PRL 110, 117202 (2013)
week ending 15 MARCH 2013
PHYSICAL REVIEW LETTERS
Robust Formation of Skyrmions and Topological Hall Effect Anomaly in Epitaxial Thin Films of MnSi Yufan Li,1,2 N. Kanazawa,1 X. Z. Yu,3 A. Tsukazaki,1 M. Kawasaki,1,3 M. Ichikawa,1 X. F. Jin,2 F. Kagawa,1 and Y. Tokura1,3 1
Department of Applied Physics and Quantum Phase Electronics Center (QPEC), University of Tokyo, Tokyo 113-8656, Japan 2 State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China 3 Cross-Correlated Materials Research Group (CMRG) and Correlated Electron Research Group (CERG), RIKEN Advanced Science Institute, Wako 351-0198, Japan (Received 16 September 2012; published 12 March 2013) Magnetotransport properties have been investigated for epitaxial thin films of B20-type MnSi grown on Si(111) substrates. Lorentz transmission electron microscopy images clearly point to the robust formation of Skyrmions over a wide temperature-magnetic field region. New features distinct from those reported previously for MnSi are observed for epitaxial films: a shorter (nearly half) period of the spin helix and Skyrmions, and a topological Hall effect anomaly consisting in 2:2 times enhancement of the amplitude and in the opposite sign with respect to bulk samples. DOI: 10.1103/PhysRevLett.110.117202
PACS numbers: 75.30.Kz, 72.25.Ba, 73.61.At, 75.70.Ak
The topological spin texture called the Skyrmion, in which the constituent spins point in all directions wrapping up a sphere, has recently been observed in the helimagnets with a noncentrosymmetric structure [1–5]. This novel magnetic structure has attracted great interest not only for its rich physics related to the quantum Berry phase (Skyrmion number) [6–8], but also for its potential applications. It is found that the Skyrmion motion can be driven by a current density as low as 105 –106 A=m2 [9–11], in contrast with the case of magnetic domain walls of conventional ferromagnets, in which the critical current density of 109 –1011 A=m2 is required [12,13]. This high current sensitivity may promise the potential application of the Skyrmion in the next-generation magnetic recording technique as well as other related spintronic devices. The Skyrmion-hosting B20-type crystal structure is cubic but noncentrosymmetric, and hence, hosts the Dzyaloshinskii-Moriya interaction. This antisymmetric spin exchange interaction competes with symmetric Heisenberg exchange and Zeeman interactions, producing rich magnetic structures, such as helical (proper screw) spin structure [14,15], conical spin structure [14,16], and field-induced ferromagnetism. The Skyrmion spin texture, which is a superposition of three helices perpendicular to the external magnetic field H, is also a consequence of the competition, but can be found only in quite a limited temperature-magnetic field (T-H) region (so-called A phase) for bulk crystals [1,17]. The coverage of the Skyrmion phase, however, turns out to be greatly enlarged in thin plates [18]; when H is applied normal to film planes, the extended Skyrmion phases have been observed by Lorentz transmission electron microscopy (TEM) in freestanding thin plate specimens, the thickness of which are reduced to Hc (see the text), reproducing the normal component plus anomalous Hall, R0 H þ Ayx .
cm-1)
−50
#1 #2 #3 #4
-1
0
nm nm nm nm
50 nm
-4
0.2
(
50
10 10 10 10
-3
0.4
0.1
ρyx (nΩ cm)
200
35K 40K 60K
-2.5
A - skew ( xy xy
ρyx (nΩ cm)
35K
2K 10K 20K 25K 30K
2K 20K 30K 60K
10K 25K 40K
35K 40K 60K
-1
0.4
0 250
2K 10K 20K 25K 30K
35K 40K 60K
0.1
(e)
-2
cm-1)
2K 10K 20K 25K 30K
M (µB/Mn)
M (µB/Mn)
(c)
∆ρxx / ρxx
∆ρxx / ρxx
5%
-100
10 nm #4
0
10
20
30
40
T(K)
FIG. 3 (color online). (a) The plot of Ayx0 =xx0 vs xx0 obtained in the 10 nm films #1–#4 and the 50 nm film. The measurement was carried out at 2 K. The solid line is the linear fitting to the results for the 10 nm films (#1–#4). (b) Axy (circles) and Axy skew (squares) of the 10 nm films. int xy xy (pentagrams) plotted for comparison with Axy skew was derived from the xy fitting (see the text). The superscripts are defined in the text.
117202-3
PHYSICAL REVIEW LETTERS
PRL 110, 117202 (2013)
thick samples. It is interesting to observe that while Axy scatters among different samples especially at low temint peratures, the temperature variations of derived sj xy þ xy reduce to a single universal, sample-independent curve. This feature presumably implies that the sample-dependent extrinsic term sj xy is negligibly small, i.e., 0 [32]. The total Hall resistivity can, therefore, be expressed as yx ¼ R0 H þ ðxx0 þ b2xx ÞM þ Tyx :
(3)
For H > Hc , Tyx is supposed to be zero, because the induced ferromagnetism has no spin chirality. Hence, R0 and b can be determined, respectively, from the intercept and the slope of the linear fitting of ðyx Mxx0 Þ=H vs 2xx M=H (not shown), with the value as determined above. In this analysis, we used the xx -H curves shown in Figs. 2(a) and 2(b). The fitted results of R0 H þ ðxx0 þ b2xx ÞM are shown as the solid lines in Figs. 2(e) and 2(f) and Figs. 4(a) and 4(b). As a crosscheck, int we also plotted int xy derived from the fitting result as xy ¼ bM in Fig. 3(b) and found that the temperature profile A skew of obtained int xy reasonably coincides with xy xy T as derived above. In this way, we can extract yx from (a) 60
2K 10K 15K
20K 25K
(b) 20
20
cm)
0
(n
30K 35K
0 −20
yx
yx
(n
cm )
40
2K 10K 15K 20K 25K
−40
−20
−60
−40
(c )
cm)
Hall
observed
ρT
(n
(n
10
20
yx
0 −10
Hall
cm )
30
R0H
T=25 K
40
(d)
A
ρyx
−20 0
0.5
1
1.5
R H
20 10 0 -10 -20 -30 -40 -50
0
T=25 K
ρT
yx
observed A
ρyx
0
2
30K 35K
0.5
1
H (T)
(e )
−10
−5
T yx
(n
2
5
10
(f )
−5
T yx
(n
cm)
0
5
10
H (T)
M−H −H yx
1
0
0
1
−10
1.5
M−H −H yx
1.5
H (T)
0
cm)
0
1.5
H (T)
0
0.5
0.5 0
5 10 15 20 25 30 35 40 45
T (K)
0
5 10 15 20 25 30 35 40 45
T (K)
FIG. 4 (color online). yx of (a) the 10 nm film and (b) the 50 nm film [magnified in the low-field region of Figs. 2(e) and 2(f), respectively]. The lines are the fitting curves for H > Hc , reproducing R0 H þ Ayx . (c) and (d) The representative yx -H curve of 25 K and its decomposition into R0 H, Ayx , and Tyx for the 10 nm film (c) and the 50 nm film (d). (e) and (f) The contour mapping of Tyx of (e) the 10 nm film and (f) the 50 nm film. The squares in (e) and (f) denote Hc defined by the kink field in M-H curves and yx -H curves.
week ending 15 MARCH 2013
the difference between the total Hall resistivity yx and the fitted curve R0 H þ ðxx0 þ b2xx ÞM below Hc . In Figs. 4(c) and 4(d) we show the representative yx -H curves measured at T ¼ 25 K for the 10 nm film and 50 nm film, respectively, and the corresponding three components R0 H, Ayx , and Tyx derived from the analysis. In the following, we discuss Tyx in the light of the Skyrmion formations. To see the global feature of Tyx , we present the contour mapping of derived Tyx as a function of T and H [Figs. 4(e) and 4(f) for the 10 nm and 50 nm films, respectively]. A finite Tyx is found in both films for T > 10 K and 0 < H < Hc , consistent with the Lorentz TEM observation, which finds the Skyrmion state at 18 K and 30 K under H ¼ 400 mT. The exclusive onset of the Hall-effect anomaly in the region where T < Tc and H < Hc appears to favor its explanation by topologically nontrivial magnetic structure, making other possible mechanisms to cause the nonlinear behavior of the normal Hall effect, e.g., the coexistence of multiple types of carriers, unlikely. Under this assumption it is possible to link the positive Tyx to the formation of the Skyrmion state and consider Figs. 4(e) and 4(f) as the magnetic phase diagrams of MnSi thin films. Obviously, the Skyrmion state as evidenced by the emergence of the THE is stabilized over a broad region in the T-H plane, spanning from 10 K to Tc and occupying almost all the region below Hc except near zero field; this is in sharp contrast to the small A phase region in bulk MnSi [1,35]. The maximum value of Tyx in the epitaxial thin films is about 10 n cm, approximately twice as large as that in bulk MnSi (4:5 n cm) [35], albeit the signs are opposite, which will be discussed later. Furthermore, for both the 10 nm and 50 nm films, the sign of Tyx flips from positive to negative when T < 5 K. This behavior is more prominent in the 10 nm film [see the raw data shown in Fig. 4(a)], where the maximum magnitude of Tyx (about 7:8 n cm) is comparable to that of the positive Tyx observed at higher temperatures. Unfortunately this temperature range (T
week ending 15 MARCH 2013
PHYSICAL REVIEW LETTERS
Robust Formation of Skyrmions and Topological Hall Effect Anomaly in Epitaxial Thin Films of MnSi Yufan Li,1,2 N. Kanazawa,1 X. Z. Yu,3 A. Tsukazaki,1 M. Kawasaki,1,3 M. Ichikawa,1 X. F. Jin,2 F. Kagawa,1 and Y. Tokura1,3 1
Department of Applied Physics and Quantum Phase Electronics Center (QPEC), University of Tokyo, Tokyo 113-8656, Japan 2 State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China 3 Cross-Correlated Materials Research Group (CMRG) and Correlated Electron Research Group (CERG), RIKEN Advanced Science Institute, Wako 351-0198, Japan (Received 16 September 2012; published 12 March 2013) Magnetotransport properties have been investigated for epitaxial thin films of B20-type MnSi grown on Si(111) substrates. Lorentz transmission electron microscopy images clearly point to the robust formation of Skyrmions over a wide temperature-magnetic field region. New features distinct from those reported previously for MnSi are observed for epitaxial films: a shorter (nearly half) period of the spin helix and Skyrmions, and a topological Hall effect anomaly consisting in 2:2 times enhancement of the amplitude and in the opposite sign with respect to bulk samples. DOI: 10.1103/PhysRevLett.110.117202
PACS numbers: 75.30.Kz, 72.25.Ba, 73.61.At, 75.70.Ak
The topological spin texture called the Skyrmion, in which the constituent spins point in all directions wrapping up a sphere, has recently been observed in the helimagnets with a noncentrosymmetric structure [1–5]. This novel magnetic structure has attracted great interest not only for its rich physics related to the quantum Berry phase (Skyrmion number) [6–8], but also for its potential applications. It is found that the Skyrmion motion can be driven by a current density as low as 105 –106 A=m2 [9–11], in contrast with the case of magnetic domain walls of conventional ferromagnets, in which the critical current density of 109 –1011 A=m2 is required [12,13]. This high current sensitivity may promise the potential application of the Skyrmion in the next-generation magnetic recording technique as well as other related spintronic devices. The Skyrmion-hosting B20-type crystal structure is cubic but noncentrosymmetric, and hence, hosts the Dzyaloshinskii-Moriya interaction. This antisymmetric spin exchange interaction competes with symmetric Heisenberg exchange and Zeeman interactions, producing rich magnetic structures, such as helical (proper screw) spin structure [14,15], conical spin structure [14,16], and field-induced ferromagnetism. The Skyrmion spin texture, which is a superposition of three helices perpendicular to the external magnetic field H, is also a consequence of the competition, but can be found only in quite a limited temperature-magnetic field (T-H) region (so-called A phase) for bulk crystals [1,17]. The coverage of the Skyrmion phase, however, turns out to be greatly enlarged in thin plates [18]; when H is applied normal to film planes, the extended Skyrmion phases have been observed by Lorentz transmission electron microscopy (TEM) in freestanding thin plate specimens, the thickness of which are reduced to Hc (see the text), reproducing the normal component plus anomalous Hall, R0 H þ Ayx .
cm-1)
−50
#1 #2 #3 #4
-1
0
nm nm nm nm
50 nm
-4
0.2
(
50
10 10 10 10
-3
0.4
0.1
ρyx (nΩ cm)
200
35K 40K 60K
-2.5
A - skew ( xy xy
ρyx (nΩ cm)
35K
2K 10K 20K 25K 30K
2K 20K 30K 60K
10K 25K 40K
35K 40K 60K
-1
0.4
0 250
2K 10K 20K 25K 30K
35K 40K 60K
0.1
(e)
-2
cm-1)
2K 10K 20K 25K 30K
M (µB/Mn)
M (µB/Mn)
(c)
∆ρxx / ρxx
∆ρxx / ρxx
5%
-100
10 nm #4
0
10
20
30
40
T(K)
FIG. 3 (color online). (a) The plot of Ayx0 =xx0 vs xx0 obtained in the 10 nm films #1–#4 and the 50 nm film. The measurement was carried out at 2 K. The solid line is the linear fitting to the results for the 10 nm films (#1–#4). (b) Axy (circles) and Axy skew (squares) of the 10 nm films. int xy xy (pentagrams) plotted for comparison with Axy skew was derived from the xy fitting (see the text). The superscripts are defined in the text.
117202-3
PHYSICAL REVIEW LETTERS
PRL 110, 117202 (2013)
thick samples. It is interesting to observe that while Axy scatters among different samples especially at low temint peratures, the temperature variations of derived sj xy þ xy reduce to a single universal, sample-independent curve. This feature presumably implies that the sample-dependent extrinsic term sj xy is negligibly small, i.e., 0 [32]. The total Hall resistivity can, therefore, be expressed as yx ¼ R0 H þ ðxx0 þ b2xx ÞM þ Tyx :
(3)
For H > Hc , Tyx is supposed to be zero, because the induced ferromagnetism has no spin chirality. Hence, R0 and b can be determined, respectively, from the intercept and the slope of the linear fitting of ðyx Mxx0 Þ=H vs 2xx M=H (not shown), with the value as determined above. In this analysis, we used the xx -H curves shown in Figs. 2(a) and 2(b). The fitted results of R0 H þ ðxx0 þ b2xx ÞM are shown as the solid lines in Figs. 2(e) and 2(f) and Figs. 4(a) and 4(b). As a crosscheck, int we also plotted int xy derived from the fitting result as xy ¼ bM in Fig. 3(b) and found that the temperature profile A skew of obtained int xy reasonably coincides with xy xy T as derived above. In this way, we can extract yx from (a) 60
2K 10K 15K
20K 25K
(b) 20
20
cm)
0
(n
30K 35K
0 −20
yx
yx
(n
cm )
40
2K 10K 15K 20K 25K
−40
−20
−60
−40
(c )
cm)
Hall
observed
ρT
(n
(n
10
20
yx
0 −10
Hall
cm )
30
R0H
T=25 K
40
(d)
A
ρyx
−20 0
0.5
1
1.5
R H
20 10 0 -10 -20 -30 -40 -50
0
T=25 K
ρT
yx
observed A
ρyx
0
2
30K 35K
0.5
1
H (T)
(e )
−10
−5
T yx
(n
2
5
10
(f )
−5
T yx
(n
cm)
0
5
10
H (T)
M−H −H yx
1
0
0
1
−10
1.5
M−H −H yx
1.5
H (T)
0
cm)
0
1.5
H (T)
0
0.5
0.5 0
5 10 15 20 25 30 35 40 45
T (K)
0
5 10 15 20 25 30 35 40 45
T (K)
FIG. 4 (color online). yx of (a) the 10 nm film and (b) the 50 nm film [magnified in the low-field region of Figs. 2(e) and 2(f), respectively]. The lines are the fitting curves for H > Hc , reproducing R0 H þ Ayx . (c) and (d) The representative yx -H curve of 25 K and its decomposition into R0 H, Ayx , and Tyx for the 10 nm film (c) and the 50 nm film (d). (e) and (f) The contour mapping of Tyx of (e) the 10 nm film and (f) the 50 nm film. The squares in (e) and (f) denote Hc defined by the kink field in M-H curves and yx -H curves.
week ending 15 MARCH 2013
the difference between the total Hall resistivity yx and the fitted curve R0 H þ ðxx0 þ b2xx ÞM below Hc . In Figs. 4(c) and 4(d) we show the representative yx -H curves measured at T ¼ 25 K for the 10 nm film and 50 nm film, respectively, and the corresponding three components R0 H, Ayx , and Tyx derived from the analysis. In the following, we discuss Tyx in the light of the Skyrmion formations. To see the global feature of Tyx , we present the contour mapping of derived Tyx as a function of T and H [Figs. 4(e) and 4(f) for the 10 nm and 50 nm films, respectively]. A finite Tyx is found in both films for T > 10 K and 0 < H < Hc , consistent with the Lorentz TEM observation, which finds the Skyrmion state at 18 K and 30 K under H ¼ 400 mT. The exclusive onset of the Hall-effect anomaly in the region where T < Tc and H < Hc appears to favor its explanation by topologically nontrivial magnetic structure, making other possible mechanisms to cause the nonlinear behavior of the normal Hall effect, e.g., the coexistence of multiple types of carriers, unlikely. Under this assumption it is possible to link the positive Tyx to the formation of the Skyrmion state and consider Figs. 4(e) and 4(f) as the magnetic phase diagrams of MnSi thin films. Obviously, the Skyrmion state as evidenced by the emergence of the THE is stabilized over a broad region in the T-H plane, spanning from 10 K to Tc and occupying almost all the region below Hc except near zero field; this is in sharp contrast to the small A phase region in bulk MnSi [1,35]. The maximum value of Tyx in the epitaxial thin films is about 10 n cm, approximately twice as large as that in bulk MnSi (4:5 n cm) [35], albeit the signs are opposite, which will be discussed later. Furthermore, for both the 10 nm and 50 nm films, the sign of Tyx flips from positive to negative when T < 5 K. This behavior is more prominent in the 10 nm film [see the raw data shown in Fig. 4(a)], where the maximum magnitude of Tyx (about 7:8 n cm) is comparable to that of the positive Tyx observed at higher temperatures. Unfortunately this temperature range (T
