Frustrated Magnet Mn₃Al₂Ge₃O₁₂ Garnet: Crystal Growth by the Optical Floating Zone Method

<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>Mn</mi><mn>3</mn></msub><msub><mi>Al</mi><mn>2</mn></msub><msub><mi>Ge</mi><mn>3</mn></msub><msub><mi mathvariant="normal">O</mi><mn>12</mn></msub></mrow></semantics></math></inline-formula> is a member of the garnet family of compounds, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>A</mi><mn>3</mn></msub><msub><mi>B</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula>(<i>C</i>O<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>4</mn></msub></semantics></math></inline-formula>)<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>3</mn></msub></semantics></math></inline-formula>, whose magnetic properties are affected by a high degree of geometrical frustration. The magnetic frustration is at the origin of the intriguing magnetic properties that these materials exhibit, such as a long range <i>hidden order</i> derived from multipoles formed from 10-spin loops in the gadolinium gallium garnet, Gd<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>3</mn></msub></semantics></math></inline-formula>Ga<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>5</mn></msub></semantics></math></inline-formula>O<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>12</mn></msub></semantics></math></inline-formula>. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>Mn</mi><mn>3</mn></msub><msub><mi>Al</mi><mn>2</mn></msub><msub><mi>Ge</mi><mn>3</mn></msub><msub><mi mathvariant="normal">O</mi><mn>12</mn></msub></mrow></semantics></math></inline-formula> garnet is isostructural to the thoroughly investigated Gd garnets, Gd<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>3</mn></msub></semantics></math></inline-formula>Ga<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>5</mn></msub></semantics></math></inline-formula>O<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>12</mn></msub></semantics></math></inline-formula> and Gd<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>3</mn></msub></semantics></math></inline-formula>Al<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>5</mn></msub></semantics></math></inline-formula>O<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>12</mn></msub></semantics></math></inline-formula>. Moreover, in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>Mn</mi><mn>3</mn></msub><msub><mi>Al</mi><mn>2</mn></msub><msub><mi>Ge</mi><mn>3</mn></msub><msub><mi mathvariant="normal">O</mi><mn>12</mn></msub></mrow></semantics></math></inline-formula>, the Heisenberg-like Mn<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mn>2</mn><mo>+</mo></mrow></msup></semantics></math></inline-formula> magnetic ions (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mo>=</mo></mrow></semantics></math></inline-formula> 0) are also arranged in corner sharing triangles that form a hyperkagomé structure. The identical crystallographic structures and similar Heisenberg-like behaviour of the magnetic ions make manganese aluminium germanium garnet the closest compound to the gadolinium garnets in its magnetic properties. Here, we report, for the first time, the growth of a large, high quality single crystal of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>Mn</mi><mn>3</mn></msub><msub><mi>Al</mi><mn>2</mn></msub><msub><mi>Ge</mi><mn>3</mn></msub><msub><mi mathvariant="normal">O</mi><mn>12</mn></msub></mrow></semantics></math></inline-formula> garnet by the floating zone method. X-ray diffraction techniques were used to characterise and confirm the high crystalline quality of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>Mn</mi><mn>3</mn></msub><msub><mi>Al</mi><mn>2</mn></msub><msub><mi>Ge</mi><mn>3</mn></msub><msub><mi mathvariant="normal">O</mi><mn>12</mn></msub></mrow></semantics></math></inline-formula> crystal boule. Temperature-dependent magnetic susceptibility measurements reveal an antiferromagnetic ordering of the Mn<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mn>2</mn><mo>+</mo></mrow></msup></semantics></math></inline-formula> ions below <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>T</mi><mi mathvariant="normal">N</mi></msub><mo>=</mo></mrow></semantics></math></inline-formula> 6.5 K. The high quality of the single crystal obtained makes it ideal for detailed investigations of the magnetic properties of the system, especially using neutron scattering techniques.