Electron localization into spin-polaron state in MnSi

Strong electron localization into a bound state has been found in both paramagnetic and ferromagnetic states of the transition metal compound MnSi by muon spin-rotation spectroscopy in magnetic fields up to 7 T and from 2 K to room temperature. This bound state, with a characteristic radius R≈0.4 nm and net spin S=24±2, is consistent with confinement of the electron’s wave function within roughly one lattice cell of MnSi and is suggested to be a spin polaron. Such spin polarons may form due to a strong exchange interaction between itinerant electrons and the magnetic electrons of Mn ions of the same 3d type; as such, they might affect the peculiar electronic and magnetic properties of MnSi. Disciplines Condensed Matter Physics | Materials Science and Engineering Comments This article is from Physical Review B 83 (2011): 410404(R), doi:10.1103/PhysRevB.83.140404. This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/ameslab_pubs/53 RAPID COMMUNICATIONS PHYSICAL REVIEW B 83, 140404(R) (2011) Electron localization into spin-polaron state in MnSi Vyacheslav G. Storchak,1,* Jess H. Brewer,2 Roger L. Lichti,3 Thomas A. Lograsso,4 and Deborah L. Schlagel4 1Russian Research Centre “Kurchatov Institute,” Kurchatov Sq. 1, Moscow 123182, Russia 2Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada V6T 1Z1 3Department of Physics, Texas Tech University, Lubbock, Texas 79409, USA 4Ames Laboratory, Iowa State University, Ames, Iowa 50011, USA (Received 15 March 2011; published 13 April 2011) Strong electron localization into a bound state has been found in both paramagnetic and ferromagnetic states of the transition metal compound MnSi by muon spin-rotation spectroscopy in magnetic fields up to 7 T and from 2 K to room temperature. This bound state, with a characteristic radius R ≈ 0.4 nm and net spin S = 24 ± 2, is consistent with confinement of the electron’s wave function within roughly one lattice cell of MnSi and is suggested to be a spin polaron. Such spin polarons may form due to a strong exchange interaction between itinerant electrons and the magnetic electrons of Mn ions of the same 3d type; as such, they might affect the peculiar electronic and magnetic properties of MnSi. DOI: 10.1103/PhysRevB.83.140404 PACS number(s): 76.75.+i, 71.70.Gm, 72.80.Ga, 74.20.Mn The transport properties of transition metal compounds near a crossover from localized to itinerant electron behavior present formidable challenges to theoretical explication, including non-Fermi-liquid (NFL) behavior when the interaction energies of the electrons are comparable to their kinetic energies.1,2 The specific quantum states that might replace the Fermi liquid remain unclear.3 It has long been recognized that the d electrons responsible for magnetism in transition metals have a dual nature; in their ground state, the itinerant electrons are described by band theory, while at elevated temperature, they exhibit properties characteristic of a system of local moments.4,5 In magnetic systems that occupy the borderline between these two extremes, the so-called “nearly ferromagnetic metals,” NFL behavior is often found in the phase diagram near a magnetically ordered phase, indicating that the NFL state may be linked to magnetic instabilities.1,2 The best-known examples include ZrZn2, Ni3Al, Pd alloys,8 UGe2, and MnSi.10–12 The latter, MnSi, represents the canonical borderline case of a weak itinerant ferromagnet in the evolution of metallic ferromagnetism away from the localized moment extreme of ferromagnetic (FM) Fe (with well-defined local magnetic moments) toward the correlated paramagnet Pd. Under ambient conditions, MnSi orders below Tc = 29.5 K into a helimagnetic phase with a rather long period of 18 nm along the 111 direction of the noncentrosymmetric cubic B20 crystal structure.13 An applied magnetic field 0.1 T unpins the helical order to align the resulting conical phase along the field; magnetic fields exceeding 0.6 T establish a spin-aligned FM state, which completes the phase diagram at ambient pressure.14 Above Tc, MnSi exhibits a CurieWeiss-type susceptibility with an effective paramagnetic (PM) moment mPM = 2.2μB per Mn, while its spontaneous magnetic moment in the FM phase is significantly smaller:mFM = 0.4μB per Mn. Although such an enhanced ratio of mPM to mFM may be accounted for by self-consistent renormalization (SCR) within the enhanced spin-fluctuation approach,4,5 ab initio calculations predict a significantly higher mFM ≈ 1μB .15,16 Accordingly, recent 29Si NMR (Ref. 16) and μSR (Ref. 17) studies have questioned the validity of the SCR model as applied to MnSi. Most recently, a number of unanticipated effects have been discovered in MnSi: the electrical resistivity at low temperature changes abruptly from the standard FL T 2 behavior to T 3/2,11,12 while the conventional long-range FM state is suppressed to give way to a phase with “partial magnetic order” at a hydrostatic pressure pc = 14.6 kbar.18 These observations contradict the predictions of the FL theory and require explanation. Furthermore, infrared optical conductivity and de Haas–van Alphen experiments indicate strong electron scattering above ∼200 K, while at low temperature, the electron effective mass m∗ is dramatically enhanced (up to 17me). All these effects suggest strong coupling to spin fluctuations, the nature of which remains unclear. The observation of partial magnetic order raises the question of spatial homogeneity of the underlying spin structure in MnSi.14 Inhomogeneous magnetism in MnSi is found at high pressure by neutron scattering,18 zero-field 29Si NMR,21 and μSR.22 The length scale of such magnetic inhomogeneities is, however, not identified. On the other hand, resistivity10 and optical conductivity19 measurements show anomalously enhanced quasiparticle-quasiparticle scattering cross sections consistent with inhomogeneities on a scale of the order of the lattice spacing. The origin of such magnetic inhomogeneities needs to be identified. In MnSi, all these unusual properties indicate strong 3d electron correlations. In fact, the entire family of B20 isostructural transition metal monosilicides exhibits discontinuous evolution of electronic and magnetic properties upon doping, from the 3d5 itinerant FM metal MnSi to the 3d6 paramagnetic semiconductor FeSi to the 3d7 diamagnetic metal CoSi.23 MnSi, FeSi, and CoSi form an isostructural dilution series of ternary and quaternary strongly correlated compounds, which not only permits conversion of a semiconductor into an unconventional metal, but also exhibits NFL behavior.24 Such unusual electronic properties are accompanied by the emerging physics of skyrmions,25–27 which clearly indicates microscopic magnetic inhomogeneities. 140404-1 1098-0121/2011/83(14)/140404(4) ©2011 American Physical Society RAPID COMMUNICATIONS STORCHAK, BREWER, LICHTI, LOGRASSO, AND SCHLAGEL PHYSICAL REVIEW B 83, 140404(R) (2011) In this Rapid Communication, we present spectroscopic evidence for electron confinement in MnSi into a bound state that we believe is a spin polaron, which can result in both microscopic magnetic inhomogeneities and an effective-mass enhancement with possible NFL behavior. A hierarchy of three well-separated energy and length scales is generally thought to determine the magnetic and electronic properties of MnSi (Ref. 18): (1) an exchange interaction that causes FM over a length scale of many lattice spacings; (2) the weak spin-orbit interaction that produces helical modulation with a long wavelength (∼18 nm at ambient pressure); and (3) a still weaker crystal anisotropy term that locks the direction of the spiral on a length scale of 1000 nm within a single domain. In strongly correlated electron systems, however, one must also take into account the much stronger exchange interaction J between itinerant carriers and localized spins, which is typically confined to within one lattice spacing. In treating this interaction, two limiting cases are important: (a) when the itinerant electron bandwidth W is large compared with J and (b) the opposite limit, when J W . The former applies to the s-f exchange in rare-earth compounds where the extremely localized f electrons are screened by other shells. The opposite extreme (W J ) provides the basis for the well-known double exchange in transition metal compounds. As odd as it may seem, this inequality is likely to be quite realistic in such compounds, where the charge carriers are often of the same d type as the localized spins.28–30 MnSi falls into an intermediate regime J/W ∼ 1: the width of its 3d band is W ≈ 2 eV,15,31 while J ≈ 0.6 eV.20 Both ab initio calculations15 and recent measurements32 show that the large density of Mn 3d states within the 3d band(s) falls at the Fermi level, ensuring a strong exchange interaction between itinerant carriers and local spins of the same d type in MnSi. Such an exchange interaction can dramatically modify the electron state via its localization into a spin polaron (SP).33 The SP is a few-body state formed by an electron that mediates a FM interaction between magnetic ions in its immediate environment, the direct coupling of which is rather weak. In such a system, an electron’s energy depends strongly on the magnetization, with the minimum energy being achieved by FM ordering28: the electron will then localize and form a FM “droplet” over the extent of its wave function in a host of any other state (in particular, PM or helimagnetic). The electron coupled to its immediate FM environment behaves as a single entity with a giant spin S, i.e., a spin polaron. In the process of electron localization, the exchange interaction is opposed by the increase of the electron kinetic energy and the entropy term due to ordering within the polaron, so the net change in the free energy F = h̄ 2 2m∗R2 + T S − J a 3