Epitaxial (001) BiFeO

1. A free-standing heterostructure comprising:

(a) a layer of BiFeO 3 , wherein the BiFeO 3 is substantially strain-free; and

(b) a layer comprising a first perovskite over which the layer of BiFeO 3 is epitaxially grown, wherein the layer comprising the first perovskite has been released from a sacrificial substrate on which it was epitaxially grown to provide removal of the sacrificial substrate, and further wherein the BiFeO 3 exhibits a coercive field of 100 kV/cm or less.

2. The free-standing heterostructure of claim 1 , wherein the first perovskite comprises SrTiO 3 .

3. The free-standing heterostructure of claim 1 , wherein the BiFeO 3 exhibits a remanent polarization of at least 55 μC/cm 2 .

4. The free-standing heterostructure of claim 1 , wherein the BiFeO 3 exhibits a remanent polarization of at least 58 μC/cm 2 .

5. The free-standing heterostructure of claim 1 , wherein the BiFeO 3 exhibits a coercive field of 90 kV/cm or less.

6. The free-standing heterostructure of claim 1 , wherein the BiFeO 3 exhibits a coercive field of 80 kV/cm or less.

7. The free-standing heterostructure of claim 1 , wherein the BiFeO 3 remains fatigue free over at least 1×10 9 cycles as measured using a switching field equal to or greater than two times the remanent polarization of the BiFeO 3 .

8. The free-standing heterostructure of claim 7 , wherein the BiFeO 3 remains fatigue free over at least 1×10 10 cycles.

9. The free-standing heterostructure of claim 1 , wherein the BiFeO 3 is from about 20 nm thick to about 5 μm thick.

10. The free-standing heterostructure of claim 1 , wherein the BiFeO 3 is from about 400 nm thick to about 600 nm thick.

11. The free-standing heterostructure of claim 1 , wherein the layer comprising the first perovskite further comprises a sublayer comprising a second perovskite, the sublayer overlying the first perovskite and underlying the BiFeO 3 .

12. The free-standing heterostructure of claim 11 , wherein the second perovskite is selected from SrRuO 3 , Sr 1-x Ca x RuO 3 (0≦x≦1), Ba 1-x Sr x RuO 3 (0≦x≦1), La 1-x Sr x MnO 3 (0.2≦x≦0.5), LaNiO 3 , IrO x , or RuO x .

13. The free-standing heterostructure of claim 1 , further comprising an electrode disposed over the BiFeO 3 .

14. The free-standing heterostructure of claim 1 , further comprising a host substrate disposed on the layer comprising the first perovskite.

15. The free-standing heterostructure of claim 14 , wherein the host substrate comprises a metal, a plastic, or a glass.

16. A method for forming a free-standing heterostructure from an as-grown, heterostructure, the method comprising releasing the as-grown heterostructure from a sacrificial substrate upon which it was grown to form the free-standing heterostructure, wherein the step of releasing provides removal of the sacrificial substrate, further wherein the as-grown heterostructure comprises a layer of BiFeO 3 and a layer comprising a first epitaxial perovskite over which the layer of BiFeO 3 is epitaxially grown, and further wherein, the BiFeO 3 in the free-standing heterostructure is substantially strain-free and exhibits a coercive field of 100 kV/cm or less.

17. The method of claim 16 , wherein releasing the as-grown heterostructure comprises removing the sacrificial substrate from the layer comprising the first epitaxial perovskite.

18. The method of claim 16 , wherein the sacrificial substrate is miscut (001) silicon.

19. The method of claim 16 , wherein the first epitaxial perovskite comprises SrTiO 3 .

20. The method of claim 16 , wherein the layer comprising the first perovskite further comprises a sublayer comprising a second perovskite, the sublayer overlying the first perovskite and underlying the BiFeO 3 .

21. The method of claim 20 , wherein the second perovskite is selected from SrRuO 3 , Sr l-x Ca x RuO 3 (0≦x≦1), Ba 1-x Sr x RuO 3 (0≦x≦1), La 1-x Sr x MnO 3 (0.2≦x≦0.5), LaNiO 3 , IrO x , or RuO x .

22. The method of claim 16 , wherein the as-gown heterostructure further comprises an electrode over the BiFeO 3 .

23. The method of claim 16 , further comprising disposing a host substrate over the layer of the first epitaxial perovskite after releasing the as-grown heterostructure.

24. The method of claim 23 , wherein the host substrate comprises a metal, a plastic, or a glass.

25. The method of claim 16 , further comprising bonding the BiFeO 3 to a supporting substrate before releasing the as-grown heterostructure.

26. The method of claim 25 , wherein the BiFeO 3 is bonded to the supporting substrate using an adhesive.

27. The method of claim 25 , further comprising disposing a host substrate over the layer comprising the first epitaxial perovskite after releasing the as-grown heterostructure.

28. The method of claim 27 , further comprising removing the supporting substrate.

29. The method of claim 16 , wherein the first epitaxial perovskite is in contact with the sacrificial substrate and wherein releasing the as-grown heterostructure comprises releasing the as-grown heterostructure at the interface between the first epitaxial perovskite and the sacrificial substrate by removing the sacrificial substrate from the first epitaxial perovskite.

30. The method of claim 29 , wherein the sacrificial substrate is miscut (001) silicon.

31. A free-standing heterostructure comprising:

(a) a layer of BiFeO 3 , wherein the BiFeO 3 is substantially strain-free; and

(b) a layer comprising a first perovskite over which the layer of BiFeO 3 is epitaxially grown, wherein the layer comprising the first perovskite has been released from a sacrificial substrate on which it was epitaxially grown to provide removal of the sacrificial substrate, and further wherein the BiFeO 3 has rhombohedral crystal symmetry.

32. The free-standing heterostructure of claim 31 , wherein the BiFeO 3 exhibits a coercive field of 100 kV/cm or less.