Towards the microscopic understanding of magnetic spin textures in chiral magnets: FeGe, MnSi and beyond B20

October 24, 2018

M. Baenitz, P. Khuntia, M. Majumder, H. Wilhelm¹, U. Roessler², H. Rosner, H. Yasuoka, M. Schmidt

¹ Diamond Light Source Ltd., Chilton, Didcot, Oxfordshire, OX11 0DE,
United Kingdom
² IFW Dresden, Postfach 270116, 01171 Dresden, Germany

The B20 systems: FeSi, FeGe and MnSi

The electronic and magnetic properties of binary compounds crystallizing in the B20 structure, such as the monosilicides and monogermanides of Mn, Cr, Fe, and Co are an active topic of research in condensed matter physics. Among them, FeSi has attracted strong interest because it is a narrow gap semiconductor with E_g = 80 meV and a non-magnetic ground state that has led to its classification as a correlated semimetal, or 'Kondo insulator'. It shares these properties with FeSb₂ and FeGa₃ (see report on Fe-based systems with ferromagnetic quantum criticality) [1,2]. In contrast to FeSi, FeGe is a metallic helimagnet as a consequence of the broken inversion symmetry and the spin orbit coupling (Dzyaloshinskii - Moriya interaction) with an ordering temperature of 278.7 K [3].

In 2004 the idea to apply pressure on FeGe single crystals to study the crossover from the chiral ferromagnet to the non-magnetic correlated semi-metal FeSi was born and continuous efforts finally succeeded in 2006 in the growth of rather large FeGe single crystals of extremely high purity [4]. So far these crystals made by M. Schmidt (from the Department of Inorganic Chemistry) are unique and this was the origin of a long standing in-depth research activity led from this institute on the various aspects on this fascinating room temperature chiral magnet. The surprising result of the pressure studies of H. Wilhelm and co-workers was that in contrast to the alloying study on FeSi_1-xGe_x, the pressurized FeGe stays metallic up to the highest applied pressures. Furthermore a very pronounced non Fermi-liquid (NFL) behaviour in the temperature dependence of the resistivity (ρ proportional T ^3/2) was found over a wide pressure range in the vicinity of the critical pressure p_c [5]. This behaviour was reminiscent to another relative in the B 20 class, MnSi, which has a much lower T_c of about 29 K. The latter attracted great attention in the context of ferromagnetic criticality [6] along with other weak ferromagnets like ZrZn₂ , Ni₃Al or CoS₂. In early 2006 Kirkpatrik and co-workers already discussed the chiral aspect (chiral order parameter) to explain puzzling neutron scattering results near T_c and the extended NFL behaviour in the ρ(T)- data near p_c (helimagnon scattering) [7,8].

Even more important was the publication by U. Roessler, A. Bogdanov and C. Pfleiderer about a “spontaneous skyrmion ground state in magnetic metals” which predicts a new long range ordered phase formed out of magnetic vortices (in analogy to the flux lattice in type II superconductors) in chiral magnets [9]. Finally 2009 this new form of matter in the ordered phase was experimentally confirmed in MnSi single crystals. Small-angle neutron scattering (SANS) experiments at selected points in the H-T- phase diagram showed magnetic modulations which are transverse to the H direction and which produce a sixfold Bragg spot pattern [10]. This was taken as an evidence for the hexagonal Skyrmion lattice (historically called “A phase”) in MnSi. The Skyrmion lattice is believed to be formed out of bundles of two dimensional spin textured objects called “Skyrmions” (SKY) forming magnetic vortices in analogy to type II superconductors. Such magnetic vortices were predicted as early as 1989 by Bogdanov and Yablonskii for helimagnets [11,12]. Based on Hall resistivity measurements, the complex spin texture in the ordered state and the impact of chiral excitations above T_c under pressure was discussed recently for MnSi [13].

In 2009 our research on FeGe was focused on A-phase signatures accompanied by the Skyrmion formation in this nearly room temperature chiral magnet (see schematic phase diagram Fig.1). In 2011 we discovered a “segmented A-Phase” with several pockets near T_cby a detailed ac magnetization study on oriented single crystals [14]. This was the first hint towards the formation of a Skyrmion lattice in FeGe bulk material (Fig.2, left). One month later Y. Tokura and co-workers confirmed the Skyrmion lattice formation in FeGe thin films by Lorentz microscopy [15]. In contrast to MnSi where the Skyrmions have a relatively small diameter (equals the helical pitch length) of about 180 Å for FeGe a diameter of about 700 Å was found which points towards large lateral regimes in the crystal with this unique chiral spin texture.

Figure 1: Schematic magnetic phase diagram of B20 helimagnets (left). Building blocks of the various phases (right): a) single Skyrmion. b) conical state c) helical state d) hexagonal Skyrmion lattice (“A phase”).

Figure 1: Schematic magnetic phase diagram of B20 helimagnets (left). Building blocks of the various phases (right): a) single Skyrmion. b) conical state c) helical state d) hexagonal Skyrmion lattice (“A phase”).

Small angle neutron scattering measurements (SANS) were conducted in 2009 on our FeGe single crystals in collaboration with S. Grigoriev (Petersburg Nuclear Physics Institute, Russia). The SANS results finally gave direct local microscopic evidence (Fig.2, right) for the formation of the hexagonal Skyrmion lattice in a sub-pocket of the segmented A-phase in the bulk sample of FeGe [16]. Recently we have also collaborated on a nuclear forward scattering study (⁵⁷Fe-Moessbauer) on FeGe under pressure which reveals an inhomogeneous chiral spin state above p_c at low temperatures with residual (non static) hyperfine fields as high as 4 T (equivalent to 0.4µ_B) [17]. Together with the early pressure experiments it is now clear that FeGe remains metallic and magnetic up to highest pressures applied (31 GPa). Furthermore the anomalous electronic transport properties (NFL-behaviour) observed well beyond p_c might originate from charge carriers scattered off inhomogeneous and twisted spin textures.

A further goal of our efforts was to prepare ⁵⁷Fe enriched FeGe crystals and to use the ⁵⁷Fe resonance to probe the magnetic phase diagram and especially the Skyrmion lattice by zero field (or field modulated) NMR. Using the effect of the small internal field (created by the magnetic ion itself) in the ordered state on the ⁵⁷Fe (I=1/2) or ⁵⁵Mn(I=5/2) nuclear spin to probe chiral magnetic textures in a helimagnet is a unique approach. Over the past decade a unique set of solid state NMR techniques far beyond standard was developed at the CPFS. Especially powerful low field- (frequency-) techniques are improved strongly. In general our microscopic study is aimed to static and dynamic magnetism of the helimagnet and for Skyrmion matter in particular to probe the dipolar coupling between the electron spins and nuclear spins and the DM-interaction itself. Furthermore Skyrmion dynamics and helical excitations across the magnetic phase diagram are a matter of further studies.

Figure 2: (left) H-T phase diagram of an FeGe single crystal for H II [100] (inset). Open and bold symbols represent the data obtained from χac(H) and χac(T), respectively. Various phases are observed below Tc = 278.2 K : a helical state with q II [100] (H < Hc1), a conical helix phase (“cone”), a field polarized state (FP) above Hc2, and a complex Skyrmion lattice region with several pockets (A0 to A3). Furthermore a broad crossover regime from the field polarized regime (FP) to the paramagnetic regime (PM) was obtained from χac(T,H) [14]. (right) Polarized SANS data on an FeGe single crystal with different polarization with respect to the incoming beam, the applied field and the crystal axis. For a) the polarization is perpendicular to the beam whereas for b) to d) the polarization is parallel to the beam [16]. — Figure 2: (left) H-T phase diagram of an FeGe single crystal for H II [100] (inset). Open and bold symbols represent the data obtained from χ_ac(H) and χ_ac(T), respectively. Various phases are observed below T_c = 278.2 K : a helical state with q II [100] (H < H_c1), a conical helix phase (“cone”), a field polarized state (FP) above H_c2, and a complex Skyrmion lattice region with several pockets (A₀to A₃). Furthermore a broad crossover regime from the field polarized regime (FP) to the paramagnetic regime (PM) was obtained from χ_ac(T,H) [14]. (right) Polarized SANS data on an FeGe single crystal with different polarization with respect to the incoming beam, the applied field and the crystal axis. For a) the polarization is perpendicular to the beam whereas for b) to d) the polarization is parallel to the beam [16].

Figure 2: (left) H-T phase diagram of an FeGe single crystal for H II [100] (inset). Open and bold symbols represent the data obtained from χ_ac(H) and χ_ac(T), respectively. Various phases are observed below T_c = 278.2 K : a helical state with q II [100] (H < H_c1), a conical helix phase (“cone”), a field polarized state (FP) above H_c2, and a complex Skyrmion lattice region with several pockets (A₀to A₃). Furthermore a broad crossover regime from the field polarized regime (FP) to the paramagnetic regime (PM) was obtained from χ_ac(T,H) [14]. (right) Polarized SANS data on an FeGe single crystal with different polarization with respect to the incoming beam, the applied field and the crystal axis. For a) the polarization is perpendicular to the beam whereas for b) to d) the polarization is parallel to the beam [16].

In contrast to neutron studies or Fe-Moessbauer, “on site” ⁵⁷Fe NMR has the capability for “line profiling” of the SKY lattice (due to the NMR line shape) and as a probe for spin dynamics of individual and collective Skyrmion excitations. The lateral dimension of about 700 Å of the FeGe-Skyrmion modulates the local field of about 150 Fe ions which should result in a significant NMR line- modulation or splitting. Our zero field NMR approach was very successful and ⁵⁷Fe NMR probes the local magnetization (hyperfine field, see Fig.3), and the dynamic susceptibility (spin lattice relaxation rate) directly "on site" [18]. It should be mentioned that so far there is no other helical SKY magnet where such studies could be performed. The reason for this is that the zero field NMR towards room temperature has to be performed in the internal fields far below 1 T (NMR frequency of about 1 MHz) which requires special NMR techniques. Here low field and/or zero field magnetic resonance is the method of choice.

Figure 3: Evolution of the 57Fe resonance line in zero field as a function of temperature. The center frequency of the line ν0(T) provides directly the hyperfine field Hhf at the Fe site (Hhf = ν0/ γN with γN = 1.3785 MHz/T). Hhf is directly proportional to the spontaneous local magnetization Mloc and could be fitted by the empirical function Hhf.0(1-tm)n with t = T/TC and m = 2 and n = 1/3 (solid line on top layer) or reasonably well by a Brillouin function with g = 2 and S = 1/2. The inset shows a typical FeGe single crystal. Magnetic resonance experiments were performed on ten 57Fe enriched FeGe crystals of approximately that size, randomly oriented [18]. — *Figure 3*: Evolution of the⁵⁷Fe resonance line in zero field as a function of temperature. The center frequency of the line ν₀(T) provides directly the hyperfine field H_hf at the Fe site (H_hf = ν₀/ γ_N with γ_N = 1.3785 MHz/T). H_hf is directly proportional to the spontaneous local magnetization M_loc and could be fitted by the empirical function H_hf.0(1-t^m)ⁿ with t = T/T_C and m = 2 and n = 1/3 (solid line on top layer) or reasonably well by a Brillouin function with g = 2 and S = 1/2. The inset shows a typical FeGe single crystal. Magnetic resonance experiments were performed on ten ⁵⁷Fe enriched FeGe crystals of approximately that size, randomly oriented [18].

*Figure 3*: Evolution of the⁵⁷Fe resonance line in zero field as a function of temperature. The center frequency of the line ν₀(T) provides directly the hyperfine field H_hf at the Fe site (H_hf = ν₀/ γ_N with γ_N = 1.3785 MHz/T). H_hf is directly proportional to the spontaneous local magnetization M_loc and could be fitted by the empirical function H_hf.0(1-t^m)ⁿ with t = T/T_C and m = 2 and n = 1/3 (solid line on top layer) or reasonably well by a Brillouin function with g = 2 and S = 1/2. The inset shows a typical FeGe single crystal. Magnetic resonance experiments were performed on ten ⁵⁷Fe enriched FeGe crystals of approximately that size, randomly oriented [18].

⁵⁵Mn on-site NMR studies on MnSi suffer from the broad NMR lines arising from the quadrupole interaction of ⁵⁵Mn with its I = 5/2 spin [19]. To overcome this problem we concentrated on ²⁹Si zero field NMR on MnSi. ²⁹Si has a I=1/2 nuclear spin but NMR studies were difficult because of the rather low natural abundance (NA=2.1 %) of the NMR active isotope. Therefore we started recently rather successful a²⁹Si zero field NMR study on ²⁹Si enriched MnSi powder in close collaboration with the group of Professor C. Krellner from the Physics Institute at the Goethe University Frankfurt. Due to the spin of I= 1/2 the NMR lines of ²⁹Si are rather narrow but on the other hand the hyperfine fields have a transferred nature which leads to rather small values and resonance frequencies on the Si nuclei. Nonetheless we were able to obtain rather sharp Si resonances in MnSi powder and in single crystals which is a promising start of this new project.

Beyond the B20 compounds

Apart from the B20 systems the cubic multiferroic Cu₂OSeO₃ is another interesting chiral magnet which hosts a Skyrmion lattice which shares the same space group P2₁3 of the B20 family [20,21]. A case study on zero field NMR on the twin isotopes ⁶³Cu (I=3/2, NA=69%) and ⁶⁵Cu (I=3/2, NA=31%) on single crystals synthesized by M. Schmidt was very successful. In contrast to the B20 systems Cu₂OSeO₃is a oxide which leads in general to a weaker hyperfine coupling between nucleus- and spin- moment. Finally it could be speculated that among the non centrosymmetric Mn-Heusler alloys there might be also candidates for non collinear chiral magnetic textures or Skyrmion lattices. We have shown for a Mn-Pt-Ga Heussler alloy that zero field NMR is a suitable tool to probe the local magnetism [22]. Recently Y. Tokura and co-workers surprisingly reported on a β-Mn type alloy the presence of Skyrmions even above room temperature [23].

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