Annual Report 2011 / 2012 - E21 - Technische Universität München

counts / stand. mon. counts / stand. mon. counts / stand. mon. counts / stand. mon.
counts / stand. mon. counts / stand. mon. counts / stand. mon. counts / stand. mon.
Chapter 1. Magnetism and Superconductivity 19
the sample with respect to the field [Figs. (d) through (h)].
We begin with panel (d) which demonstrates that the pattern
for field perpendicular to the neutron beam is also perpendicular
to the field. Further, Figs. (e) through (h) show
the six-fold pattern for field parallel to the neutron beam.
The six-fold pattern in the plane perpendicular to the field
is thereby roughly aligned along 〈100〉, consistent with very
weak magnetic anisotropy terms that are sixth order in spinorbit
coupling and small demagnetizing fields (see, e.g., [3]
[4]). As demonstrated for the binary P2 1 3 compounds, the
six-fold pattern arises from a triple-k state, with Σ i k i = 0,
coupled to the uniform magnetization and stabilized by thermal
Gaussian fluctuations. The topology of the triple-k state
is that of a skyrmion lattice, i.e., the winding number is 1
per magnetic unit cell. This has been confirmed experimentally
in MnSi by means of Renninger scans in SANS [11] and
the topological Hall signal [12]. We therefore interpret the
A-phase in Cu 2 OSeO 3 as a skyrmion lattice.
q y
(Å -1 )
q y
(Å -1 )
0.02
0.01
0
-0.01
0.01
0
-0.01
a)
ᐸ100ᐳ
-0.02
0.02
c)
-0.02
0.02
e)
q y
(Å -1 )
q y
(Å -1 )
0.01
0
0.01
0
-0.01
-0.02
-0.02
ᐸ110ᐳ
ᐸ100ᐳ
B = 0
T = 5.0 K
B || ᐸ110ᐳ
B = 58 mT
T = 5.0 K
ᐸ110ᐳ
ᐸ100ᐳ
-0.01
B = 21 mT
B || ᐸ100ᐳ T = 57.3 K
-0.02
0.02
g)
ᐸ110ᐳ
50
22.9
10.5
4.8
2.2
1
50
22.9
10.5
4.8
2.2
1
10
7.3
5.3
3.8
2.8
2
10
7.3
5.3
3.8
2.8
B = 24 mT
B || ᐸ111ᐳ T = 57.0 K
2
-0.01 0 0.01 0.02
q x
(Å -1 )
b)
d)
f)
ᐸ100ᐳ
h)
ᐸ110ᐳ
ᐸ100ᐳ
B || ᐸ110ᐳ
ᐸ110ᐳ
ᐸ100ᐳ
B = 0
T = 5.0 K
B || ᐸ110ᐳ
ᐸ110ᐳ
B = 19 mT
T = 57.3 K
ᐸ110ᐳ
B = 19 mT
T = 57.3 K
ᐸ110ᐳ
50
22.9
10.5
4.8
2.2
1
15
12.5
10.4
8.7
7.2
6
10
7.3
5.3
3.8
2.8
2
10
7.3
5.3
3.8
B = 22 mT
2.8
T = 57.0 K
B random orientation
2
-0.02 -0.01 0 0.01 0.02
q x
(Å -1 )
Figure 2: Typical integrated small-angle neutron scattering
rocking scans in Cu 2OSeO 3. (a) Zero-field scattering pattern
along 〈100〉, characteristic of helimagnetic order along 〈100〉. (b)
Zero-field scattering pattern along 〈110〉, characteristic of helimagnetic
order along 〈100〉. (c) Typical scattering pattern in the
field range B c1 < B < B c2 for T < T c. (d) Scattering pattern
in the A phase for magnetic field perpendicular to the neutron
beam. Panels (e) through (h): Typical scattering pattern in the A
phase for magnetic field parallel to the neutron beam for various
orientations.
Thus, bulk samples of Cu 2 OSeO 3 represent the first example
of helimagnetic order in a structural sibling of the
B20 compounds that is nonbinary, an oxide, a compound
with a nonferromagnetic leading-order exchange interaction,
and an insulator. Being an insulator, the skyrmion lattice in
Cu 2 OSeO 3 thereby promises an emergent electrodynamics
akin to that observed in its binary siblings [7] [8], where
electric fields may now be used to manipulate the skyrmions.
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