Frustrated Magnetism

In frustrated magnetic materials, the competing interactions cannot be simultaneously satisfied leading to unusual low temperature behaviour.

We study the nature of the ground states, as well as unusual excitations, in these frustrated materials.

Low Dimensional Systems

1D and 2D magnets can be made of chains or ladders of spins, with S ≥ 1/2 and Ising, XY, or Heisenberg character.

These systems offer the chance to study unusual magnetic ground states and excitations, and to compare experimental results with theories for model systems.

Permanent Magnetism

​Permanent magnets are pervasive in both established and developing technologies.

Found in motors and generators, transducers, magnetomechanical devices and magnetic field and imaging systems, there is a multi-billion pound worldwide market for them.

Pyrochlores and Spin Ice

A₂B₂O₇ pyrochlores consist of two interpenetrating networks of corner linked tetrahedra. With the A sublattice occupied by magnetic rare-earth (RE) ions, the anisotropic crystallographic environments along with quantum and dipolar interactions, lead to magnetic properties that include: order by disorder in Er₂Ti₂O₇ [1], frustrated Heisenberg antiferromagnetism in Gd₂Ti₂O₇ [2], and (quantum) spin ice in, for example, (Ho/Dy)₂Ti₂O₇, [3-5] Yb₂Ti₂O₇ [6] and Nd₂Zr₂O₇ [7].

Spin ice adopts a highly correlated but disordered ground state where the local magnetisation fulfils the divergence free “ice rule" with two spins pointing in and two out of each tetrahedron. Classical excitations above the spin ice manifold are defects that, by reversing the orientation of a single moment, locally violate the ice rule and so the divergence free condition. This leads to monopole physics [7], as well as under certain circumstances, fragmentation [7].

Selected Warwick papers

[1] J. D. M. Champion et al., Phys. Rev. B 68, 020401 (2003); S. S. Sosin et al., Phys. Rev. B 82, 094428 (2010).

[2] O. A. Petrenko et al., Phys. Rev. B 70, 012402 (2004); Phys. Rev. B 85, 180412(R) (2012), J.A.M. Paddison et al. npjQuantumMater. 6, 99 (2021).

[3] O. A. Petrenko et al., Phys. Rev. B 68, 012406 (2003).

[4] T. Fennel et al., Phys. Rev. B 70, 134408 (2004); Phys. Rev. B 72, 224411 (2005).

[5] S. Erfanifam et al., Phys. Rev. B 84, 220404 (2011); Phys. Rev. B 90, 064409 (2014).

[6] L.-J. Chang et al., Nature Commun. 3, 992 (2012); Phys. Rev. B 89, 184416 (2014); E. Lhotel et al., Phys. Rev. B 89, 224419 (2014); A. Mostaed et al., Phys. Rev. B 95, 094431 (2017).

[7] E. Lhotel et al., Phys. Rev. Lett. 115, 197202 (2015); S. Petit et al., Nat. Phys. 12, 746 (2016); C. Paulsen et al., Nat. Phys. 12, 661 (2016); N. Martin et al., Phys. Rev. X 7, 041028 (2017), C. Paulsen et al. Nature Commun. 10, 1509 (2019); M Léger et al. Phys. Rev. Letts. 126, 247201 (2021).

Academic staff

• Prof. Geetha Balakrishnan
• Prof. Martin LeesLink opens in a new window
• Dr Oleg PetrenkoLink opens in a new window

Molecular Magnets

Gaining control of the building blocks of magnetic materials and thereby achieving particular characteristics could make possible the design and growth of bespoke magnetic devices. Progress in the synthesis of molecular materials, and especially coordination polymers, represents a significant step towards this goal.

Coordination polymers are self-organising materials consisting of arrays of metal ions linked via molecular ligands. Here, the choice of initial components dictates the form of the final product, enabling many different polymeric architectures to be obtained. These materials are thus a route to study magnetism.

We use high- and low-field magnetometry to understand the balance of competing interactions in low-dimensional magnet systems constructed from organic and molecular building blocks. Materials can be studied that are near-ideal realisations of model quantum systems, allowing the predictions of quantum theory to be tested in the laboratory.

Selected Warwick papers

W. J. A. Blackmore et al., New J. Phys. 21, 093025 (2019); Inorg. Chem. 61, 141-153 (2022).

J. Brambleby et al., Phys. Rev. B 92, 134406 (2015); Phys. Rev. B 95, 024404 (2017); Phys. Rev. B 95, 134435 (2017).

V. Chandrasekhar et al., Polyhedron 72, 35 (2014).

S.P.M. Curley Phys. Rev. Mater. 5, 034401 (2021); Phys. Rev. B 104, 214435 (2021).

L.H.R. Dos Santos et al., JACS 138, 2280 (2016).

P. A. Goddard et al., Phys. Rev. B 93, 094430 (2016).

T. Lancaster et al., Phys. Rev. Lett. 112, 207201 (2014).

J. Lui et al., Phys. Rev. Lett. 122, 057207 (2019).

J. L. Manson et al., Sci. Rep. 8, 4745 (2018); Polyhedron 180, 114379 (2020); JACS 143, 4633 (2021).

R. C. Williams et al., Phys. Rev. Res. 2, 013082 (2020).

Academic Staff:

• Prof. Paul Goddard

Rare Earth Transition Metal Magnets

There is a growing demand for stronger and cheaper magnetic materials. Most strong magnets are comprised of rare-earth (RE) and transition metal (TM) atoms arranged in specific crystal structures. The TM element, such as iron or cobalt, helps the ferromagnetism to persist to high temperatures and the RE component, such as neodymium or samarium, is there to generate a large magnetisation which is hard to reorientate away from an 'easy' direction specified by the crystal structure.

One well-known RE-TM permanent magnet class, based on SmCo₅ has excellent high temperature performance but the cost and availability of cobalt can be a problem. There is now a concerted effort worldwide to come up with new permanent magnetic materials with improved magnetic characteristics and reduced dependence on critical elements.

PRETAMAGLink opens in a new window

Investigation of the physics underlying the principles of design of rare earth - transition metal permanent magnets:EP/M028941/1Link opens in a new window

In our PRETAMAGLink opens in a new window research programme we use ab-initio magnetic materials modelling, applied and tested in parallel with state-of-the-art sample synthesis, characterisation and experimental investigation. These studies are aimed at understanding intrinsic magnetic properties and refining the design principles of RE-TM magnets.

Selected Warwick papers

C. E. Patrick et al., Phys. Rev. Materials 1, 024411 (2017).

C. E. Patrick et al., Phys. Rev. Lett. 120, 097202 (2018).

S. Kumar et al., Appl. Phys. Lett. 116, 102408 (2020).

S. Kumar et al., J. Phys.: Condens. Matter 32, 255802 (2020).

Academic Staff:

• Prof. Geetha BalakrishnanLink opens in a new window
• Prof. Martin LeesLink opens in a new window

Also Prof. Julie StauntonLink opens in a new window and Prof. Rachel EdwardsLink opens in a new window (Ultrasound).

SrRE₂O₄ (RE = Gd, Ho, Dy, or Er)

The family of rare-earth (RE) strontium oxides has recently been identified as a useful addition to a small group of compounds where the combination of geometrical frustration, magnetic low dimensionality, and single-ion physics results in the stabilisation of highly unusual ground states at temperatures much lower than those expected from the strength of the magnetic interactions [1].

A wide variety of unconventional magnetic properties observed in these compounds includes a coexistence of long-range antiferromagnetic and short-range incommensurate order in SrEr₂O₄ [2], two types of short-range order in SrHo₂O₄ [3], and the absence of the longer-range magnetic correlations in SrDy₂O₄ down to the lowest experimentally available temperatures [4] and complex magnetic ordering in SrGd₂O₄ [5].

Selected Warwick papers

[1] O. A. Petrenko, Low Temp. Phys. 40, 106 (2014). G. Balakrishnan et al., J. Phys.: Condens. Matter 21, 012202 (2009).

[2] O. A. Petrenko et al., Phys. Rev. B 78, 184410 (2008); T. J. Hayes et al., Phys. Rev. B 84, 174435 (2011); J. Phys. Soc. Jpn. 81, 024708 (2012).

[3] O. Young et al., J. Phys.: Conf.
Ser. 391, 012081 (2012); Phys. Rev. B 88, 024411 (2013); Crystals 9, 488 (2019).

[4] T. H. Cheffings et al., J. Phys.: Condens. Matter 25, 256001 (2013), O.A. Petrenko Phys. Rev. B.95, 104442 (2017).

[5] N. Qureshi et al. Phys. Rev. B 105, 014425 (2022); Phys. Rev. B 106, 224426 (2022).

Academic staff

• Dr Oleg Petrenko
• Prof. Geetha BalakrishnanLink opens in a new window

Ca₃Co₂O₆ Ising spin chain

Ca₃Co₂2O₆ is a rare example of a material where ferromagnetic 1D Ising spin chains are coupled through a much weaker antiferro-magnetic (AFM) exchange on a triangular lattice [1-6]. Ca₃Co₂O₆ orders at T_N = 25 K in longitudinal amplitude-modulated spin-density-wave (SDW) along the c axis [3-6].

On cooling the magnetisation exhibits a significant field, temperature, and time dependence, and there is a very rare order-order transition from the SDW to a commensurate AFM phase [5]. The application of a magnetic field produces a sequence of equally spaced steps in the magnetisation, that are reminiscent of quantum tunnelling of magnetisation in molecular magnets.

Selected Warwick papers

[1] V. Hardy et al., Phys. Rev. B 70, 214439 (2004); Phys. Rev. B 70, 064424 (2004); Phys. Rev. B 70, 104423 (2004).

[2] A. Maignan et al., J. Mater. Chem. 14, 1231 (2004).

[3] O. A. Petrenko et al., Eur. Phys. J. B 47, 79 (2005).

[4] A. Bombardi et al., Phys. Rev. B 78, 100406 (2008).

[5] S. Agrestini et al., Phys. Rev. B 77, 140403 (2008); Phys. Rev. Lett. 101, 097207 (2008); Phys. Rev. Lett. 106, 197204 (2011).

[6] J. A. M. Paddison et al., Phys. Rev. B 90, 014411 (2014).

Academic Staff:

• Prof. Martin Lees
• Dr Oleg PetrenkoLink opens in a new window

Other Magnetic Systems

Gadolinium Gallium Garnet Gd₃Ga₅O₁₂ is a frustrated magnetic system that exhibits a spin-liquid state above a spin-glass transition at T_g ≈ 0.14 K, that is far below the anti-ferromagnetic interaction strength of ~2 K. Liquid-like magnetic diffuse scattering and persistence of strong spin fluctuations are observed in neutron scattering to low T [1-3]. Suppression of conventional magnetic order allows “hidden” order to emerge in its place [4].

Selected Warwick papers

[1] O. A. Petrenko et al., Phys. Rev. Lett. 80, 4570 (1998).

[2] J. A. Quilliam et al., Phys. Rev. B 87, 174421 (2013).

[3] N. d’ Ambrumenil et al., Phys. Rev. Lett. 114, 227203 (2015).

[4] J. A. M. Paddison et al., Science 350, 179 (2015).

Hydrothermally prepared magnetic oxides

We work with Prof. Richard Walton and his Group in Chemistry who prepare magnetic oxides via hydrothermal methods. Materials of interest include ruthenates [1], bismuth based compounds [2], and chromites [3], with new structures or potential for applications.

Selected Warwick papers

[1] C. I. Hiley et al., Phys. Rev. B 92, 104413 (2015); Angew. Chem. Int. Ed. 53, 4423 (2014); R. J. Darton et al., Cryst.Growth Des. 10, 3819 (2010).

[2] K. Sardar et al., Chem. Mater. 24, 4192 (2012); J. Phys: Cond. Matter 24, 045904 (2012).

[3] L. M. Daniels et al., Inorg. Chem. 52, 12161 (2013); K. Sardar et al., Chem. Mater. 23, 48 (2011).