The notion of a simple ordered state implies homogeneity. If the order is established by a broken symmetry, the elementary Landau theory of phase transitions shows that only one symmetry mode describes this state. At the exact points of phase coexistence, domain states composed of large regions of different phases can be stabilized by long-range interactions. In uniaxial antiferromagnets, so-called metamagnetism is an example of such behaviour where antiferromagnetic and field-induced, spin-polarized paramagnetic/ferromagnetic states coexist at a jump-like transition in the magnetic phase diagram. Here, by combining experiments with theoretical analysis, we show that a different type of mixed state between antiferromagnetism and ferromagnetism can be created in certain non-centrosymmetric materials. In small-angle neutron scattering experiments, we observe a field-driven spin state in the layered antiferromagnet Ca3Ru2O7, which is modulated on a scale between 8 and 20 nm and has both antiferromagnetic and ferromagnetic parts. We call this state a metamagnetic texture and attribute its appearance to the chiral twisting effects of the asymmetric Dzyaloshinskii–Moriya exchange. The observation can be understood as an extraordinary coexistence—in one thermodynamic state—of spin orders that belong to different symmetries. The complex nature of this metamagnetic state is demonstrated experimentally by measurements of anomalies in electronic transport that reflect the spin polarization in the metamagnetic texture; determination of the magnetic orbital moments, which support the existence of strong spin–orbit effects, is a pre-requisite for the mechanism of twisted magnetic states in this material. Our findings provide an example of a rich and largely unexplored class of textured states. Such textures mediate between different ordering modes near phase coexistence, and produce extremely rich phase diagrams.
Access optionsAccess options
Subscribe to Journal
Get full journal access for 1 year
only $15.58 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Becquerel, J. & van den Handel, J. Le métamagnétisme. J. Phys. Radium 10, 10–13 (1939).
Becquerel, J. Le métamagnétisme. In Reunion d’ étude sur le magnétisme. Généralités et magnéto-optique. Strasbourg, 21–25 Mai 1939 97–139 (Institut International de Coopération Intellectuelle, 1940).
Stryjewski, E. & Giordano, N. Metamagnetism. Adv. Phys. 26, 487–650 (1977).
Néel, L. Les métamagnétiques ou substances antiferromagnétiques à champ seuil. Nuovo Cimento 6, 942–960 (1957).
Bar’yakhtar, V. G., Bogdanov, A. N. & Yablonskii, D. A. The physics of magnetic domains. Usp. Fiz. Nauk 156, 47–92 (1988).
Dzyaloshinskii, I. E. Theory of helicoidal structures in antiferromagnets. 1. Nonmetals. Sov. Phys. JETP 19, 960–971 (1964).
Levanyuk, A. P. Incommensurate Phases in Dielectrics (eds Blinc, R. & Levanyuk, A. P.) (North Holland, 1986).
Cummins, H. Z. Experimental studies of structurally incommensurate crystal phases. Phys. Rep. 185, 211–409 (1990).
De Gennes, P. G. Short range order effects in the isotropic phase of nematics and cholesterics. Mol. Cryst. Liquid Cryst. 12, 193–214 (1971).
Wright, D. C. & Mermin, N. D. Crystalline liquids: the blue phases. Rev. Mod. Phys. 61, 385–432 (1989).
Meiboom, S., Sethna, J. P., Anderson, P. W. & Brinkman, W. F. Theory of the blue phase of cholesteric liquid crystals. Phys. Rev. Lett. 46, 1216–1219 (1981).
Nakanishi, O., Yanase, A., Hasegawa, A. & Kataoka, M. The origin of the helical spin density wave in MnSi. Solid State Commun. 35, 995–998 (1980).
Bak, P. & Jensen, M. H. Theory of helical magnetic structures and phase transitions in MnSi and FeGe. J. Phys. C 13, L881–L885 (1980).
Bogdanov, A. N. New localized solutions of the nonlinear field equations. JETP Lett. 62, 247–251 (1995).
Bogdanov, A. N., Rößler, U. K., Wolf, M. & Müller, K.-H. Magnetic structures and reorientation transitions in noncentrosymmetric uniaxial antiferromagnets. Phys. Rev. B 66, 214410 (2002).
Bogdanov, A. N. & Yablonskii, D. A. Thermodynamically stable ‘vortices’ in magnetically ordered crystals. The mixed state of magnets. Zh. Eksp. Teor. Fiz. 95, 178–182 (1989).
Rößler, U. K., Bogdanov, A. N. & Pfleiderer, C. Spontaneous skyrmion ground states in magnetic metals. Nature 442, 797–801 (2006).
Mühlbauer, S. et al. Skyrmion lattice in a chiral magnet. Science 323, 915–919 (2009).
Yu, X. Z. et al. Real-space observation of a two-dimensional skyrmion crystal. Nature 465, 901–904 (2010).
Jungwirth, T. et al. The multiple directions of antiferromagnetic spintronics. Nat. Phys. 14, 200–203 (2018).
Gomonay, O., Baltz, V., Brataas, A. & Tserkovnyak, Y. Antiferromagnetic spin textures and dynamics. Nat. Phys. 14, 213–216 (2018).
Duine, R. A., Lee, K.-J., Parkin, S. S. P. & Stiles, M. D. Synthetic antiferromagnetic spintronics. Nat. Phys. 14, 217–219 (2018).
Yoshida, Y. et al. Crystal and magnetic structure of Ca3Ru2O7. Phys. Rev. B 72, 054412 (2005).
Bao, W., Mao, Z. Q., Qu, Z. & Lynn, J. W. Spin valve effect and magnetoresistivity in single crystalline Ca3Ru2O7. Phys. Rev. Lett. 100, 247203 (2008).
Liu, G. Q. Mott transition and magnetic anisotropy in Ca3Ru2O7. Phys. Rev. B 84, 235137 (2011).
Yoshida, Y. et al. Quasi-two-dimensional metallic ground state of Ca3Ru2O7. Phys. Rev. B 69, 220411(R) (2004).
Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys. 82, 1539–1592 (2010).
McCall, S., Cao, G. & Crow, J. E. Impact of magnetic fields on anisotropy in Ca3Ru2O7. Phys. Rev. B 67, 094427 (2003).
Cao, G. et al. Orbitally driven behaviour: Mott transition, quantum oscillations and colossal magnetoresistance in bilayered Ca3Ru2O7. New J. Phys. 6, 159 (2004).
Fobes, D., Peng, J., Qu, Z., Liu, T. J. & Mao, Z. Q. Magnetic phase transitions and bulk spin-valve effect tuned by in-plane field orientation in Ca3Ru2O7. Phys. Rev. B 84, 014406 (2011).
Dewhurst, C. D. et al. The small-angle neutron scattering instrument D33 at the Institut Laue Langevin. J. Appl. Cryst. 49, 1–14 (2015).
Ke, X., Peng, J., Tian, W., Hong, T. & Mao, Z. Q. Commensurate-incommensurate magnetic phase transition in the Fe-doped bilayer ruthenate Ca3Ru2O7. Phys. Rev. B 89, 220407(R) (2014).
Zhu, M. et al. Tuning the competing phases of bilayer ruthenate Ca3Ru2O7 via dilute Mn impurities and magnetic field. Phys. Rev. B 95, 144426 (2017).
Zheludev, A. et al. Field-induced incommensurate-to-commensurate transition in Ba2CuGe2O7. Phys. Rev. B 57, 2968–2978 (1998).
Agrestini, S. et al. Nature of the magnetic order in Ca3Co2O6. Phys. Rev. Lett. 101, 097202 (2008).
Gao, S. et al. Spiral spin-liquid and the emergence of a vortex-like state in MnSc2S4. Nat. Phys. 13, 157–161 (2017).
Jensen, J. & Mackintosh, A. R. Rare Earth Magnetism (Clarendon, 1991).
Levanyuk, A. P. Thermodynamical theory of phase-transitions with appearance of an incommensurate superstructure in ferroelectrics NaNO2 and SC(NH2)2. Fiz. Tverd. Tela 18, 1927–1932 (1976).
Stefanovskii, E. P. Exchange-relativistic modulated magnetic-structures in multisublattice rhombic antiferromagnets. Fiz. Tverd. Tela 28, 3452–3456 (1986).
Yablonskii, D. A. & Medvedeva, L. I. Classification of magnetic structures in compounds with the Fe2P-structure. Physica B 167, 125–132 (1990).
Aizu, K. Investigation of incommensurate phases of the ‘Twiny’ gradient form as compared with incommensurate phases of the simple gradient form. J. Phys. Soc. Jpn 58, 4501–4510 (1989).
Zavorotnev, Yu. D. & Medvedyeva, L. I. Long-period incommensurate structures in crystals with a triangular arrangement of magnetic ions. J. Magn. Magn. Mater. 248, 402–412 (2002).
Zavorotnev, Yu. D. & Medvedeva, L. I. Characteristics of irreducible vectors rotating in superstructures with two one-component order parameters. Crystallogr. Rep. 47, 1003–1006 (2002).
Milward, G. C., Calderon, M. J. & Littlewood, P. B. Electronically soft phases in manganites. Nature 433, 607–611 (2005).
Bar’yakhtar, V. G., Stefanovskij, E. P. & Yablonskii, D. A. Theory of magnetic structure and electric polarization of Cr2BeO4 system. Pisma Zh. Eksp. Teor. Fiz. 42, 258–260 (1985).
Ronning, F. et al. Electronic in-plane symmetry breaking at field-tuned quantum criticality in CeRhIn5. Nature 548, 313–317 (2017).
Tolédano J. C. & Tolédano P. The Landau Theory of Phase Transitions (World Scientific, 1987).
Koepernik, K. & Eschrig, H. Full-potential nonorthogonal local-orbital minimum-basis band-structure scheme. Phys. Rev. B 59, 1743 (1999).
Sokolov, D. A. & Cubitt, R. Probing the Magnetic Field Driven Modulated Structure and Exotic Magnetism in Ca 3 Ru 2 O 7 (Institut Laue–Langevin, 2018); https://doi.org/10.5291/ILL-DATA.5-42-462
We thank U. Nitzsche for technical support with FPLO. N.K. acknowledges the support from JSPS KAKENHI (nos JP17H06136 and JP18K04715) and JST-Mirai Program (no. JPMJMI18A3) in Japan. D.A.S. thanks C. Geibel for the critical reading of the manuscript and constructive comments. Access to NG7 SANS was provided by the Center for High Resolution Neutron Scattering, a partnership between the National Institute of Standards and Technology and the National Science Foundation under agreement no. DMR-1508249. We thank J. Krzywon and Y. Qiang for technical support during the SANS experiment at NIST. This work is partly based on experiments performed at the Swiss spallation neutron source SINQ, Paul Scherrer Institute, Villigen, Switzerland. Certain commercial equipment, instruments, or materials are identified in this article to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.
The authors declare no competing interests.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Figs. 1–8 and Supplementary references 1–17.
About this article
Nature Physics (2019)