VOLUME 85, NUMBER 16 P H Y S I C A L R E V I E W L E T T E R S 16 OCTOBER 2000

Observation of Charge-Density Wave Domains on the Cr(110) Surface
by Low-Temperature Scanning Tunneling Microscopy

K.-F. Braun, S. Fölsch,* G. Meyer, and K.-H. Rieder
Institut für Experimentalphysik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany
(Received 11 April 2000)
We have studied the Cr(110) surface with low-temperature scanning tunneling microscopy at 6 to
145 K. For tunneling voltages below 6150 mV we observe a surface charge-density wave (CDW) with
a wavelength of 42 Å and wave fronts aligned with the [001] in-plane direction. The observed wave
pattern is identified as the surface projection of the bulk CDW's arising from the spin-density wave
ground state of Cr with the Q vector parallel to [100] and [010], respectively. The bulk CDW with Q
parallel to the [001] in-plane direction appears, however, to be strongly suppressed at the Cr(110) surface.

PACS numbers: 75.30.Pd, 61.16.Ch, 75.30.Fv

The spin-density wave ground state of the itinerant anti- The experiments were carried out with a homebuilt ul-
ferromagnet chromium [1,2] is the subject of long-standing trahigh vacuum (UHV) LT-STM which operated at tem-
scientific interest concerning its fundamental nature and, peratures between 6 and 300 K. The Cr(110) surface
more recently, its technological implications [2]. Below was cleaned by extensive Ne1 sputtering and simultaneous
the Néel temperature TN 311 K bulk Cr exhibits static annealing cycles up to 970 K (1 keV, 4 mA). It is known
spin-density waves (SDW) due to wave vector nesting of from literature that UHV cleaning of Cr surfaces is a
the electron and hole Fermi surfaces [3]. As a result of the tedious task owing to persistent segregation of bulk con-
nesting condition, the wave vector Q is incommensurate taminants [18]. In the present case, the applied treatment
with the lattice and may point along any of the three finally yielded a well-ordered surface with terraces typi-
100 directions of the bcc Cr lattice. The SDW may be cally 600 Å in size and segregated contaminants (pre-
either longitudinal (S k Q below TSF) or transversal dominantly nitrogen [18]) reduced to an estimated surface
(S Q above TSF) in character, where S denotes the spin concentration below 8%. The exemplary STM image
polarization and TSF 123 K is the spin flip transition in Fig. 1(a) was taken in constant current mode at 6 K
temperature. The SDW is accompanied by a strain wave (750 Å 3 560 Å, 1000 MV tunneling resistance, Ut
and a charge-density wave (CDW) with half the period of 21 V referring to the sample with respect to the tip) and
the SDW [47]. As an important issue to technological shows seven terraces which are separated by monatomic
applications, SDW's play a crucial role in the giant steps preferentially aligned with the [001] direction and
magnetoresistance effect [8] in Cr Fe superlattices which the close-packed 111 direction. The crystallographic ori-
is triggered by oscillatory magnetic coupling across the entation and the centered rectangular unit cell is inferred
antiferromagnetic Cr spacer layer [9,10]. Up to now, from the inset in Fig. 1(a) 20 Å 3 18 Å, 0.1 MV, Ut
all experimental information available on the structural 10 mV demonstrating atomic resolution of the Cr(110)
features of SDW's and CDW's in bulk Cr or in thin Cr surface. Residual surface contaminants are imaged as de-
films is based on spatially averaging approaches such as pletions on top of the flat terraces. It is noted that these
neutron [1] and x-ray diffraction [1,2,57] or spectro- contaminants tend to form elongated aggregates which are
scopic techniques [11,12]. In this Letter, we present for aligned with the close-packed 111 directions within the
the first time a local probe study of CDW's at a Cr sur- surface plane. Figure 1(b) shows the same surface area
face by low-temperature scanning tunneling microscopy imaged at a reduced tunneling voltage of Ut 210 mV
(LT-STM). We show that the antiferromagnetic (AFM) and 10 MV tunneling resistance. Under these conditions,
surface domain structure of Cr can be imaged indirectly a wavelike surface modulation with a corrugation ampli-
via CDW's accompanying the SDW ground state. Besides tude of 0.15 Å is observed which is characterized by a
the recently published work of Scholl et al. [13], this periodic length of 42 Å and wave fronts aligned with the
is-to our knowledge-the only experimental study to [001] direction. The wave pattern persists over the entire
date that gives access to the microscopic domain structure temperature range investigated; the only effect of tempera-
of an AFM surface on the nanometer scale. The present ture increase is a successive decrease in corrugation am-
observations are also remarkable in the sense that they plitude down to 0.05 Å at 145 K. The overall wave
arise from the surface projection of a 3D bulk CDW. pattern shows no dispersive behavior (i.e., the wavelength
In contrast, only surface charge-density modulations does not change with Ut) and appears to be largely undis-
associated with surface-localized states [14,15] or with turbed by steps, adsorbates, or segregated surface contami-
CDW's in quasi-1D [16] or 2D layered materials [17] nants. Hence, it is not associated with a surface state [19]
have been observed by STM so far. which would show the well known Friedel oscillations.

VOLUME 85, NUMBER 16 P H Y S I C A L R E V I E W L E T T E R S 16 OCTOBER 2000

FIG. 2. Voltage-dependent magnitude of the surface wave in
Fig. 1(b) at 6 K; (a) exemplary line scans 190 Å in length
taken along 110 at Ut 27 mV (upper curve) and at Ut
2275 mV (lower curve). (b) Mean corrugation amplitude ver-
FIG. 1. (a) STM image taken at 6 K 750 Å 3 560 Å, sus Ut measured at constant tunneling resistance (20 MV, black
1000 MV, Ut 21 V with seven Cr(110) terraces separated dots) and at constant current (1.6 nA, empty dots). The charge-
by monatomic steps; segregated surface contaminants are density modulation is strongly enhanced for Ut below 6150 mV
imaged as dark dots. The inset 20 Å 3 18 Å, 0.1 MV, Ut with respect to EF.
10 mV demonstrates atomic resolution and shows the centered
rectangular surface unit cell. (b) Same area as (a) imaged at re- value of U
duced sample bias of 210 mV and 10 MV tunneling resistance t is increased. In Fig. 2(b) the mean amplitude
of the surface wave is shown as a function of U
showing a surface wave with a wavelength of 42 Å and wave t mea-
fronts aligned with the [001] direction. The wave pattern is sured at constant tunneling current (I 1.6 nA, empty
attributed to a surface charge-density modulation arising from dots) and at a fixed tunneling resistance of 20 MV; see
the bulk CDW's of Cr with Q k 100 and Q k 010 . full dots (constant tunneling resistance ensures identical
tip-sample distances for different Ut). In both cases the
By varying the sample bias we find that the wave pattern charge-density modulation is strongly enhanced for Ut be-
shows up for tunneling performed close to the Fermi level low about 6150 mV and shows a pronounced maximum at
only; its amplitude, on the other hand, is insensitive to the EF, demonstrating that the corrugation amplitude is solely
tunneling resistance (i.e., the tip-sample distance) which determined by the tunneling voltage. Hence, the energetic
was varied between 0.1 and 1000 MV. We thus conclude range of electronic Cr states contributing to the observed
that the charge-density modulation observed here is not surface wave is obviously confined to the vicinity of the
due to a topographical modulation of the surface. Fermi energy. We interpret this characteristic feature as an
The voltage-dependent magnitude of the observed wave unambiguous fingerprint of the CDW accompanying the
pattern indicates that we are dealing with a surface charge- SDW ground state of Cr which originates from electron
density wave coupled to the well known bulk CDW of Cr. and hole Fermi surface nesting [3].
This is apparent from Fig. 2 which illustrates the measured Next, we verify the assignment to a surface-projected
corrugation amplitude of the surface wave for different Ut. CDW on the basis of known spatial characteristics of the
Figure 2(a) shows two line scans 190 Å in length taken at bulk CDW in Cr [1,2]. According to neutron and x-ray
6 K along the 110 direction (i.e., perpendicular to the diffraction data the intrinsic bulk CDW occupies equally
wave fronts). While the modulation is clearly observed populated domains with the Q vector pointing along any of
at Ut 27 mV with a mean amplitude of 0.16 Å, it is the three 100 lattice directions. The bulk wavelength is
largely suppressed at Ut 2275 mV. We further find temperature dependent and reaches a low-temperature limit
a continuous lateral shift of the modulation as a function of lbulk 29.5 Å below 20 K [5]. In contrast, the nor-
of the tunneling voltage. Comparison of the line scans in mal direction of the surface wave fronts shown in Fig. 1(b)
Fig. 2(a) shows that the phase shift relative to the modula- points along the 110 in-plane direction and the period-
tion measured close to EF approaches p when the absolute icity length measures 42 Å. This apparent discrepancy is
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VOLUME 85, NUMBER 16 P H Y S I C A L R E V I E W L E T T E R S 16 OCTOBER 2000

resolved by the scheme in Fig. 3 which illustrates the wave shows a constant current topograph 310 Å 3 190 Å,
front arrangement of the three possible bulk CDW domains 18 MV, Ut 20 mV, 135 K of the related wave pat-
(labeled as A, B, and C) relative to the (110) surface plane. tern with equidistant wave fronts running along the 110
For domain A, planar wave fronts with Q k 001 inter- direction. For comparison, Fig. 4(b) reproduces the
sect the (110) plane at a distance identical to lbulk. On dominant surface CDW at the same scale. The crystallo-
the other hand, the wave fronts connected with domains graphic orientation of images [as indicated in Fig. 4(d)] is
B and C (Q k 010 and Q k 100 ) produce intersection chosen so that wave fronts of the domain with Q k 001
lines running along the 001 in-plane direction (see bold
p [Fig. 4(a)] are aligned vertically whereas those of the
lines in Fig. 3) with a spacing of 2 lbulk. In the tempera-
p dominant domain [Fig. 4(b)] run along the horizontal
ture range from 6 to 145 K the quantity 2 lbulk amounts direction. At the present measuring temperature, the mean
according to Ref. [5] to 41.7 42.9 Å, which-within the corrugation of the surface CDW with Q k 001 is about
range of experimental accuracy-agrees very well with 2 times smaller compared to that found for its dominant
our measured value of 42 Å. The wave pattern observed counterpart with Q k 010 and Q k 100 , respectively.
here is thus identified as a surface charge-density modu- A wave front separation of 30 Å is deduced from
lation induced by the two bulk CDW domains with Q Fig. 4(a) which agrees well with the expected value of
pointing either along the [010] or the [100] out-of-plane lbulk for this domain labeled as A in Fig. 3. It is worth
direction. noting that for domain A no such voltage-dependent phase
The major portion of our experimental data reveals sur- shift is observed as it occurs for domains B and C with
face wave patterns analogous to the exemplary case shown Q k 010 and Q k 100 [cf. Fig. 2(a)]. Although we
in Fig. 1(b). Hence, the bulk CDW with Q pointing along cannot yet give a definite physical explanation for the
the [001] in-plane direction (cf. domain A in Fig. 3) ap- phase shift found for domains B and C, it is reasonable
pears to be largely suppressed at the Cr(110) surface. This from the point of symmetry that no phase shift occurs for
finding is consistent with x-ray diffraction data on Cr(100) domain A: In this case, the planar wave fronts of the
[7] and (100)-oriented Cr films [6] which show that CDW corresponding bulk CDW are oriented perpendicular to
modes with Q oriented within the surface plane are the (110) surface plane which preserves mirror symmetry
quenched in the surface-near region. In a few cases, with respect to the (001) plane. Figure 4(c) shows a
however, we have also detected a surface charge-density surface area 990 Å 3 810 Å, 18 MV, Ut 20 mV,
modulation connected with the remaining bulk CDW do- 135 K) in which the surface CDW with Q k 001 (top
main with Q parallel to the [001] in-plane direction. right) coexists with two CDW domains with Q k 010
There is some indication that this rarely observed sur- or Q k 100 (left and lower right). As a guide to
face CDW is pinned by defects since it usually occurs the eye, respective wave front positions are depicted
in the vicinity of extended step bunches. Figure 4(a) schematically by lines in Fig. 4(d). It is remarkable to
note that the domain wall width estimated from Figs. 4(c)
and 4(d) is within only a few nm. This finding cor-
roborates previous ideas concerning domain walls in
bulk Cr [20,21]: In the transversal SDW state S Q
two spin polarization domains may form for each Q
domain. Polarization walls within single Q domains can
be moved reversibly by external strain or magnetic fields
and exhibit wall widths in the range of 100 nm [20].
Walls between SDW domains with different Q, on the
other hand, are much harder to move and are expected to
be extremely narrow (typically a few lattice constants in
width [21]). Our experimental result shows that we are
able to verify the latter case by direct spatial observation.
To summarize, we have presented evidence that the bulk
CDW which accompanies the SDW in Cr gives rise to
significant charge-density modulations at the Cr surface.
The possibility to study these modulations by LT-STM
FIG. 3. Schematic wave front arrangement of the three pos- is remarkable for several reasons: First of all, the sur-
sible bulk CDW domains of Cr (labeled as A, B, and C) relative face domain structure of Cr in its antiferromagnetic SDW
to the (110) surface plane. While planar wave fronts of domain ground state can be imaged and verified indirectly on the
A Q k 001 intersect the (110) plane at a distance identical
to the bulk wavelength l atomic scale, since the observed wave patterns are specific
bulk, the wave fronts connected with
domains B and C (Q k 010 and Q k 100 ) produce intersec- to the particular bulk CDW domains involved. Second, this
tion lines (bold lines) running along the [001] in-plane direction
p experimental approach allows one to investigate local sur-
with a spacing of 2 lbulk. face phenomena associated with the CDW (and thereby the

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VOLUME 85, NUMBER 16 P H Y S I C A L R E V I E W L E T T E R S 16 OCTOBER 2000

FIG. 4. (a) STM image 310 Å 3 190 Å, 18MV, Ut
20 mV, 135 K) showing the surface charge-density modulation
arising from the bulk CDW domain with Q k 001 ; wave
fronts run along the 110 direction with a spacing of 30 Å
(cf. domain A, Fig. 3). For direct comparison, the dominant
surface CDW is reproduced in (b). (c) 990 Å 3 810 Å surface
area (18 MV, Ut 20 mV, 135 K) in which the surface
CDW with Q k 001 (top right) coexists with two dominant
CDW domains with Q k 100 or Q k 010 , respectively
(left and lower right). (d) Scheme of respective wave front
positions extracted from (c). Because of enhanced contrast,
surface contaminants appear more pronounced in (a) and (c) as
compared to (b).

direct observation of the SDW with the help of ferro-
magnetic STM tips. Apart from these interesting issues,
our future experiments aim at local spectroscopic mea-
surements in order to complement the spatially averaged
spectroscopic information on the SDW ground state of Cr
available to date [12].
This research was supported by the Deutsche For-
schungsgemeinschaft (Sfb 290, TP A5).

*Corresponding author.
Electronic address: foelsch@physik.fu-berlin.de
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