We acknowledge discussions with G. Stiehl, R. Haislmaier, A. SenGupta, V. Gopalan, W. Wang, W. Wu and E. Barnard and technical support with the electron microscopy from E. J. Kirkland, M. Thomas and J. Grazul. Research primarily supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under Award No. DE-SC0002334, which supported the work of J.A.Mu. (2010–2014), C.M.B., M.E.H., J.A.Mo., H.D., A.F.R., R.He., Q.M., H.P., R.M., C.J.F., P.S., D.A.M. and D.G.S. Substrate preparation was performed in part at the Cornell NanoScale Facility, a member of the National Nanotechnology Coordinated Infrastructure (NNCI), which is supported by the National Science Foundation (Grant ECCS-15420819). The electron microscopy studies made use of the electron microscopy facility of the Cornell Center for Materials Research, a National Science Foundation (NSF) Materials Research Science and Engineering Centers programme (DMR 1120296) and NSF IMR-0417392. X-ray dichroism was performed at the Advanced Light Source at Lawrence Berkeley National Laboratory. The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under Contract No. DE-AC02-05CH11231. J.A.Mu. acknowledges fellowship support from the Army Research Office in the form of a National Defense Science and Engineering Graduate Fellowship and from the National Science Foundation in the form of a Graduate Research Fellowship. J.A.Mu. was funded (July 2015–) by C-SPINS, one of six centres of STARnet, a Semiconductor Research Corporation programme, sponsored by MARCO and DARPA. J.T.H. acknowledges support from the Semiconductor Research Corporation (SRC) under grant 2014-IN-2534. J.D.C. acknowledges support from SRC-FAME, one of six centres of STARnet, a Semiconductor Research Corporation programme sponsored by MARCO and DARPA. S.M.D. acknowledges the support of a National Research Council NIST postdoctoral research associateship. Z.L. acknowledges support from the NSF under Grant No. EEC-1160504 NSF Nanosystems Engineering Research Center for Translational Applications of Nanoscale Multiferroic Systems (TANMS). A.F. is supported by the Swiss National Science Foundation. R.Ho. and L.F.K. acknowledge support by the David and Lucile Packard Foundation. E.P. acknowledges support from the National Science Foundation in the form of a Graduate Research Fellowship (DGE-1144153). Certain commercial equipment, instruments, or materials are identified in this paper 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.