# THE KINEMATICS AND CHEMISTRY OF RED HORIZONTAL BRANCH
STARS IN THE SAGITTARIUS STREAMS

W.B.SHI11affiliationmark:  22affiliationmark:  Y.Q.CHEN11affiliationmark:
K.CARRELL11affiliationmark:  and G.ZHAO11affiliationmark:  22affiliationmark:
† 1 Key Laboratory of Optical Astronomy, National Astronomical Observatories,
Chinese Academy of Sciences, Beijing 100012, China<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>2 Shandong Provincial Key
Laboratory of Optical Astronomy and Solar-Terrestrial Environment, School of
Space Science and Physics, Shandong University at Weihai, Weihai 264209, China

###### Abstract

We have selelcted 556 Red Horizontal Branch (RHB) stars along the streams of
the Sagittarius dwarf galaxy (Sgr) from SDSS DR7 spectroscopic data using a
theoretical model. The metallicity and $\alpha$-elements distributions are
investigated for stars in the Sgr streams and for Galactic stars at the same
locations. We find that the Sgr stars have two peaks in the metallicity
distribution while the Galactic stars have a more prominent metal-poor peak.
Meanwhile, [$\alpha$/Fe] ratios of the Sgr stars are lower than those of the
Galactic stars. Among the Sgr stars, we find a difference in the metallicity
distribution between the leading and trailing arms of the Sgr tidal tails. The
metallicity and [$\alpha$/Fe] distribution of the leading arm is similar to
that of the Galaxy. The trailing arm is composed mainly of a metal rich
component and [$\alpha$/Fe] is obviously lower than that of the Galactic
stars. The metallicity gradient is -(1.8 $\pm$ 0.3)$\times 10^{-3}$ dex
degree-1 in the first wrap of the trailing arm and -(1.5 $\pm$ 0.4)$\times
10^{-3}$ dex degree-1 in the first wrap of the leading arm. No significant
gradient exists along the second wraps of the leading or trailing arms. It
seems that the Sgr dwarf galaxy initially lost the metal poor component in the
second wrap (older) arms due to the tidal force of our Galaxy and then the
metal rich component is disrupted in the first wrap (younger) arms. Finally,
we found that the velocity dispersion of the trailing arm from
$88^{\circ}<\Lambda_{\odot}<112^{\circ}$ is $\sigma$ = 9.808 $\pm$ 1.0 km s-1,
which is consistent with previous work in the literature.

Galaxy: halo — galaxy: Sagittarius — stars: red horizontal-branch

##  1 Introduction

The Sagittarius dwarf galaxy is the second nearest galaxy to our Milky
Way(assuming the Canis Major dwarf galaxy is the nearest). The Sgr is
currently being disrupted under the strain of the Milky Way. Studying the
metallicity and kinematic distributions of Sgr stars has now become an
important issue. Many works on chemical abundances of the Sgr stars have been
done based on high resolution spectra. Bellazzini et al. (2008) selected 321
RGB stars in the Sgr nucleus and give the average [Fe/H]$\sim$ -0.45 dex from
the infrared Ca II triplet. Carretta et al. (2010) derived homogeneous
elemental abundances with 27 red giant stars belonging to the Sgr nucleus and
found on average [Fe/H] $\sim$ -0.61 dex – -0.74 dex. Keller et al. (2010)
observed 11 M giant stars with the Gemini South telescope which indicated the
[Fe/H] of stars decreases along the tidal stream. Chou et al. (2007) present a
reliable measurement on M giants with high resolution at different points
along the tidal stream and show a significant metallicity gradient. They found
a median [Fe/H]$\sim$-0.4 in the core that decreases to -1.1 dex over the
leading arm.

However, these works based on high resolution spectra have small samples of
stars. Based on low resolution spectra Yanny et al. (2009) traced the Sgr
tidal streams with red K/M-giants from the SDSS survey. They found an average
[Fe/H] in the range -0.8$\pm$0.2 with 33 K/M-giant stars in two areas. Carlin
et al. (2012) derived metallicity from low-resolution spectra of stars along a
stretch of the Sgr stream and find a constant [Fe/H]$\sim$-1.15. Thus far, the
metallicity and abundance studies of the Sgr tails have been less detailed in
large samples of stars and in various locations, which are the advantages of
the present work. We analyze the metallicity distribution at different points
along the tidal streams of the Sgr with low resolution data for a large sample
of stars.

The SDSS spectroscopic survey and the LAMOST project (Zhao et al., 2006), will
provide a large sample of Red Horizontal Branch (RHB) stars with low
resolution spectra in the Sgr. Currently, the spectroscopic data of the SDSS
survey provides stellar parameters, distances, radial velocities and
metallicities for many stars spread across a wide area. In this work, we
investigate the properties of Sgr RHB stars from SDSS and compare them with
stars in the Milky Way. We present the procedure for selecting the RHB stars
in Sect.2 and give the metallicity analysis in Sect.3. In Sect.4 we test the
theoretical model and sample selection, and a summary is given in Sect.5.

##  2 Sample selection

We obtained 8535 RHB Stars, 5391 with (U,V,W) and 3144 stars without, from
SDSS DR7 low resolution spectral data (Chen et al., 2010). We choose the Sgr
stars with the aid of a theoretical model by Law & Majewski (2010). Law &
Majewski (2010) provide a model of the Sgr orbiting in a triaxial Galactic
potential with $10^{5}$ points. The model divides the $10^{5}$ points into
four parts: leading arm 1 and 2 and trailing arm 1 and 2. The model is based
on observational data from 2MASS and SDSS (for more details please see Law &
Majewski (2010)).

We select our sample stars by using the Law & Majewski (2010) model as a
reference to provide cuts on the RHB stars. Firstly, we obtain 3512 stars from
the full 8535 RHB star sample using Ra-Dec positions. Secondly, we choose RHB
stars in the Sagittarius leading and trailing tidal tails using a
Distance-$\Lambda_{\odot}$ map of the Law & Majewski (2010) model. Here
$\Lambda_{\odot}$ is the Sgr longitude scale along the orbital plane. We
obtain 586 stars in leading arm 1, 585 stars in leading arm 2, 973 stars in
trailing arm 1 and 502 stars in trailing arm 2 from the 3512 stars. The first
and second wrap of the Law & Majewski (2010) model is denoted by arm 1 and 2
respectively. Third, we select stars to be likely members of the Sgr stream
based on their radial velocities, which are appropriate for the Sgr stream at
these positions based on Sgr debris models (Chou et al., 2010). Specifically,
we select stars with a $V_{gsr}$(the velocity in the Galactic standard of
rest)-$\Lambda_{\odot}$ map (Figure 1). A local standard of rest rotation
velocity of 220 km s-1 is adopted for the Sun, for consistency with Law &
Majewski (2010). We also calculate $V_{gsr}$ with the same equation as Law &
Majewski (2010) for consistency, i.e. $V_{gsr}=rv+9.0\cos b\cos l+232.0\cos
b\sin l+7.0\sin b$ km s-1. With the $V_{gsr}$ criteria, 118 stars satisfy the
cuts on leading arm 1 in both the Distance-$\Lambda_{\odot}$ and
$V_{gsr}$-$\Lambda_{\odot}$ maps from 586 stars. In a similar way, 80, 329 and
47 stars in the leading arm group 2, trailing arm group 1 and trailing arm
group 2, are selected from 585, 973 and 502 stars, respectively (see Figure
1). There are 18 RHB stars overlapped in the leading arm and trailing arm. We
omit these overlapping stars from the leading and trailing arm groups. Finally
there are 102, 78, 327 and 31 RHB stars in leading arm 1 and 2 and trailing
arm 1 and 2, respectively (shown in the $X_{GC}$-$Z_{GC}$ map of Figure 2). We
adopt 556 (including 18 overlapping stars) as the total number of RHB stars in
our Sgr samples. The table of our Sgr samples is provided in a electronic
version.

Leading arm 1

Leading arm 2

Trailing arm 1

Trailing arm 2

Figure 1: Selected RHB stars with the Law & Majewski (2010) model (red points)
in a $V_{gsr}$-$\Lambda_{\odot}$ map. We obtain 118 stars (green points) from
586 stars (green points + yellow points + black points) in leading arm 1 and
80 stars (green points) from 585 stars (green points + yellow points + black
points) in leading arm 2. We obtain 329 stars (blue points) from 973 stars
(blue points + yellow points \+ black points) in trailing arm 1 and 47 stars
(blue points) from 502 stars (blue points + yellow points + black points) in
trailing arm 2. The yellow points indicate the Galactic RHB stars. We replaced
the high density stars for a generalization which is shown as the black boxes.
For clearly dividing the stars into Sgr and Galaxy components, we omit the
stars (black points) located at the edge of the model.

Leading arm stars in Sgr

Trailing arm stars in Sgr

Leading arm stars in Galaxy

Trailing arm stars in Galaxy

Figure 2: Spatial distribution of target stars in the debris streams of Sgr.
Upper panels: A plot of Sgr RHB stars in the leading and trailing arms in an
$X_{GC}$-$Z_{GC}$ map. Green and blue points indicate arm 1 and arm 2
respectively in the leading and trailing arms. The large black point indicates
the location of the Galactic Center, while the asterisk indicates the location
of the Sun. Lower panels: A plot of the Galactic RHB stars in an
$X_{GC}$-$Z_{GC}$ map.

For comparison, we selected a sample of Galactic stars with the same positions
but different velocities from the Sgr tidal stars. That is, we select Galactic
RHB stars from the full 8535 star sample by finding stars that satisfy the Ra-
Dec criteria and the Distance-$\Lambda_{\odot}$ criteria of the Law & Majewski
(2010) model, but do not satisfy the $V_{gsr}$-$\Lambda_{\odot}$ criteria
mentioned above. In Figure 1 the yellow points indicate Galactic RHB stars. We
excluded the high density stars with a generalization which is shown as the
black boxes in order to reduce the potential effect from the undetected stream
stars in the Galaxy, see Figure 1. Again, 159 overlapping stars at the
positions of the leading and trailing arms are removed from the leading and
trailing sample. Finally, there are 202, 164, 347 and 129 Galactic stars at
the positions of leading arm 1 and 2 and trailing arm 1 and 2, respectively
(shown in the $X_{GC}$-$Z_{GC}$ map of Figure 2). We adopt 1001 (including 159
overlapping stars) as the total number of RHB stars in our Galaxy sample. The
table of Galactic samples is also provided in a electronic version.

##  3 Results and Discussions

###  3.1 Comparing the kinematics and chemistry of RHB stars in the Sgr and in
the Galaxy

In Figure 3, we plot the histograms of [Fe/H], $V_{r}$, and [$\alpha$/Fe] and
the distribution map of [Fe/H]-[$\alpha$/Fe] for RHB stars in the Sgr (556)
and Galaxy (1001). One sees that the value of $V_{r}$ for all RHB stars in the
Sgr have a sharp peak at -140 km s-1, while there is a large dispersion in the
distribution for the Galactic RHB stars. This is mainly due to the selection
effect. We set a dashed line at -90 km s-1 in the $V_{r}$ histogram to define
the lower velocity group and analyze the metallity distribution of those lower
velocity stars. Clearly, the lower velocity stars are more than half of all
the stars in the Sgr, but the lower velocity stars are only a small part of
all the Galactic stars. Meanwhile, the Galactic stars are dominated by a metal
poor component while the Sgr stars have a significant contribution from a more
metal rich component. The distribution of [Fe/H] in the Sgr stars has two
peaks, one at -1.3 dex and one at -0.8 dex. There are also two peaks in the
[Fe/H] distribution of Galactic RHB stars, which are at the same [Fe/H] value,
but the peak at -0.8 dex is less pronounced and could be due to Sgr stars near
the edges of our selection criteria. Yanny et al. (2009) show that the giant
branch in the Sgr leading tidal tail is consistent with those of globular
clusters with [Fe/H] of -1.0 $\pm$ 0.5. They also find that the 33 identified
Sgr K/M-giant stars have metallicities of -0.8 $\pm$ 0.2. Our results are
similar to the distribution of [Fe/H] in Yanny et al. (2009). We also show the
lower velocity stars with a dashed line in the histograms of [Fe/H] and
[$\alpha$/Fe]. For the Sgr stars, the dashed line shows two peaks in the
[Fe/H] histogram and the two components have equal contributions, while the
solid line shows a bigger contribution from the peak at -1.3 dex than that
from the peak at -0.8 dex. For Galactic RHB stars, the dashed line is similar
to the solid line.

All RHB stars in Sgr

All RHB stars in Galaxy

Figure 3: We compare all RHB stars (red solid lines) in the Sgr (556) and
Galaxy (1001). Blue dashed lines show the stars whose $V_{r}$ is less than -90
km s-1. Left (right) panels show RHB stars in the Sgr (Galaxy).

From the [Fe/H]-[$\alpha$/Fe] map in Figure 3, we can see that the
[$\alpha$/Fe] of most stars is lower than 0.2 dex in Sgr, while that of most
Galactic stars is larger than 0.2 dex. The low [$\alpha$/Fe] stars mainly come
from the metal rich component of the Sgr tidals at -0.8 dex. These results are
consistent with the results of early dwarf galaxy fragments. [$\alpha$/Fe]
deficiencies were found by Smecker-Hane & McWilliam (2002), McWilliam &
Smecker-Hane (2005), Sbordone et al. (2007) and Carretta et al. (2010) for the
more metal-rich stars in the Sgr (McWilliam (2010)). The existence of some
Galactic stars in our sample may lead to analysis error, but they could also
be real since there are plenty of examples of Galactic halo stars with low
[$\alpha$/Fe] (e.g. Nissen & Schuster (1997) and Brown et al. (1997)).

###  3.2 Comparing the properties of Sgr RHB stars in the leading and trailing
arms

Leading arm stars in Sgr

Leading arm stars in Galaxy

Figure 4: Same as Figure 3 but for comparing RHB stars in the leading arm of
the Sgr (180) and Galaxy (366).

Trailing arm stars in Sgr

Trailing arm stars in Galaxy

Figure 5: Same as Figure 3 but for comparing RHB stars in the trailing arm of
the Sgr (358) and Galaxy (476).

It is interesting to compare the properties of RHB stars between the leading
and trailing arms of the Sgr tidal tails. Firstly, the distribution of $V_{r}$
for the RHB stars have big differences between the leading and trailing arms
(Figures 4 \- 5). There are two peaks, -20 km s-1 and -100 km s-1, in the
$V_{r}$ histogram of leading arm stars. The distribution of the Sgr leading
arm stars is similiar with that of the Galactic RHB stars, which also presents
two peaks. Meanwhile, nearly all the trailing arm stars are centered around
one peak near -140 km s-1. The dashed line corresponds to low velocity stars
with $V_{r}$ less than -90 km s-1 in the $V_{r}$ histogram, the same as in
Figure 3. Again, this difference comes from the predictions of the Law &
Majewski (2010) model. We find that the metallicity distribution of the stars
also has large differences between the two arms (Figures 4 \- 5). The
metallicity distribution of RHB stars in the leading arm is similar to that of
the Galactic stars both in the solid and dashed lines. The metal rich peak is
not clear and the metal poor peak is prominent in the leading arm. The [Fe/H]
distribution of the trailing arm stars has two peaks and the metal rich peak
is significant, as shown in the solid line and even more clearly for low
velocity stars as shown in the dashed line.

From the [$\alpha$/Fe] histograms of Figures 4 \- 5, we can see that the
distributions of leading arm RHB stars is also similar with that of Galactic
stars both in the solid and dashed lines, while trailing arm stars show most
stars have lower values of [$\alpha$/Fe], which is different from the Galactic
stars. The properties of the trailing arm RHB stars are more consistent with
the core of the Sgr: [Fe/H] is more metal rich than that of the Galaxy and
[$\alpha$/Fe] is lower than that of Galactic halo stars. It is unexplained
that the leading arm stars do not follow the chemical history of the Sgr core.
Further work is necessary to investigate the leading arm of the Sgr tidals.

###  3.3 The metallicity gradient along the leading and trailing arms

Figure 6: [Fe/H] as a function of angular distance from the main body of Sgr
along the leading arm (left panels) and trailing arm (right panels). The upper
panels show the individual points. In the lower panels, the distribution of
[Fe/H] is displayed as the median. The solid line shows the result of a least-
squares linear fit to the median data. The metallicity gradient is -(1.5 $\pm$
0.4)$\times 10^{-3}$ dex degree-1 in leading arm 1 and -(1.8 $\pm$ 0.3)$\times
10^{-3}$ dex degree-1 in trailing arm 1. The fitted line shows that the
metallicity is nearly flat in leading arm 2 and trailing arm 2.

Figure 7: [$\alpha$/Fe] as a function of angular distance from the main body
of Sgr along the leading arm (left panels) and trailing arm (right panels).
The [$\alpha$/Fe] gradient is (0.67 $\pm$ 0.15)$\times 10^{-3}$ dex degree-1
in leading arm 1 and (0.86 $\pm$ 0.12) $\times 10^{-3}$ dex degree-1 in
trailing arm 1. There is no obvious trend in leading arm 2 or trailing arm 2
except for the fluctuations of individual points.

We would like to see if the metallicity is a function of orbital longitude
along the Sgr leading and trailing tidal streams. Figures 6 and 7 give the
distributions of $\Lambda_{\odot}$-[Fe/H] and $\Lambda_{\odot}$-[$\alpha$/Fe]
for RHB stars. There is a metallicity gradient in trailing arm 1 while there
is a lower one in leading arm 1\. We find that in the trailing arm, when
moving farther from the Sgr core along arm 1 and then to arm 2, the
metallicity shifts to more metal poor values, which suggests an evolution
toward more ancient stars since metal poor RHB stars must be older than metal
rich RHB stars. This is in agreement with dwarf galaxy formation theories
where the more metal rich core of the galaxy is surrounded by older and more
metal poor stars since it is this outer, older and metal poor population that
will be tidally stripped before the younger, inner component. Our results also
agree with the gradient found by Chou et al. (2007) and is similar to Figure
15 of Law & Majewski (2010), which gives the distribution of
$\Lambda_{\odot}$-[Fe/H]. However, Yanny et al. (2009) have studied the
metallicity of blue horizontal-branch (BHB) stars as a function of
$\Lambda_{\odot}$ and find that there is no significant trend in the BHB
metallicity. It is possible that the BHB stars in Yanny et al. (2009) are the
old and metal poor component of the Sgr, which is not easily distinguished
from the Galactic components with the same properties, in contrast with our
comparison sample.

###  3.4 Sgr RHB stars in the bright and faint streams

A recent paper by Koposov et al. (2012) suggests the tidal debris of the Sgr
is actually two separate streams of stars separated by $\sim 10^{\circ}$ in
the Sgr orbital coordinate system. Their work is an extension of the work of
Belokurov et al. (2006) who found two branches of the leading arm debris in
the north Galactic cap. The brighter and thicker stream is claimed to have
more than one stellar population with a large fraction being metal-rich. The
fainter and thinner stream is said to be primarily a single, metal-poor
population. No estimate of the metallicity of either stream is given by
Koposov et al. (2012), but using our RHB sample we can make a qualitative
comparison.

Figure 8: The metallicity distribution of stars belonging to the bright stream
of Koposov et al. (2012). The stars were selected based on the positions and
distances given in their Tables 1 and 2.

As we have shown, our Sgr RHB sample is somewhat metal-rich. Further, since
the brighter stream is also the more metal-rich one according to Koposov et
al. (2012), we expect our RHB sample to be composed primarily of stars from
this stream. To check if this is the case, we separate our sample into stars
belonging to the bright and faint streams using the positions and distances
given in Tables 1 and 2 of Koposov et al. (2012). There are 84 stars (80, 2
and 2 from trailing arm, leading arm and overlapping group, respectively) in
the bright stream and 5 stars (all from the trailing arm) in the faint stream.
The metallicity distribution of the stars in the bright stream is shown in
Figure 8. As expected, most of the stars are metal-rich.

We do not have enough stars in the faint stream to make a meaningful
comparison. This could be due to a couple of factors. One reason we may not
have many stars corresponding to the faint stream is because our selection
criteria are based on the model of Law & Majewski (2010). This selection may
preclude these stars simply based on positions and/or kinematics. Another
possibility is that the metal-poor faint stream has little or no RHB
component. A more detailed description of the two streams is necessary in
order to distinguish between these two possibilities.

##  4 Error Estimate and Model Test

###  4.1 Comparing with Besançon model

In order to estimate the level of contamination from halo RHB stars we use the
Besançon model of the Galaxy (Robin et al., 2003). We selected stars from all
possible Galactic components and applied our selection criteria mentioned
above.

We find that the possible contribution from the halo in our sample varies
greatly depending on the area. In particular, the leading arm areas we select
will suffer from more contamination than the trailing arm areas because of the
closer distances, lower velocities, and wider spread in velocities, all of
which will increase the number of expected halo stars. Further, in the second
wraps of the tidal tails the model constraints are not as strong and therefore
allow for more contamination. Our cleanest sample is that for trailing arm 1
in part because of the larger distances, but more importantly, from the narrow
range of velocities with large negative values. We also have the largest
sample of RHB stars in trailing arm 1 so we expect the results from this area
to be the best and most robust.

The fact that our metallicity gradients for trailing arm 1 and leading arm 1
are so similar and agree within errors means that contamination in our sample
is small and/or has little effect on our results. We also point out that halo
contamination is not unique to our RHB sample and disentangling the halo
component from the Sgr component is very difficult since the stars are at the
same distances and have the same velocities. Previous work using similar
selection criteria as our work will also suffer from the same problem (such as
Yanny et al. (2009); Monaco et al. (2007); Keller et al. (2010); Correnti et
al. (2010); Carlin et al. (2012); Koposov et al. (2012)).

###  4.2 Error Analysis

In the current models (especially in Law & Majewski (2010)), the younger
segments of tidal debris are constrained to match the 2MASS/SDSS observations
while the older segments are regarded as predictions for where tidal debris
might be expected if it extends beyond that which is currently traced by
2MASS/SDSS. The dynamical ’age’ of a particle in the Law & Majewski (2010)
model is given by the parameter ’Pcol’ where values of Pcol $<=$ 3 correspond
to tidal debris observed by 2MASS/SDSS. In our analysis, we use stars whose
’Pcol’ range from 1 to 7 in the model. For more accuracy we could only use the
tidal debris previously observed by 2MASS/SDSS. These parts nearly correspond
to the first wrap of the leading and trailing arms. This would restrict our
results to only arm 1 of the leading and trailing arms. With this sample, the
results become stronger and thus our results are reliable. In particular, the
metallicity and [$\alpha$/Fe] gradients are only detectable in arm 1 of the
leading and trailing arms.

We vary our ranges by 10% in distance and velocity for the sample selection to
obtain a larger or smaller sample and perform the same analysis procedure. The
results are very similar with the original ones. This indicates that the
sample selection criteria are reasonable and the results are robust.

###  4.3 Distance distributions for stars with $\Lambda_{\odot}<130^{\circ}$
as a model test

$70^{\circ}<\Lambda_{\odot}\leq 80^{\circ}$

$80^{\circ}<\Lambda_{\odot}\leq 90^{\circ}$

$90^{\circ}<\Lambda_{\odot}\leq 100^{\circ}$

$100^{\circ}<\Lambda_{\odot}\leq 110^{\circ}$

$110^{\circ}<\Lambda_{\odot}\leq 120^{\circ}$

$120^{\circ}<\Lambda_{\odot}\leq 130^{\circ}$

Figure 9: The distance distribution of RHB stars for
$\Lambda_{\odot}<130^{\circ}$. Each panel shows the stars in a $10^{\circ}$
bin. The dashed lines show the range of model distances in trailing arm 1.

In our sample there are a significant number of stars in trailing arm 1 with
$\Lambda_{\odot}<130^{\circ}$, but not enough stars for good statistics in
other areas. We thus investigate the distance distributions of our RHB stars
and compare them with model predictions since we expect that Galactic stars
have a broad distribution and there should be an overdensity when the Sgr
stream passes through the Galactic field. Figure 9 shows the distance
distributions of RHB stars and dashed lines show the distance range given in
the model for Sgr trailing arm 1 for $\Lambda_{\odot}<130^{\circ}$ with a bin
width of $10^{\circ}$. One sees that almost all bins show distance peaks
within the model predicted ranges despite the significant selection effect of
the SDSS spectroscopic survey. It seems that the distance prediction in the
Law & Majewski (2010) model is correct and our sample selection of RHB stars
based on this model is reasonable.

###  4.4 The velocity dispersion at $88^{\circ}<\Lambda_{\odot}<112^{\circ}$
as a model test

Figure 10: Left panel: radial velocity as a function of longitude of the Sgr
orbital plane for our RHB stars. The polynomial fit to the distribution is
also plotted. Right panel: distribution of the differences between the
polynomial fit and the data. A Gaussian fit is also shown.

Our sample has the largest number of stars at
$88^{\circ}<\Lambda_{\odot}<112^{\circ}$, which covers a similar area as
Majewski et al. (2004) and Monaco et al. (2007). Thus, we investigate the
velocity dispersion for this area so that we can compare our result to these
works and provide a test to the model prediction. In the left panel of Figure
10, we plot Vgsr as a function of the Sgr longitude $\Lambda_{\odot}$. The
solid line is a polynomial fit to the data and it describes a characteristic
trend of decreasing Vgsr with increasing $\Lambda_{\odot}$ along the Sgr
trailing tail, as already discussed by Majewski et al. (2004) and Monaco et
al. (2007). The fit is for $88^{\circ}<\Lambda_{\odot}<112^{\circ}$ because
for $\Lambda_{\odot}<90^{\circ}$ an increase of the velocity dispersion is
evident (see Majewski et al. (2004) and Monaco et al. (2007)). The right panel
shows residuals of our sample stars with respect to the polynomial fit. The
distribution is fit with a Gaussian of width $\sigma$=9.808$\pm$1.0 km s-1
using 119 stars. Monaco et al. (2007) give a velocity dispersion of
$\sigma$=8.3$\pm$0.9 km s-1 using 41 stars with high resolution spectroscopy
and Majewski et al. (2004) give $\sigma$=10.4$\pm$1.3 km s-1 for stars with
low resolution spectroscopy. These three values are consistent within errors.
The agreement indicates that the Law & Majewski (2010) model prediction is
reasonable, which is what our sample star selection is based on. These parts
of the trailing tail are dynamically colder than the Sgr core, which has
dispersions of 11.17 km s-1 and 11.4 km s-1 in Monaco et al. (2005).

##  5 Summary

In this paper we present the properties of the metallicity and
$\alpha$-abundance distributions for a large sample of RHB stars belonging to
the Sgr tidal streams. The Sgr stars have two components in [Fe/H] while the
Galactic stars have a more prominent metal-poor one. [$\alpha$/Fe] is lower
for the Sgr stars than for Milky Way stars, especially along the trailing arm.
There are metallicity gradients along the streams of Sgr, with a value of
-(1.8 $\pm$ 0.3)$\times 10^{-3}$ dex degree-1 in trailing arm 1 and of -(1.5
$\pm$ 0.4)$\times 10^{-3}$ dex degree-1 in leading arm 1. No significant
gradient exists along trailing arm 2 or leading arm 2. Stars belonging to more
ancient wraps of the streams in arm 2 are more metal-poor.

We test the model and sample selection in four aspects as follows. First, by
comparing with the Besançon model of the Galaxy we find that contamination
from the Galactic halo is small for the largest sample of RHB stars in
trailing arm 1. Then we change the selection range for the width of the
leading and trailing arms and find no significant difference. Third we
investigated the distance distribution of RHB stars in trailing arm 1
($\Lambda_{\odot}<130^{\circ}$) and the peaks fall within the model prediction
ranges. Fourth we test the velocity dispersion for the Sgr trailing tail at
$88^{\circ}<\Lambda_{\odot}<112^{\circ}$ and found a value of
$\sigma$=9.808$\pm$1.0 km s-1, which is consistent with the results of
Majewski et al. (2004) and Monaco et al. (2007).

With the upcoming LAMOST spectroscopic survey, we can expect to analyze RHB
stars in the Sgr for an even larger sample and in different Galactic locations
in order to further study the chemical history of the Sgr galaxy.

We thank the referees for their helpful comments which significantly improved
the paper. This work was supported by the National Natural Science Foundation
of China (Grant No.11178013, 11073026, 11150110135 and 10978015), and by the
Provincial Natural Science Foundation of ShanDong (Y2008A08 and ZR2010AM006).

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# Magnetic excitations in double perovskite iridates La2$\mathit{M}$IrO6
($\mathit{M}$ = Co, Ni, and Zn) mediated by 3$\mathit{d}$-5$\mathit{d}$
hybridization

Wentao Jin<EMAIL_ADDRESS>Department of Physics, University of Toronto,
Toronto, Ontario, M5S 1A7, Canada  School of Physics, Beihang University,
Beijing 100191, China  Sae Hwan Chun  Department of Physics, University of
Toronto, Toronto, Ontario, M5S 1A7, Canada  Pohang Accelerator Laboratory,
Pohang, Gyeongbuk 37673, Republic of Korea  Jungho Kim  Advanced Photon
Source, Argonne National Laboratory, Argonne, Illinois 60439, USA  Diego Casa
Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439,
USA  Jacob P. C. Ruff  Cornell High Energy Synchrotron Source, Cornell
University, Ithaca, New York 14853, USA  C. J. Won  Department of Physics,
Inha University, Incheon 22212, Republic of Korea  Laboratory for Pohang
Emergent Materials and Max Plank POSTECH Center for Complex Phase Materials,
Pohang University of Science and Technology, Pohang 37673, Republic of Korea
K. D. Lee  Department of Physics, Inha University, Incheon 22212, Republic of
Korea  N. Hur  Department of Physics, Inha University, Incheon 22212, Republic
of Korea  Young-June Kim<EMAIL_ADDRESS>Department of Physics,
University of Toronto, Toronto, Ontario, M5S 1A7, Canada

(August 27, 2024)

###### Abstract

By performing resonant inelastic x-ray scattering (RIXS) measurements at the
Ir $\mathit{L_{\mathrm{3}}}$ edge, we have investigated the low-energy
elementary excitations in a series of double perovskite iridate single
crystals, La2$\mathit{M}$IrO6 ($\mathit{M}$ = Co, Ni, and Zn). Almost
dispersionless magnetic excitations at $\mathds{\sim}$ 42(6) meV and
$\mathds{\sim}$ 35(5) meV have been observed in crystals containing magnetic
3$\mathit{d}$ ions, La2CoIrO6 and La2NiIrO6, respectively. In contrast, this
low-energy magnetic excitation is absent in La2ZnIrO6 in which the
3$\mathit{d}$ ions are non-magnetic, suggesting the importance of
3$\mathit{d}$-5$\mathit{d}$ hybridization in the magnetic properties of these
double perovskite iridates. The magnetic excitation is suppressed completely
above the magnetic ordering temperature, suggesting the inadequacy of using a
simple spin Hamiltonian to describe magnetism of these materials.

##  I Introduction

Transition metal oxides with 4$\mathit{d}$ and 5$\mathit{d}$ elements have
attracted tremendous interest in the past decade, due to the possible
realization of exotic quantum states such as spin-orbital assisted Mott
insulators,KimBJ_08 ; Plumb_14  quantum spin liquids,Banerjee_16 ; Takagi_19
and Weyl semimetals,Wan_11  arising from the delicate interplay between the
strong spin-orbit coupling (SOC), crystal-field splitting, and Coulomb
repulsion.Witczak-Krempa_14 ; Rau_16  Especially, the largely extended
5$\mathit{d}$ orbitals render a relatively weaker electronic correlation
compared with that of the 3$\mathit{d}$ transition metal (TM), leading to
various attempts aiming to combine the strong correlation of the 3$\mathit{d}$
TM and strong SOC of the 5$\mathit{d}$ TM by engineering
3$\mathit{d}$-5$\mathit{d}$ heterostructures.Matsuno_15 ; Nichols_16 ; Hao_18
Double perovskite (DP) iridates with the formula of
$\mathit{A_{\mathrm{2}}B}$IrO6, in which $\mathit{A}$ is a rare-earth or
alkaline-earth metal and $\mathit{B}$ is a 3$\mathit{d}$ TM, respectively,
offer a unique possibility to realize such a 3$\mathit{d}$-5$\mathit{d}$
combination even within the bulk structure. The topic of $3d-5d$ coupled
magnetism in DP structure has been the subject of extensive research efforts
over the years. Cook_14 ; Morrow_13 ; Vasala_15 ; Plumb_13 ; Laguna-Marco_15 ;
Vogl_18 ; LeeM_18 ; Yuan_18 ; Taylor_18 ; Granado_19 ; Bhowal_20 ; Yuan_21

La2$\mathit{M}$IrO6 with either magnetic ($\mathit{M}$ = Mn, Co, Ni, Cu) or
nonmagnetic ($\mathit{M}$ = Mg, Zn) $\mathit{M}^{2+}$ ions adopts the
$\mathit{B}$-site ordered rock-salt structure with a monoclinic symmetry
(space group $\mathit{P}$21/$\mathit{n}$),Vasala_15 ; Currie_95  which can be
regarded as two interpenetrating simple perovskite lattices La$\mathit{M}$O3
and LaIrO3 with alternating $\mathit{M}^{2+}$O6 and Ir4+O6 octahedra. With the
5$\mathit{d}^{5}$ electronic configuration, the Ir $\mathit{t}$2g manifold
splits into a fully filled $\mathit{j_{\mathrm{eff}}}$ = 3/2 quartet and a
half filled $\mathit{j_{\mathrm{eff}}}$ = 1/2 doublet in the presence of
strong SOC. As a result, a spin-orbital entangled $\mathit{j_{\mathrm{eff}}}$
= 1/2 Mott insulator is expected as their electronic ground state.Cao_13  Such
a $\mathit{j_{\mathrm{eff}}}$ = 1/2 state associated with the Ir4+ ions on a
quasi-face-centered cubic lattice can host the long-sought Kitaev
interactions,Kitaev_06 ; Jackeli_09 ; Kimchi_14  which drives numerous
theoretical and experimental studies in recent years on the magnetism of DP
iridates La2$\mathit{M}$IrO6.

In the case of La2MgIrO6 and La2ZnIrO6 with nonmagnetic $\mathit{M}^{2+}$ ions
occupying the $\mathit{B}$-site, the Ir4+ sublattice was found to order in a
collinear and canted antiferromagnetic (AFM) structure below
$\mathit{T_{\mathrm{N}}}$ = 12 K and 7.5 K, respectively, with a $\mathit{k}$
= 0 propagation vector.Cao_13  The canted antiferromagnetism in La2ZnIrO6
(LZIO) was modeled by a spin Hamiltonian incorporating both the Heisenberg
exchange and the Dzyaloshinskii–Moriya interaction due to the octahedral
titing and strong deviation of the Zn-O-Ir angle from 180∘.Zhu_15  On the
other hand, in the presence of a magnetic $\mathit{M}^{2+}$ ion in
La2$\mathit{M}$IrO6, the magnetic ground state is more complicated due to the
interplay between 3$\mathit{d}$ and 5$\mathit{d}$ magnetism. For example,
La2MnIrO6 undergoes a ferromagnetic (FM) transition at
$\mathit{T_{\mathrm{C}}}$ = 130 K,Demazeau_94  whereas La2CuIrO6 exhibits an
AFM transition into a noncollinear magnetic structure with $\mathit{k}$ =
(1/2, 0, 1/2).Manna_16  La2CoIrO6 (LCIO) display a ferrimagnetic order below
$\mathit{T_{\mathrm{C}}}$ $\mathds{\sim}$ 95 K as revealed by neutron powder
diffraction. Narayanan_10 ; LeeS_18  In this noncollinear magnetic order with
$\mathit{k}$ = 0, the moments of both the Co and Ir sublattice are ordered
antiferromagnetically in the $\mathit{ac}$ plane and canted along the
$\mathit{b}$ axis, giving rise to ferromagnetic moments. In addition,
La2NiIrO6 (LNIO) was recently determined to be a noncollinear antiferromagnet
with $\mathit{k}$ = (1/2, 1/2, 0), showing only the $\mathit{a}$\- and
$\mathit{c}$\- spin components with simultaneous ordering of Ni2+ and Ir4+
moments.Ferreira_21

Although many experimental studies have been carried out to understand the
static magnetic order in the DP iridates La2$\mathit{M}$IrO6, information
about the spin dynamics have been scarce. For LZIO, a recent inelastic neutron
scattering study found gapped spin-wave excitations with very weak dispersion,
suggesting strong exchange anisotropies and a possible dominant Kitaev
interaction associated with the monoclinically distorted DP lattice.Aczel_16
The recent combined nuclear magnetic resonance (NMR) and electron spin
resonance (ESR) measurements have revealed pronounced quasi-static spin
correlations in both LZIO and LCIO persisting at temperatures far above their
magnetic phase transitions, signifying substantial magnetic frustration
inherently existing in these DP iridates composed of two intersecting fcc
sublattices.Iakovleva_18  However, it is still not clear how the magnetism is
translated between the 3$\mathit{d}$ magnetic TM and 5$\mathit{d}$ Ir4+ ions,
and what roles the 3$\mathit{d}$ magnetic TM ions is playing in the spin
dynamics of the Ir sublattice. In this paper, the low-energy magnetic
excitations of Ir4+ pseudospins in a series of DP iridates,
La2$\mathit{M}$IrO6 ($\mathit{M}$ = Co, Ni, and Zn), are systematically
studied using resonant inelastic x-ray scattering (RIXS) measurements at the
Ir $\mathit{L}_{3}$ edge. A large excitation gap of $\mathds{\sim}$ 40 meV was
observed in both LCIO and LNIO, but not in LZIO, indicating the important role
of the 3$\mathit{d}$ magnetic ions in mediating the spin exciations of the Ir
sublattice.

##  II Experimental Details

RIXS experiments were performed at the 27 ID-B beamline of the Advanced Photon
Source (APS) at Argonne National Laboratory using the MERIX
instrumentation.Gog_09  A double-bounce diamond(111) primary monochromator, a
channel-cut Si(844) secondary monochromator, and a spherical (2 m radius)
diced Si(844) analyzer crystal were used to obtain an overall energy
resolution of $\mathds{\sim}$ 25 meV [full width at half-maximum (FWHM)] at
the incident photon energy $\mathit{E_{i}}$ = 11.214 keV (near the Ir
$\mathit{L_{\mathrm{3}}}$ edge, 2$\mathit{p}$ $\mathds{\rightarrow}$
5$\mathit{d}$). The incident beam was focused to a size of 40 × 20 $\mu$m2
($\mathit{H}$ × $\mathit{V}$) at the sample position. A MYTHEN strip detector
was used, and the horizontal scattering geometry with the scattering angle
2$\theta$ close to 90∘ was adopted to minimize the elastic background
intensity. The sample temperature was controlled between 5 and 300 K in a
closed-cycle refrigerator.

Single crystals of La2$\mathit{M}$IrO6 ($\mathit{M}$ = Co, Ni, and Zn) were
synthesized using the PbO-PbF2 flux method. The polycrystalline samples of
La2$\mathit{M}$IrO6 were firstly prepared by solid-state reaction. The
stoichiometric mixtures of pre-dried La2O3, Co3O4/NiO/ZnO, and IrO2 powders
were ground, pelletized, and sintered at 1150 ℃ twice with an intermediate
grinding. The obtained polycrystalline sample La2$\mathit{M}$IrO6 were then
mixed with the PbO-PbF2 flux inside a Pt crucible covered by an AlO2OO3
thermal mass. The mixture were heated up to 1300 ℃ for 6 h followed by a slow
cooling procedure of 3-5 ℃/h to 1000 ℃, after which millimeter-size crystals
were obtained and seperated from the bulk.

Using the monoclinic notation, the crystals used in the RIXS experiments were
polished with the [0, 1, 0], [0, 0, 1] and [1, 1, 0] directions parallel to
the surface normals for LCIO, LNIO and LZIO, respectively. Structural
characterizations of the LCIO and LNIO single crystals were performed at the
A2 beamline of the Cornell High Energy Synchrotron Source (CHESS) using high-
energy x-ray diffraction with $\mathit{E_{i}}$ = 60 keV, at both $\mathit{T}$
= 280 K and $\mathit{T}$ = 100 K. The dc magnetization data of the same
crystals used in synchrotron x-ray measurements were collected using a Quantum
Design magnetic property measurement system (MPMS).

As shown in Figure S1 in the Supplemental Material,SM  at room temperature,
all the diffraction spots of the La2$\mathit{M}$IrO6 ($\mathit{M}$ = Co and
Ni) single crystals fit well with a monoclinic lattice ($\mathit{a}$
$\mathds{\approx}$ 5.58 Å, $\mathit{b}$ $\mathds{\approx}$ 5.67 Å,
$\mathit{c}$ $\mathds{\approx}$ 7.91 Å, $\beta$ $\mathds{\approx}$ 89.9∘) with
the formation of multiple twins (note that $\mathit{d_{\mathrm{110}}}$
$\mathds{\approx}$ $\mathit{d_{\mathrm{002}}}$), evidenced by the appearances
of (odd/2, odd/2, 0) reflections. This is consistent with the previously
reported monoclinic symmetry for DP iridates.Currie_95  Upon cooling down to
100 K, the diffraction patterns do not show any visible change for both
compounds, indicating the robustness of the monoclinic structure with
decreasing temperature. Therefore, throughout this paper we will use the
monoclinic notation to describe their crystal structure. The sharpness of all
diffraction spots confirms the high quality of the single-crystal samples.
Although we did not carry out single-crystal diffraction studies on LZIO, we
expect an equally good crystal quality for it, given that all three crystals
were grown using the same methods.

##  III Results

RIXS measurements were performed to understand the low-energy elementary
excitations in all three compounds. RIXS at the Ir $\mathit{L_{\mathrm{3}}}$
edge, as a second order process involving x-ray absorption and emission
connected by an intermediate Ir-5$\mathit{d}$ state,Ament_11 ; KimYJ_18  can
sensitively probe the $\mathit{d}$-$\mathit{d}$ crystal-field
excitations,Gretarsson_13 ; Aczel_19  magnetic excitations,KimJH_214 ;
KimJH_327 ; Lu_17 ; Chun_18  and even phonon excitationsMeyers_18 ; Vale_19
in various iridates.

Figure 1: The RIXS spectra with the energy transfer below 1 eV obtained at the
base temperature for LCIO (a), LNIO (b) and LZIO (c), taken at $\mathit{Q}$ =
(0, 7.2, 0), (0, 1.5, 10) and (5, 5, 0.5), respectively. The dashed lines
represent the instrumental resolution.

Figure 1 shows the RIXS spectra in a wide energy transfer range below 1 eV
obtained at the base temperature at $\mathit{Q}$ = (0, 7.2, 0), (0, 1.5, 10)
and (5, 5, 0.5), for LCIO (a), LNIO (b) and LZIO (c), respectively, revealing
multiple common excitation features for all three compounds, labeled A, B, and
C. It is worth noting the similarity between all three spectra, indicating
similar Ir electronic states. This observation is consistent with the recent
hard x-ray photoelectron spectroscopy (HAXPES) study by Takegami et al., in
which little difference between the Ir electronic structure for these three
samples was observed.Takegami_20  Our results are also consistent with the
RIXS spectrum reported for LZIO in Ref. Aczel_19, , where features B and C at
the energy transfers of $\hbar\omega\sim$ 0.6$\mathds{-}$0.7 eV were
attributed to the intraband $\mathit{t_{\mathrm{2g}}}$ crystal-field
excitations from the $\mathit{j_{\mathrm{eff}}}$ = 3/2 quartet to the
$\mathit{j_{\mathrm{eff}}}$ = 1/2 doublet, seperated due to the noncubic
crystal-field splitting of the $\mathit{j_{\mathrm{eff}}}$ = 3/2 manifold at
the Ir4+ sites. The origin of feature A around 0.3 eV is still not clear yet,
which might be related to the 3$\mathit{d}$-5$\mathit{d}$ magnetic
hybridization, as this mode is evidently stronger in LCIO and LNIO compared
with that in LZIO. A similar feature, attributed to
5$\mathit{d}$-4$\mathit{d}$ hopping, was observed in the recent RIXS study of
Ag3LiIr2O6.de la Torre_21  We also note that a mode with a comparable energy
($\hbar\omega\sim$ 0.42 eV) was observed in the RIXS spectra of Na2IrO3, which
was assigned to the particle-hole exciton across the charge gap.Gretarsson_13
Note that these three materials are all semiconductors with similar gap sizes.
The activation gap of 0.26 eV and 0.34 eV were estimated from the resitivity
measurements on LCIO and LZIO, respectively.Narayanan_10 ; Gao_20  For LNIO,
the density functional calculation estimates that the gap is also of a similar
size around $\sim$ 0.2 eV.Wang_12  Therefore, peak A could also be due to the
enhanced exciton contribution near the charge gap. These excitations above 0.2
eV are beyond the scope of this paper, and they will not be further discussed
here.

Comparing the base-temperature RIXS spectrum of the three compounds below 0.2
eV, it is noticeable that a low-energy mode around 40 meV (labeled M) exists
in both LCIO and LNIO, which is however absent in LZIO. For LZIO, there is
only a sharp elastic peak below 0.2 eV, which is limited by the instrumental
resolution (the dashed line). To obtain some insights on the origin of the
low-energy mode M, the incident energy dependence of this mode was measured at
5 K at $\mathit{Q}$ = (0, 7.2, 0) for LCIO. As shown in Fig. 2, it exhibits a
resonant behavior around $\mathit{E_{i}}$ = 11.214 keV. As this energy is
about 3 eV below the main Ir $\mathit{L_{\mathrm{3}}}$ absorption edge as
determined by the fluorescence line, we can conclude that the RIXS process for
M involves an intermediate state in which an Ir 2$\mathit{p_{\mathrm{3/2}}}$
core electron is excited into the Ir 5$\mathit{d}$
$\mathit{t_{\mathrm{\mathrm{2}g}}}$ states, instead of the
2$\mathit{p_{\mathrm{3/2}}}$ $\mathds{\rightarrow}$ 5$\mathit{d}$
$\mathit{e_{\mathrm{g}}}$ transition. Since the lowest-energy electronic
excitations between the $\mathit{j_{\mathrm{eff}}}$ states occurs with a much
higher energy scale ($\mathds{\sim}$ 0.6 eV), the possible origin of M around
40 meV can be either magnetic or phonon excitations, both of which are
expected to appear around this energy scale.

Figure 2: The incident energy dependence of the RIXS spectrum of LCIO, taken
at $\mathit{T}$ = 5 K and $\mathit{Q}$ = (0, 7.2, 0). The dashed line marks
the low-energy mode M, with the maximal intensity achieved at $\mathit{E_{i}}$
= 11.214 keV.  Figure 3: (a) The RIXS spectrum of LCIO collected at different
temperature at $\mathit{Q}$ = (0, 7.2, 0), in which the shaded bar marks the
mode M. (b) The integrated intensity of mode M as a function of temperature,
as well as the dc magnetization of the LCIO single crystal measured with an
applied field of 0.2 T along the $\mathit{b}$ axis in the field-cooling
process. (c)-(h) The RIXS spectra at the Stokes side at 5 K (c), 30 K (d), 50
K (e), 70 K (f), 90 K (g) and 110 K (h), respectively, subtracted by that of
150 K after the Bose factor correction. The dotted and solid lines present the
sloping background and the fittings using a Gaussian profile.

To further understand the origin of mode M, the RIXS spectrum of LCIO at
$\mathit{Q}$ = (0, 7.2, 0) is measured as a function of temperature. As shown
in Fig. 3(a), the amplitude of the elastic line increases upon warming up,
which is commonly observed in RIXS experiments and typically ascribed to
thermal diffuse scattering. In contrast, the intensity of mode M is suppressed
gradually with increasing temperature. The RIXS spectra for $\mathit{T}$ > 90
K are very similar, indicating that the excitation spetrum does not change any
more above $\mathds{\sim}$ 90 K. Therefore, we decided to use the highest-
temperature (150 K) spectrum as a background to tease out the temperature
dependence of the mode M, after correcting the Bose population factor,
$n(E)$=1/$(e^{E/k_{\mathrm{B}}T}-1)$, for the energy loss side. Note that the
magnetic ordering temperature, $\mathit{T_{\mathrm{C}}}$, is determined to be
75 K by dc magnetization measurements (Fig. 3(b)). As shown in Fig. 3(c-h),
below 70 K, the mode M with the energy of $\mathds{\sim}$ 42(6) meV becomes
clearly visible after such a correction and subtraction. With increasing
temperature, this mode fades away and gets buried into the sloping background
finally, strongly supporting its magnetic origin. This mode M can be fitted
using a Gaussian profile superimposed on the sloping background, by which its
integrated intensity can be extracted. A comparison between the intensity of
mode M and the dc magnetization of the LCIO single crystal measured in an
applied field of 0.2 T (Fig. 3(b)) further corroborates our assignment of M as
the magnetic excitation. We also note that below 70 K, some additional
spectral weight remains below 20 meV even after the Bose factor correction and
background subtraction, whose origin is unclear yet, although the incomplete
subtraction is still a possibility. To clarify the nature of this additional
feature, further RIXS measurements with even higher resolution is needed.

The same procedure of data treatment for LNIO is also carried out. As shown in
Fig. S2 in the Supplemental Material,SM  the mode M in LNIO displays a similar
temperature dependence to that in LCIO, but it persists only below 50 K. This
is consistent with the fact that the LNIO single crystal undergoes an
antiferromagnetic-type transition below $\mathit{T_{\mathrm{N}}}$
$\mathds{\sim}$ 42 K, as evidenced from the magnetization data. After the Bose
factor correction and background subtraction, the energy of mode M in LNIO can
be determined to be $\mathds{\sim}$ 35(5) meV. Therefore, by combining the
results from both LCIO and LNIO, we can reach the conclusion that the mode M,
appearing in the RIXS spectra of both compounds, is clearly associated with
the magnetic excitations of ordered Ir4+ moments.

Figure 4: The $\mathit{Q}$-dependence of the low-energy RIXS spetrum of LCIO
(a-c), LNIO (d-f), and LZIO (g-i), collected at the base temperature. The
shaded bars in (a-f) mark the magnetic excitation existing in LCIO and LNIO.

The $\mathit{Q}$-dependence of the low-energy RIXS spetrum of all three
samples along the reciprocal $\mathit{H,}$ $\mathit{K},$ $\mathit{L}$
directions were measured at the base temperature for LCIO (Fig. 4(a-c)), LNIO
(Fig. 4(d-f)), and LZIO (Fig. 4(g-i)). Note that a sizable temperature-
independent background is present in the RIXS spectra, as reflected by pretty
similar profiles for LCIO for $\mathit{T}$ > 90 K (see Fig. 3(a)). Within the
experimental uncertainty, the energy of mode M stays almost constant,
indicating an almost dispersionless magnetic excitation for LCIO and LNIO with
a very large excitation gap of $\mathds{\sim}$ 42 meV and $\mathds{\sim}$ 35
meV, respectively. In contrast, this feature is not observed for different
$\mathit{Q}$ values in LZIO with non-magnetic 3$\mathit{d}$ Zn2+ ions,
supporting that the observed mode M in LCIO and LNIO originate from the
3$\mathit{d}$-5$\mathit{d}$ magnetic hybridization. As the shaded bars in Fig.
4(a-f) show, the energy of this magnetic excitation is higher in LCIO than
that in LNIO, probably indicating a larger magnetic energy scale in LCIO.

##  IV Discussion And Conclusion

We presented two compelling pieces of evidence for the magnetic origin of the
observed non-dispersive excitation around 40 meV in LCIO and LNIO. One is its
temperature dependence, which tracks the magnetic order closely. The other is
the fact that this mode is absent in LZIO, whose magnetic behavior is distinct
from the other two compounds. Although tempting, it is not straigtforward to
associate this with a magnon mode. The fact that the mode is almost
dispersionless is unusual for a magnon mode. It is certainly possible that
this excitation is composed of multiple magnon modes. With the energy
resolution of the present RIXS instrumentation, we were not able to resolve
any fine structure, which prevents us from comparing it with theoretical
dispersion relations. Another possibility for this excitation could be a
hybrid phonon-magnon mode. It is well known that optical phonon modes are
fairly non-dispersive, and if phonon modes are strongly coupled to the magnon,
the momentum and temperature dependence could be explained. In fact, the
anomalous temperature dependence of the Raman $\mathit{A_{\mathrm{1g}}}$ mode
in a DP Ba2FeReO6 was attributed to a strong coupling between the bond-
stretching mode and magnetic order.Raman  Recently, Lee et al. also pointed
out the existence of such a mode in LCIO based on their neutron powder
diffraction data.LeeS_18  These studies certainly support the idea of this
mode arising from the magnetoelastic coupling. However, the difference in the
excitation energy of about 15% between LCIO and LNIO would be difficult to
explain, since these two compounds have an almost identical structure and the
phonon energies are expected to be similar.

The absence of mode M in our RIXS spectra of LZIO clearly indicates that this
magnetic excitation observed in LCIO and LNIO arises from the hybridization
between the unpaired 5$\mathit{d}$ and 3$\mathit{d}$ electrons, which was
proposed previously to explain the x-ray magnetic circular dichroism (XMCD)
results of LCIO.Kolchinskaya_12  The 5$\mathit{d}$–3$\mathit{d}$ hybridization
was the subject of the recent x-ray absorption spectroscopy
investigationLeeM_18  as well as the HAXPES study.Takegami_20  In particular,
the latter study showed that the Ir-O hybridization is very strong in both
$\sigma$ and $\pi$ symmetry. The DFT calculation in this study also shows
strongly hybridized Ni and Co states near the Fermi level, which is absent for
the Zn states in LZIO.Takegami_20  The strong antiferromagnetic interaction
between Co/Ni and Ir in these compounds can be understood considering the
oxygen mediated hybridization. Since Co and Ni can only have unoccupied states
with minority spin direction, the parallel spin configuration for Ir would be
forbidden (See Fig. 6 in Ref. LeeM_18, ). Then one can understand the
difference in the magnetic energy scale of LCIO and LNIO as arising from
difference in hybridization due to slight structural difference. Specifically,
the Ir-O-Co angle is $\sim 154^{\circ}$, while the Ir-O-Ni angle is $\sim
150^{\circ}$,Narayanan_10 ; Wang_12  meaning that the Ir-O-Co bond is closer
to 180∘ that gives rise to stronger antiferromagnetic interaction.

For LZIO, in which the 3$\mathit{d}$ shell of Zn2+ is completely filled and
there is no medium of unpaired 3$\mathit{d}$ electrons, such a high-energy
magnetic excitation is absent. We note that magnetic excitations arising from
Ir moments were observed around 2 meV in a recent inelastic neutron scattering
study,Aczel_16  which is indistinguishable from the elastic line with the
current RIXS resolution. It is interesting to note that despite different
ground-state magnetic structure, LCIO and LNIO seem to have similar magnetic
excitations due to antiferromagnetic superexchange-like coupling between Ir
and Co/Ni. Our results provides a solid evidence that such a
3$\mathit{d}$-5$\mathit{d}$ magnetic coupling is playing an imporant role in
the magnetism of the DP iridates, similar to the case in the DP
rhenates.Plumb_13 ; Yuan_18  Further theoretical studies on these materials
will be of great importance to understand the detailed magnetic interactions
in them.

Another interesting observation is that from Fig. 3(b) and Fig. S2(b), the
feature M in either LCIO or LNIO disappears above the magnetic ordering
temperature. This is somewhat surprising, since classical spin systems
described by a spin Hamiltonian typically show broadening and softening of the
zone-boundary magnons, instead of a complete suppression as observed
here.Huberman ; Wan  The observed suppression of magnetic mode above the
transition temperature, however, is consistent with other recent studies on
iridate materials. For example, a similarly dramatic temperature dependence
was observed for a layered compound Sr3Ir2O7 and a pyrochlore compound
Eu2Ir2O7.KimJH_327 ; Chun_18  These studies suggest that charge fluctuations
are important in iridates and that the Hamiltonian beyond a simple spin model
is required to account for the magnetic excitations in these materials.

In conclusion, the low-energy elementary excitations in a series of double
perovskite iridate single crystals including LCIO, LNIO and LZIO are
investigated by means of RIXS measurements at the Ir $\mathit{L_{\mathrm{3}}}$
edge. Clear magnetic excitations with a large excitation gap of
$\mathds{\sim}$ 42(6) meV and $\mathds{\sim}$ 35(5) meV were observed, for
LCIO and LNIO, respectively. This magnetic excitation disappears above the
magnetic ordering temperature, suggesting the inadequacy of a local spin model
for describing magnetism of these double perovskite iridates. The absence of
such a magnetic excitation in LZIO, in which the 3$\mathit{d}$ ions are non-
magnetic, suggests the importance of 3$\mathit{d}$-5$\mathit{d}$ hybridization
in the magnetism of the DP iridates.

###### Acknowledgements.

The authors would like to acknowledge valuable discussions with Bo Yuan and
Shoushu Gong. Work at the University of Toronto was supported by the Natural
Sciences and Engineering Research Council of Canada, through Discovery and
CREATE program, and Canada Foundation for Innovation. W.J acknowledges the
support by the National Natural Science Foundation of China (Grant No.
12074023). C.J.W. was supported by the National Research Foundation of Korea
(Grant No. 2016K1A4A4A01922028 and 2020M3H4A2084417). Use of the Advanced
Photon Source at Argonne National Laboratory is supported by the U.S.
Department of Energy, Office of Science, under Contract No. DE-AC02-06CH11357.

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