity of all MnSi samples was
responds to a strong dissipation of the charge transport. less than 2 µΩcm.
Theabruptdropoftheelectricalresistivitywhenthema-
The experiments were performed at the BACH beam
terialis cooledthroughT suggests that this dissipation
C line [20] of the ELETTRA synchrotron in Trieste. XAS
is due to a coupling to magnetic fluctuations.
was performed in total electron yield (TEY), measuring
Here,usingX-rayAbsorptionSpectroscopy(XAS),X- roughly the first 50 ˚A of the surface, and total fluores-
2

500400300200 104 102 100 98 90 85 80
Si 2p
Mn 3s
C 1s
O 1s
)
U.
A. Si 2s
(
s
nt
u
o
C C KLL O KLL

Si-O Si-Mn
500400300200 104 102 100 98 90 85 80
Binding energy (eV)
FIG.2: (Coloronline). XPSspectraofMnSibeforeandafter
FIG. 1: (Color). Mn sublattice of MnSi. The corners of
cleaving. In the right part of the figure one can see the high
the triangles, all of which are equilateral, correspond to the
resolution spectraof theMn3s levelsmeasured with aninci-
positions of the Mn-atoms.
dent photon energy of 418 eV and the Si 2p levels measured
withanincidentphotonenergyof196eVbeforecleavingand
142eVaftercleaving; intheleft partasurveyfrom theSi2s
totheO 1s is displayed measured at 655 eV incident photon
cence yield (TFY), measuring down to 200 nm in the
energy. Thebluecurverepresentsthespectrumaftercleaving,
bulk. The XAS spectra were normalized to the incident
theredcurvewasrecordedbeforecleaving. Aftercleavingthe
photonflux,theresolutioninTEYwas150meVand400
highbindingenergycomponentoftheSi2plineissuppressed
meV in TFY. The fluorescence experiments were done ,theMn3slevelsplittingdiminishesandtheCandO1slines
recording the fluorescent decay of Mn 3d −→ 2p and are also suppressed.
2p−→3s levels on a CCD detector.
Large single crystals were cleaved in situ prior to the
measurements in order to obtain clean surfaces; the sur- ofthe Si2plevelissuppressed,theMn3slevelssplitting
face quality was checked with XPS, Fig. 2. The base diminishes to a much smaller value and the carbon and
pressureinthemeasurementchamberwas1·10−10mbar. oxygen 1s lines are suppressed.
XAS and XPS spectra were recorded at room tempera- In Fig. 3 we display the Mn L2,3 XAS spectrum of
ture within minutes after cleaving. The contamination MnSimeasuredbothinTEYandTFY; one cansee that
of the surface before and after cleaving was checked by the two spectra are almost identical, indicating that we
oxygen and carbon 1s photoemission. The cleaved sur- are probing indeed the bulk. The two main peaks corre-
faceofthesamplewasscannedspatiallywithstepsof100 spondtothe2p1/2(642eV)and2p3/2(653eV)spin-orbit
µm and XPS was recorded at each position. This anal- split components of the 2p core level. In a one particle
ysis showed that a significant carbon contamination is picture these two edges have the same spectral shape,
presentonthe borderofthesample. Thiscontamination as illustrated by a first principles calculation using the
affects dramaticallythe shape of the TEY XAS. Only at Local Density Approximation (LDA, black line in Fig.
least 150 µm away from the sample’s border, where the 3). Self consistent LDA-LMTO (Local Density Approx-
XPS reveals a very clean surface, we could have a TEY imation - Linear Muffin Tin Orbital) calculations have
spectrum in agreement with the TFY one, representa- been performed for 64-atom supercells; one of the Mn
tive of the bulk properties of the material. In the XPS atoms has a core hole. The groundstate of the calcu-
spectra, recorded in the middle of a cleaved sample, the lation was ferromagnetic, adopting three different states
oxygen and carbon 1s lines are completely suppressed of magnetic polarizationcharacterizedby localmoments
with respect to the noncleavedsample,as shownin Fig. of 0.4, 0.8 and 1 µ , labelled as such in Fig. 3. The
B
2. Theanalysisofthesurfacerevealedthatcarbon,MnO XAS spectrum corresponds to a broadened sum of the
and SiO2 are the main contaminants. The XPS of Si 2p unoccupied local spin Mn-d DOS functions. A known
levels shows a component around 102 eV associated to problem of band calculations in MnSi is the predicted
SiO2; the Mn 3s splitting on the sample before cleaving value of the local moment on the transition metal atom
was 6.3 eV, in agreement with earlier reports for MnO [6]. This quantity is strongly dependent on the unit cell
[21]. Inthe cleavedsample the highbinding energypeak dimensionandtends to behigherthenthe measuredone
3

Photon Energy (eV)
640 645 650 655 640 645 650 655 640 645 650 655
TFY 4 5 6 7 8
d d d d d
TEY 5
6 d
)
. 3d 6
U d
. 7
A
d
(

n
o

i
t
p
r
o
s
b
0.4
A B

0.8
B
1
B
6

Atomic d Mixed Valence LDA
FIG. 3: (Color). Left panel: Mn L2,3 edge measured XAS together with atomic multiplet calculation for a 3d6 ground state.
TheTFYexperimenthasaresolutionof0.4eV(redopensymbols);theTEYexperimenthasaresolution of0.2eV(blueopen
symbols). Middlepanel: theexperimentalspectraareplottedtogetherwiththeMnmixedvalenceatomicmultipletscalculations
inacubiccrystalfield(blackline);belowthislineispossibletoseethecontributionfromthedifferentconfigurations. Thedark
bluelinerepresentsthesuperpositionofthed4,d5,d6 andd7 configurationswiththeweightsgivenbythebinomialdistribution
intableI,whichcorrespondtothenoninteractingparticlepicture. Rightpanel: theLDAcalculationsareplottedfor3different
valueof thelattice parameter together with the experimentalspectra.
when the lattice constant has the experimentally deter- fieldenvironmentof2.4,2.6and3eV.Furthermoreleast
mined dimension of 4.558 ˚A. We checked the influence meansquarefitstothedataoftheweightedsuperposition
of this effect on the XAS spectrum in 3 cases, chang- of 4 single valence spectra, d4,d5,d6,d7 and d5,d6,d7,d8
ing the lattice constant: the local moment of Mn is 0.4 were performed. The least mean square routine tends
4 8
µ (the experimentally measured value) for a lattice pa- to give a negligible weight to the d and d configura-
B
rameter a = 4.36˚A, 0.8 for a = 4.5˚A and 1 µ for the tions. We estimate the error bars of this approach as
B
measured lattice constant a = 4.55˚A. This is shown in the maximumspreadofvalues obtainedforthe d5,d6,d7
the right panel of Fig. 3; this effect weakly modifies the configurations in the two cases for the 3 mentioned val-
XAS spectrum and cannot explain the strong departure ues of the crystal field. The crystal field is estimated
from the measured one. It is evident that LDA calcula- from the band splitting observed in the high symmetry
tions arenarrowerandcannotreplicate the XAS spectra points of the band calculations [5]. In the best fit the
for MnSi. In the middle panel of Fig. 3 we compare relativeweights of the different valences are found to be:
the experimentalspectrawithatomicmodelcalculations 0%d4,21%d5,55%d6,24%d7,0%d8 inacrystalfieldof2.6
performed with a standard computer program [22]. We eV. In Fig. 4 we plot the inverse of the χ2 obtained fit-
calculate the XAS spectra for several different configu- tingtheexperimentaldatatothecombinationofd4+d5,
4 5 6 7 8 5 6 6 7 7 8
rations: Mn 3d ,3d ,3d ,3d and d in a cubic crystal d +d , d +d and d +d respectively. This calcula-
4
tion shows that the fitting quality is peaked around the
6 TABLE I: Theoretical P(N) assuming non interacting parti-
d configurationandsupportstheconclusionthatalarge
contribution to the XAS spectrum comes from the 3d6 cles, [PNI(N)], experimental P(N) obtained from the mixed-
valence fit to the XAS spectrum, [Pexp(N)]. The values
configuration. of ∆(N) correspond to the shift of the energies E(2p −→
3dN+1),withrespecttotheoutputoftheCowancode,ofthe
final state multiplets; the cubic crystal field parameter was
2.6 eV for all configurations.
) 5
.
U N PNI(N) Pexp(N) ∆(N)
. 0 0.0001 - -
A 4
( 1 0.0015 - -

y 2 0.011 - -
t 3
li 3 0.042 - -
a
u 4 0.111 - -
2
Q 5 0.193 0.21 2
6 0.251 0.55 0.38 eV
t
i 1
F 7 0.215 0.24 3.72 eV
8 0.121 - -
0 9 0.04 - -
10 0.006 - -
0 1 2 3 4 5 6 7 8 9 10
N
FIG. 4: (Color online). We display the inverse χ2 for the interaction in the 3d shell of Mn. For the d6 configura-
fits to the experimental data of the superposition of d4+d5, tion of Mn Ueff = F0 −J −C = 1eV [23], where F0
d5+d6, d6+d7 and d7+d8 respectively. is the intra-shell Coulomb repulsion, J is the intra-shell
exchange interaction and C takes into account all the
IntheleftpanelofFig. 3wedisplayacalculationforan multipolecontributionsoftheCoulombandexchangein-
atomic3d6groundstate;thissimplecalculationalsodoes teraction. The overall3d band-width of MnSi is about 6
not represent satisfactorily the experiments. The better eV, but this value in part reflects a relative shift of the
agreementbetweentheexperimentsandtheatomicmul- different group of bands, representing the crystal field
tiplet mixed valence calculation emphasizes two impor- splitting. The width of each of the sub-bands is approx-
tant properties of the electronic configuration of MnSi: imatively 2.5 eV, hence U = 0.4W in this compound.
(i)thedominantconfigurationis3d6;(ii)experimentally, This value implies that MnSi has to be considered as an
the valence fluctuations are given by: itinerant system. On the other hand the valence fluc-
tuations should be strongly suppressed as compared to
p(N)=P(N0)·exp[−(N −N0)2] (1) the non interacting picture, and this indeed corresponds
δN to what we observed experimentally. As a result of final
state interference effects [24, 25], the values of P(5) and
where δNexp = 0.92 and N0 = 6. For non interacting
P(7) given in table I and Fig. 3 are probably somewhat
particlesdistributedover103dbands,havingtheaverage
underestimated.
occupation of 6 electrons (N0 =6), P(N) is given by the
InFig. 6wepresentthephotoemissionspectrumofthe
binomial equation:
Mn 3s core level measured at an incident photon energy
N! of 418 eV and the fluorescence spectrum measured at a
P (N)=0.6N0.410−N10! (2)
NI N!(10−N)! photon energy of 660 eV; since photoemission is a very
surface sensitive technique, we cross check our results
(NI = non interacting), which is to a very good approx- acquiring the correspondingfluorescence spectrum when
imation given by Eq. 1 with N0 = 6 and δNNI = 2.3. possible. The Mn 3s photoemission shows a shoulder
Thusthevalue δNNI =2.5givesameasureofthevalence onthe highenergysideofthe spectrum. Mostlikely,the
δNexp
suppression in the ground state. In table I we show the mixedvalencegroundstatewediscussedbeforeisrespon-
probability ofhaving N electrons onan ionas a function sible for this weak shoulder visible in the 3s spectrum.
of the occupation number in a LDA picture, together Theasymmetryofthe3slevelsphotoemissionininsulat-
with the experimental findings. In Fig. 5 one can see ing Mn compounds, such as MnO, MnF2 or manganites,
the fit to Eq. 1 for the experimentally derived P(N) and has been shown to be caused by the many-body interac-
the theoretical ones. The sharp suppression of valence tionbetweenthe core-holeandthe localized3delectrons
fluctuations in the ground state of Mn observed experi- [21, 26]. In this case the role of the exchange interaction
mentallyislikelytheconsequenceoftheon-siteCoulomb is predominant and, when the orbital moment does not
5
0.8 Photon energy (eV)
PXAS(N)
8 6 4 2 0 555 560 565 570
0.7 PNI(N)
0.6 GGaauussssiiaann ffiitt,, NNeNxI=p=20.2.953 ELDxpA A.U.) XFS U.)
0.5 s ( A.
N) 0.4 unt s (
P( o nt
0.3 n c ou
o c
0.2 ctr on
0.1 otoel XPS Phot
0.0 h
P

-0.1
0 1 2 3 4 5 6 7 8 9 10
N 8 6 4 2 0 95 90 8 5 80 75
FIG. 5: (Color online). The theoretical and experimentally Binding Energy (eV)
derived values of P(N) are plotted together with the fit to
FIG. 6: (color online). Top panel: Valence Band photoemis-
Eq. 1. From thesefitswe extract thevaluesfor δN and thus
δNNI = 2.6 sionmeasuredatanincidentphotonenergyof104eVtogether
δNexp with LDA calculations. Lower panel: Photoemission (blue
open symbols) measured at 418 eV incident photon energy
and fluorescent (red open symbols) spectra of Mn 3s levels
measured at 660 eV incident photon energy.
contribute to the total magnetic moment of the charge
carriers, a direct relation between the 3s level splitting
and the spin magnetic moment is valid. On the other
hand,itiswellknownthatthisrelationdoesn’tholdany
Our observations evidence the fact that in this class
longer in more metallic systems [27]. When the elec- of materials it is not justified to neglect completely the
tronegativity of the ligand atom decreases, the charge electron electron correlations. The discrepancy between
transfer satellites and the screening of the final state be-
the single particle scenario and the experiment is cor-
come more important, as a result it is not possible any roborated by the comparison in Fig. 3 (a) of the LDA-
longer to attribute the peaks in the 3s spectra to pure
predictionoftheXASspectrumtotheexperimentaldata.
spin states. Usually, in more covalent systems, the 3s
It would be tempting to attribute this discrepancy to
levels splitting is smaller than what one would expect in the fact that XAS is a high energy probe, and that the
thelocalizedscenariobecauseoftheseeffects. Webelieve
observed spectra correspond to the final state with an
thatthis isthe caseinMnSi,whosemetallicbehaviorre-
extra core-hole present. However, (i) both in the band-
flects the covalent nature of the Mn-Si bonding. calculation as well as in the atomic multiplet calcula-
In Fig. 6 we compare the experimental valence band tionsshowninFig.3(a)thepresenceofthecore-holehas
photoemission spectra with the LDA calculations. The been taken into account, (ii) theoretically these spectra
calculations includes the radial matrix elements but ig- are expected to be a very sensitive fingerprint of the ini-
nores the k-conservationbetween initial and final states. tialstateelectronicconfiguration,(iii)thesameconcerns
This is a reasonable approximation in the limit of large would apply to the transition metal oxide family, where
photon energy[28]. In the calculation a peak is evident XAS has been quite successful probes of the magnetic
around 2.8 eV away from the Fermi edge, a similar fea- properties [30, 31, 32, 33]. Moreover, also valence band
tureisvisibleintheexperimentalspectrum,althoughits photoemission,whereno corehole is present,is inconsis-
position is only 1.8 eV away from the Fermi edge. The tent with the LDA approach. The cross check of the re-
valence band photoemission spectra have been collected sults by means of different techniques, electron counting
usingthreeincomingphotonenergies: 86eV,104eVand and photon counting techniques, make us confident that
196eVandnoappreciablechangeswhereobserved. Also we are indeed probing the electronic structure of bulk
in this case the agreement between the calculation and MnSi. Our estimated value for U/W around 0.4 classi-
the experiment is not satisfactorily. The valence band fies MnSi in a class of materials where none of the two
photoemission on MnSi has already been reported to- approximationsisparticularlygood: completely neglect-
getherwiththeLDAcalculationinRef. 29. Theauthors ingtheelectron-electroninteractionsorconsideringthem
pointoutthatthemajordeviationsfromtherawspectra asdominant. ThehelicalmagneticstructureofMnSihas
andthecalculationsareascribabletotheonsiteCoulomb been explained in terms of the Dyaloshinskii-Moryia in-
repulsions, in agreement with our conclusion. teraction; the interplay between spin-orbit coupling and
6
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